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Title: A Budget of Paradoxes, Volume I (of II)

Author: Augustus De Morgan

Editor: David Eugene Smith

Release Date: October 20, 2007 [EBook #23100]

Language: English

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Transcriber's note: A few typographical errors have been corrected: they
are listed at the end of the text.

       *       *       *       *       *


BY AUGUSTUS DE MORGAN

A BUDGET OF
PARADOXES

REPRINTED WITH THE AUTHOR'S ADDITIONS FROM THE ATHENAEUM



SECOND EDITION EDITED BY DAVID EUGENE SMITH

WITH A NEW INTRODUCTION BY ERNEST NAGEL

PROFESSOR OF PHILOSOPHY, COLUMBIA UNIVERSITY

UNABRIDGED EDITION--TWO VOLUMES BOUND AS ONE



Volume I



DOVER PUBLICATIONS, INC., NEW YORK

       *       *       *       *       *


PREFACE TO THE FIRST EDITION.

(1872)

It is not without hesitation that I have taken upon myself the editorship
of a work left avowedly imperfect by the author, and, from its
miscellaneous and discursive character, difficult of completion with due
regard to editorial limitations by a less able hand.

Had the author lived to carry out his purpose he would have looked through
his Budget again, amplifying and probably rearranging some of its contents.
He had collected materials for further illustration of Paradox of the kind
treated of in this book; and he meant to write a second part, in which the
contradictions and inconsistencies of orthodox learning would have been
subjected to the same scrutiny and castigation as heterodox ignorance had
already received.

It will be seen that the present volume contains more than the _Athenæum_
Budget. Some of the additions formed a Supplement to the original articles.
These supplementary paragraphs were, by the author, placed after those to
which they respectively referred, being distinguished from the rest of the
text by brackets. I have omitted these brackets as useless, except where
they were needed to indicate subsequent writing.

Another and a larger portion of the work consists of discussion of matters
of contemporary interest, for the Budget was in some degree a receptacle
for the author's thoughts on any literary, scientific, or social question.
Having grown thus gradually to its present size, the book as it was left
was not quite in a fit condition for publication, but the alterations which
have been made are slight and few, being in most cases verbal, and such as
the sense absolutely required, or transpositions of sentences to secure
coherence with the rest, in places where the author, in his more recent
insertion of them, had overlooked the connection in which they stood. In no
case has the meaning been in any degree modified or interfered with.

One rather large omission must be mentioned here. It is an account of the
quarrel between Sir James South and Mr. Troughton on the mounting, etc. of
the equatorial telescope at Campden Hill. At some future time when the
affair has passed entirely out of the memory of living Astronomers, the
appreciative sketch, which is omitted in this edition of the Budget, will
be an interesting piece of history and study of character.[1]

A very small portion of Mr. James Smith's circle-squaring has been left
out, with a still smaller portion of Mr. De Morgan's answers to that
Cyclometrical Paradoxer.

In more than one place repetitions, which would have disappeared under the
author's revision, have been allowed to remain, because they could not have
been taken away without leaving a hiatus, not easy to fill up without
damage to the author's meaning.

I give these explanations in obedience to the rules laid down for the
guidance of editors at page 15.[2] If any apology for the fragmentary
character of the book be thought necessary, it may be found in the author's
own words at page 281 of the second volume.[3]

The publication of the Budget could not have been delayed without lessening
the interest attaching to the writer's thoughts upon questions of our own
day. I trust that, incomplete as the work is compared with what it might
have been, I shall not be held mistaken in giving it to the world. Rather
let me hope that it will be welcomed as an old friend returning under great
disadvantages, but bringing a pleasant remembrance of the amusement which
its weekly appearance in the _Athenæum_ gave to both writer and reader.

The Paradoxes are dealt with in chronological order. This will be a guide
to the reader, and with the alphabetical Index of Names, etc., will, I
trust, obviate all difficulty of reference.

SOPHIA DE MORGAN.

    6 MERTON ROAD, PRIMROSE HILL.

       *       *       *       *       *


PREFACE TO THE SECOND EDITION.

If Mrs. De Morgan felt called upon to confess her hesitation at taking upon
herself the labor of editing these Paradoxes, much more should one who was
born two generations later, who lives in another land and who was reared
amid different influences, confess to the same feeling when undertaking to
revise this curious medley. But when we consider the nature of the work,
the fact that its present rarity deprives so many readers of the enjoyment
of its delicious satire, and the further fact that allusions that were
commonplace a half century ago are now forgotten, it is evident that some
one should take up the work and perform it _con amore_.

Having long been an admirer of De Morgan, having continued his work in the
bibliography of early arithmetics, and having worked in his library among
the books of which he was so fond, it is possible that the present editor,
whatever may be his other shortcomings, may undertake the labor with as
much of sympathy as any one who is in a position to perform it. With this
thought in mind, two definite rules were laid down at the beginning of the
task: (1) That no alteration in the text should be made, save in slightly
modernizing spelling and punctuation and in the case of manifest
typographical errors; (2) That whenever a note appeared it should show at
once its authorship, to the end that the material of the original edition
might appear intact.

In considering, however, the unbroken sequence of items that form the
Budget, it seems clear that readers would be greatly aided if the various
leading topics were separated in some convenient manner. After considerable
thought it was decided to insert brief captions from time to time that
might aid the eye in selecting the larger subjects of the text. In some
parts of the work these could easily be taken from the original folio
heads, but usually they had to be written anew. While, therefore, the
present editor accepts the responsibility for the captions of the various
subdivisions, he has endeavored to insert them in harmony with the original
text.

As to the footnotes, the first edition had only a few, some due to De
Morgan himself and others to Mrs. De Morgan. In the present edition those
due to the former are signed A. De M., and those due to Mrs. De Morgan
appear with her initials, S. E. De M. For all other footnotes the present
editor is responsible. In preparing them the effort has been made to
elucidate the text by supplying such information as the casual reader might
wish as he passes over the pages. Hundreds of names are referred to in the
text that were more or less known in England half a century ago, but are
now forgotten there and were never familiar elsewhere. Many books that were
then current have now passed out of memory, and much that agitated England
in De Morgan's prime seems now like ancient history. Even with respect to
well-known names, a little information as to dates and publications will
often be welcome, although the editor recognizes that it will quite as
often be superfluous. In order, therefore, to derive the pleasure that
should come from reading the Budget, the reader should have easy access to
the information that the notes are intended to supply. That they furnish
too much here and too little there is to be expected. They are a human
product, and if they fail to serve their purpose in all respects it is
hoped that this failure will not seriously interfere with the reader's
pleasure.

In general the present editor has refrained from expressing any opinions
that would strike a discordant note in the reading of the text as De Morgan
left it. The temptation is great to add to the discussion at various
points, but it is a temptation to be resisted. To furnish such information
as shall make the reading more pleasant, rather than to attempt to improve
upon one of the most delicious bits of satire of the nineteenth century,
has been the editor's wish. It would have been an agreeable task to review
the history of circle squaring, of the trisection problem, and of the
duplication of the cube. This, however, would be to go too far afield. For
the benefit of those who wish to investigate the subject the editor can
only refer to such works and articles as the following: F. Rudio,
_Archimedes, Huygens, Lambert, Legendre,--mit einer Uebersicht über die
Geschichte des Problemes von der Quadratur des Zirkels_, Leipsic, 1892;
Thomas Muir, "Circle," in the eleventh edition of the _Encyclopædia
Britannica_; the various histories of mathematics; and to his own article
on "The Incommensurability of [pi]" in Prof. J. W. A. Young's _Monographs
on Topics of Modern Mathematics_, New York, 1911.

The editor wishes to express his appreciation and thanks to Dr. Paul Carus,
editor of _The Monist_ and _The Open Court_ for the opportunity of
undertaking this work; to James Earl Russell, LL.D., Dean of Teachers
College, Columbia University, for his encouragement in its prosecution; to
Miss Caroline Eustis Seely for her intelligent and painstaking assistance
in securing material for the notes; and to Miss Lydia G. Robinson and Miss
Anna A. Kugler for their aid and helpful suggestions in connection with the
proof-sheets. Without the generous help of all five this work would have
been impossible.

DAVID EUGENE SMITH.

    TEACHERS COLLEGE, COLUMBIA UNIVERSITY.

       *       *       *       *       *


A BUDGET OF PARADOXES

{1}

INTRODUCTORY.

If I had before me a fly and an elephant, having never seen more than one
such magnitude of either kind; and if the fly were to endeavor to persuade
me that he was larger than the elephant, I might by possibility be placed
in a difficulty. The apparently little creature might use such arguments
about the effect of distance, and might appeal to such laws of sight and
hearing as I, if unlearned in those things, might be unable wholly to
reject. But if there were a thousand flies, all buzzing, to appearance,
about the great creature; and, to a fly, declaring, each one for himself,
that he was bigger than the quadruped; and all giving different and
frequently contradictory reasons; and each one despising and opposing the
reasons of the others--I should feel quite at my ease. I should certainly
say, My little friends, the case of each one of you is destroyed by the
rest. I intend to show flies in the swarm, with a few larger animals, for
reasons to be given.

In every age of the world there has been an established system, which has
been opposed from time to time by isolated and dissentient reformers. The
established system has sometimes fallen, slowly and gradually: it has
either been upset by the rising influence of some one man, or it has been
sapped by gradual change of opinion in the many.

I have insisted on the isolated character of the dissentients, as an
element of the _a priori_ probabilities of the case. Show me a schism,
especially a growing schism, and it is another thing. The homeopathists,
for instance, shall be, if any one so think, as wrong as St. John Long; but
an {2} organized opposition, supported by the efforts of many acting in
concert, appealing to common arguments and experience, with perpetual
succession and a common seal, as the Queen says in the charter, is, be the
merit of the schism what it may, a thing wholly different from the case of
the isolated opponent in the mode of opposition to it which reason points
out.

During the last two centuries and a half, physical knowledge has been
gradually made to rest upon a basis which it had not before. It has become
_mathematical_. The question now is, not whether this or that hypothesis is
better or worse to the pure thought, but whether it accords with observed
phenomena in those consequences which can be shown necessarily to follow
from it, if it be true. Even in those sciences which are not yet under the
dominion of mathematics, and perhaps never will be, a working copy of the
mathematical process has been made. This is not known to the followers of
those sciences who are not themselves mathematicians and who very often
exalt their horns against the mathematics in consequence. They might as
well be squaring the circle, for any sense they show in this particular.

A great many individuals, ever since the rise of the mathematical method,
have, each for himself, attacked its direct and indirect consequences. I
shall not here stop to point out how the very accuracy of exact science
gives better aim than the preceding state of things could give. I shall
call each of these persons a _paradoxer_, and his system a _paradox_. I use
the word in the old sense: a paradox is something which is apart from
general opinion, either in subject-matter, method, or conclusion.

Many of the things brought forward would now be called _crotchets_, which
is the nearest word we have to old _paradox_. But there is this difference,
that by calling a thing a _crotchet_ we mean to speak lightly of it; which
was not the necessary sense of _paradox_. Thus in the sixteenth century
many spoke of the earth's motion as the _paradox of {3} Copernicus_, who
held the ingenuity of that theory in very high esteem, and some, I think,
who even inclined towards it. In the seventeenth century, the depravation
of meaning took place, in England at least. Phillips says _paradox_ is "a
thing which seemeth strange"--here is the old meaning: after a colon he
proceeds--"and absurd, and is contrary to common opinion," which is an
addition due to his own time.

Some of my readers are hardly inclined to think that the word _paradox_
could once have had no disparagement in its meaning; still less that
persons could have applied it to themselves. I chance to have met with a
case in point against them. It is Spinoza's _Philosophia Scripturæ
Interpres, Exercitatio Paradoxa_, printed anonymously at Eleutheropolis, in
1666. This place was one of several cities in the clouds, to which the
cuckoos resorted who were driven away by the other birds; that is, a
feigned place of printing, adopted by those who would have caught it if
orthodoxy could have caught them. Thus, in 1656, the works of Socinus could
only be printed at Irenopolis. The author deserves his self-imposed title,
as in the following:[4]

"Quanto sane satius fuisset illam [Trinitatem] pro mysterio non habuisse,
et Philosophiæ ope, antequam quod esset statuerent, secundum veræ logices
præcepta quid esset cum Cl. Kleckermanno investigasse; tanto fervore ac
labore in profundissimas speluncas et obscurissimos metaphysicarum
speculationum atque fictionum recessus se recipere ut ab adversariorum
telis sententiam suam in tuto collocarent. {4} Profecto magnus ille vir ...
dogma illud, quamvis apud theologos eo nomine non multum gratiæ iniverit,
ita ex immotis Philosophiæ fundamentis explicat ac demonstrat, ut paucis
tantum immutatis, atque additis, nihil amplius animus veritate sincere
deditus desiderare possit."

This is properly paradox, though also heterodox. It supposes, contrary to
all opinion, orthodox and heterodox, that philosophy can, with slight
changes, explain the Athanasian doctrine so as to be at least compatible
with orthodoxy. The author would stand almost alone, if not quite; and this
is what he meant. I have met with the counter-paradox. I have heard it
maintained that the doctrine as it stands, in all its mystery is _a priori_
more likely than any other to have been Revelation, if such a thing were to
be; and that it might almost have been predicted.

After looking into books of paradoxes for more than thirty years, and
holding conversation with many persons who have written them, and many who
might have done so, there is one point on which my mind is fully made up.
The manner in which a paradoxer will show himself, as to sense or nonsense,
will not depend upon what he maintains, but upon whether he has or has not
made a sufficient knowledge of what has been done by others, _especially as
to the mode of doing it_, a preliminary to inventing knowledge for himself.
That a little knowledge is a dangerous thing is one of the most fallacious
of proverbs. A person of small knowledge is in danger of trying to make his
_little_ do the work of _more_; but a person without any is in more danger
of making his _no_ knowledge do the work of _some_. Take the speculations
on the tides as an instance. Persons with nothing but a little geometry
have certainly exposed themselves in their modes of objecting to results
which require the higher mathematics to be known before an independent
opinion can be formed on sufficient grounds. But persons with no geometry
at all have done the same thing much more completely. {5}

There is a line to be drawn which is constantly put aside in the arguments
held by paradoxers in favor of their right to instruct the world. Most
persons must, or at least will, like the lady in Cadogan Place,[5] form and
express an immense variety of opinions on an immense variety of subjects;
and all persons must be their own guides in many things. So far all is
well. But there are many who, in carrying the expression of their own
opinions beyond the usual tone of private conversation, whether they go no
further than attempts at oral proselytism, or whether they commit
themselves to the press, do not reflect that they have ceased to stand upon
the ground on which their process is defensible. Aspiring to lead _others_,
they have never given themselves the fair chance of being first led by
_other_ others into something better than they can start for themselves;
and that they should first do this is what both those classes of others
have a fair right to expect. New knowledge, when to any purpose, must come
by contemplation of old knowledge in every matter which concerns thought;
mechanical contrivance sometimes, not very often, escapes this rule. All
the men who are now called discoverers, in every matter ruled by thought,
have been men versed in the minds of their predecessors, and learned in
what had been before them. There is not one exception. I do not say that
every man has made direct acquaintance with the whole of his mental
ancestry; many have, as I may say, only known their grandfathers by the
report of their fathers. But even on this point it is remarkable how many
of the greatest names in all departments of knowledge have been real
antiquaries in their several subjects.

I may cite, among those who have wrought strongly upon opinion or practice
in science, Aristotle, Plato, Ptolemy, Euclid, Archimedes, Roger Bacon,
Copernicus, Francis Bacon, Ramus, Tycho Brahé, Galileo, Napier, Descartes,
Leibnitz, Newton, Locke. I take none but names known out of their {6}
fields of work; and all were learned as well as sagacious. I have chosen my
instances: if any one will undertake to show a person of little or no
knowledge who has established himself in a great matter of pure thought,
let him bring forward his man, and we shall see.

This is the true way of putting off those who plague others with their
great discoveries. The first demand made should be--Mr. Moses, before I
allow you to lead me over the Red Sea, I must have you show that you are
learned in all the wisdom of the Egyptians upon your own subject. The plea
that it is unlikely that this or that unknown person should succeed where
Newton, etc. have failed, or should show Newton, etc. to be wrong, is
utterly null and void. It was worthily versified by Sylvanus Morgan (the
great herald who in his _Sphere of Gentry_ gave coat armor to "Gentleman
Jesus," as he said), who sang of Copernicus as follows (1652):

 "If Tellus winged be,
  The earth a motion round;
  Then much deceived are they
  Who nere before it found.
  Solomon was the wisest,
  His wit nere this attained;
  Cease, then, Copernicus,
  Thy hypothesis is vain."

Newton, etc. were once unknown; but they made themselves known by what they
knew, and then brought forward what they could do; which I see is as good
verse as that of Herald Sylvanus. The demand for previous knowledge
disposes of twenty-nine cases out of thirty, and the thirtieth is worth
listening to.

I have not set down Copernicus, Galileo, etc. among the paradoxers, merely
because everybody knows them; if my list were quite complete, they would
have been in it. But the reader will find Gilbert, the great precursor of
sound magnetical theory; and several others on whom no censure can be cast,
though some of their paradoxes are inadmissible, {7} some unprovoked, and
some capital jokes, true or false: the author of _Vestiges of Creation_ is
an instance. I expect that my old correspondent, General Perronet Thompson,
will admit that his geometry is part and parcel of my plan; and also that,
if that plan embraced politics, he would claim a place for his _Catechism
on the Corn Laws_, a work at one time paradoxical, but which had more to do
with the abolition of the bread-tax than Sir Robert Peel.

My intention in publishing this Budget in the _Athenæum_ is _to enable
those who have been puzzled by one or two discoverers to see how they look
in a lump_. The only question is, has the selection been fairly made? To
this my answer is, that no selection at all has been made. The books are,
without exception, those which I have in my own library; and I have taken
_all_--I mean all of the kind: Heaven forbid that I should be supposed to
have no other books! But I may have been a collector, influenced in choice
by bias? I answer that I never have collected books of this sort--that is,
I have never searched for them, never made up my mind to look out for this
book or that. I have bought what happened to come in my way at show or
auction; I have retained what came in as part of the _undescribed_ portion
of miscellaneous auction lots; I have received a few from friends who found
them among what they called their rubbish; and I have preserved books sent
to me for review. In not a few instances the books have been bound up with
others, unmentioned at the back; and for years I knew no more I had them
than I knew I had Lord Macclesfield's speech on moving the change of Style,
which, after I had searched shops, etc. for it in vain, I found had been
reposing on my own shelves for many years, at the end of a summary of
Leibnitz's philosophy. Consequently, I may positively affirm that the
following list is formed by accident and circumstance alone, and that it
truly represents the casualties of about a third of a century. For
instance, the large proportion of works {8} on the quadrature of the circle
is not my doing: it is the natural share of this subject in the actual run
of events.

[I keep to my plan of inserting only such books as I possessed in 1863,
except by casual notice in aid of my remarks. I have found several books on
my shelves which ought to have been inserted. These have their titles set
out at the commencement of their articles, in leading paragraphs; the
casuals are without this formality.[6]]

Before proceeding to open the Budget, I say something on my personal
knowledge of the class of discoverers who square the circle, upset Newton,
etc. I suspect I know more of the English class than any man in Britain. I
never kept any reckoning; but I know that one year with another--and less
of late years than in earlier time--I have talked to more than five in each
year, giving more than a hundred and fifty specimens. Of this I am sure,
that it is my own fault if they have not been a thousand. Nobody knows how
they swarm, except those to whom they naturally resort. They are in all
ranks and occupations, of all ages and characters. They are very earnest
people, and their purpose is _bona fide_ the dissemination of their
paradoxes. A great many--the mass, indeed--are illiterate, and a great many
waste their means, and are in or approaching penury. But I must say that
never, in any one instance, has the quadrature of the circle, or the like,
been made a pretext for begging; even to be asked to purchase a book is of
the very rarest occurrence--it has happened, and that is all.

These discoverers despise one another: if there were the concert among them
which there is among foreign mendicants, a man who admitted one to a
conference would be plagued to death. I once gave something to a very
genteel French applicant, who overtook me in the street, at my own door,
saying he had picked up my handkerchief: whether he picked it up in my
pocket for an introduction, I know not. {9} But that day week came another
Frenchman to my house, and that day fortnight a French lady; both failed,
and I had no more trouble. The same thing happened with Poles. It is not so
with circle-squarers, etc.: they know nothing of each other. Some will read
this list, and will say I am right enough, generally speaking, but that
there _is_ an exception, if I could but see it.

I do not mean, by my confession of the manner in which I have sinned
against the twenty-four hours, to hold myself out as accessible to personal
explanation of new plans. Quite the contrary: I consider myself as having
made my report, and being discharged from further attendance on the
subject. I will not, from henceforward, talk to any squarer of the circle,
trisector of the angle, duplicator of the cube, constructor of perpetual
motion, subverter of gravitation, stagnator of the earth, builder of the
universe, etc. I will receive any writings or books which require no
answer, and read them when I please: I will certainly preserve them--this
list may be enlarged at some future time.

There are three subjects which I have hardly anything upon; astrology,
mechanism, and the infallible way of winning at play. I have never cared to
preserve astrology. The mechanists make models, and not books. The
infallible winners--though I have seen a few--think their secret too
valuable, and prefer _mutare quadrata rotundis_--to turn dice into coin--at
the gaming-house: verily they have their reward.

I shall now select, to the mystic number seven, instances of my personal
knowledge of those who think they have discovered, in illustration of as
many misconceptions.

1. _Attempt by help of the old philosophy, the discoverer not being in
possession of modern knowledge._ A poor schoolmaster, in rags, introduced
himself to a scientific friend with whom I was talking, and announced that
he had found out the composition of the sun. "How was that done?"--"By
consideration of the four elements."--"What are {10} they?"--"Of course,
fire, air, earth, and water."--"Did you not know that air, earth, and
water, have long been known to be no elements at all, but
compounds?"--"What do you mean, sir? Who ever heard of such a thing?"

2. _The notion that difficulties are enigmas, to be overcome in a moment by
a lucky thought._ A nobleman of very high rank, now long dead, read an
article by me on the quadrature, in an early number of the _Penny
Magazine_. He had, I suppose, school recollections of geometry. He put
pencil to paper, drew a circle, and constructed what seemed likely to
answer, and, indeed, was--as he said--certain, if only this bit were equal
to that; which of course it was not. He forwarded his diagram to the
Secretary of the Diffusion Society, to be handed to the author of the
article, in case the difficulty should happen to be therein overcome.

3. _Discovery at all hazards, to get on in the world._ Thirty years ago, an
officer of rank, just come from foreign service, and trying for a
decoration from the Crown, found that his claims were of doubtful amount,
and was told by a friend that so and so, who had got the order, had the
additional claim of scientific distinction. Now this officer, while abroad,
had bethought himself one day, that there really could be no difficulty in
finding the circumference of a circle: if a circle were rolled upon a
straight line until the undermost point came undermost again, there would
be the straight line equal to the circle. He came to me, saying that he did
not feel equal to the statement of his claim in this respect, but that if
some clever fellow would put the thing in a proper light, he thought his
affair might be managed. I was clever enough to put the thing in a proper
light to himself, to this extent at least, that, though perhaps they were
wrong, the advisers of the Crown would never put the letters K.C.B. to such
a circle as his.

4. _The notion that mathematicians cannot find the circle for common
purposes._ A working man measured the altitude of a cylinder accurately,
and--I think the process of {11} Archimedes was one of his
proceedings--found its bulk. He then calculated the ratio of the
circumference to the diameter, and found it answered very well on other
modes of trial. His result was about 3.14. He came to London, and somebody
sent him to me. Like many others of his pursuit, he seemed to have turned
the whole force of his mind upon one of his points, on which alone he would
be open to refutation. He had read some of Kater's experiments, and had got
the Act of 1825 on weights and measures. Say what I would, he had for a
long time but one answer--"Sir! I go upon Captain Kater and the Act of
Parliament." But I fixed him at last. I happened to have on the table a
proof-sheet of the _Astronomical Memoirs_, in which were a large number of
observed places of the planets compared with prediction, and asked him
whether it could be possible that persons who did not know the circle
better than he had found it could make the calculations, of which I gave
him a notion, so accurately? He was perfectly astonished, and took the
titles of some books which he said he would read.

5. _Application for the reward from abroad._ Many years ago, about
twenty-eight, I think, a Jesuit came from South America, with a quadrature,
and a cutting from a newspaper announcing that a reward was ready for the
discovery in England. On this evidence he came over. After satisfying him
that nothing had ever been offered here, I discussed his quadrature, which
was of no use. I succeeded better when I told him of Richard White, also a
Jesuit, and author of a quadrature published before 1648, under the name of
_Chrysæspis_, of which I can give no account, having never seen it. This
White (_Albius_) is the only quadrator who was ever convinced of his error.
My Jesuit was struck by the instance, and promised to read more
geometry--he was no Clavius--before he published his book. He relapsed,
however, for I saw his book advertised in a few days. I may say, as
sufficient proof of my being no collector, that I had not the curiosity to
buy his book; and my friend the {12} Jesuit did not send me a copy, which
he ought to have done, after the hour I had given him.

6. _Application for the reward at home._ An agricultural laborer squared
the circle, and brought the proceeds to London. He left his papers with me,
one of which was the copy of a letter to the Lord Chancellor, desiring his
Lordship to hand over forthwith 100,000 pounds, the amount of the alleged
offer of reward. He did not go quite so far as M. de Vausenville, who, I
think in 1778, brought an action against the Academy of Sciences to recover
a reward to which he held himself entitled. I returned the papers, with a
note, stating that he had not the knowledge requisite to see in what the
problem consisted. I got for answer a letter in which I was told that a
person who could not see that he had done the thing should "change his
business, and appropriate his time and attention to a Sunday-school, to
learn what he could, and keep the _litle_ children from _durting_ their
_close_." I also received a letter from a friend of the quadrator,
informing me that I knew his friend had succeeded, and had been heard to
say so. These letters were printed--without the names of the writers--for
the amusement of the readers of _Notes and Queries_, First Series, xii. 57,
and they will appear again in the sequel.

[There are many who have such a deep respect for any attempt at thought
that they are shocked at ridicule even of those who have made themselves
conspicuous by pretending to lead the world in matters which they have not
studied. Among my anonyms is a gentleman who is angry at my treatment of
the "poor but thoughtful" man who is described in my introduction as
recommending me to go to a Sunday-school because I informed him that he did
not know in what the difficulty of quadrature consisted. My impugner quite
forgets that this man's "thoughtfulness" chiefly consisted in his demanding
a hundred thousand pounds from the Lord Chancellor for his discovery; and I
may add, that his greatest stretch of invention was finding out that "the
clergy" {13} were the means of his modest request being unnoticed. I
mention this letter because it affords occasion to note a very common
error, namely, that men unread in their subjects have, by natural wisdom,
been great benefactors of mankind. My critic says, "Shakspeare, whom the
Pro^r (_sic_) may admit to be a wisish man, though an object of contempt as
to learning ..." Shakespeare an object of contempt as to learning! Though
not myself a thoroughgoing Shakespearean--and adopting the first half of
the opinion given by George III, "What! is there not sad stuff? only one
must not say so"--I am strongly of opinion that he throws out the masonic
signs of learning in almost every scene, to all who know what they are. And
this over and above every kind of direct evidence. First, foremost, and
enough, the evidence of Ben Jonson that he had "little Latin and less
Greek"; then Shakespeare had as much Greek as Jonson would call _some_,
even when he was depreciating. To have any Greek at all was in those days
exceptional. In Shakespeare's youth St. Paul's and Merchant Taylor's
schools were to have masters learned in good and clean Latin literature,
_and also in Greek if such may be gotten_. When Jonson spoke as above, he
intended to put Shakespeare low among the learned, but not out of their
pale; and he spoke as a rival dramatist, who was proud of his own learned
sock; and it may be a subject of inquiry how much Latin _he_ would call
_little_. If Shakespeare's learning on certain points be very much less
visible than Jonson's, it is partly because Shakespeare's writings hold it
in chemical combination, Jonson's in mechanical aggregation.]

7. An elderly man came to me to show me how the universe was created. There
was one molecule, which by vibration became--Heaven knows how!--the Sun.
Further vibration produced Mercury, and so on. I suspect the nebular
hypothesis had got into the poor man's head by reading, in some singular
mixture with what it found there. Some modifications of vibration gave
heat, electricity, etc. I {14} listened until my informant ceased to
vibrate--which is always the shortest way--and then said, "Our knowledge of
elastic fluids is imperfect." "Sir!" said he, "I see you perceive the truth
of what I have said, and I will reward your attention by telling you what I
seldom disclose, never, except to those who can receive my theory--the
little molecule whose vibrations have given rise to our solar system is the
Logos of St. John's Gospel!" He went away to Dr. Lardner, who would not go
into the solar system at all--the first molecule settled the question. So
hard upon poor discoverers are men of science who are not antiquaries in
their subject! On leaving, he said, "Sir, Mr. De Morgan received me in a
very different way! he heard me attentively, and I left him perfectly
satisfied of the truth of my system." I have had much reason to think that
many discoverers, of all classes, believe they have convinced every one who
is not peremptory to the verge of incivility.

My list is given in chronological order. My readers will understand that my
general expressions, where slighting or contemptuous, refer to the
ignorant, who teach before they have learned. In every instance, those of
whom I am able to speak with respect, whether as right or wrong, have
sought knowledge in the subject they were to handle before they completed
their speculations. I shall further illustrate this at the conclusion of my
list.

Before I begin the list, I give prominence to the following letter,
addressed by me to the _Correspondent_ of October 28, 1865. Some of my
paradoxers attribute to me articles in this or that journal; and others may
think--I know some do think--they know me as the writer of reviews of some
of the very books noticed here. The following remarks will explain the way
in which they may be right, and in which they may be wrong. {15}

       *       *       *       *       *

THE EDITORIAL SYSTEM.

"Sir,--I have reason to think that many persons have a very inaccurate
notion of the _Editorial System_. What I call by this name has grown up in
the last _centenary_--a word I may use to signify the hundred years now
ending, and to avoid the ambiguity of _century_. It cannot conveniently be
explained by editors themselves, and _edited_ journals generally do not
like to say much about it. In _your_ paper perhaps, in which editorial
duties differ somewhat from those of ordinary journals, the common system
may be freely spoken of.

"When a reviewed author, as very often happens, writes to the editor of the
reviewing journal to complain of what has been said of him, he
frequently--even more often than not--complains of 'your reviewer.' He
sometimes presumes that 'you' have, 'through inadvertence' in this
instance, 'allowed some incompetent person to lower the character of your
usually accurate pages.' Sometimes he talks of 'your scribe,' and, in
extreme cases, even of 'your hack.' All this shows perfect ignorance of the
journal system, except where it is done under the notion of letting the
editor down easy. But the editor never accepts the mercy.

"All that is in a journal, except what is marked as from a correspondent,
either by the editor himself or by the correspondent's real or fictitious
signature, is published entirely on editorial responsibility, as much as if
the editor had written it himself. The editor, therefore, may claim, and
does claim and exercise, unlimited right of omission, addition, and
alteration. This is so well understood that the editor performs his last
function on the last revise without the 'contributor' knowing what is done.
The word _contributor_ is the proper one; it implies that he furnishes
materials without stating what he furnishes or how much of it is accepted,
or whether he be the only contributor. All this applies both to political
and literary journals. No editor acknowledges {16} the right of a
contributor to withdraw an article, if he should find alterations in the
proof sent to him for correction which would make him wish that the article
should not appear. If the _demand_ for suppression were made--I say nothing
about what might be granted to _request_--the answer would be, 'It is not
your article, but mine; I have all the responsibility; if it should contain
a libel, I could not give you up, even at your own desire. You have
furnished me with materials, on the known and common understanding that I
was to use them at my discretion, and you have no right to impede my
operations by making the appearance of the article depend on your
approbation of my use of your materials.'

"There is something to be said for this system, and something against it--I
mean simply on its own merits. But the all-conquering argument in its favor
is, that the only practicable alternative is the modern French plan of no
articles without the signature of the writers. I need not discuss this
plan; there is no collective party in favor of it. Some may think it is not
the only alternative; they have not produced any intermediate proposal in
which any dozen of persons have concurred. Many will say, Is not all this,
though perfectly correct, well known to be matter of form? Is it not
practically the course of events that an engaged contributor writes the
article, and sends it to the editor, who admits it as
written--substantially, at least? And is it not often very well known, by
style and in other ways, who it was wrote the article? This system is
matter of form just as much as loaded pistols are matter of form so long as
the wearer is not assailed; but matter of form takes the form of matter in
the pulling of a trigger, so soon as the need arises. Editors and
contributors who can work together find each other out by elective
affinity, so that the common run of events settles down into most articles
appearing much as they are written. And there are two safety-valves; that
is, when judicious persons come together. In the first place, the editor
himself, when he has selected his contributor, feels that {17} the
contributor is likely to know his business better than an editor can teach
him; in fact, it is on that principle that the selection is made. But he
feels that he is more competent than the writer to judge questions of
strength and of tone, especially when the general purpose of the journal is
considered, of which the editor is the judge without appeal. An editor who
meddles with substantive matter is likely to be wrong, even when he knows
the subject; but one who prunes what he deems excess, is likely to be
right, even when he does not know the subject. In the second place, a
contributor knows that he is supplying an editor, and learns, without
suppressing truth or suggesting falsehood, to make the tone of his
communications suit the periodical in which they are to appear. Hence it
very often arises that a reviewed author, who thinks he knows the name of
his reviewer, and proclaims it with expressions of dissatisfaction, is only
wrong in supposing that his critic has given all his mind. It has happened
to myself more than once, to be announced as the author of articles which I
could not have signed, because they did not go far enough to warrant my
affixing my name to them as to a sufficient expression of my own opinion.

"There are two other ways in which a reviewed author may be wrong about his
critic. An editor frequently makes slight insertions or omissions--I mean
slight in quantity of type--as he goes over the last proof; this he does in
a comparative hurry, and it may chance that he does not know the full sting
of his little alteration. The very bit which the writer of the book most
complains of may not have been seen by the person who is called the writer
of the article until after the appearance of the journal; nay, if he be one
of those--few, I daresay--who do not read their own articles, may never
have been seen by him at all. Possibly, the insertion or omission would not
have been made if the editor could have had one minute's conversation with
his contributor. Sometimes it actually contradicts something which is {18}
allowed to remain in another part of the article; and sometimes, especially
in the case of omission, it renders other parts of the article
unintelligible. These are disadvantages of the system, and a judicious
editor is not very free with his _unus et alter pannus_. Next, readers in
general, when they see the pages of a journal with the articles so nicely
fitting, and so many ending with the page or column, have very little
notion of the cutting and carving which goes to the process. At the very
last moment arises the necessity of some trimming of this kind; and the
editor, who would gladly call the writer to counsel if he could, is obliged
to strike out ten or twelve lines. He must do his best, but it may chance
that the omission selected would take from the writer the power of owning
the article. A few years ago, an able opponent of mine wrote to a journal
some criticisms upon an article which he expressly attributed to me. I
replied as if I were the writer, which, in a sense, I was. But if any one
had required of me an unmodified 'Yes' or 'No' to the question whether I
wrote the article, I must, of two falsehoods, have chosen 'No': for certain
omissions, dictated by the necessities of space and time, would have
amounted, had my signature been affixed, to a silent surrender of points
which, in my own character, I must have strongly insisted on, unless I had
chosen to admit certain inferences against what I had previously published
in my own name. I may here add that the forms of journalism obliged me in
this case to remind my opponent that it could not be permitted to me, _in
that journal_, either to acknowledge or deny the authorship of the
articles. The cautions derived from the above remarks are particularly
wanted with reference to the editorial comments upon letters of complaint.
There is often no time to send these letters to the contributor, and even
when this can be done, an editor is--and very properly--never of so
editorial a mind as when he is revising the comments of a contributor upon
an assailant of the article. He is then in a better position as to
information, and a more {19} critical position as to responsibility. Of
course, an editor never meddles, except under notice, with the letter of a
correspondent, whether of a complainant, of a casual informant, or of a
contributor who sees reason to become a correspondent. Omissions must
sometimes be made when a grievance is too highly spiced. It did once happen
to me that a waggish editor made an insertion without notice in a letter
signed by me with some fiction, which insertion contained the name of a
friend of mine, with a satire which I did not believe, and should not have
written if I had. To my strong rebuke, he replied--'I know it was very
wrong; but human nature could not resist.' But this was the only occasion
on which such a thing ever happened to me.

"I daresay what I have written may give some of your readers to understand
some of the _pericula et commoda_ of modern journalism. I have known men of
deep learning and science as ignorant of the prevailing system as any
uneducated reader of a newspaper in a country town. I may perhaps induce
some writers not to be too sure about this, that, or the other person. They
may detect their reviewer, and they may be safe in attributing to him the
general matter and tone of the article. But about one and another point,
especially if it be a short and stinging point, they may very easily chance
to be wrong. It has happened to myself, and within a few weeks to
publication, to be wrong in two ways in reading a past article--to
attribute to editorial insertion what was really my own, and to attribute
to myself what was really editorial insertion."



What is a man to do who is asked whether he wrote an article? He may, of
course, refuse to answer; which is regarded as an admission. He may say, as
Swift did to Serjeant Bettesworth, "Sir, when I was a young man, a friend
of mine advised me, whenever I was asked whether I had written a certain
paper, to deny it; and I accordingly tell that I did _not_ write it." He
may say, as I often do, {20} when charged with having invented a joke,
story, or epigram, "I want all the credit I can get, and therefore I always
acknowledge all that is attributed to me, truly or not; the story, etc.
_is_ mine." But for serious earnest, in the matter of imputed criticism,
the answer may be, "The article was of my material, but the editor has not
let it stand as I gave it; I cannot own it as a whole." He may then refuse
to be particular as to the amount of the editor's interference. Of this
there are two extreme cases. The editor may have expunged nothing but a
qualifying adverb. Or he may have done as follows. We all remember the
account of Adam which satirizes woman, but eulogizes her if every second
and third line be transposed. As in:

 "Adam could find no solid peace
    When Eve was given him for a mate,
  Till he beheld a woman's face,
    Adam was in a happy state."

If this had been the article, and a gallant editor had made the
transpositions, the author could not with truth acknowledge. If the
alteration were only an omitted adverb, or a few things of the sort, the
author could not with truth deny. In all that comes between, every man must
be his own casuist. I stared, when I was a boy, to hear grave persons
approve of Sir Walter Scott's downright denial that he was the author of
Waverley, in answer to the Prince Regent's downright question. If I
remember rightly, Samuel Johnson would have approved of the same course.

It is known that, whatever the law gives, it also gives all that is
necessary to full possession; thus a man whose land is environed by land of
others has a right of way over the land of these others. By analogy, it is
argued that when a man has a right to his secret, he has a right to all
that is necessary to keep it, and that is not unlawful. If, then, he can
only keep his secret by denial, he has a right to denial. This I admit to
be an answer against all men except the denier himself; if conscience and
self-respect will allow {21} it, no one can impeach it. But the question
cannot be solved on a case. That question is, A lie, is it _malum in se_,
without reference to meaning and circumstances? This is a question with two
sides to it. Cases may be invented in which a lie is the only way of
preventing a murder, or in which a lie may otherwise save a life. In these
cases it is difficult to acquit, and almost impossible to blame; discretion
introduced, the line becomes very hard to draw.

I know but one work which has precisely--as at first appears--the character
and object of my Budget. It is the _Review of the Works of the Royal
Society of London_, by Sir John Hill, M.D. (1751 and 1780, 4to.). This man
offended many: the Royal Society, by his work, the medical profession, by
inventing and selling extra-pharmacopoeian doses; Garrick, by resenting the
rejection of a play. So Garrick wrote:

 "For physic and farces his equal there scarce is;
  His farces are physic; his physic a farce is."

I have fired at the Royal Society and at the medical profession, but I have
given a wide berth to the drama and its wits; so there is no epigram out
against me, as yet. He was very able and very eccentric. Dr. Thomson
(_Hist. Roy. Soc._) says he has no humor, but Dr. Thomson was a man who
never would have discovered humor.

Mr. Weld (_Hist. Roy. Soc._) backs Dr. Thomson, but with a remarkable
addition. Having followed his predecessor in observing that the
_Transactions_ in Martin Folkes's time have an unusual proportion of
trifling and puerile papers, he says that Hill's book is a poor attempt at
humor, and glaringly exhibits the feelings of a disappointed man. It is
probable, he adds, that the points told with some effect on the Society;
for shortly after its publication the _Transactions_ possess a much higher
scientific value.

I copy an account which I gave elsewhere.

When the Royal Society was founded, the Fellows set {22} to work to prove
all things, that they might hold fast that which was good. They bent
themselves to the question whether sprats were young herrings. They made a
circle of the powder of a unicorn's horn, and set a spider in the middle of
it; "but it immediately ran out." They tried several times, and the spider
"once made some stay in the powder." They inquired into Kenelm Digby's
sympathetic powder. "Magnetic cures being discoursed of, Sir Gilbert Talbot
promised to communicate what he knew of sympathetical cures; and those
members who had any of the powder of sympathy, were desired to bring some
of it at the next meeting."

June 21, 1661, certain gentlemen were appointed "curators of the proposal
of tormenting a man with the sympathetic powder"; I cannot find any record
of the result. And so they went on until the time of Sir John Hill's
satire, in 1751. This once well-known work is, in my judgment, the greatest
compliment the Royal Society ever received. It brought forward a number of
what are now feeble and childish researches in the Philosophical
Transactions. It showed that the inquirers had actually been inquiring; and
that they did not pronounce decision about "natural _knowledge_" by help of
"_natural_ knowledge." But for this, Hill would neither have known what to
assail, nor how. Matters are now entirely changed. The scientific bodies
are far too well established to risk themselves. _Ibit qui zonam perdidit:_

    "Let him take castles who has ne'er a groat."

These great institutions are now without any collective purpose, except
that of promoting individual energy; they print for their contributors, and
guard themselves by a general declaration that they will not be answerable
for the things they print. Of course they will not put forward anything for
everybody; but a writer of a certain reputation, or matter of a certain
look of plausibility and safety, {23} will find admission. This is as it
should be; the pasturer of flocks and herds and the hunters of wild beasts
are two very different bodies, with very different policies. The scientific
academies are what a spiritualist might call "publishing mediums," and
_their_ spirits fall occasionally into writing which looks as if minds in
the higher state were not always impervious to nonsense.

The following joke is attributed to Sir John Hill. I cannot honestly say I
believe it; but it shows that his contemporaries did not believe he had no
humor. Good stories are always in some sort of keeping with the characters
on which they are fastened. Sir John Hill contrived a communication to the
Royal Society from Portsmouth, to the effect that a sailor had broken his
leg in a fall from the mast-head; that bandages and a plentiful application
of tarwater had made him, in three days, able to use his leg as well as
ever. While this communication was under grave discussion--it must be
remembered that many then thought tarwater had extraordinary remedial
properties--the joker contrived that a second letter should be delivered,
which stated that the writer had forgotten, in his previous communication,
to mention that the leg was a wooden leg! Horace Walpole told this story, I
suppose for the first time; he is good authority for the fact of
circulation, but for nothing more.

Sir John Hill's book is droll and cutting satire. Dr. Maty, (Sec. Royal
Society) wrote thus of it in the _Journal Britannique_ (Feb. 1751), of
which he was editor:

"Il est fâcheux que cet ingénieux Naturaliste, qui nous a déjà donné et qui
nous prépare encore des ouvrages plus utiles, emploie à cette odieuse tâche
une plume qu'il trempe dans le fiel et dans l'absinthe. Il est vrai que
plusieurs de ses remarques sont fondées, et qu'à l'erreur qu'il indique, il
joint en même tems la correction. Mais il n'est pas toujours équitable, et
ne manque jamais d'insulter. Que peut {24} après tout prouver son livre, si
ce n'est que la quarante-cinquième partie d'un très-ample et très-utile
Recueil n'est pas exempte d'erreurs? Devoit-il confondre avec des Ecrivains
superficiels, dont la Liberté du Corps ne permet pas de restreindre la
fertilité, cette foule de savans du Premier ordre, dont les Ecrits ont orné
et ornent encore les Transactions? A-t-il oublié qu'on y a vu fréquemment
les noms des Boyle, des Newton, des Halley, des De Moivres, des Hans
Sloane, etc.? Et qu'on y trouve encore ceux des Ward, des Bradley, des
Graham, des Ellicot, des Watson, et d'un Auteur que Mr. Hill préfère à tous
les autres, je veux dire de Mr. Hill lui-même?"[7]

This was the only answer; but it was no answer at all. Hill's object was to
expose the absurdities; he therefore collected the absurdities. I feel sure
that Hill was a benefactor of the Royal Society; and much more than he
would have been if he had softened their errors and enhanced their praises.
No reviewer will object to me that I have omitted Young, Laplace, etc. But
then my book has a true title. Hill should not have called his a review of
the "Works."

It was charged against Sir John Hill that he had tried to become a Fellow
of the Royal Society and had failed. This he denied, and challenged the
production of the certificate which a candidate always sends in, and which
is preserved. {25} But perhaps he could not get so far as a
certificate--that is, could not find any one to recommend him; he was a
likely man to be in such a predicament. As I have myself run foul of the
Society on some little points, I conceive it possible that I may fall under
a like suspicion. Whether I could have been a Fellow, I cannot know; as the
gentleman said who was asked if he could play the violin, I never tried. I
have always had a high opinion of the Society upon its whole history. A
person used to historical inquiry learns to look at wholes; the
Universities of Oxford and Cambridge, the College of Physicians, etc. are
taken in all their duration. But those who are not historians--I mean not
possessed of the habit of history--hold a mass of opinions about current
things which lead them into all kinds of confusion when they try to look
back. Not to give an instance which will offend any set of existing
men--this merely because I can do without it--let us take the country at
large. Magna Charta for ever! glorious safeguard of our liberties! _Nullus
liber homo capiatur aut imprisonetur ... aut aliquo modo destruatur, nisi
per judicium parium_ ....[8] _Liber homo: frank home_; a capital thing for
him--but how about the _villeins_? Oh, there are none _now_! But there
were. Who cares for villains, or barbarians, or helots? And so England, and
Athens, and Sparta, were free States; all the freemen in them were free.
Long after Magna Charta, villains were sold with their "chattels and
offspring," named in that order. Long after Magna Charta, it was law that
"Le Seigniour poit rob, naufrer, et chastiser son villein a son volunt,
salve que il ne poit luy maim."[9]

The Royal Society was founded as a co-operative body, and co-operation was
its purpose. The early charters, etc. do not contain a trace of the
intention to create a _scientific distinction_, a kind of Legion of Honor.
It is clear that the {26} qualification was ability and willingness to do
good work for the promotion of natural knowledge, no matter in how many
persons, nor of what position in society. Charles II gave a smart rebuke
for exclusiveness, as elsewhere mentioned. In time arose, almost of course,
the idea of distinction attaching to the title; and when I first began to
know the Society, it was in this state. Gentlemen of good social position
were freely elected if they were really educated men; but the moment a
claimant was announced as resting on his science, there was a disposition
to inquire whether he was scientific enough. The maxim of the poet was
adopted; and the Fellows were practically divided into _Drink-deeps_ and
_Taste-nots_.

I was, in early life, much repelled by the tone taken by the Fellows of the
Society with respect to their very mixed body. A man high in science--some
thirty-seven years ago (about 1830)--gave me some encouragement, as he
thought. "We shall have you a Fellow of the Royal Society in time," said
he. Umph! thought I: for I had that day heard of some recent elections, the
united science of which would not have demonstrated I. 1, nor explained the
action of a pump. Truly an elevation to look up at! It came, further, to my
knowledge that the Royal Society--if I might judge by the claims made by
very influential Fellows--considered itself as entitled to the best of
everything: second-best being left for the newer bodies. A secretary, in
returning thanks for the Royal at an anniversary of the Astronomical, gave
rather a lecture to the company on the positive duty of all present to send
the very best to the old body, and the absolute right of the old body to
expect it. An old friend of mine, on a similar occasion, stated as a fact
that the thing was always done, as well as that it ought to be done.

Of late years this pretension has been made by a President of the Society.
In 1855, Lord Rosse presented a confidential memorandum to the Council on
the expediency of enlarging their number. He says, "In a Council so small
it {27} is impossible to secure a satisfactory representation of the
leading scientific Societies, and it is scarcely to be expected that, under
such circumstances, they will continue to publish inferior papers while
they send the best to our _Transactions_."

And, again, with all the Societies represented on the Council, "even if
every Science had its Society, and if they published everything,
withholding their best papers [i.e., from the Royal Society], which they
would not be likely to do, still there would remain to the Royal Society
...." Lord Rosse seems to imagine that the minor Societies themselves
transfer their best papers to the Royal Society; that if, for instance, the
Astronomical Society were to receive from A.B. a paper of unusual merit,
the Society would transfer it to the Royal Society. This is quite wrong:
any preference of the Royal to another Society is the work of the
contributor himself. But it shows how well hafted is the Royal Society's
claim, that a President should acquire the notion that it is acknowledged
and acted upon by the other Societies, in their joint and corporate
capacities. To the pretension thus made I never could give any sympathy.
When I first heard Mr. Christie, Sec. R. S., set it forth at the
anniversary dinner of the Astronomical Society, I remembered the Baron in
Walter Scott:

 "Of Gilbert the Galliard a heriot he sought,
  Saying, Give thy best steed as a vassal ought."

And I remembered the answer:

 "Lord and Earl though thou be, I trow
  I can rein Buck's-foot better than thou."

Fully conceding that the Royal Society is entitled to preeminent rank and
all the respect due to age and services, I could not, nor can I now, see
any more obligation in a contributor to send his best to that Society than
he can make out to be due to himself. This pretension, in my mind, was
hooked on, by my historical mode of viewing things already mentioned, to my
knowledge of the fact that the Royal {28} Society--the chief fault,
perhaps, lying with its President, Sir Joseph Banks--had sternly set itself
against the formation of other societies; the Geological and Astronomical,
for instance, though it must be added that the chief rebels came out of the
Society itself. And so a certain not very defined dislike was generated in
my mind--an anti-aristocratic affair--to the body which seemed to me a
little too uplifted. This would, I daresay, have worn off; but a more
formidable objection arose. My views of physical science gradually arranged
themselves into a form which would have rendered F.R.S., as attached to my
name, a false representation symbol. The Royal Society is the great
fortress of general physics: and in the philosophy of our day, as to
general physics, there is something which makes the banner of the R.S. one
under which I cannot march. Everybody who saw the three letters after my
name would infer certain things as to my mode of thought which would not be
true inference. It would take much space to explain this in full. I may
hereafter, perhaps, write a budget of collected results of the _a priori
philosophy_, the nibbling at the small end of omniscience, and the effect
it has had on common life, from the family parlor to the jury-box, from the
girls'-school to the vestry-meeting. There are in the Society those who
would, were there no others, prevent my criticism, be its conclusions true
or false, from having any basis; but they are in the minority.

There is no objection to be made to the principles of philosophy in vogue
at the Society, when they are stated as principles; but there is an
omniscience in daily practice which the principles repudiate. In like
manner, the most retaliatory Christians have a perfect form of round words
about behavior to those who injure them; none of them are as candid as a
little boy I knew, who, to his mother's admonition, You should love your
enemies, answered--Catch me at it!

Years ago, a change took place which would alone have {29} put a sufficient
difficulty in the way. The co-operative body got tired of getting funds
from and lending name to persons who had little or no science, and wanted
F.R.S. to be in every case a Fellow Really Scientific. Accordingly, the
number of yearly elections was limited to fifteen recommended by the
Council, unless the general body should choose to elect more; which it does
not do. The election is now a competitive examination: it is no longer--Are
you able and willing to promote natural knowledge; it is--Are you one of
the upper fifteen of those who make such claim. In the list of
candidates--a list rapidly growing in number--each year shows from thirty
to forty of those whom Newton and Boyle would have gladly welcomed as
fellow-laborers. And though the rejected of one year may be the accepted of
the next--or of the next but one, or but two, if self-respect will permit
the candidate to hang on--yet the time is clearly coming when many of those
who ought to be welcomed will be excluded for life, or else shelved at
last, when past work, with a scientific peerage. Coupled with this attempt
to create a kind of order of knighthood is an absurdity so glaring that it
should always be kept before the general eye. This distinction, this mark
set by science upon successful investigation, is of necessity a
class-distinction. Rowan Hamilton, one of the greatest names of our day in
mathematical science, never could attach F.R.S. to his name--_he could not
afford it_. There is a condition precedent--Four Red Sovereigns. It is four
pounds a year, or--to those who have contributed to the Transactions--forty
pounds down. This is as it should be: the Society must be supported. But it
is not as it should be that a kind of title of honor should be forged, that
a body should take upon itself to confer distinctions _for science_, when
it is in the background--and kept there when the distinction is
trumpeted--that the wearer is a man who can spare four pounds a year. I am
well aware that in England a person who is not gifted either by nature or
art, with this amount of money power, {30} is, with the mass, a very
second-rate sort of Newton, whatever he may be in the field of
investigation. Even men of science, so called, have this feeling. I know
that the _scientific advisers_ of the Admiralty, who, years ago, received
100 pounds a year each for his trouble, were sneered at by a wealthy
pretender as "fellows to whom a hundred a year is an object." Dr. Thomas
Young was one of them. To a bookish man--I mean a man who can manage to
collect books--there is no tax. To myself, for example, 40 pounds worth of
books deducted from my shelves, and the life-use of the Society's splendid
library instead, would have been a capital exchange. But there may be, and
are, men who want books, and cannot pay the Society's price. The Council
would be very liberal in allowing books to be consulted. I have no doubt
that if a known investigator were to call and ask to look at certain books,
the Assistant-Secretary would forthwith seat him with the books before him,
absence of F.R.S. not in any wise withstanding. But this is not like having
the right to consult any book on any day, and to take it away, if farther
wanted.

So much for the Royal Society as concerns myself. I must add that there is
not a spark of party feeling against those who wilfully remain outside. The
better minds of course know better; and the smaller _savants_ look
complacently on the idea of an outer world which makes _élite_ of them. I
have done such a thing as serve on a committee of the Society, and report
on a paper: they had the sense to ask, and I had the sense to see that none
of my opinions were compromised by compliance. And I will be of any use
which does not involve the status of _homo trium literarum_; as I have
elsewhere explained, I would gladly be _Fautor Realis Scientiæ_, but I
would not be taken for _Falsæ Rationis Sacerdos_.

Nothing worse will ever happen to me than the smile which individuals
bestow on a man who does not _groove_. Wisdom, like religion, belongs to
majorities; who can {31} wonder that it should be so thought, when it is so
clearly pictured in the New Testament from one end to the other?

The counterpart of _paradox_, the isolated opinion of one or of few, is the
general opinion held by all the rest; and the counterpart of false and
absurd paradox is what is called the "vulgar error," the _pseudodox_. There
is one great work on this last subject, the _Pseudodoxia Epidemica_ of Sir
Thomas Browne, the famous author of the _Religio Medici_; it usually goes
by the name of Browne "On Vulgar Errors" (1st ed. 1646; 6th, 1672). A
careful analysis of this work would show that vulgar errors are frequently
opposed by scientific errors; but good sense is always good sense, and
Browne's book has a vast quantity of it.

As an example of bad philosophy brought against bad observation. The
Amphisbæna serpent was supposed to have two heads, one at each end; partly
from its shape, partly because it runs backwards as well as forwards. On
this Sir Thomas Browne makes the following remarks:

"And were there any such species or natural kind of animal, it would be
hard to make good those six positions of body which, according to the three
dimensions, are ascribed unto every Animal; that is, _infra_, _supra_,
_ante_, _retro_, _dextrosum_, _sinistrosum_: for if (as it is determined)
that be the anterior and upper part wherein the senses are placed, and that
the posterior and lower part which is opposite thereunto, there is no
inferior or former part in this Animal; for the senses, being placed at
both extreams, doth make both ends anterior, which is impossible; the terms
being Relative, which mutually subsist, and are not without each other. And
therefore this duplicity was ill contrived to place one head at both
extreams, and had been more tolerable to have settled three or four at one.
And therefore also Poets have been more reasonable than Philosophers, and
_Geryon_ or _Cerberus_ less monstrous than _Amphisbæna_." {32}

There may be paradox upon paradox: and there is a good instance in the
eighth century in the case of Virgil, an Irishman, Bishop of Salzburg and
afterwards Saint, and his quarrels with Boniface, an Englishman, Archbishop
of Mentz, also afterwards Saint. All we know about the matter is, that
there exists a letter of 748 from Pope Zachary, citing Virgil--then, it
seems, at most a simple priest, though the Pope was not sure even of
that--to Rome to answer the charge of maintaining that there is another
world (_mundus_) under our earth (_terra_), with another sun and another
moon. Nothing more is known: the letter contains threats in the event of
the charge being true; and there history drops the matter. Since Virgil was
afterwards a Bishop and a Saint, we may fairly conclude that he died in the
full flower of his orthodox reputation. It has been supposed--and it seems
probable--that Virgil maintained that the earth is peopled all the way
round, so that under some spots there are antipodes; that his
contemporaries, with very dim ideas about the roundness of the earth, and
most of them with none at all, interpreted him as putting another earth
under ours--turned the other way, probably, like the second piece of
bread-and-butter in a sandwich, with a sun and moon of its own. In the
eighth century this would infallibly have led to an underground Gospel, an
underground Pope, and an underground Avignon for him to live in. When, in
later times, the idea of inhabitants for the planets was started, it was
immediately asked whether they had sinned, whether Jesus Christ died for
_them_, whether their wine and their water could be lawfully used in the
sacraments, etc.

On so small a basis as the above has been constructed a companion case to
the persecution of Galileo. On one side the positive assertion, with
indignant comment, that Virgil was deposed for antipodal heresy, on the
other, serious attempts at justification, palliation, or mystification.
Some writers say that Virgil was found guilty; others that he gave
satisfactory explanation, and became very good friends with {33} Boniface:
for all which see Bayle. Some have maintained that the antipodist was a
different person from the canonized bishop: there is a second Virgil, made
to order. When your shoes pinch, and will not stretch, always throw them
away and get another pair: the same with your facts. Baronius was not up to
the plan of a substitute: his commentator Pagi (probably writing about
1690) argues for it in a manner which I think Baronius would not have
approved. This Virgil was perhaps a slippery fellow. The Pope says he hears
that Virgil pretended licence from him to claim one of some new bishoprics:
this he declares is totally false. It is part of the argument that such a
man as this could not have been created a Bishop and a Saint: on this point
there will be opinions and opinions.[10]

Lactantius, four centuries before, had laughed at the antipodes in a manner
which seems to be ridicule thrown on the idea of the earth's roundness.
Ptolemy, without reference to the antipodes, describes the extent of the
inhabited part of the globe in a way which shows that he could have had no
objection to men turned opposite ways. Probably, in the eighth century, the
roundness of the earth was matter of thought only to astronomers. It should
always be remembered, especially by those who affirm persecution of a true
opinion, that but for our knowing from Lactantius that the antipodal notion
had been matter of assertion and denial among theologians, we could never
have had any great confidence in Virgil really having maintained the simple
theory of the existence of antipodes. And even now we are not entitled to
affirm it as having historical proof: the evidence {34} goes to Virgil
having been charged with very absurd notions, which it seems more likely
than not were the absurd constructions which ignorant contemporaries put
upon sensible opinions of his.

One curious part of this discussion is that neither side has allowed Pope
Zachary to produce evidence to character. He shall have been an Urban, say
the astronomers; an Urban he ought to have been, say the theologians. What
sort of man was Zachary? He was eminently sensible and conciliatory; he
contrived to make northern barbarians hear reason in a way which puts him
high among that section of the early popes who had the knack of managing
uneducated swordsmen. He kept the peace in Italy to an extent which
historians mention with admiration. Even Bale, that Maharajah of
pope-haters, allows himself to quote in favor of Zachary, that "multa
Papalem dignitatem decentia, eademque præclara (scilicet) opera
confecit."[11] And this, though so willing to find fault that, speaking of
Zachary putting a little geographical description of the earth on the
portico of the Lateran Church, he insinuates that it was intended to affirm
that the Pope was lord of the whole. Nor can he say how long Zachary held
the see, except by announcing his death in 752, "cum decem annis
pestilentiæ sedi præfuisset."[12]

There was another quarrel between Virgil and Boniface which is an
illustration. An ignorant priest had baptized "in nomine Patri_a_, et
Fili_a_ et Spiritu_a_ Sancta." Boniface declared the rite null and void:
Virgil maintained the contrary; and Zachary decided in favor of Virgil, on
the ground that the absurd form was only ignorance of Latin, and not
heresy. It is hard to believe that this man deposed a priest for asserting
the whole globe to be inhabited. To me the little information that we have
seems {35} to indicate--but not with certainty--that Virgil maintained the
antipodes: that his ignorant contemporaries travestied his theory into that
of an underground cosmos; that the Pope cited him to Rome to explain his
system, which, as reported, looked like what all would then have affirmed
to be heresy; that he gave satisfactory explanations, and was dismissed
with honor. It may be that the educated Greek monk, Zachary, knew his
Ptolemy well enough to guess what the asserted heretic would say; we have
seen that he seems to have patronized geography. The _description_ of the
earth, according to historians, was a _map_; this Pope may have been more
ready than another to prick up his ears at any rumor of geographical
heresy, from hope of information. And Virgil, who may have entered the
sacred presence as frightened as Jacquard, when Napoleon I sent for him and
said, with a stern voice and threatening gesture, "You are the man who can
tie a knot in a stretched string," may have departed as well pleased as
Jacquard with the riband and pension which the interview was worth to him.

A word more about Baronius. If he had been pope, as he would have been but
for the opposition of the Spaniards, and if he had lived ten years longer
than he did, and if Clavius, who would have been his astronomical adviser,
had lived five years longer than he did, it is probable, nay almost
certain, that the great exhibition, the proceeding against Galileo, would
not have furnished a joke against theology in all time to come. For
Baronius was sensible and witty enough to say that in the Scriptures the
Holy Spirit intended to teach how to go to Heaven, not how Heaven goes; and
Clavius, in his last years, confessed that the whole system of the heavens
had broken down, and must be mended.

The manner in which the Galileo case, a reality, and the Virgil case, a
fiction, have been hawked against the Roman see are enough to show that the
Pope and his adherents have not cared much about physical philosophy. In
truth, orthodoxy has always had other fish to fry. Physics, which {36} in
modern times has almost usurped the name _philosophy_, in England at least,
has felt a little disposed to clothe herself with all the honors of
persecution which belong to the real owner of the name. But the bishops,
etc. of the Middle Ages knew that the contest between nominalism and
realism, for instance, had a hundred times more bearing upon orthodoxy than
anything in astronomy, etc. A wrong notion about _substance_ might play the
mischief with _transubstantiation_.

The question of the earth's motion was the single point in which orthodoxy
came into real contact with science. Many students of physics were
suspected of magic, many of atheism: but, stupid as the mistake may have
been, it was _bona fide_ the magic or the atheism, not the physics, which
was assailed. In the astronomical case it was the very doctrine, as a
doctrine, independently of consequences, which was the _corpus delicti_:
and this because it contradicted the Bible. And so it did; for the
stability of the earth is as clearly assumed from one end of the Old
Testament to the other as the solidity of iron. Those who take the Bible to
be _totidem verbis_ dictated by the God of Truth can refuse to believe it;
and they make strange reasons. They undertake, _a priori_, to settle Divine
intentions. The Holy Spirit did not _mean_ to teach natural philosophy:
this they know beforehand; or else they infer it from finding that the
earth does move, and the Bible says it does not. Of course, ignorance
apart, every word is truth, or the writer did not mean truth. But this puts
the whole book on its trial: for we never can find out what the writer
meant, until we otherwise find out what is true. Those who like may, of
course, declare for an inspiration over which they are to be viceroys; but
common sense will either accept verbal meaning or deny verbal inspiration.

       *       *       *       *       *


{37}

A BUDGET OF PARADOXES.

VOLUME I.

THE STORY OF BURIDAN'S ASS.

    Questiones Morales, folio, 1489 [Paris]. By T. Buridan.

This is the title from the Hartwell Catalogue of Law Books. I suppose it is
what is elsewhere called the "Commentary on the Ethics of Aristotle,"
printed in 1489.[13] Buridan[14] (died about 1358) is the creator of the
famous ass which, as _Burdin's_[15] ass, was current in Burgundy, perhaps
is, as a vulgar proverb. Spinoza[16] says it was a jenny ass, and that a
man would not have been so foolish; but whether the compliment is paid to
human or to masculine character does not appear--perhaps to both in one.
The story _told_ about the famous paradox is very curious. The Queen of
France, Joanna or Jeanne, was in the habit of sewing her lovers up in
sacks, and throwing them into the Seine; not for blabbing, but that they
might not blab--certainly the safer plan. Buridan was exempted, and, in
gratitude, invented the sophism. What it has to do with the matter {38} has
never been explained. Assuredly _qui facit per alium facit per se_ will
convict Buridan of prating. The argument is as follows, and is seldom told
in full. Buridan was for free-will--that is, will which determines conduct,
let motives be ever so evenly balanced. An ass is _equally_ pressed by
hunger and by thirst; a bundle of hay is on one side, a pail of water on
the other. Surely, you will say, he will not be ass enough to die for want
of food or drink; he will then make a choice--that is, will choose between
alternatives of equal force. The problem became famous in the schools; some
allowed the poor donkey to die of indecision; some denied the possibility
of the balance, which was no answer at all.



MICHAEL SCOTT'S DEVILS.

The following question is more difficult, and involves free-will to all who
answer--"Which you please." If the northern hemisphere were land, and all
the southern hemisphere water, ought we to call the northern hemisphere an
island, or the southern hemisphere a lake? Both the questions would be good
exercises for paradoxers who must be kept employed, like Michael
Scott's[17] devils. The wizard {39} knew nothing about squaring the circle,
etc., so he set them to make ropes out of sea sand, which puzzled them.
Stupid devils; much of our glass is sea sand, and it makes beautiful
thread. Had Michael set them to square the circle or to find a perpetual
motion, he would have done his work much better. But all this is
conjecture: who knows that I have not hit on the very plan he adopted?
Perhaps the whole race of paradoxers on hopeless subjects are Michael's
subordinates, condemned to transmigration after transmigration, until their
task is done.

The above was not a bad guess. A little after the time when the famous
Pascal papers[18] were produced, I came into possession of a correspondence
which, but for these papers, I should have held too incredible to be put
before the world. But when one sheep leaps the ditch, another will follow:
so I gave the following account in the _Athenæum_ of October 5, 1867:

"The recorded story is that Michael Scott, being bound by contract to
produce perpetual employment for a number of young demons, was worried out
of his life in inventing jobs for them, until at last he set them to make
ropes out of sea sand, which they never could do. We have obtained a very
curious correspondence between the wizard Michael and his demon-slaves; but
we do not feel at liberty to say how it came into our hands. We much regret
that we did not receive it in time for the British Association. It appears
that the story, true as far as it goes, was never finished. The demons
easily conquered the rope difficulty, by the simple process of making the
sand into glass, and spinning the glass into thread, which they twisted.
Michael, thoroughly disconcerted, hit upon the plan of setting some to {40}
square the circle, others to find the perpetual motion, etc. He commanded
each of them to transmigrate from one human body into another, until their
tasks were done. This explains the whole succession of cyclometers, and all
the heroes of the Budget. Some of this correspondence is very recent; it is
much blotted, and we are not quite sure of its meaning: it is full of
figurative allusions to driving something illegible down a steep into the
sea. It looks like a humble petition to be allowed some diversion in the
intervals of transmigration; and the answer is--

  Rumpat et serpens iter institutum,[19]

--a line of Horace, which the demons interpret as a direction to come
athwart the proceedings of the Institute by a sly trick. Until we saw this,
we were suspicious of M. Libri,[20] the unvarying blunders of the
correspondence look like knowledge. To be always out of the road requires a
map: genuine ignorance occasionally lapses into truth. We thought it
possible M. Libri might have played the trick to show how easily the French
are deceived; but with our present information, our minds are at rest on
the subject. We see M. Chasles does not like to avow the real source of
information: he will not confess himself a spiritualist."



PHILO OF GADARA.

Philo of Gadara[21] is asserted by Montucla,[22] on the {41} authority of
Eutocius,[23] the commentator on Archimedes, to have squared the circle
within the _ten-thousandth_ part of a unit, that is, to _four_ places of
decimals. A modern classical dictionary represents it as done by Philo to
_ten thousand_ places of decimals. Lacroix comments on Montucla to the
effect that _myriad_ (in Greek _ten thousand_) is here used as we use it,
vaguely, for an immense number. On looking into Eutocius, I find that not
one definite word is said about the extent to which Philo carried the
matter. I give a translation of the passage:

"We ought to know that Apollonius Pergæus, in his Ocytocium [this work is
lost], demonstrated the same by other numbers, and came nearer, which seems
more accurate, but has nothing to do with Archimedes; for, as before said,
he aimed only at going near enough for the wants of life. Neither is Porus
of Nicæa fair when he takes Archimedes to task for not giving a line
accurately equal to the circumference. He says in his Cerii that his
teacher, Philo of Gadara, had given a more accurate approximation ([Greek:
eis akribesterous arithmous agagein]) than that of Archimedes, or than 7 to
22. But all these [the rest as well as Philo] miss the intention. They
multiply and divide by _tens of thousands_, which no one can easily do,
unless he be versed in the logistics [fractional computation] of Magnus
[now unknown]."

Montucla, or his source, ought not to have made this mistake. He had been
at the Greek to correct Philo _Gadetanus_, as he had often been called, and
he had brought away {42} and quoted [Greek: apo Gadarôn]. Had he read two
sentences further, he would have found the mistake.

We here detect a person quite unnoticed hitherto by the moderns, Magnus the
arithmetician. The phrase is ironical; it is as if we should say, "To do
this a man must be deep in Cocker."[24] Accordingly, Magnus, Baveme,[25]
and Cocker, are three personifications of arithmetic; and there may be
more.



ON SQUARING THE CIRCLE.

Aristotle, treating of the category of relation, denies that the quadrature
has been found, but appears to assume that it can be done. Boethius,[26] in
his comment on the passage, says that it has been done since Aristotle, but
that the demonstration is too long for him to give. Those who have no
notion of the quadrature question may look at the _English Cyclopædia_,
art. "Quadrature of the Circle."

    Tetragonismus. Id est circuli quadratura per Campanum, Archimedem
    Syracusanum, atque Boetium mathematicæ perspicacissimos adinventa.--At
    the end, Impressum Venetiis per Ioan. Bapti. Sessa. Anno ab
    incarnatione Domini, 1503. Die 28 Augusti.

{43}

This book has never been noticed in the history of the subject, and I
cannot find any mention of it. The quadrature of Campanus[27] takes the
ratio of Archimedes,[28] 7 to 22 to be absolutely correct; the account
given of Archimedes is not a translation of his book; and that of Boetius
has more than is in Boet_h_ius. This book must stand, with the next, as the
earliest in print on the subject, until further showing: Murhard[29] and
Kastner[30] have nothing so early. It is edited by Lucas Gauricus,[31] who
has given a short preface. Luca Gaurico, Bishop of Civita Ducale, an
astrologer of astrologers, published this work at about thirty years of
age, and lived to eighty-two. His works are collected in folios, but I do
not know whether they contain this production. The poor fellow could never
tell his own fortune, because his father neglected to note the hour and
minute of his birth. But if there had been anything in astrology, he could
have worked back, as Adams[32] and Leverrier[33] did when they caught {44}
Neptune: at sixty he could have examined every minute of his day of birth,
by the events of his life, and so would have found the right minute. He
could then have gone on, by rules of prophecy. Gauricus was the
mathematical teacher of Joseph Scaliger,[34] who did him no credit, as we
shall see.



BOVILLUS ON THE QUADRATURE PROBLEM.

    In hoc opere contenta Epitome.... Liber de quadratura Circuli....
    Paris, 1503, folio.

The quadrator is Charles Bovillus,[35] who adopted the views of Cardinal
Cusa,[36] presently mentioned. Montucla is hard on his compatriot, who, he
says, was only saved from the laughter of geometers by his obscurity.
Persons must guard against most historians of mathematics in one point:
they frequently attribute to _his own_ age the obscurity which a writer has
in _their own_ time. This tract was printed by Henry Stephens,[37] at the
instigation of Faber Stapulensis,[38] {45} and is recorded by Dechales,[39]
etc. It was also introduced into the _Margarita Philosophica_ of 1815,[40]
in the same appendix with the new perspective from Viator. This is not
extreme obscurity, by any means. The quadrature deserved it; but that is
another point.

It is stated by Montucla that Bovillus makes [pi] = [root]10. But Montucla
cites a work of 1507, _Introductorium Geometricum_, which I have never
seen.[41] He finds in it an account which Bovillus gives of the quadrature
of the peasant laborer, and describes it as agreeing with his own. But the
description makes [pi] = 3-1/8, which it thus appears Bovillus could not
distinguish from [root]10. It seems also that this 3-1/8, about which we
shall see so much in the sequel, takes its rise in the thoughtful head of a
poor laborer. It does him great honor, being so near the truth, and he
having no means of instruction. In our day, when an ignorant person chooses
to bring his fancy forward in opposition to demonstration which he will not
study, he is deservedly laughed at.

{46}



THE STORY OF LACOMME'S ATTEMPT AT QUADRATURE.

Mr. James Smith,[42] of Liverpool--hereinafter notorified--attributes the
first announcement of 3-1/8 to M. Joseph Lacomme, a French well-sinker, of
whom he gives the following account:

"In the year 1836, at which time Lacomme could neither read nor write, he
had constructed a circular reservoir and wished to know the quantity of
stone that would be required to pave the bottom, and for this purpose
called on a professor of mathematics. On putting his question and giving
the diameter, he was surprised at getting the following answer from the
Professor: _'Qu'il lui était impossible de le lui dire au juste, attendu
que personne n'avait encore pu trouver d'une manière exacte le rapport de
la circonférence au diametre.'_[43] From this he was led to attempt the
solution of the problem. His first process was purely mechanical, and he
was so far convinced he had made the discovery that he took to educating
himself, and became an expert arithmetician, and then found that
arithmetical results agreed with his mechanical experiments. He appears to
have eked out a bare existence for many years by teaching arithmetic, all
the time struggling to get a hearing from some of the learned societies,
but without success. In the year 1855 he found his way to Paris, where, as
if by accident, he made the acquaintance of a young gentleman, son of M.
Winter, a commissioner of police, and taught him his peculiar methods of
calculation. The young man was so enchanted that he strongly recommended
Lacomme to his father, and {47} subsequently through M. Winter he obtained
an introduction to the President of the Society of Arts and Sciences of
Paris. A committee of the society was appointed to examine and report upon
his discovery, and the society at its _séance_ of March 17, 1856, awarded a
silver medal of the first class to M. Joseph Lacomme for his discovery of
the true ratio of diameter to circumference in a circle. He subsequently
received three other medals from other societies. While writing this I have
his likeness before me, with his medals on his breast, which stands as a
frontispiece to a short biography of this extraordinary man, for which I am
indebted to the gentleman who did me the honor to publish a French
translation of the pamphlet I distributed at the meeting of the British
Association for the Advancement of Science, at Oxford, in
1860."--_Correspondent_, May 3, 1866.

My inquiries show that the story of the medals is not incredible. There are
at Paris little private societies which have not so much claim to be
exponents of scientific opinion as our own Mechanics' Institutes. Some of
them were intended to give a false lustre: as the "Institut Historique,"
the members of which are "Membre de l'Institut Historique." That M. Lacomme
should have got four medals from societies of this class is very possible:
that he should have received one from any society at Paris which has the
least claim to give one is as yet simply incredible.



NICOLAUS OF CUSA'S ATTEMPT.

    Nicolai de Cusa Opera Omnia. Venice, 1514. 3 vols. folio.

The real title is "Hæc accurata recognitio trium voluminum operum clariss.
P. Nicolai Cusæ ... proxime sequens pagina monstrat."[44] Cardinal Cusa,
who died in 1464, is one of the earliest modern attempters. His quadrature
is found in the second volume, and is now quite unreadable.

{48} In these early days every quadrator found a geometrical opponent, who
finished him. Regimontanus[45] did this office for the Cardinal.



HENRY CORNELIUS AGRIPPA.

    De Occulta Philosophia libri III. By Henry Cornelius Agrippa. Lyons,
    1550, 8vo.

    De incertitudine et vanitate scientiarum. By the same. Cologne, 1531,
    8vo.

The first editions of these works were of 1530, as well as I can make out;
but the first was in progress in 1510.[46] In the second work Agrippa
repents of having wasted time on the magic of the first; but all those who
actually deal with demons are destined to eternal fire with Jamnes and
Mambres and Simon Magus. This means, as is the fact, that his occult
philosophy did not actually enter upon _black_ magic, but confined itself
to the power of the stars, of numbers, etc. The fourth book, which appeared
after the death of Agrippa, and really concerns dealing with evil spirits,
is undoubtedly spurious. It is very difficult to make out what Agrippa
really believed on the subject. I have introduced his books as the most
marked specimens of treatises on magic, a paradox of our day, though not
far from orthodoxy in his; and here I should have ended my notice, if I had
not casually found something more interesting to the reader of our day.

{49}



WHICH LEADS TO WALTER SCOTT.

Walter Scott, it is well known, was curious on all matters connected with
magic, and has used them very widely. But it is hardly known how much pains
he has taken to be correct, and to give the real thing. The most decided
detail of a magical process which is found in his writings is that of
Dousterswivel in _The Antiquary_; and it is obvious, by his accuracy of
process, that he does not intend the adept for a mere impostor, but for one
who had a lurking belief in the efficacy of his own processes, coupled with
intent to make a fraudulent use of them. The materials for the process are
taken from Agrippa. I first quote Mr. Dousterswivel:

"... I take a silver plate when she [the moon] is in her fifteenth mansion,
which mansion is in de head of _Libra_, and I engrave upon one side de
worts _Schedbarschemoth Scharta_ch_an_ [_ch_ should be _t_]--dat is, de
Intelligence of de Intelligence of de moon--and I make his picture like a
flying serpent with a turkey-cock's head--vary well--Then upon this side I
make de table of de moon, which is a square of nine, multiplied into
itself, with eighty-one numbers [nine] on every side and diameter nine...."

In the _De Occulta Philosophia_, p. 290, we find that the fifteenth mansion
of the moon _incipit capite Libræ_, and is good _pro extrahendis
thesauris_, the object being to discover hidden treasure. In p. 246, we
learn that a _silver_ plate must be used with the moon. In p. 248, we have
the words which denote the Intelligence, etc. But, owing to the falling of
a number into a wrong line, or the misplacement of a line, one or
other--which takes place in all the editions I have examined--Scott has,
sad to say, got hold of the wrong words; he has written down the _demon of
the demons_ of the moon. Instead of the gibberish above, it should have
been _Malcha betarsisim hed beruah schenhakim_. In p. 253, we have the
magic square of the moon, with eighty-one numbers, and the symbol for the
Intelligence, which Scott likens to a flying {50} serpent with a
turkey-cock's head. He was obliged to say something; but I will stake my
character--and so save a woodcut--on the scratches being more like a pair
of legs, one shorter than the other, without a body, jumping over a
six-barred gate placed side uppermost. Those who thought that Scott forged
his own nonsense, will henceforth stand corrected. As to the spirit
Peolphan, etc., no doubt Scott got it from the authors he elsewhere
mentions, Nicolaus Remigius[47] and Petrus Thyracus; but this last word
should be Thyræus.

The tendency of Scott's mind towards prophecy is very marked, and it is
always fulfilled. Hyder, in his disguise, calls out to Tippoo: "Cursed is
the prince who barters justice for lust; he shall die in the gate by the
sword of the stranger." Tippoo was killed in a gateway at Seringapatam.[48]



FINAEUS ON CIRCLE SQUARING.

    Orontii Finaei ... Quadratura Circuli. Paris, 1544, 4to.

Orontius[49] squared the circle out of all comprehension; but he was killed
by a feather from his own wing. His {51} former pupil, John Buteo,[50] the
same who--I believe for the first time--calculated the question of Noah's
ark, as to its power to hold all the animals and stores, unsquared him
completely. Orontius was the author of very many works, and died in 1555.
Among the laudatory verses which, as was usual, precede this work, there is
one of a rare character: a congratulatory ode to the wife of the author.
The French now call this writer Oronce Finée; but there is much difficulty
about delatinization. Is this more correct than Oronce Fine, which the
translator of De Thou uses? Or than Horonce Phine, which older writers
give? I cannot understand why M. de Viette[51] should be called Viète,
because his Latin name is Vieta. It is difficult to restore Buteo; for not
only now is _butor_ a blockhead as well as a bird, but we really cannot
know what kind of bird Buteo stood for. We may be sure that Madame Fine was
Denise Blanche; for Dionysia Candida can mean nothing else. Let her shade
rejoice in the fame which Hubertus Sussannæus has given her.

I ought to add that the quadrature of Orontius, and solutions of all the
other difficulties, were first published in _De Rebus Mathematicis Hactenus
Desideratis_,[52] of which I have not the date.



{52}

DUCHESNE, AND A DISQUISITION ON ETYMOLOGY.

    Nicolai Raymari Ursi Dithmarsi Fundamentum Astronomicum, id est, nova
    doctrina sinuum et triangulorum.... Strasburg, 1588, 4to.[53]

People choose the name of this astronomer for themselves: I take _Ursus_,
because he _was_ a bear. This book gave the quadrature of Simon
Duchesne,[54] or à Quercu, which excited Peter Metius,[55] as presently
noticed. It also gave that unintelligible reference to Justus Byrgius which
has been used in the discussion about the invention of logarithms.[56]

The real name of Duchesne is Van der Eycke. I have met with a tract in
Dutch, _Letterkundige Aanteekeningen_, upon Van Eycke, Van Ceulen,[57]
etc., by J. J. Dodt van Flensburg,[58] which I make out to be since 1841 in
date. I should {53} much like a translation of this tract to be printed,
say in the _Phil. Mag._ Dutch would be clear English if it were properly
spelt. For example, _learn-master_ would be seen at once to be _teacher_;
but they will spell it _leermeester_. _Of these_ they write as _van deze_;
_widow_ they make _weduwe_. All this is plain to me, who never saw a Dutch
dictionary in my life; but many of their misspellings are quite
unconquerable.



FALCO'S RARE TRACT.

    Jacobus Falco Valentinus, miles Ordinis Montesiani, hanc circuli
    quadraturam invenit. Antwerp, 1589, 4to.[59]

The attempt is more than commonly worthless; but as Montucla and others
have referred to the verses at the end, and as the tract is of the rarest,
I will quote them:

      _Circulus loquitur._
  Vocabar ante circulus
  Eramque curvus undique
  Ut alta solis orbita
  Et arcus ille nubium.
  Eram figura nobilis
  Carensque sola origine
  Carensque sola termino.
  Modo indecora prodeo
  Novisque foedor angulis.
  Nec hoc peregit Archytas[60]
  Neque Icari pater neque
  Tuus, Iapete, filius.
  Quis ergo casus aut Deus
  Meam quadravit aream?

      _Respondet auctor._
  Ad alta Turiæ ostia
  Lacumque limpidissimum
  Sita est beata civitas
  {54}
  Parum Saguntus abfuit
  Abestque Sucro plusculum.
  Hic est poeta quispiam
  Libenter astra consulens
  Sibique semper arrogans
  Negata doctioribus,
  Senex ubique cogitans
  Sui frequenter immemor
  Nec explicare circinum
  Nec exarare lineas
  Sciens ut ipse prædicat.
  Hic ergo bellus artifex
  Tuam quadravit aream.[61]

Falco's verses are pretty, if the U-mysteries be correct; but of these
things I have forgotten--what I knew. [One mistake has been pointed out to
me: it is Arch[=y]tas].

As a specimen of the way in which history is written, I copy the account
which Montucla--who is accurate when he writes about what he has
seen--gives of these verses. He gives the date 1587; he places the verses
at the beginning instead of the end; he says the circle thanks its
quadrator affectionately; and he says the good and modest chevalier gives
all the glory to the patron saint of his order. All of little consequence,
as it happens; but writing at second-hand makes as complete mistakes about
more important matters.

{55}



BUNGUS ON THE MYSTERY OF NUMBER.

    Petri Bungi Bergomatis Numerorum mysteria. Bergomi [Bergamo], 1591,
    4to. Second Edition.

The first edition is said to be of 1585;[62] the third, Paris, 1618. Bungus
is not for my purpose on his own score, but those who gave the numbers
their mysterious characters: he is but a collector. He quotes or uses 402
authors, as we are informed by his list; this just beats Warburton,[63]
whom some eulogist or satirist, I forget which, holds up as having used 400
authors in some one work. Bungus goes through 1, 2, 3, etc., and gives the
account of everything remarkable in which each number occurs; his accounts
not being always mysterious. The numbers which have nothing to say for
themselves are omitted: thus there is a gap between 50 and 60. In treating
666, Bungus, a good Catholic, could not compliment the Pope with it, but he
fixes it on Martin Luther with a little forcing. If from A to I represent
1-10, from K to S 10-90, and from T to Z 100-500, we see:

   M   A   R   T   I   N     L   U   T   E   R   A
  30   1  80  100  9  40    20  200 100  5  80   1

which gives 666. Again, in Hebrew, _Lulter_ does the same:

  [Hebrew:   R    T    L    W   L]
            200  400  30    6  30

And thus two can play at any game. The second is better than the first: to
Latinize the surname and not the Christian {56} name is very unscholarlike.
The last number mentioned is a thousand millions; all greater numbers are
dismissed in half a page. Then follows an accurate distinction between
_number_ and _multitude_--a thing much wanted both in arithmetic and logic.



WHICH LEADS TO A STORY ABOUT THE ROYAL SOCIETY.

What may be the use of such a book as this? The last occasion on which it
was used was the following. Fifteen or sixteen years ago the Royal Society
determined to restrict the number of yearly admissions to fifteen men of
science, and noblemen _ad libitum_; the men of science being selected and
recommended by the Council, with a power, since practically surrendered, to
the Society to elect more. This plan appears to me to be directly against
the spirit of their charter, the true intent of which is, that all who are
fit should be allowed to promote natural knowledge in association, from and
after the time at which they are both fit and willing. It is also working
more absurdly from year to year; the tariff of fifteen per annum will soon
amount to the practical exclusion of many who would be very useful. This
begins to be felt already, I suspect. But, as appears above, the body of
the Society has the remedy in its own hands. When the alteration was
discussed by the Council, my friend the late Mr. Galloway,[64] then one of
the body, opposed it strongly, and inquired particularly into the reason
why _fifteen_, of all numbers, was the one to be selected. Was it because
fifteen is seven and eight, typifying the Old Testament Sabbath, and the
New Testament day of the resurrection following? Was it because Paul strove
fifteen days against Peter, proving that he was a doctor both of the Old
and New Testament? Was it because the prophet Hosea bought a lady {57} for
fifteen pieces of silver? Was it because, according to Micah, seven
shepherds and eight chiefs should waste the Assyrians? Was it because
Ecclesiastes commands equal reverence to be given to both Testaments--such
was the interpretation--in the words "Give a portion to seven, and also to
eight"? Was it because the waters of the Deluge rose fifteen cubits above
the mountains?--or because they lasted fifteen decades of days? Was it
because Ezekiel's temple had fifteen steps? Was it because Jacob's ladder
has been supposed to have had fifteen steps? Was it because fifteen years
were added to the life of Hezekiah? Was it because the feast of unleavened
bread was on the fifteenth day of the month? Was it because the scene of
the Ascension was fifteen stadia from Jerusalem? Was it because the
stone-masons and porters employed in Solomon's temple amounted to fifteen
myriads? etc. The Council were amused and astounded by the volley of
fifteens which was fired at them; they knowing nothing about Bungus, of
which Mr. Galloway--who did not, as the French say, indicate his
sources--possessed the copy now before me. In giving this anecdote I give a
specimen of the book, which is exceedingly rare. Should another edition
ever appear, which is not very probable, he would be but a bungling Bungus
who should forget the _fifteen_ of the Royal Society.



AND ALSO TO A QUESTION OF EVIDENCE.

[I make a remark on the different colors which the same person gives to one
story, according to the bias under which he tells it. My friend Galloway
told me how he had quizzed the Council of the Royal Society, to my great
amusement. Whenever I am struck by the words of any one, I carry away a
vivid recollection of position, gestures, tones, etc. I do not know whether
this be common or uncommon. I never recall this joke without seeing before
me my friend, leaning against his bookcase, with Bungus open in his hand,
and a certain half-depreciatory tone which he often used {58} when speaking
of himself. Long after his death, an F.R.S. who was present at the
discussion, told me the story. I did not say I had heard it, but I watched
him, with Galloway at the bookcase before me. I wanted to see whether the
two would agree as to the fact of an enormous budget of fifteens having
been fired at the Council, and they did agree perfectly. But when the
paragraph of the Budget appeared in the _Athenæum_, my friend, who seemed
rather to object to the _showing-up_, assured me that the thing was grossly
exaggerated; there was indeed a fifteen or two, but nothing like the number
I had given. I had, however, taken sharp note of the previous narration.



AND TO ANOTHER QUESTION OF EVIDENCE.

I will give another instance. An Indian officer gave me an account of an
elephant, as follows. A detachment was on the march, and one of the
gun-carriages got a wheel off the track, so that it was also off the
ground, and hanging over a precipice. If the bullocks had moved a step,
carriages, bullocks, and all must have been precipitated. No one knew what
could be done until some one proposed to bring up an elephant, and let him
manage it his own way. The elephant took a moment's survey of the fix, put
his trunk under the axle of the free wheel, and waited. The surrounders,
who saw what he meant, moved the bullocks gently forward, the elephant
followed, supporting the axle, until there was ground under the wheel, when
he let it quietly down. From all I had heard of the elephant, this was not
too much to believe. But when, years afterwards, I reminded my friend of
his story, he assured me that I had misunderstood him, that the elephant
was _directed_ to put his trunk under the wheel, and saw in a moment why.
This is reasonable sagacity, and very likely the correct account; but I am
quite sure that, in the fit of elephant-worship under which the story was
first told, it was told as I have first stated it.] {59}



GIORDANO BRUNO AND HIS PARADOXES.

    [Jordani Bruni Nolani de Monade, Numero et Figura ... item de
    Innumerabilibus, Immenso, et Infigurabili ... Frankfort, 1591, 8vo.[65]

I cannot imagine how I came to omit a writer whom I have known so many
years, unless the following story will explain it. The officer reproved the
boatswain for perpetual swearing; the boatswain answered that he heard the
officers swear. "Only in an emergency," said the officer. "That's just it,"
replied the other; "a boatswain's life is a life of 'mergency." Giordano
Bruno was all paradox; and my mind was not alive to his paradoxes, just as
my ears might have become dead to the boatswain's oaths. He was, as has
been said, a vorticist before Descartes,[66] an optimist before Leibnitz, a
Copernican before Galileo. It would be easy to collect a hundred strange
opinions of his. He was born about 1550, and was roasted alive at Rome,
February 17, 1600, for the maintenance and defence of the holy Church, and
the rights and liberties of the same. These last words are from the writ of
our own good James I, under which Leggatt[67] was roasted at Smithfield, in
March 1612; and if I had a copy of the instrument under which Wightman[68]
was roasted at Lichfield, a month afterwards, I daresay I should {60} find
something quite as edifying. I extract an account which I gave of Bruno in
the _Comp. Alm._ for 1855:

"He was first a Dominican priest, then a Calvinist; and was roasted alive
at Rome, in 1600, for as many heresies of opinion, religious and
philosophical, as ever lit one fire. Some defenders of the papal cause have
at least worded their accusations so to be understood as imputing to him
villainous actions. But it is positively certain that his death was due to
opinions alone, and that retractation, even after sentence, would have
saved him. There exists a remarkable letter, written from Rome on the very
day of the murder, by Scioppius[69] (the celebrated scholar, a waspish
convert from Lutheranism, known by his hatred to Protestants and Jesuits)
to Rittershusius,[70] a well-known Lutheran writer on civil and canon law,
whose works are in the index of prohibited books. This letter has been
reprinted by Libri (vol. iv. p. 407). The writer informs his friend (whom
he wished to convince that even a Lutheran would have burnt Bruno) that all
Rome would tell him that Bruno died for Lutheranism; but this is because
the Italians do not know the difference between one heresy and another, in
which simplicity (says the writer) may God preserve them. That is to say,
they knew the difference between a live heretic and a roasted one by actual
inspection, but had no idea of the difference between a Lutheran and a
Calvinist. The countrymen of Boccaccio would have smiled at the idea which
the German scholar entertained of them. They said Bruno was burnt for
Lutheranism, a name under which they classed all Protestants: and they are
better witnesses than Schopp, or Scioppius. He then proceeds to describe to
his Protestant friend (to whom he would certainly not have omitted any act
which both their churches would have condemned) the mass of opinions with
which Bruno was charged; as that there {61} are innumerable worlds, that
souls migrate, that Moses was a magician, that the Scriptures are a dream,
that only the Hebrews descended from Adam and Eve, that the devils would be
saved, that Christ was a magician and deservedly put to death, etc. In
fact, says he, Bruno has advanced all that was ever brought forward by all
heathen philosophers, and by all heretics, ancient and modern. A time for
retractation was given, both before sentence and after, which should be
noted, as well for the wretched palliation which it may afford, as for the
additional proof it gives that opinions, and opinions only, brought him to
the stake. In this medley of charges the Scriptures are a dream, while
Adam, Eve, devils, and salvation are truths, and the Saviour a deceiver. We
have examined no work of Bruno except the _De Monade_, etc., mentioned in
the text. A strong though strange _theism_ runs through the whole, and
Moses, Christ, the Fathers, etc., are cited in a manner which excites no
remark either way. Among the versions of the cause of Bruno's death is
_atheism_: but this word was very often used to denote rejection of
revelation, not merely in the common course of dispute, but by such
writers, for instance, as Brucker[71] and Morhof.[72] Thus Morhof says of
the _De Monade, etc._, that it exhibits no manifest signs of atheism. What
he means by the word is clear enough, when he thus speaks of a work which
acknowledges God in hundreds of places, and rejects opinions as blasphemous
in several. The work of Bruno in which his astronomical opinions are
contained is _De Monade, etc._ (Frankfort, 1591, 8vo). He is the most
thorough-going Copernican possible, and throws out almost every opinion,
true or false, which has ever been discussed by astronomers, from the
theory of innumerable inhabited worlds and systems to that {62} of the
planetary nature of comets. Libri (vol. iv)[73] has reprinted the most
striking part of his expressions of Copernican opinion."



THIS LEADS TO THE CHURCH QUESTION.

The Satanic doctrine that a church may employ force in aid of its dogma is
supposed to be obsolete in England, except as an individual paradox; but
this is difficult to settle. Opinions are much divided as to what the Roman
Church would do in England, if she could: any one who doubts that she
claims the right does not deserve an answer. When the hopes of the
Tractarian section of the High Church were in bloom, before the most
conspicuous intellects among them had _transgressed_ their ministry, that
they might go to their own place, I had the curiosity to see how far it
could be ascertained whether they held the only doctrine which makes me the
personal enemy of a sect. I found in one of their tracts the assumption of
a right to persecute, modified by an asserted conviction that force was not
efficient. I cannot now say that this tract was one of the celebrated
ninety; and on looking at the collection I find it so poorly furnished with
contents, etc., that nothing but searching through three thick volumes
would decide. In these volumes I find, augmenting as we go on, declarations
about the character and power of "the Church" which have a suspicious
appearance. The suspicion is increased by that curious piece of sophistry,
No. 87, on religious reserve. The queer paradoxes of that tract leave us in
doubt as to everything but this, that the church(man) is not bound to give
his whole counsel in all things, and not bound to say what the things are
in which he does not give it. It is likely enough that some of the "rights
and liberties" are but scantily described. There is now no fear; but the
time was when, if not fear, there might be a looking for of fear to come;
nobody could then be so {63} sure as we now are that the lion was only
asleep. There was every appearance of a harder fight at hand than was
really found needful.

Among other exquisite quirks of interpretation in the No. 87 above
mentioned is the following. God himself employs reserve; he is said to be
decked with light as with a garment (the old or prayer-book version of
Psalm civ. 2). To an ordinary apprehension this would be a strong image of
display, manifestation, revelation; but there is something more. "Does not
a garment veil in some measure that which it clothes? Is not that very
light concealment?"

This No. 87, admitted into a series, fixes upon the managers of the series,
who permitted its introduction, a strong presumption of that underhand
intent with which they were charged. At the same time it is honorable to
our liberty that this series could be published: though its promoters were
greatly shocked when the Essayists and Bishop Colenso[74] took a swing on
the other side. When No. 90 was under discussion, Dr. Maitland,[75] the
librarian at Lambeth, asked Archbishop Howley[76] a question about No. 89.
"I did not so much as know there _was_ a No. 89," was the answer. I am
almost sure I have seen this in print, and quite sure that Dr. Maitland
told it to me. It is creditable that there was so much freedom; but No. 90
was _too bad_, and was stopped.

The Tractarian mania has now (October 1866) settled down into a chronic
vestment disease, complicated with fits of transubstantiation, which has
taken the name of {64} _Ritualism_. The common sense of our national
character will not put up with a continuance of this grotesque folly;
millinery in all its branches will at last be advertised only over the
proper shops. I am told that the Ritualists give short and practical
sermons; if so, they may do good in the end. The English Establishment has
always contained those who want an excitement; the New Testament, in its
plain meaning, can do little for them. Since the Revolution, Jacobitism,
Wesleyanism, Evangelicism, Puseyism,[77] and Ritualism, have come on in
turn, and have furnished hot water for those who could not wash without it.
If the Ritualists should succeed in substituting short and practical
teaching for the high-spiced lectures of the doctrinalists, they will be
remembered with praise. John the Baptist would perhaps not have brought all
Jerusalem out into the wilderness by his plain and good sermons: it was the
camel's hair and the locusts which got him a congregation, and which,
perhaps, added force to his precepts. When at school I heard a dialogue,
between an usher and the man who cleaned the shoes, about Mr. ----, a
minister, a very corporate body with due area of waistcoat. "He is a man of
great erudition," said the first. "Ah, yes sir," said Joe; "any one can see
that who looks at that silk waistcoat."]



OF THOMAS GEPHYRANDER SALICETUS.

[When I said at the outset that I had only taken books from my own store, I
should have added that I did not make any search for information given as
_part_ of a work. Had I looked _through_ all my books, I might have made
some curious additions. For instance, in Schott's _Magia Naturalis_[78]
{65} (vol. iii. pp. 756-778) is an account of the quadrature of
Gephyra_u_der, as he is misprinted in Montucla. He was Thomas Gephyrander
Salicetus; and he published two editions, in 1608 and 1609.[79] I never
even heard of a copy of either. His work is of the extreme of absurdity: he
makes a distinction between geometrical and arithmetical fractions, and
evolves theorems from it. More curious than his quadrature is his name;
what are we to make of it? If a German, he is probably a German form of
_Bridgeman_. and Salicetus refers him to _Weiden_. But _Thomas_ was hardly
a German Christian name of his time; of 526 German philosophers,
physicians, lawyers, and theologians who were biographed by Melchior
Adam,[80] only two are of this name. Of these one is Thomas Erastus,[81]
the physician whose theological writings against the Church as a separate
power have given the name of Erastians to those who follow his doctrine,
whether they have heard of him or not. Erastus is little known;
accordingly, some have supposed that he must be Erastus, the friend of St.
Paul and Timothy (Acts xix. 22; 2 Tim. iv. 20; Rom. xvi. 23), but what this
gentleman did to earn the character is not hinted at. Few words would have
done: Gaius (Rom. xvi. 23) has an immortality which many more noted men
have missed, given by John Bunyan, out of seven words of St. Paul. I was
once told that the Erastians got their name from _Blastus_, and I could not
solve _bl = er_: at last I remembered that Blastus was a _chamberlain_[82]
as well as Erastus; hence the association which {66} caused the mistake.
The real heresiarch was a physician who died in 1583; his heresy was
promulgated in a work, published immediately after his death by his widow,
_De Excommunicatione Ecclesiastica_. He denied the power of excommunication
on the principle above stated; and was answered by Besa.[83] The work was
translated by Dr. R. Lee[84] (Edinb. 1844, 8vo). The other is Thomas
Grynæus,[85] a theologian, nephew of Simon, who first printed Euclid in
Greek; of him Adam says that of works he published none, of learned sons
four. If Gephyrander were a Frenchman, his name is not so easily guessed
at; but he must have been of La Saussaye. The account given by Schott is
taken from a certain Father Philip Colbinus, who wrote against him.

In some manuscripts lately given to the Royal Society, David Gregory,[86]
who seems to have seen Gephyrander's work, calls him Salicetus
_Westphalus_, which is probably on the title-page. But the only Weiden I
can find is in Bavaria. Murhard has both editions in his Catalogue, but had
plainly never seen the books: he gives the author as Thomas Gep. Hyandrus,
Salicettus Westphalus. Murhard is a very old referee of mine; but who the
_non nominandus_ was to see Montucla's _Gephyrander_ in Murhard's _Gep.
Hyandrus_, both writers being usually accurate?]



NAPIER ON REVELATIONS.

    A plain discoverie of the whole Revelation of St. John ... whereunto
    are annexed certain oracles of Sibylla.... Set Foorth by John Napeir L.
    of Marchiston. London, 1611, 4to.[87]

{67}

The first edition was Edinburgh, 1593,[88] 4to. Napier[89] always believed
that his great mission was to upset the Pope, and that logarithms, and such
things, were merely episodes and relaxations. It is a pity that so many
books have been written about this matter, while Napier, as good as any, is
forgotten and unread. He is one of the first who gave us the six thousand
years. "There is a sentence of the house of Elias reserved in all ages,
bearing these words: The world shall stand six thousand years, and then it
shall be consumed by fire: two thousand yeares voide or without lawe, two
thousand yeares under the law, and two thousand yeares shall be the daies
of the Messias...."

I give Napier's parting salute: it is a killing dilemma:

"In summar conclusion, if thou o _Rome_ aledges thyselfe reformed, and to
beleeue true Christianisme, then beleeue Saint _John_ the Disciple, whome
Christ loued, publikely here in this Reuelation proclaiming thy wracke, but
if thou remain Ethnick in thy priuate thoghts, beleeuing[90] the old
Oracles of the _Sibyls_ reuerently keeped somtime in thy _Capitol_: then
doth here this _Sibyll_ proclame also thy wracke. Repent therefore alwayes,
in this thy latter breath, as thou louest thine Eternall salvation.
_Amen_."

--Strange that Napier should not have seen that this appeal could not
succeed, unless the prophecies of the Apocalypse were no true prophecies at
all.

{68}



OF GILBERT'S DE MAGNETE.

    De Magnete magneticisque corporibus, et de magno magnete tellure. By
    William Gilbert. London, 1600, folio.--There is a second edition; and a
    third, according to Watt.[91]

Of the great work on the magnet there is no need to speak, though it was a
paradox in its day. The posthumous work of Gilbert, "De Mundo nostro
sublunari philosophia nova" (Amsterdam, 1651, 4to)[92] is, as the title
indicates, confined to the physics of the globe and its atmosphere. It has
never excited attention: I should hope it would be examined with our
present lights.



OF GIOVANNI BATISTA PORTA.

    Elementorum Curvilineorium Libri tres. By John Baptista Porta. Rome,
    1610, 4to.[93]

This is a ridiculous attempt, which defies description, except that it is
all about lunules. Porta was a voluminous writer. His printer announces
fourteen works printed, and four to come, besides thirteen plays printed,
and eleven waiting. His name is, and will be, current in treatises on
physics for more reasons than one.

{69}



CATALDI ON THE QUADRATURE.

    Trattato della quadratura del cerchio. Di Pietro Antonio Cataldi.
    Bologna, 1612, folio.[94]

Rheticus,[95] Vieta, and Cataldi are the three untiring computers of
Germany, France, and Italy; Napier in Scotland, and Briggs[96] in England,
come just after them. This work claims a place as beginning with the
quadrature of Pellegrino Borello[97] of Reggio, who will have the circle to
be exactly 3 diameters and 69/484 of a diameter. Cataldi, taking Van
Ceulen's approximation, works hard at the finding of integers which nearly
represent the ratio. He had not then the _continued fraction_, a mode of
representation which he gave the next year in his work on the square root.
He has but twenty of Van Ceulen's thirty places, which he takes from
Clavius[98]: and any one might be puzzled to know whence the Italians got
the result; Van Ceulen, in 1612, not having been translated from Dutch. But
Clavius names his comrade Gruenberger, and attributes the approximation to
them {70} jointly; "Lud. a Collen et Chr. Gruenbergerus[99] invenerunt,"
which he had no right to do, unless, to his private knowledge, Gruenberger
had verified Van Ceulen. And Gruenberger only handed over twenty of the
places. But here is one instance, out of many, of the polyglot character of
the Jesuit body, and its advantages in literature.



OF LANSBERGIUS.

    Philippi Lausbergii Cyclometriæ Novæ Libri Duo. Middleburg, 1616,
    4to.[100]

This is one of the legitimate quadratures, on which I shall here only
remark that by candlelight it is quadrature under difficulties, for all the
diagrams are in red ink.



A TEXT LEADING TO REMARKS ON PRESTER JOHN.

    Recherches Curieuses des Mesures du Monde. By S. C. de V. Paris, 1626,
    8vo (pp. 48).[101]

It is written by some Count for his son; and if all the French nobility
would have given their sons the same kind of instruction about rank, the
old French aristocracy would have been as prosperous at this moment as the
English peerage and squireage. I sent the tract to Capt. Speke,[102]
shortly after his arrival in England, thinking he might like {71} to see
the old names of the Ethiopian provinces. But I first made a copy of all
that relates to Prester John,[103] himself a paradox. The tract contains,
_inter alia_, an account of the four empires; of the great Turk, the great
Tartar, the great Sophy, and the great Prester John. This word _great_
(_grand_), which was long used in the phrase "the great Turk," is a generic
adjunct to an emperor. Of the Tartars it is said that "c'est vne nation
prophane et barbaresque, sale et vilaine, qui mangent la chair demie cruë,
qui boiuent du laict de jument, et qui n'vsent de nappes et seruiettes que
pour essuyer leurs bouches et leurs mains."[104] Many persons have heard of
Prester John, and have a very indistinct idea of him. I give all that is
said about him, since the recent discussions about the Nile may give an
interest to the old notions of geography.

"Le grand Prestre Jean qui est le quatriesme en rang, est Empereur
d'Ethiopie, et des Abyssins, et se vante d'estre issu de la race de Dauid,
comme estant descendu de la Royne de Saba, Royne d'Ethiopie, laquelle
estant venuë en Hierusalem pour voir la sagesse de Salomon, enuiron l'an du
monde 2952, s'en retourna grosse d'vn fils qu'ils nomment Moylech, duquel
ils disent estre descendus en ligne directe. Et ainsi il se glorifie
d'estre le plus ancien Monarque de la terre, disant que son Empire a duré
plus de trois mil ans, ce que nul autre Empire ne peut dire. Aussi met-il
en ses tiltres ce qui s'ensuit: Nous, N. Souuerain en mes Royaumes,
vniquement aymé de Dieu, colomne de la foy, sorty de la race de Inda, etc.
Les limites de cet Empire touchent à la mer Rouge, et aux montagnes d'Azuma
vers {72} l'Orient, et du costé de l'Occident, il est borné du fleuue du
Nil, qui le separe de la Nubie, vers le Septentrion il a l'Ægypte, et au
Midy les Royaumes de Congo, et de Mozambique, sa longueur contenant
quarante degré, qui font mille vingt cinq lieuës, et ce depuis Congo ou
Mozambique qui sont au Midy, iusqu'en Ægypte qui est au Septentrion, et sa
largeur contenant depuis le Nil qui est à l'Occident, iusqu'aux montagnes
d'Azuma, qui sont à l'Orient, sept cens vingt cinq lieues, qui font vingt
neuf degrez. Cét empire a sous soy trente grandes Prouinces, sçavoir,
Medra, Gaga, Alchy, Cedalon, Mantro, Finazam, Barnaquez, Ambiam, Fungy,
Angoté, Cigremaon, Gorga, Cafatez, Zastanla, Zeth, Barly, Belangana, Tygra,
Gorgany, Barganaza, d'Ancut, Dargaly, Ambiacatina, Caracogly, Amara, Maon
(_sic_), Guegiera, Bally, Dobora et Macheda. Toutes ces Prouinces cy dessus
sont situées iustement sous la ligne equinoxiale, entres les Tropiques de
Capricorne, et de Cancer. Mais elles s'approchent de nostre Tropique, de
deux cens cinquante lieuës plus qu'elles ne font de l'autre Tropique. Ce
mot de Prestre Jean signifie grand Seigneur, et n'est pas Prestre comme
plusieurs pense, il a esté tousiours Chrestien, mais souuent Schismatique:
maintenant il est Catholique, et reconnaist le Pape pour Souuerain Pontife.
I'ay veu quelqu'vn des ses Euesques, estant en Hierusalem, auec lequel i'ay
conferé souuent par le moyen de nostre trucheman: il estoit d'vn port graue
et serieux, succiur (_sic_) en son parler, mais subtil à merueilles en tout
ce qu'il disoit. Il prenoit grand plaisir au recit que je luy faisais de
nos belles ceremonies, et de la grauité de nos Prelats en leurs habits
Pontificaux, et autres choses que je laisse pour dire, que l'Ethiopien est
ioyoux et gaillard, ne ressemblant en rien a la saleté du Tartare, ny à
l'affreux regard du miserable Arabe, mais ils sont fins et cauteleux, et ne
se fient en personne, soupçonneux à merueilles, et fort devotieux, ils ne
sont du tout noirs comme l'on croit, i'entens parler de ceux qui ne sont
pas sous la ligne Equinoxiale, ny trop proches {73} d'icelle, car ceux qui
sont dessous sont les Mores que nous voyons."[105]

It will be observed that the author speaks of his conversation with an
Ethiopian bishop, about that bishop's sovereign. Something must have passed
between the two which satisfied the writer that the bishop acknowledged his
own sovereign under some title answering to Prester John.

{74}



CONCERNING A TRACT BY FIENUS.

    De Cometa anni 1618 dissertationes Thomæ Fieni[106] et Liberti
    Fromondi[107] ... Equidem Thomæ Fieni epistolica quæstio, An verum sit
    Coelum moveri et Terram quiescere? London, 1670, 8vo.

This tract of Fienus against the motion of the earth is a reprint of one
published in 1619.[108] I have given an account of it as a good summary of
arguments of the time, in the _Companion to the Almanac_ for 1836.

{75}



ON SNELL'S WORK.

    Willebrordi Snellii. R. F. Cyclometricus. Leyden, 1621, 4to.

This is a celebrated work on the approximative quadrature, which, having
the suspicious word _cyclometricus_, must be noticed here for
distinction.[109]



ON BACON'S NOVUM ORGANUM.

1620. In this year, Francis Bacon[110] published his _Novum Organum_,[111]
which was long held in England--but not until the last century--to be the
work which taught Newton and all his successors how to philosophize. That
Newton never mentions Bacon, nor alludes in any way to his works, passed
for nothing. Here and there a paradoxer ventured not to find all this
teaching in Bacon, but he was pronounced blind. In our day it begins to be
seen that, great as Bacon was, and great as his book really is, he is not
the philosophical father of modern discovery.

But old prepossession will find reason for anything. A learned friend of
mine wrote to me that he had discovered proof that Newton owned Bacon for
his master: the proof was that Newton, in some of his earlier writings,
used the {76} phrase _experimentum crucis_, which is Bacon's. Newton may
have read some of Bacon, though no proof of it appears. I have a dim idea
that I once saw the two words attributed to the alchemists: if so, there is
another explanation; for Newton was deeply read in the alchemists.

I subjoin a review which I wrote of the splendid edition of Bacon by
Spedding,[112] Ellis,[113] and Heath.[114] All the opinions therein
expressed had been formed by me long before: most of the materials were
collected for another purpose.



    The Works of Francis Bacon. Edited by James Spedding, R. Leslie Ellis,
    and Douglas D. Heath. 5 vols.[115]

No knowledge of nature without experiment and observation: so said
Aristotle, so said Bacon, so acted Copernicus, Tycho Brahé,[116] Gilbert,
Kepler, Galileo, Harvey, etc., before Bacon wrote.[117] No derived
knowledge _until_ experiment and observation are concluded: so said Bacon,
and no one else. We do not mean to say that he laid down his principle in
these words, or that he carried it to the utmost extreme: we mean that
Bacon's ruling idea was the {77} collection of enormous masses of facts,
and then digested processes of arrangement and elimination, so artistically
contrived, that a man of common intelligence, without any unusual sagacity,
should be able to announce the truth sought for. Let Bacon speak for
himself, in his editor's English:

"But the course I propose for the discovery of sciences is such as leaves
but little to the acuteness and strength of wits, but places all wits and
understandings nearly on a level. For, as in the drawing of a straight line
or a perfect circle, much depends on the steadiness and practice of the
hand, if it be done by aim of hand only, but if with the aid of rule or
compass little or nothing, so it is exactly with my plan.... For my way of
discovering sciences goes far to level men's wits, and leaves but little to
individual excellence; because it performs everything by the surest rules
and demonstrations."

To show that we do not strain Bacon's meaning, we add what is said by
Hooke,[118] whom we have already mentioned as his professed disciple, and,
we believe, his only disciple of the day of Newton. We must, however,
remind the reader that Hooke was very little of a mathematician, and spoke
of algebra from his own idea of what others had told him:

"The intellect is not to be suffered to act without its helps, but is
continually to be assisted by some method or engine, which shall be as a
guide to regulate its actions, so as that it shall not be able to act
amiss. Of this engine, no man except the incomparable Verulam hath had any
thoughts and he indeed hath promoted it to a very good pitch; but there is
yet somewhat more to be added, which he seemed to want time to complete. By
this, as by that {78} art of algebra in geometry, 'twill be very easy to
proceed in any natural inquiry, regularly and certainly.... For as 'tis
very hard for the most acute wit to find out any difficult problem in
geometry without the help of algebra ... and altogether as easy for the
meanest capacity acting by that method to complete and perfect it, so will
it be in the inquiry after natural knowledge."

Bacon did not live to mature the whole of this plan. Are we really to
believe that if he had completed the _Instauratio_ we who write this--and
who feel ourselves growing bigger as we write it--should have been on a
level with Newton in physical discovery? Bacon asks this belief of us, and
does not get it. But it may be said, Your business is with what he _did_
leave, and with its consequences. Be it so. Mr. Ellis says: "That his
method is impracticable cannot, I think, be denied, if we reflect not only
that it never has produced any result, but also that the process by which
scientific truths have been established cannot be so presented as even to
appear to be in accordance with it." That this is very true is well known
to all who have studied the history of discovery: those who deny it are
bound to establish either that some great discovery has been made by
Bacon's method--we mean by the part peculiar to Bacon--or, better still, to
show that some new discovery can be made, by actually making it. No general
talk about _induction_: no reliance upon the mere fact that certain
experiments or observations have been made; let us see where _Bacon's
induction_ has been actually used or can be used. Mere induction,
_enumeratio simplex_, is spoken of by himself with contempt, as utterly
incompetent. For Bacon knew well that a thousand instances may be
contradicted by the thousand and first: so that no enumeration of
instances, however large, is "sure demonstration," so long any are left.

The immortal Harvey, who was _inventing_--we use the word in its old
sense--the circulation of the blood, while {79} Bacon was in the full flow
of thought upon his system, may be trusted to say whether, when the system
appeared, he found any likeness in it to his own processes, or what would
have been any help to him, if he had waited for the _Novum Organum_. He
said of Bacon, "He writes philosophy like a Lord Chancellor." This has been
generally supposed to be only a sneer at the _sutor ultra crepidam_; but we
cannot help suspecting that there was more intended by it. To us, Bacon is
eminently the philosopher of _error prevented_, not of _progress
facilitated_. When we throw off the idea of being _led right_, and betake
ourselves to that of being _kept from going wrong_, we read his writings
with a sense of their usefulness, his genius, and their probable effect
upon purely experimental science, which we can be conscious of upon no
other supposition. It amuses us to have to add that the part of Aristotle's
logic of which he saw the value was the book on _refutation of fallacies_.
Now is this not the notion of things to which the bias of a practised
lawyer might lead him? In the case which is before the Court, generally
speaking, truth lurks somewhere about the facts, and the elimination of all
error will show it in the residuum. The two senses of the word _law_ come
in so as to look almost like a play upon words. The judge can apply the law
so soon as the facts are settled: the physical philosopher has to deduce
the law from the facts. Wait, says the judge, until the facts are
determined: did the prisoner take the goods with felonious intent? did the
defendant give what amounts to a warranty? or the like. Wait, says Bacon,
until all the facts, or all the obtainable facts, are brought in: apply my
rules of separation to the facts, and the result shall come out as easily
as by ruler and compasses. We think it possible that Harvey might allude to
the legal character of Bacon's notions: we can hardly conceive so acute a
man, after seeing what manner of writer Bacon was, meaning only that he was
a lawyer and had better stick to his business. We do ourselves believe that
Bacon's philosophy {80} more resembles the action of mind of a common-law
judge--not a Chancellor--than that of the physical inquirers who have been
supposed to follow in his steps. It seems to us that Bacon's argument is,
there can be nothing of law but what must be either perceptible, or
mechanically deducible, when all the results of law, as exhibited in
phenomena, are before us. Now the truth is, that the physical philosopher
has frequently to conceive law which never was in his previous thought--to
educe the unknown, not to choose among the known. Physical discovery would
be very easy work if the inquirer could lay down his this, his that, and
his t'other, and say, "Now, one of these it must be; let us proceed to try
which." Often has he done this, and failed; often has the truth turned out
to be neither this, that, nor t'other. Bacon seems to us to think that the
philosopher is a judge who has to choose, upon ascertained facts, which of
known statutes is to rule the decision: he appears to us more like a person
who is to write the statute-book, with no guide except the cases and
decisions presented in all their confusion and all their conflict.

Let us take the well-known first aphorism of the _Novum Organum_:

"Man being the servant and interpreter of nature, can do and understand so
much, and so much only, as he has observed in fact or in thought of the
course of nature: beyond this he neither knows anything nor can do
anything."

This aphorism is placed by Sir John Herschel[119] at the head of his
_Discourse on the Study of Natural Philosophy_: a book containing notions
of discovery far beyond any of which Bacon ever dreamed; and this because
it was written {81} after discovery, instead of before. Sir John Herschel,
in his version, has avoided the translation of _re vel mente observaverit_,
and gives us only "by his observation of the order of nature." In making
this the opening of an excellent sermon, he has imitated the theologians,
who often employ the whole time of the discourse in stuffing matter into
the text, instead of drawing matter out of it. By _observation_ he
(Herschel) means the whole course of discovery, observation, hypothesis,
deduction, comparison, etc. The type of the Baconian philosopher as it
stood in his mind, had been derived from a noble example, his own father,
William Herschel,[120] an inquirer whose processes would have been held by
Bacon to have been vague, insufficient, compounded of chance work and
sagacity, and too meagre of facts to deserve the name of induction. In
another work, his treatise on Astronomy,[121] Sir John Herschel, after
noting that a popular account can only place the reader on the threshold,
proceeds to speak as follows of all the higher departments of science. The
italics are his own:

"Admission to its sanctuary, and to the privileges and feelings of a
votary, is only to be gained by one means--_sound and sufficient knowledge
of mathematics, the great instrument of all exact inquiry, without which no
man can ever make such advances in this or any other of the higher
departments of science as can entitle him to form an independent opinion on
any subject of discussion within their range_."

How is this? Man can know no more than he gets from observation, and yet
mathematics is the great instrument of all exact inquiry. Are the results
of mathematical deduction results of observation? We think it likely that
{82} Sir John Herschel would reply that Bacon, in coupling together
_observare re_ and _observare mente_, has done what some wags said Newton
afterwards did in his study-door--cut a large hole of exit for the large
cat, and a little hole for the little cat.[122] But Bacon did no such
thing: he never included any deduction under observation. To mathematics he
had a dislike. He averred that logic and mathematics should be the
handmaids, not the mistresses, of philosophy. He meant that they should
play a subordinate and subsequent part in the dressing of the vast mass of
facts by which discovery was to be rendered equally accessible to Newton
and to us. Bacon himself was very ignorant of all that had been done by
mathematics; and, strange to say, he especially objected to astronomy being
handed over to the mathematicians. Leverrier and Adams, calculating an
unknown planet into visible existence by enormous heaps of algebra, furnish
the last comment of note on this specimen of the goodness of Bacon's views.
The following account of his knowledge of what had been done in his own day
or before it, is Mr. Spedding's collection of casual remarks in Mr. Ellis's
several prefaces:

"Though he paid great attention to astronomy, discussed carefully the
methods in which it ought to be studied, constructed for the satisfaction
of his own mind an elaborate theory of the heavens, and listened eagerly
for the news from the stars brought by Galileo's telescope, he appears to
have been utterly ignorant of the discoveries which had just been made by
Kepler's calculations. Though he complained in 1623 of the want of
compendious methods for facilitating arithmetical computations, especially
with regard to the doctrine of Series, and fully recognized the importance
of them as an aid to physical inquiries--he does not say a word about
Napier's Logarithms, which had been published only nine years before and
reprinted more than once in the {83} interval. He complained that no
considerable advance had made in geometry beyond Euclid, without taking any
notice of what had been done by Archimedes and Apollonius. He saw the
importance of determining accurately the specific gravity of different
substances, and himself attempted to form a table of them by a rude process
of his own, without knowing of the more scientific though still imperfect
methods previously employed by Archimedes, Ghetaldus,[123] and Porta. He
speaks of the [Greek: heurêka] of Archimedes in a manner which implies that
he did not clearly apprehend either the nature of the problem to be solved
or the principles upon which the solution depended. In reviewing the
progress of mechanics, he makes no mention of Archimedes himself, or of
Stevinus,[124] Galileo, Guldinus,[125] or Ghetaldus. He makes no allusion
to the theory of equilibrium. He observes that a ball of one pound weight
will fall nearly as fast through the air as a ball of two, without alluding
to the theory of the acceleration of falling bodies, which had been made
known by Galileo more than thirty years before. He proposes an inquiry with
regard to the lever--namely, whether in a balance with arms of different
length but equal weight the distance from the fulcrum has any effect upon
the inclination,--though the theory of the lever was as well understood in
his own time as it is now. In making an experiment {84} of his own to
ascertain the cause of the motion of a windmill, he overlooks an obvious
circumstance which makes the experiment inconclusive, and an equally
obvious variation of the same experiment which would have shown him that
his theory was false. He speaks of the poles of the earth as fixed, in a
manner which seems to imply that he was not acquainted with the precession
of the equinoxes; and in another place, of the north pole being above and
the south pole below, as a reason why in our hemisphere the north winds
predominate over the south."

Much of this was known before, but such a summary of Bacon's want of
knowledge of the science of his own time was never yet collected in one
place. We may add, that Bacon seems to have been as ignorant of
Wright's[126] memorable addition to the resources of navigation as of
Napier's addition to the means of calculation. Mathematics was beginning to
be the great instrument of exact inquiry: Bacon threw the science aside,
from ignorance, just at the time when his enormous sagacity, applied to
knowledge, would have made him see the part it was to play. If Newton had
taken Bacon for his master, not he, but somebody else, would have been
Newton.[127]



ON METEOROLOGICAL OBSERVATORIES.

There is an attempt at induction going on, which has yielded little or no
fruit, the observations made in the meteorological observatories. This
attempt is carried on in a manner which would have caused Bacon to dance
for joy; for he lived in times when Chancellors did dance. {85} Russia,
says M. Biot,[128] is covered by an army of meteorographs, with generals,
high officers, subalterns, and privates with fixed and defined duties of
observation. Other countries have also their systematic observations. And
what has come of it? Nothing, says M. Biot, and nothing will ever come of
it; the veteran mathematician and experimental philosopher declares, as
does Mr. Ellis, that no single branch of science has ever been fruitfully
explored in this way. There is no _special object_, he says. Any one would
suppose that M. Biot's opinion, given to the French Government upon the
proposal to construct meteorological observatories in Algeria (_Comptes
Rendus_, vol. xli, Dec. 31, 1855), was written to support the mythical
Bacon, modern physics, against the real Bacon of the _Novum Organum_. There
is no _special object_. In these words lies the difference between the two
methods.



[In the report to the Greenwich Board of Visitors for 1867 Mr. Airy,[129]
speaking of the increase of meteorological observatories, remarks, "Whether
the effect of this movement will be that millions of useless observations
will be added to the millions that already exist, or whether something may
be expected to result which will lead to a meteorological theory, I cannot
hazard a conjecture." This _is_ a conjecture, and a very obvious one: if
Mr. Airy would have given 2-3/4d. for the chance of a meteorological theory
formed by masses of observations, he would never have said what I have
quoted.]



BASIS OF MODERN DISCOVERY.

Modern discoveries have not been made by large collections of facts, with
subsequent discussion, separation, and {86} resulting deduction of a truth
thus rendered perceptible. A few facts have suggested an _hypothesis_,
which means a _supposition_, proper to explain them. The necessary results
of this supposition are worked out, and then, and not till then, other
facts are examined to see if these ulterior results are found in nature.
The trial of the hypothesis is the _special object_: prior to which,
hypothesis must have been started, not by rule, but by that sagacity of
which no description can be given, precisely because the very owners of it
do not act under laws perceptible to themselves.[130] The inventor of
hypothesis, if pressed to explain his method, must answer as did Zerah
Colburn,[131] when asked for his mode of instantaneous calculation. When
the poor boy had been bothered for some time in this manner, he cried out
in a huff, "God put it into my head, and I can't put it into yours."[132]
{87} Wrong hypotheses, rightly worked from, have produced more useful
results than unguided observation. But this is not the Baconian plan.
Charles the Second, when informed of the state of navigation, founded a
Baconian observatory at Greenwich, to observe, observe, observe away at the
moon, until her motions were known sufficiently well to render her useful
in guiding the seaman. And no doubt Flamsteed's[133] observations, twenty
or thirty of them at least, were of signal use. But how? A somewhat
fanciful thinker, one Kepler, had hit upon the approximate orbits of the
planets by trying one hypothesis after another: he found the _ellipse_,
which the Platonists, well despised of Bacon, and who would have despised
him as heartily if they had known him, had investigated and put ready to
hand nearly 2000 years before.[134] The sun in the focus, the motions of
the planet more and more rapid as they approach the sun, led Kepler--and
Bacon would have reproved him for his rashness--to imagine that a force
residing in the sun might move the planets, a force inversely as the
distance. Bouillaud,[135] upon a fanciful analogy, rejected the inverse
distance, {88} and, rejecting the force altogether, declared that if such a
thing there were, it would be as the inverse _square_ of the distance.
Newton, ready prepared with the mathematics of the subject, tried the fall
of the moon towards the earth, away from her tangent, and found that, as
compared with the fall of a stone, the law of the inverse square did hold
for the moon. He deduced the ellipse, he proceeded to deduce the effect of
the disturbance of the sun upon the moon, upon the assumed theory of
_universal_ gravitation. He found result after result of his theory in
conformity with observed fact: and, by aid of Flamsteed's observations,
which amended what mathematicians call his _constants_, he constructed his
lunar theory. Had it not been for Newton, the whole dynasty of Greenwich
astronomers, from Flamsteed of happy memory, to Airy whom Heaven
preserve,[136] might have worked away at nightly observation and daily
reduction, without any remarkable result: looking forward, as to a
millennium, to the time when any man of moderate intelligence was to see
the whole explanation. What are large collections of facts for? To make
theories _from_, says Bacon: to try ready-made theories _by_, says the
history of discovery: it's all the same, says the idolater: nonsense, say
we!

Time and space run short: how odd it is that of the three leading ideas of
mechanics, time, space, and matter, the first two should always fail a
reviewer before the third. We might dwell upon many points, especially if
we attempted a more descriptive account of the valuable edition before us.
No one need imagine that the editors, by their uncompromising attack upon
the notion of Bacon's influence common even among mathematicians and
experimental philosophers, have lowered the glory of the great man whom it
was, many will think, their business to defend through thick and thin. They
have given a clearer notion of his {89} excellencies, and a better idea of
the power of his mind, than ever we saw given before. Such a correction as
theirs must have come, and soon, for as Hallam says--after noting that the
_Novum Organum_ was _never published separately in England_, Bacon has
probably been more read in the last thirty years--now forty--than in the
two hundred years which preceded. He will now be more read than ever he
was. The history of the intellectual world is the history of the worship of
one idol after another. No sooner is it clear that a Hercules has appeared
among men, than all that imagination can conceive of strength is attributed
to him, and his labors are recorded in the heavens. The time arrives when,
as in the case of Aristotle, a new deity is found, and the old one is
consigned to shame and reproach. A reaction may afterwards take place, and
this is now happening in the case of the Greek philosopher. The end of the
process is, that the opposing deities take their places, side by side, in a
Pantheon dedicated not to gods, but to heroes.



THE REAL VALUE OF BACON'S WORKS.

Passing over the success of Bacon's own endeavors to improve the details of
physical science, which was next to nothing, and of his method as a whole,
which has never been practised, we might say much of the good influence of
his writings. Sound wisdom, set in sparkling wit, must instruct and amuse
to the end of time: and, as against error, we repeat that Bacon is soundly
wise, so far as he goes. There is hardly a form of human error within his
scope which he did not detect, expose, and attach to a satirical metaphor
which never ceases to sting. He is largely indebted to a very extensive
reading; but the thoughts of others fall into his text with such a
close-fitting compactness that he can make even the words of the Sacred
Writers pass for his own. A saying of the prophet Daniel, rather a
hackneyed quotation in our day, _Multi pertransibunt, et augebitur
scientia_, stands in the title-page of the first edition {90} of Montucla's
_History of Mathematics_ as a quotation from Bacon--and it is not the only
place in which this mistake occurs. When the truth of the matter, as to
Bacon's system, is fully recognized, we have little fear that there will be
a reaction against the man. First, because Bacon will always live to speak
for himself, for he will not cease to be read: secondly, because those who
seek the truth will find it in the best edition of his works, and will be
most ably led to know what Bacon was, in the very books which first showed
at large what he _was not_.



THE CONGREGATION OF THE INDEX, ON COPERNICUS.

In this year (1620) appeared the corrections under which the Congregation
of the Index--i.e., the Committee of Cardinals which superintended the
_Index_ of forbidden books--proposed to allow the work of Copernicus to be
read. I insert these conditions in full, because they are often alluded to,
and I know of no source of reference accessible to a twentieth part of
those who take interest in the question.

By a decree of the Congregation of the Index, dated March 5, 1616, the work
of Copernicus, and another of Didacus Astunica,[137] are suspended _donec
corrigantur_, as teaching:

"Falsam illam doctrinam Pythagoricam, divinæ que Scripturæ omnino
adversantem, de mobilitate Terræ et immobilitate Solis."[138]

But a work of the Carmelite Foscarini[139] is:

{91}

"Omnino prohibendum atque damnandum," because "ostendere conatur præfatam
doctrinam ... consonam esse veritati et non adversari Sacræ
Scripturæ."[140]

Works which teach the false doctrine of the earth's motion are to be
corrected; those which declare the doctrine conformable to Scripture are to
be utterly prohibited.

In a "Monitum ad Nicolai Copernici lectorem, ejusque emendatio, permissio,
et correctio," dated 1620 without the month or day, permission is given to
reprint the work of Copernicus with certain alterations; and, by
implication, to read existing copies after correction in writing. In the
preamble the author is called _nobilis astrologus_; not a compliment to his
birth, which was humble, but to his fame. The suspension was because:

"Sacræ Scripturæ, ejusque veræ et Catholicæ interpretationi repugnantia
(quod in homine Christiano minime tolerandum) non _per hypothesin_
tractare, sed _ut verissima_ adstruere non dubitat!"[141]

And the corrections relate:

"Locis in quibus non _ex hypothesi_, sed _asserendo_ de situ et motu Terræ
disputat."[142]

That is, the earth's motion may be an hypothesis for elucidation of the
heavenly motions, but must not be asserted as a fact.



(In Pref. circa finem.) "_Copernicus._ Si fortasse erunt [Greek:
mataiologoi], qui cum omnium Mathematum ignari sint, tamen de illis
judicium sibi summunt, propter aliquem locum scripturæ, male ad suum
propositum detortum, ausi fuerint meum {92} hoc institutum reprehendere ac
insectari: illos nihil moror adeo ut etiam illorum judicium tanquam
temerarium contemnam. Non enim obscurum est Lactantium, celebrem alioqui
scriptorem, sed Mathematicum parum, admodum pueriliter de forma terræ
loqui, cum deridet eos, qui terram globi formam habere prodiderunt. Itaque
non debet mirum videri studiosis, si qui tales nos etiam videbunt.
Mathemata Mathematicis scribuntur, quibus et hi nostri labores, si me non
fallit opinio, videbuntur etiam Reipub. ecclesiasticæ conducere aliquid....
_Emend._ Ibi _si fortasse_ dele omnia, usque ad verbum _hi nostri labores_
et sic accommoda--_Coeterum hi nostri labores_."[143]

All the allusion to Lactantius, who laughed at the notion of the earth
being round, which was afterwards found true, is to be struck out.



(Cap. 5. lib. i. p. 3) "_Copernicus._ Si tamen attentius rem consideremus,
videbitur hæc quæstio nondum absoluta, et ideireo minime contemnenda.
_Emend._ Si tamen attentius rem consideremus, nihil refert an Terram in
medio Mundi, an extra Medium existere, quoad solvendas coelestium motuum
apparentias existimemus."[144]

{93}

We must not say the question is not yet settled, but only that it may be
settled either way, so far as mere explanation of the celestial motions is
concerned.



(Cap. 8. lib. i.) "Totum hoc caput potest expungi, quia ex professo tractat
de veritate motus Terræ, dum solvit veterum rationes probantes ejus
quietem. Cum tamen problematice videatur loqui; ut studiosis satisfiat,
seriesque et ordo libri integer maneat; emendetur ut infra."[145]

A chapter which seems to assert the motion should perhaps be expunged; but
it may perhaps be problematical; and, not to break up the book, must be
amended as below.



(p. 6.) "_Copernicus._ Cur ergo hesitamus adhuc, mobilitatem illi formæ suæ
a natura congruentem concedere, magisquam quod totus labatur mundus, cujus
finis ignoratur, scirique nequit, neque fateamur ipsius cotidianæ
revolutionis in coelo apparentiam esse, et in terra veritatem? Et hæc
perinde se habere, ac si diceret Virgilianus Æneas: Provehimur portu ...
_Emend._ Cur ergo non possum mobilitatem illi formæ suæ concedere, magisque
quod totus labatur mundus, cujus finis ignoratur scirique nequit, et quæ
apparent in coelo, perinde se habere ac si ..."[146]

{94}

"Why should we hesitate to allow the earth's motion," must be altered into
"I cannot concede the earth's motion."



(p. 7.) "_Copernicus._ Addo etiam, quod satis absurdum videretur,
continenti sive locanti motum adscribi, et non potius contento et locato,
quod est terra. _Emend._ Addo etiam difficilius non esse contento et
locato, quod est Terra, motum adscribere, quam continenti."[147]

We must not say it is absurd to refuse motion to the _contained_ and
_located_, and to give it to the containing and locating; say that neither
is more difficult than the other.



(p. 7.) "_Copernicus._ Vides ergo quod ex his omnibus probabilior sit
mobilitas Terræ, quam ejus quies, præsertim in cotidiana revolutione,
tanquam terræ maxime propria. _Emend._ _Vides_ ... delendus est usque ad
finem capitis."[148]

Strike out the whole of the chapter from this to the end; it says that the
motion of the earth is the most probable hypothesis.



(Cap. 9. lib. i. p. 7.) "_Copernicus._ Cum igitur nihil prohibeat
mobilitatem Terræ, videndum nunc arbitror, an etiam plures illi motus
conveniant, ut possit una errantium syderum existimari. _Emend._ Cum igitur
Terram moveri assumpserim, videndum nunc arbitror, an etiam illi plures
possint convenire motus."[149]

{95}

We must not say that nothing prohibits the motion of the earth, only that
having _assumed_ it, we may inquire whether our explanations require
several motions.



(Cap. 10. lib. i. p. 9.) "_Copernicus._ Non pudet nos fateri ... hoc potius
in mobilitate terræ verificari. _Emend._ Non pudet nos assumere ... hoc
consequenter in mobilitate verificari."[150]

(Cap. 10. lib. i. p. 10.) "_Copernicus._ Tanta nimirum est divina hæc. Opt.
Max. fabrica. _Emend._ Dele illa verba postrema."[151]

(Cap. ii. lib. i.[152]) "_Copernicus._ De triplici motu telluris
demonstratio. _Emend._ De hypothesi triplicis motus Terræ, ejusque
demonstratione."[153]

(Cap. 10. lib. iv. p. 122.[154]) "_Copernicus._ De magnitudine horum trium
siderum, Solis, Lunæ, et Terræ. _Emend._ Dele verba _horum trium siderum_,
quia terra non est sidus, ut facit eam Copernicus."[155]

We must not say we are not ashamed to _acknowledge_; _assume_ is the word.
We must not call this assumption a _Divine work_. A chapter must not be
headed _demonstration_, but _hypothesis_. The earth must not be called a
_star_; the word implies motion.

It will be seen that it does not take much to reduce Copernicus to pure
hypothesis. No personal injury being done to the author--who indeed had
been 17 years out of {96} reach--the treatment of his book is now an
excellent joke. It is obvious that the Cardinals of the Index were a little
ashamed of their position, and made a mere excuse of a few corrections.
Their mode of dealing with chap. 8, this _problematice videtur loqui, ut
studiosis satisfiat_,[156] is an excuse to avoid corrections. But they
struck out the stinging allusion to Lactantius[157] in the preface, little
thinking, honest men, for they really believed what they said--that the
light of Lactantius would grow dark before the brightness of their own.



THE CONVOCATION AT OXFORD EQUALLY AT FAULT.

1622. I make no reference to the case of Galileo, except this. I have
pointed out (_Penny Cycl. Suppl._ "Galileo"; _Engl. Cycl._ "Motion of the
Earth") that it is clear the absurdity was the act of the _Italian_
Inquisition--for the private and personal pleasure of the Pope, who _knew_
that the course he took would not commit him as _Pope_--and not of the body
which calls itself the _Church_. Let the dirty proceeding have its right
name. The Jesuit Riccioli,[158] the stoutest and most learned
Anti-Copernican in Europe, and the Puritan Wilkins, a strong Copernican and
Pope-hater, are equally positive that the Roman _Church_ never pronounced
any decision: and this in the time immediately following the ridiculous
proceeding of the Inquisition. In like manner a decision of the Convocation
of Oxford is not a law of the _English_ Church; which is fortunate, for
that Convocation, in 1622, came to a decision quite as absurd, and a great
deal {97} more wicked than the declaration against the motion of the earth.
The second was a foolish mistake; the first was a disgusting surrender of
right feeling. The story is told without disapprobation by Anthony Wood,
who never exaggerated anything against the university of which he is
writing eulogistic history.

In 1622, one William Knight[159] put forward in a sermon preached before
the University certain theses which, looking at the state of the times, may
have been improper and possibly of seditious intent. One of them was that
the bishop might excommunicate the civil magistrate: this proposition the
clerical body could not approve, and designated it by the term
_erronea_,[160] the mildest going. But Knight also declared as follows:

"Subditis mere privatis, si Tyrannus tanquam latro aut stuprator in ipsos
faciat impetum, et ipsi nec potestatem ordinariam implorare, nec alia
ratione effugere periculum possint, in presenti periculo se et suos contra
tyrannum, sicut contra privatum grassatorem, defendere licet."[161]

That is, a man may defend his purse or a woman her honor, against the
personal attack of a king, as against that of a private person, if no other
means of safety can be found. The Convocation sent Knight to prison,
declared the proposition _"falsa_, periculosa, et _impia_," and enacted
that all applicants for degrees should subscribe this censure, and make
oath that they would neither hold, teach, nor defend Knight's opinions.

The thesis, in the form given, was unnecessary and improper. Though strong
opinions of the king's rights were advanced at the time, yet no one
ventured to say that, {98} ministers and advisers apart, the king might
_personally_ break the law; and we know that the first and only attempt
which his successor made brought on the crisis which cost him his throne
and his head. But the declaration that the proposition was _false_ far
exceeds in all that is disreputable the decision of the Inquisition against
the earth's motion. We do not mention this little matter in England. Knight
was a Puritan, and Neal[162] gives a short account of his sermon. From
comparison with Wood,[163] I judge that the theses, as given, were not
Knight's words, but the digest which it was customary to make in criminal
proceedings against opinion. This heightens the joke, for it appears that
the qualifiers of the Convocation took pains to present their condemnation
of Knight in the terms which would most unequivocally make their censure
condemn themselves. This proceeding took place in the interval between the
two proceedings against Galileo: it is left undetermined whether we must
say pot-kettle-pot or kettle-pot-kettle.



    Liberti Fromondi.... Ant-Aristarchus, sive orbis terræ immobilis.
    Antwerp, 1631, 8vo.[164]

This book contains the evidence of an ardent opponent of Galileo to the
fact, that Roman Catholics of the day did not consider the decree of the
_Index_ or of the _Inquisition_ as a declaration of their _Church_. Fromond
would have been glad to say as much, and tries to come near it, but
confesses he must abstain. See _Penny Cyclop. Suppl._ "Galileo," and _Eng.
Cycl._ "Motion of the Earth." The author of a celebrated article in the
_Dublin Review_, in defence of the {99} Church of Rome, seeing that
Drinkwater Bethune[165] makes use of the authority of Fromondus, but for
another purpose, sneers at him for bringing up a "musty old Professor." If
he had known Fromondus, and used him he would have helped his own case,
which is very meagre for want of knowledge.[166]



    Advis à Monseigneur l'eminentissime Cardinal Duc de Richelieu, sur la
    Proposition faicte par le Sieur Morin pour l'invention des longitudes.
    Paris, 1634, 8vo.[167]

This is the Official Report of the Commissioners appointed by the Cardinal,
of whom Pascal is the one now best known, to consider Morin's plan. See the
full account in Delambre, _Hist. Astr. Mod._ ii. 236, etc.



THE METIUS APPROXIMATION.

    Arithmetica et Geometria practica. By Adrian Metius. Leyden, 1640,
    4to.[168]

This book contains the celebrated approximation _guessed at_ by his father,
Peter Metius,[169] namely that the diameter is {100} to the circumference
as 113 to 355. The error is at the rate of about a foot in 2,000 miles.
Peter Metius, having his attention called to the subject by the false
quadrature of Duchesne, found that the ratio lay between 333/106 and
377/120. He then took the liberty of taking the mean of both numerators and
denominators, giving 355/113. He had no right to presume that this mean was
better than either of the extremes; nor does it appear positively that he
did so. He published nothing; but his son Adrian,[170] when Van Ceulen's
work showed how near his father's result came to the truth, first made it
known in the work above. (See _Eng. Cyclop._, art. "Quadrature.")



ON INHABITABLE PLANETS.

    A discourse concerning a new world and another planet, in two books.
    London, 1640, 8vo.[171]

    Cosmotheoros: or conjectures concerning the planetary worlds and their
    inhabitants. Written in Latin, by Christianus Huyghens. This
    translation was first published in 1698. Glasgow, 1757, 8vo. [The
    original is also of 1698.][172]

The first work is by Bishop Wilkins, being the third edition, [first in
1638] of the first book, "That the Moon may be a Planet"; and the first
edition of the second work, {101} "That the Earth may be a Planet." [See
more under the reprint of 1802.] Whether other planets be inhabited or not,
that is, crowded with organisations some of them having consciousness, is
not for me to decide; but I should be much surprised if, on going to one of
them, I should find it otherwise. The whole dispute tacitly assumes that,
if the stars and planets be inhabited, it must be by things of which we can
form some idea. But for aught we know, what number of such bodies there
are, so many organisms may there be, of which we have no way of thinking
nor of speaking. This is seldom remembered. In like manner it is usually
forgotten that the _matter_ of other planets may be of different chemistry
from ours. There may be no oxygen and hydrogen in Jupiter, which may have
_gens_ of its own.[173] But this must not be said: it would limit the
omniscience of the _a priori_ school of physical inquirers, the larger half
of the whole, and would be very _unphilosophical_. Nine-tenths of my best
paradoxers come out from among this larger half, because they are just a
little more than of it at their entrance.

There was a discussion on the subject some years ago, which began with

    The plurality of worlds: an Essay. London, 1853, 8vo. [By Dr. Wm.
    Whewell, Master of Trinity College, Cambridge]. A dialogue on the
    plurality of worlds, being a supplement to the Essay on that subject.
    [First found in the second edition, 1854; removed to the end in
    subsequent editions, and separate copies issued.][174]

A work of skeptical character, insisting on analogies which prohibit the
positive conclusion that the planets, stars, etc., are what we should call
_inhabited_ worlds. It produced {102} several works and a large amount of
controversy in reviews. The last predecessor of whom I know was

    Plurality of Worlds.... By Alexander Maxwell. Second Edition. London,
    1820, 8vo.

This work is directed against the plurality by an author who does not admit
modern astronomy. It was occasioned by Dr. Chalmers's[175] celebrated
discourses on religion in connection with astronomy. The notes contain many
citations on the gravity controversy, from authors now very little read:
and this is its present value. I find no mention of Maxwell, not even in
Watt.[176] He communicated with mankind without the medium of a publisher;
and, from Vieta till now, this method has always been favorable to loss of
books.

A correspondent informs me that Alex. Maxwell, who wrote on the plurality
of worlds, in 1820, was a law-bookseller and publisher (probably his own
publisher) in Bell Yard. He had peculiar notions, which he was fond of
discussing with his customers. He was a bit of a Swedenborgian.



INHABITED PLANETS IN FICTION.

There is a class of hypothetical creations which do not belong to my
subject, because they are _acknowledged_ to be fictions, as those of
Lucian,[177] Rabelais,[178] Swift, Francis {103} Godwin,[179] Voltaire,
etc. All who have more positive notions as to either the composition or
organization of other worlds, than the reasonable conclusion that our
Architect must be quite able to construct millions of other buildings on
millions of other plans, ought to rank with the writers just mentioned, in
all but self-knowledge. Of every one of their systems I say, as the Irish
Bishop said of Gulliver's book,--I don't believe half of it. Huyghens had
been preceded by Fontenelle,[180] who attracted more attention. Huyghens is
very fanciful and very positive; but he gives a true account of his method.
"But since there's no hopes of a Mercury to carry us such a journey, we
shall e'en be contented with what's in our power: we shall suppose
ourselves there...." And yet he says, "We have proved that they live in
societies, have hands and feet...." Kircher[181] had gone to the stars
before him, but would not find any life in them, either animal or
vegetable.

The question of the inhabitants of a particular planet is one which has
truth on one side or the other: either there are some inhabitants, or there
are none. Fortunately, it is of no consequence which is true. But there are
many cases where the balance is equally one of truth and falsehood, in
which the choice is a matter of importance. My work selects, for the most
part, sins against demonstration: but the world is full of questions of
fact or opinion, in which a struggling minority will become a majority, or
else will {104} be gradually annihilated: and each of the cases subdivides
into results of good, and results of evil. What is to be done?

 "Periculosum est credere et non credere;
  Hippolitus obiit quia novercæ creditum est;
  Cassandræ quia non creditum ruit Ilium:
  Ergo exploranda est veritas multum prius
  Quam stulta prove judicet sententia."[182]



    Nova Demonstratio immobilitatis terræ petita ex virtute magnetica. By
    Jacobus Grandamicus. Flexiae (La Flèche), 1645, 4to.[183]

No magnetic body can move about its poles: the earth is a magnetic body,
therefore, etc. The iron and its magnetism are typical of two natures in
one person; so it is said, "Si exaltatus fuero à terra, omnia traham ad me
ipsum."[184]



A VENETIAN BUDGET OF PARADOXES.

    Le glorie degli incogniti, o vero gli huomini illustri dell' accademia
    de' signori incogniti di Venetia. Venice, 1647, 4to.

This work is somewhat like a part of my own: it is a budget of Venetian
nobodies who wished to be somebodies; but paradox is not the only means
employed. It is of a serio-comic character, gives genuine portraits in
copperplate, and grave lists of works; but satirical accounts. The
astrologer Andrew Argoli[185] is there, and his son; both of whom, with
some of the others, have place in modern works {105} on biography. Argoli's
discovery that logarithms facilitate easy processes, but increase the labor
of difficult ones, is worth recording.



    Controversiæ de vera circuli mensura ... inter ... C. S. Longomontanum
    et Jo. Pellium.[186] Amsterdam, 1647, 4to.

Longomontanus,[187] a Danish astronomer of merit, squared the circle in
1644: he found out that the diameter 43 gives the square root of 18252 for
the circumference; which gives 3.14185... for the ratio. Pell answered him,
and being a kind of circulating medium, managed to engage in the
controversy names known and unknown, as Roberval, Hobbes, Carcavi, Lord
Charles Cavendish, Pallieur, Mersenne, Tassius, Baron Wolzogen, Descartes,
Cavalieri and Golius.[188] Among them, of course, Longomontanus was made
{106} mincemeat: but he is said to have insisted on the discovery of his
epitaph.[189]

{107}



THE CIRCULATING MEDIA OF MATHEMATICS.

The great circulating mediums, who wrote to everybody, heard from
everybody, and sent extracts to everybody else, have been Father Mersenne,
John Collins, and the late Professor Schumacher: all "late" no doubt, but
only the last recent enough to be so styled. If M.C.S. should ever again
stand for "Member of the Corresponding Society," it should raise an
acrostic thought of the three. There is an allusion to Mersenne's
occupation in Hobbes's reply to him. He wanted to give Hobbes, who was very
ill at Paris, the Roman Eucharist: but Hobbes said, "I have settled all
that long ago; when did you hear from Gassendi?" We are reminded of
William's answer to Burnet. John Collins disseminated Newton, among others.
Schumacher ought to have been called the postmaster-general of astronomy,
as Collins was called the attorney-general of mathematics.[190]

{108}



THE SYMPATHETIC POWDER.

    A late discourse ... by Sir Kenelme Digby.... Rendered into English by
    R. White. London, 1658, 12mo.

On this work see _Notes and Queries_, 2d series, vii. 231, 299, 445, viii.
190. It contains the celebrated sympathetic powder. I am still in much
doubt as to the connection of Digby with this tract.[191] Without entering
on the subject here, I observe that in Birch's _History of the Royal
Society_,[192] to which both Digby and White belonged, Digby, though he
brought many things before the Society, never mentioned the powder, which
is connected only with the names of Evelyn[193] and Sir Gilbert
Talbot.[194] The sympathetic powder was that which cured by anointing the
weapon with its salve instead of the wound. I have long been convinced that
it was efficacious. The directions were to keep the {109} wound clean and
cool, and to take care of diet, rubbing the salve on the knife or
sword.[195] If we remember the dreadful notions upon drugs which prevailed,
both as to quantity and quality, we shall readily see that any way of _not_
dressing the wound would have been useful. If the physicians had taken the
hint, had been careful of diet etc., and had poured the little barrels of
medicine down the throat of a practicable doll, _they_ would have had their
magical cures as well as the surgeons.[196] Matters are much improved now;
the quantity of medicine given, even by orthodox physicians, would have
been called infinitesimal by their professional ancestors. Accordingly, the
College of Physicians has a right to abandon its motto, which is _Ars
longa, vita brevis_, meaning _Practice is long, so life is short_.



HOBBES AS A MATHEMATICIAN.

    Examinatio et emendatio Mathematicæ Hodiernæ. By Thomas Hobbes. London,
    1666, 4to.

In six dialogues: the sixth contains a quadrature of the circle.[197] But
there is another edition of this work, without place or date on the
title-page, in which the quadrature is omitted. This seems to be connected
with the publication {110} of another quadrature, without date, but about
1670, as may be judged from its professing to answer a tract of Wallis,
printed in 1669.[198] The title is "Quadratura circuli, cubatio sphæræ,
duplicatio cubi," 4to.[199] Hobbes, who began in 1655, was very wrong in
his quadrature; but, though not a Gregory St. Vincent,[200] he was not the
ignoramus in geometry that he is sometimes supposed. His writings,
erroneous as they are in many things, contain acute remarks on points of
principle. He is wronged by being coupled with Joseph Scaliger, as the two
great instances of men of letters who have come into geometry to help the
mathematicians out of their difficulty. I have never seen Scaliger's
quadrature,[201] except in the answers of Adrianus Romanus,[202] Vieta and
Clavius, and in the extracts of Kastner.[203] Scaliger had no right to such
strong opponents: Erasmus or Bentley might just as well have tried the
problem, and either would have done much better in any twenty minutes of
his life.[204]



AN ESTIMATE OF SCALIGER.

Scaliger inspired some mathematicians with great respect for his
geometrical knowledge. Vieta, the first man of his time, who answered him,
had such regard for his opponent {111} as made him conceal Scaliger's name.
Not that he is very respectful in his manner of proceeding: the following
dry quiz on his opponent's logic must have been very cutting, being true.
"In grammaticis, dare navibus Austros, et dare naves Austris, sunt æque
significantia. Sed in Geometricis, aliud est adsumpsisse circulum BCD non
esse majorem triginta sex segmentis BCDF, aliud circulo BCD non esse majora
triginta sex segmenta BCDF. Illa adsumptiuncula vera est, hæc falsa."[205]
Isaac Casaubon,[206] in one of his letters to De Thou,[207] relates that,
he and another paying a visit to Vieta, the conversation fell upon
Scaliger, of whom the host said that he believed Scaliger was the only man
who perfectly understood mathematical writers, especially the Greek ones:
and that he thought more of Scaliger when wrong than of many others when
right; "pluris se Scaligerum vel errantem facere quam multos [Greek:
katorthountas]."[208] This must have been before Scaliger's quadrature
(1594). There is an old story of some one saying, "Mallem cum Scaligero
errare, quam cum Clavio recte sapere."[209] This I cannot help suspecting
to have been a version of Vieta's speech with Clavius satirically inserted,
on account of the great hostility which Vieta showed towards Clavius in the
latter years of his life.

Montucla could not have read with care either Scaliger's quadrature or
Clavius's refutation. He gives the first a wrong date: he assures the world
that there is no question about Scaliger's quadrature being wrong, in the
eyes of geometers at least: and he states that Clavius mortified him {112}
extremely by showing that it made the circle less than its inscribed
dodecagon, which is, of course, equivalent to asserting that a straight
line is not always the shortest distance between two points. Did _Clavius_
show this? No, it was Scaliger himself who showed it, boasted of it, and
declared it to be a "noble paradox" that a theorem false in geometry is
true in arithmetic; a thing, he says with great triumph, not noticed by
Archimedes himself! He says in so many words that the periphery of the
dodecagon is greater than that of the circle; and that the more sides there
are to the inscribed figure, the more does it exceed the circle in which it
is. And here _are_ the words, on the independent testimonies of Clavius and
Kastner:

"Ambitus dodecagoni circulo inscribendi plus potest quam circuli ambitus.
Et quanto deinceps plurium laterum fuerit polygonum circulo inscribendum,
tanto plus poterit ambitus polygoni quam ambitus circuli."[210]

There is much resemblance between Joseph Scaliger and William
Hamilton,[211] in a certain impetuousity of character, and inaptitude to
think of quantity. Scaliger maintained that the arc of a circle is less
than its chord in arithmetic, though greater in geometry; Hamilton arrived
at two quantities which are identical, but the greater the one the less the
other. But, on the whole, I liken Hamilton rather to Julius than to Joseph.
On this last hero of literature I repeat Thomas Edwards,[212] who says that
a man is unlearned who, be his other knowledge what it may, does not {113}
understand the subject he writes about. And now one of many instances in
which literature gives to literature character in science. Anthony
Teissier,[213] the learned annotator of De Thou's biographies, says of
Finæus, "Il se vanta sans raison avoir trouvé la quadrature du cercle; la
gloire de cette admirable découverte était réservée à Joseph Scalinger,
comme l'a écrit Scévole de St. Marthe."[214]



JOHN GRAUNT AS A PARADOXER.

    Natural and Political Observations ... upon the Bills of Mortality. By
    John Graunt, citizen of London. London, 1662, 4to.[215]

This is a celebrated book, the first great work upon mortality. But the
author, going _ultra crepidam_, has attributed to the motion of the moon in
her orbit all the tremors which she gets from a shaky telescope.[216] But
there is another paradox about this book: the above absurd opinion is
attributed to that excellent mechanist, Sir William Petty, who passed his
days among the astronomers. Graunt did not write his own book! Anthony
Wood[217] hints that Petty "assisted, or put into a way" his old
benefactor: no doubt the two friends talked the matter over many a time.
Burnet and Pepys[218] state that Petty wrote the book. It is enough for me
that {114} Graunt, whose honesty was never impeached, uses the plainest
incidental professions of authorship throughout; that he was elected into
the Royal Society because he was the author; that Petty refers to him as
author in scores of places, and published an edition, as editor, after
Graunt's death, with Graunt's name of course. The note on Graunt in the
_Biographia Britannica_ may be consulted; it seems to me decisive. Mr.
C. B. Hodge, an able actuary, has done the best that can be done on the
other side in the _Assurance Magazine_, viii. 234. If I may say what is in
my mind, without imputation of disrespect, I suspect some actuaries have a
bias: they would rather have Petty the greater for their Coryphæus than
Graunt the less.[219]

Pepys is an ordinary gossip: but Burnet's account has an animus which is of
a worse kind. He talks of "one Graunt, a Papist, under whose name Sir
William Petty[220] published his observations on the bills of mortality."
He then gives the cock without a bull story of Graunt being a trustee of
the New River Company, and shutting up the cocks and carrying off their
keys, just before the fire of London, by which a supply of water was
delayed.[221] It was one of the first objections made to Burnet's work,
that Graunt was _not_ a trustee at the time; and Maitland, the historian of
London, ascertained from the books of the Company that he was not admitted
until twenty-three days after the breaking out of the fire. Graunt's first
admission {115} to the Company took place on the very day on which a
committee was appointed to inquire into the cause of the fire. So much for
Burnet. I incline to the view that Graunt's setting London on fire strongly
corroborates his having written on the bills of mortality: every practical
man takes stock before he commences a grand operation in business.



MANKIND A GULLIBLE LOT.

    De Cometis: or a discourse of the natures and effects of Comets, as
    they are philosophically, historically, and astrologically considered.
    With a brief (yet full) account of the III late Comets, or blazing
    stars, visible to all Europe. And what (in a natural way of judicature)
    they portend. Together with some observations on the nativity of the
    Grand Seignior. By John Gadbury, [Greek: Philomathêmatikos]. London,
    1665, 4to.

Gadbury, though his name descends only in astrology, was a well-informed
astronomer.[222] D'Israeli[223] sets down Gadbury, Lilly, Wharton, Booker,
etc., as rank rogues: I think him quite wrong. The easy belief in roguery
and intentional imposture which prevails in educated society is, to my
mind, a greater presumption against the honesty of mankind than all the
roguery and imposture itself. Putting aside mere swindling for the sake of
gain, and looking at speculation and paradox, I find very little reason to
suspect wilful deceit.[224] My opinion of mankind is founded upon the {116}
mournful fact that, so far as I can see, they find within themselves the
means of believing in a thousand times as much as there is to believe in,
judging by experience. I do not say anything against Isaac D'Israeli for
talking his time. We are all in the team, and we all go the road, but we do
not all draw.



A FORERUNNER OF A WRITTEN ESPERANTO.

    An essay towards a real character and a philosophical language. By John
    Wilkins [Dean of Ripon, afterwards Bishop of Chester].[225] London,
    1668, folio.

This work is celebrated, but little known. Its object gives it a right to a
place among paradoxes. It proposes a language--if that be the proper
name--in which _things_ and their relations shall be denoted by signs, not
_words_: so that any person, whatever may be his mother tongue, may read it
in his own words. This is an obvious possibility, and, I am afraid, an
obvious impracticability. One man may construct such a system--Bishop
Wilkins has done it--but where is the man who will learn it? The second
tongue makes a language, as the second blow makes a fray. There has been
very little curiosity about his performance, the work is scarce; and I do
not know where to refer the reader for any account of its details, except,
to the partial reprint of Wilkins presently mentioned under 1802, in which
there is an unsatisfactory abstract. There is nothing in the _Biographia
Britannica_, except discussion of Anthony Wood's statement that the hint
was derived from Dalgarno's book, {117} _De Signis_, 1661.[226] Hamilton
(_Discussions_, Art. 5, "Dalgarno") does not say a word on this point,
beyond quoting Wood; and Hamilton, though he did now and then write about
his countrymen with a rough-nibbed pen, knew perfectly well how to protect
their priorities.



GREGOIRE DE ST. VINCENT.

    Problema Austriacum. Plus ultra Quadratura Circuli. Auctore P. Gregorio
    a Sancto Vincentio Soc. Jesu., Antwerp, 1647, folio.--Opus Geometricum
    posthumum ad Mesolabium. By the same. Gandavi [Ghent], 1668,
    folio.[227]

The first book has more than 1200 pages, on all kinds of geometry. Gregory
St. Vincent is the greatest of circle-squarers, and his investigations led
him into many truths: he found the property of the area of the
hyperbola[228] which led to Napier's logarithms being called _hyperbolic_.
Montucla says of him, with sly truth, that no one has ever squared the
circle with so much genius, or, excepting his principal object, with so
much success.[229] His reputation, and the many merits of his work, led to
a sharp controversy on his quadrature, which ended in its complete exposure
by Huyghens and others. He had a small school of followers, who defended
him in print.

{118}



RENE DE SLUSE.

    Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liège], 1668,
    4to.[230]

The Mesolabum is the solution of the problem of finding two mean
proportionals, which Euclid's geometry does not attain. Slusius is a true
geometer, and uses the ellipse, etc.: but he is sometimes ranked with the
trisecters, for which reason I place him here, with this explanation.

The finding of two mean proportionals is the preliminary to the famous old
problem of the duplication of the cube, proposed by Apollo (not Apollonius)
himself. D'Israeli speaks of the "six follies of science,"--the quadrature,
the duplication, the perpetual motion, the philosopher's stone, magic, and
astrology. He might as well have added the trisection, to make the mystic
number seven: but had he done so, he would still have been very lenient;
only seven follies in all science, from mathematics to chemistry! Science
might have said to such a judge--as convicts used to say who got seven
years, expecting it for life, "Thank you, my Lord, and may you sit there
till they are over,"--may the Curiosities of Literature outlive the Follies
of Science!



JAMES GREGORY.

1668. In this year James Gregory, in his _Vera Circuli et Hyperbolæ
Quadratura_,[231] held himself to have proved that {119} the _geometrical_
quadrature of the circle is impossible. Few mathematicians read this very
abstruse speculation, and opinion is somewhat divided. The regular
circle-squarers attempt the _arithmetical_ quadrature, which has long been
proved to be impossible. Very few attempt the geometrical quadrature. One
of the last is Malacarne, an Italian, who published his _Solution
Géométrique_, at Paris, in 1825. His method would make the circumference
less than three times the diameter.



BEAULIEU'S QUADRATURE.

    La Géométrie Françoise, ou la Pratique aisée.... La quadracture du
    cercle. Par le Sieur de Beaulieu, Ingénieur, Géographe du Roi ...
    Paris, 1676, 8vo. [not Pontault de Beaulieu, the celebrated
    topographer; he died in 1674].[232]

If this book had been a fair specimen, I might have pointed to it in
connection with contemporary English works, and made a scornful comparison.
But it is not a fair specimen. Beaulieu was attached to the Royal
Household, and throughout the century it may be suspected that the
household forced a royal road to geometry. Fifty years before, Beaugrand,
the king's secretary, made a fool of himself, and [so?] contrived to pass
for a geometer. He had interest enough to get Desargues, the most powerful
geometer of his time,[233] the teacher and friend of Pascal, prohibited
from {120} lecturing. See some letters on the History of Perspective, which
I wrote in the _Athenæum_, in October and November, 1861. Montucla, who
does not seem to know the true secret of Beaugrand's greatness, describes
him as "un certain M. de Beaugrand, mathématicien, fort mal traité par
Descartes, et à ce qu'il paroit avec justice."[234]

Beaulieu's quadrature amounts to a geometrical construction[235] which
gives [pi] = [root]10. His depth may be ascertained from the following
extracts. First on Copernicus:

"Copernic, Allemand, ne s'est pas moins rendu illustre par ses doctes
écrits; et nous pourrions dire de luy, qu'il seroit le seul et unique en la
force de ses Problèmes, si sa trop grande présomption ne l'avoit porté à
avancer en cette Science une proposition aussi absurde, qu'elle est contre
la Foy et raison, en faisant la circonférence d'un Cercle fixe, immobile,
et le centre mobile, sur lequel principe Géométrique, il a avancé en son
Traitté Astrologique le Soleil fixe, et la Terre mobile."[236]

I digress here to point out that though our quadrators, etc., very often,
and our historians sometimes, assert that men of the character of
Copernicus, etc., were treated with contempt and abuse until their day of
ascendancy came, nothing can be more incorrect. From Tycho Brahé[237] to
Beaulieu, there is but one expression of admiration for the genius of
Copernicus. There is an exception, which, I {121} believe, has been quite
misunderstood. Maurolycus,[238] in his _De Sphæra_, written many years
before its posthumous publication in 1575, and which it is not certain he
would have published, speaking of the safety with which various authors may
be read after his cautions, says, "Toleratur et Nicolaus Copernicus qui
Solem fixum et Terram _in girum circumverti_ posuit: et scutica potius, aut
flagello, quam reprehensione dignus est."[239] Maurolycus was a mild and
somewhat contemptuous satirist, when expressing disapproval: as we should
now say, he pooh-poohed his opponents; but, unless the above be an
instance, he was never savage nor impetuous. I am fully satisfied that the
meaning of the sentence is, that Copernicus, who turned the earth like a
boy's top, ought rather to have a whip given him wherewith to keep up his
plaything than a serious refutation. To speak of _tolerating_ a person _as
being_ more worthy of a flogging than an argument, is almost a
contradiction.

I will now extract Beaulieu's treatise on algebra, entire.

"L'Algebre est la science curieuse des Sçavans et specialement d'un General
d'Armée ou Capitaine, pour promptement ranger une Armée en bataille, et
nombre de Mousquetaires et Piquiers qui composent les bataillons d'icelle,
outre les figures de l'Arithmetique. Cette science a 5 figures
particulieres en cette sorte. P signifie _plus_ au commerce, et à l'Armée
_Piquiers_. M signifie _moins_, et _Mousquetaire_ en l'Art des bataillons.
[It is quite true that P and M were used for _plus_ and _minus_ in a great
many old works.] R signifie _racine_ en la mesure du Cube, et en l'Armée
_rang_. Q signifie _quaré_ en l'un et l'autre usage. C signifie _cube_ en
la mesure, et _Cavallerie_ en la composition des bataillons et escadrons.
Quant à l'operation de cette science, c'est {122} d'additionner un _plus_
d'avec _plus_, la somme sera _plus_, et _moins_ d'avec _plus_, on soustrait
le moindre du _plus_, et la reste est la somme requise ou nombre trouvé. Je
dis seulement cecy en passant pour ceux qui n'en sçavent rien du
tout."[240]

This is the algebra of the Royal Household, seventy-three years after the
death of Vieta. Quære, is it possible that the fame of Vieta, who himself
held very high stations in the household all his life, could have given
people the notion that when such an officer chose to declare himself an
algebraist, he must be one indeed? This would explain Beaugrand, Beaulieu,
and all the _beaux_. Beaugrand--not only secretary to the king, but
"mathematician" to the Duke of Orleans--I wonder what his "fool" could have
been like, if indeed he kept the offices separate,--would have been in my
list if I had possessed his _Geostatique_, published about 1638.[241] He
makes bodies diminish in weight as they approach the earth, because the
effect of a weight on a lever is less as it approaches the fulcrum.

{123}



SIR MATTHEW HALE.

    Remarks upon two late ingenious discourses.... By Dr. Henry More.[242]
    London, 1676, 8vo.

In 1673 and 1675, Matthew Hale,[243] then Chief Justice, published two
tracts, an "Essay touching Gravitation," and "Difficiles Nugæ" on the
Torricellian experiment. Here are the answers by the learned and voluminous
Henry More. The whole would be useful to any one engaged in research about
ante-Newtonian notions of gravitation.



    Observations touching the principles of natural motions; and especially
    touching rarefaction and condensation.... By the author of _Difficiles
    Nugæ_. London, 1677, 8vo.

This is another tract of Chief Justice Hale, published the year after his
death. The reader will remember that _motion_, in old philosophy, meant any
change from state to state: what we now describe as _motion_ was _local
motion_. This is a very philosophical book, about _flux_ and _materia
prima_, _virtus activa_ and _essentialis_, and other fundamentals. I think
Stephen Hales, the author of the "Vegetable Statics," has the writings of
the Chief Justice sometimes attributed to him, which is very puny justice
indeed.[244] Matthew Hale died in 1676, and from his devotion to science it
probably arose that his famous _Pleas of the Crown_[245] and other law
works did not appear until after his death. One of his {124} contemporaries
was the astronomer Thomas Street, whose _Caroline Tables_[246] were several
times printed: another contemporary was his brother judge, Sir Thomas
Street.[247] But of the astronomer absolutely nothing is known: it is very
unlikely that he and the judge were the same person, but there is not a bit
of positive evidence either for or against, so far as can be ascertained.
Halley[248]--no less a person--published two editions of the _Caroline
Tables_, no doubt after the death of the author: strange indeed that
neither Halley nor any one else should leave evidence that Street was born
or died.

Matthew Hale gave rise to an instance of the lengths a lawyer will go when
before a jury who cannot detect him. Sir Samuel Shepherd,[249] the Attorney
General, in opening Hone's[250] first trial, calls him "one who was the
most learned man that ever adorned the Bench, the most even man that ever
blessed domestic life, the _most eminent man that ever advanced the
progress of science_, and one of the [very moderate] best and most purely
religious men that ever lived."

{125}



ON THE DISCOVERY OF ANTIMONY.

    Basil Valentine his triumphant Chariot of Antimony, with annotations of
    Theodore Kirkringius, M.D. With the true book of the learned Synesius,
    a Greek abbot, taken out of the Emperour's library, concerning the
    Philosopher's Stone. London, 1678, 8vo.[251]

There are said to be three Hamburg editions of the collected works of
Valentine, who discovered the common antimony, and is said to have given
the name _antimoine_, in a curious way. Finding that the pigs of his
convent throve upon it, he gave it to his brethren, who died of it.[252]
The impulse given to chemistry by R. Boyle[253] seems to have brought out a
vast number of translations, as in the following tract:



ON ALCHEMY.

    _Collectanea Chymica_: A collection of ten several treatises in
    chymistry, concerning the liquor Alkehest, the Mercury of Philosophers,
    and other curiosities worthy the perusal. Written by Eir.
    Philaletha,[254] Anonymus, J. B. Van-Helmont,[255] Dr. Fr. {126}
    Antonie,[256] Bernhard Earl of Trevisan,[257] Sir Geo. Ripley,[258]
    Rog. Bacon,[259] Geo. Starkie,[260] Sir Hugh Platt,[261] and the Tomb
    of Semiramis. See more in the contents. London, 1684, 8vo.

In the advertisements at the ends of these tracts there are upwards of a
hundred English tracts, nearly all of the period, and most of them
translations. Alchemy looks up since the chemists have found perfectly
different substances composed of the same elements and proportions. It is
true the chemists cannot yet _transmute_; but they may in time: they poke
about most assiduously. It seems, then, that the conviction that alchemy
_must_ be impossible was a delusion: but we do not mention it.

{127}

The astrologers and the alchemists caught it in company in the following,
of which I have an unreferenced note.

"Mendacem et futilem hominem nominare qui volunt, calendariographum dicunt;
at qui sceleratum simul ac impostorem, chimicum.[262]

 "Crede ratem ventis corpus ne crede chimistis;
      Est quævis chimica tutior aura fide."[263]

Among the smaller paradoxes of the day is that of the _Times_ newspaper,
which always spells it _chymistry_: but so, I believe, do Johnson, Walker,
and others. The Arabic work is very likely formed from the Greek: but it
may be connected either with [Greek: chêmeia] or with [Greek: chumeia].



    Lettre d'un gentil-homme de province à une dame de qualité, sur le
    sujet de la Comète. Paris, 1681, 4to.

An opponent of astrology, whom I strongly suspect to have been one of the
members of the Academy of Sciences under the name of a country
gentleman,[264] writes very good sense on the tremors excited by comets.



    The Petitioning-Comet: or a brief Chronology of all the famous Comets
    and their events, that have happened from the birth of Christ to this
    very day. Together with a modest enquiry into this present comet,
    London, 1681, 4to.

A satirical tract against the cometic prophecy:

"This present comet (it's true) is of a menacing aspect, but if the _new
parliament_ (for whose convention so many good men pray) continue long to
sit, I fear not but the star will lose its virulence and malignancy, or at
least its portent be averted from this our nation; which being the humble
request to God of all good men, makes me thus entitle it, a
Petitioning-Comet."

{128}

The following anecdote is new to me:

"Queen Elizabeth (1558) being then at Richmond, and being disswaded from
looking on a comet which did then appear, made answer, _jacta est alea_,
the dice are thrown; thereby intimating that the pre-order'd providence of
God was above the influence of any star or comet."

The argument was worth nothing: for the comet might have been _on the dice_
with the event; the astrologers said no more, at least the more rational
ones, who were about half of the whole.



    An astrological and theological discourse upon this present great
    conjunction (the like whereof hath not (likely) been in some ages)
    ushered in by a great comet. London, 1682, 4to. By C. N.[265]

The author foretells the approaching "sabbatical jubilee," but will not fix
the date: he recounts the failures of his predecessors.



    A judgment of the comet which became first generally visible to us in
    Dublin, December 13, about 15 minutes before 5 in the evening, A.D.
    1680. By a person of quality. Dublin, 1682, 4to.

The author argues against cometic astrology with great ability.



    A prophecy on the conjunction of Saturn and Jupiter in this present
    year 1682. With some prophetical predictions of what is likely to ensue
    therefrom in the year 1684. By John Case, Student in physic and
    astrology.[266] London, 1682, 4to.

{129}

According to this writer, great conjunctions of Jupiter and Saturn occur
"in the fiery trigon," about once in 800 years. Of these there are to be
seven: six happened in the several times of Enoch, Noah, Moses, Solomon,
Christ, Charlemagne. The seventh, which is to happen at "the lamb's
marriage with the bride," seems to be that of 1682; but this is only
vaguely hinted.



    De Quadrature van de Circkel. By Jacob Marcelis. Amsterdam, 1698, 4to.

    Ampliatie en demonstratie wegens de Quadrature ... By Jacob Marcelis.
    Amsterdam, 1699, 4to.

    Eenvoudig vertoog briev-wys geschrevem am J. Marcelis ... Amsterdam,
    1702, 4to.

    De sleutel en openinge van de quadrature ... Amsterdam, 1704, 4to.

Who shall contradict Jacob Marcelis?[267] He says the circumference
contains the diameter exactly times

    1008449087377541679894282184894
  3 --------------------------------
    6997183637540819440035239271702

But he does not come very near, as the young arithmetician will find.



MATHEMATICAL THEOLOGY.

    Theologiæ Christianæ Principia Mathematica. Auctore Johanne Craig.[268]
    London, 1699, 4to.

This is a celebrated speculation, and has been reprinted abroad, and
seriously answered. Craig is known in the early history of fluxions, and
was a good mathematician. {130} He professed to calculate, on the
hypothesis that the suspicions against historical evidence increase with
the square of the time, how long it will take the evidence of Christianity
to die out. He finds, by formulæ, that had it been oral only, it would have
gone out A.D. 800; but, by aid of the written evidence, it will last till
A.D. 3150. At this period he places the second coming, which is deferred
until the extinction of evidence, on the authority of the question "When
the Son of Man cometh, shall he find faith on the earth?" It is a pity that
Craig's theory was not adopted: it would have spared a hundred treatises on
the end of the world, founded on no better knowledge than his, and many of
them falsified by the event. The most recent (October, 1863) is a tract in
proof of Louis Napoleon being Antichrist, the Beast, the eighth Head, etc.;
and the present dispensation is to close soon after 1864.

In order rightly to judge Craig, who added speculations on the variations
of pleasure and pain treated as functions of time, it is necessary to
remember that in Newton's day the idea of force, as a quantity to be
measured, and as following a law of variation, was very new: so likewise
was that of probability, or belief, as an object of measurement.[269] The
success of the _Principia_ of Newton put it into many heads to speculate
about applying notions of quantity to other things not then brought under
measurement. Craig imitated Newton's title, and evidently thought he was
making a step in advance: but it is not every one who can plough with
Samson's heifer.

It is likely enough that Craig took a hint, directly or indirectly, from
Mohammedan writers, who make a reply to the argument that the Koran has not
the evidence derived {131} from miracles. They say that, as evidence of
Christian miracles is daily becoming weaker, a time must at last arrive
when it will fail of affording assurance that they were miracles at all:
whence would arise the necessity of another prophet and other miracles.
Lee,[270] the Cambridge Orientalist, from whom the above words are taken,
almost certainly never heard of Craig or his theory.



THE ARISTOCRAT AS A SCIENTIST.

    Copernicans of all sorts convicted ... to which is added a Treatise of
    the Magnet. By the Hon. Edw. Howard, of Berks. London, 1705, 8vo.

Not all the blood of all the Howards will gain respect for a writer who
maintains that eclipses admit no possible explanation under the Copernican
hypothesis, and who asks how a man can "go 200 yards to any place if the
moving superficies of the earth does carry it from him?" Horace Walpole, at
the beginning of his _Royal and Noble Authors_, has mottoed his book with
the Cardinal's address to Ariosto, "Dove diavolo, Messer Ludovico, avete
pigliato tante coglionerie?"[271] Walter Scott says you could hardly pick
out, on any principle of selection--except badness itself, he means of
course--the same number of plebeian authors whose works are so bad. But his
implied satire on aristocratic writing forgets two points. First, during a
large period of our history, when persons of rank condescended to write,
they veiled themselves under "a person of honor," "a person of quality,"
and the like, when not wholly undescribed. Not one of these has Walpole
got; he omits, {132} for instance, Lord Brounker's[272] translation of
Descartes on Music. Secondly, Walpole only takes the heads of houses: this
cuts both ways; he equally eliminates the Hon. Robert Boyle and the
precious Edward Howard. The last writer is hardly out of the time in which
aristocracy suppressed its names; the avowal was then usually meant to make
the author's greatness useful to the book. In our day, literary peers and
honorables are very favorably known, and contain an eminent class.[273]
They rough it like others, and if such a specimen as Edw. Howard were now
to appear, he would be greeted with

 "Hereditary noodle! knowest thou not
  Who would be wise, himself must make him so?"



THE LONGITUDE PROBLEM.

    A new and easy method to find the longitude at land or sea. London,
    1710, 4to.

This tract is a little earlier than the great epoch of such publications
(1714), and professes to find the longitude by the observed altitudes of
the moon and two stars.[274] {133}



    A new method for discovering the longitude both at sea and land, humbly
    proposed to the consideration of the public.[275] By Wm. Whiston[276]
    and Humphry Ditton.[277] London, 1714, 8vo.

This is the celebrated tract, written by the two Arian heretics. Swift,
whose orthodoxy was as undoubted as his meekness, wrote upon it the
epigram--if, indeed, that be epigram of which the point is pious
wish--which has been so often recited for the purity of its style, a purity
which transcends modern printing. Perhaps some readers may think that Swift
cared little for Whiston and Ditton, except as a chance hearing of their
plan pointed them out as good marks. But it was not so: the clique had
their eye on the guilty pair before the publication of the tract. The
preface is dated July 7; and ten days afterwards Arbuthnot[278] writes as
follows to Swift:

"Whiston has at last published his project of the longitude; the most
ridiculous thing that ever was thought on. But a pox on him! he has spoiled
one of my papers of Scriblerus, which was a proposition for the longitude
not very unlike his, to this purpose; that since there was no pole for east
and west, that all the princes of Europe should join and build two
prodigious poles, upon high mountains, {134} with a vast lighthouse to
serve for a polestar. I was thinking of a calculation of the time, charges,
and dimensions. Now you must understand his project is by lighthouses, and
explosion of bombs at a certain hour."

The plan was certainly impracticable; but Whiston and Ditton might have
retorted that they were nearer to the longitude than their satirist to the
kingdom of heaven, or even to a bishopric. Arbuthnot, I think, here and
elsewhere, reveals himself as the calculator who kept Swift right in his
proportions in the matter of the Lilliputians, Brobdingnagians, etc. Swift
was very ignorant about things connected with number. He writes to Stella
that he has discovered that leap-year comes every four years, and that all
his life he had thought it came every three years. Did he begin with the
mistake of Cæsar's priests? Whether or no, when I find the person who did
not understand leap-year inventing satellites of Mars in correct accordance
with Kepler's third law, I feel sure he must have had help.



THE AURORA BOREALIS.

    An essay concerning the late apparition in the heavens on the 6th of
    March. Proving by mathematical, logical, and moral arguments, that it
    cou'd not have been produced meerly by the ordinary course of nature,
    but must of necessity be a prodigy. Humbly offered to the consideration
    of the Royal Society. London, 1716, 8vo.

The prodigy, as described, was what we should call a very decided and
unusual aurora borealis. The inference was, that men's sins were bringing
on the end of the world. The author thinks that if one of the old
"threatening prophets" were then alive, he would give "something like the
following." I quote a few sentences of the notion which the author had of
the way in which Ezekiel, for instance, would have addressed his Maker in
the reign of George the First:

"Begin! Begin! O Sovereign, for once, with an {135} effectual clap of
thunder.... O Deity! either thunder to us no more, or when you thunder, do
it home, and strike with vengeance to the mark.... 'Tis not enough to raise
a storm, unless you follow it with a blow, and the thunder without the
bolt, signifies just nothing at all.... Are then your lightnings of so
short a sight, that they don't know how to hit, unless a mountain stands
like a barrier in their way? Or perhaps so many eyes open in the firmament
make you lose your aim when you shoot the arrow? Is it this? No! but, my
dear Lord, it is your custom never to take hold of your arms till you have
first bound round your majestic countenance with gathered mists and
clouds."



    The principles of the Philosophy of the Expansive and Contractive
    Forces ... By Robert Greene,[279] M.A., Fellow of Clare Hall.
    Cambridge, 1727, folio.

Sanderson[280] writes to Jones,[281] "The gentleman has been reputed mad
for these two years last past, but never gave the world such ample
testimony of it before." This was said of a former work of Greene's, on
solid geometry, published in 1712, in which he gives a quadrature.[282] He
gives the same or another, I do not know which, in the present work, in
which the circle is 3-1/5 diameters. This volume is of 981 good folio
pages, and treats of all things, mental and material. The author is not at
all mad, only wrong on {136} many points. It is the weakness of the
orthodox follower of any received system to impute insanity to the solitary
dissentient: which is voted (in due time) a very wrong opinion about
Copernicus, Columbus, or Galileo, but quite right about Robert Greene. If
misconceptions, acted on by too much self-opinion, be sufficient evidence
of madness, it would be a curious inquiry what is the least per-centage of
the reigning school which has been insane at any one time. Greene is one of
the sources for Newton being led to think of gravitation by the fall of an
apple: his authority is the gossip of Martin Folkes.[283] Probably Folkes
had it from Newton's niece, Mrs. Conduitt, whom Voltaire acknowledges as
_his authority_.[284] It is in the draft found among Conduitt's papers of
memoranda to be sent to Fontenelle. But Fontenelle, though a great retailer
of anecdote, does not mention it in his _éloge_ of Newton; whence it may be
suspected that it was left out in the copy forwarded to France. D'Israeli
has got an improvement on the story: the apple "struck him a smart blow on
the head": no doubt taking him just on the organ of causality. He was
"surprised at the force of the stroke" from so small an apple: but then the
apple had a mission; Homer would have said {137} it was Minerva in the form
of an apple. "This led him to consider the accelerating motion of falling
bodies," which Galileo had settled long before: "from whence he deduced the
principle of gravity," which many had considered before him, but no one had
_deduced anything from it_. I cannot imagine whence D'Israeli got the rap
on the head, I mean got it for Newton: this is very unlike his usual
accounts of things. The story is pleasant and possible: its only defect is
that various writings, well known to Newton, a very _learned_
mathematician, had given more suggestion than a whole sack of apples could
have done, if they had tumbled on that mighty head all at once. And
Pemberton, speaking from Newton himself, says nothing more than that the
idea of the moon being retained by the same force which causes the fall of
bodies struck him for the first time while meditating in a garden. One
particular tree at Woolsthorpe has been selected as the gallows of the
appleshaped goddess: it died in 1820, and Mr. Turnor[285] kept the wood;
but Sir D. Brewster[286] brought away a bit of root in 1814, and must have
had it on his conscience for 43 years that he may have killed the tree.
Kepler's suggestion of gravitation with the inverse distance, and
Bouillaud's proposed substitution of the inverse square of the distance,
are things which Newton knew better than his modern readers. I discovered
two anagrams on his name, which are quite conclusive; the notion of
gravitation was _not new_; but Newton _went on_. Some wandering spirit,
probably whose business it was to resent any liberty taken with Newton's
name, put into the head of a friend of mine _eighty-one_ anagrams on my own
pair, some of which hit harder than any apple.

{138}



DE MORGAN ANAGRAMS.

This friend, whom I must not name, has since made it up to about 800
anagrams on my name, of which I have seen about 650. Two of them I have
joined in the title-page: the reader may find the sense. A few of the
others are personal remarks.

 "Great gun! do us a sum!"

is a sneer at my pursuits: but,

 "Go! great sum! [Integral]a u^{n} du"

is more dignified.

 "Sunt agro! gaudemus,"[287]

is happy as applied to one of whom it may be said:

 "Ne'er out of town; 'tis such a horrid life;
   But duly sends his family and wife."

 "Adsum, nugator, suge!"[288]

is addressed to a student who continues talking after the lecture has
commenced: oh! the rascal!

 "Graduatus sum! nego"[289]

applies to one who declined to subscribe for an M.A. degree.

 "Usage mounts guard"

symbolizes a person of very fixed habits.

 "Gus! Gus! a mature don!
    August man! sure, god!
  And Gus must argue, O!
    Snug as mud to argue,
  Must argue on gauds.
    A mad rogue stung us.
  Gag a numerous stud
    Go! turn us! damage us!
  Tug us! O drag us! Amen.
    Grudge us! moan at us!
  {139}
  Daunt us! gag us more!
    Dog-ear us, man! gut us!
  D---- us! a rogue tugs!"

are addressed to me by the circle-squarers; and,

 "O! Gus! tug a mean surd!"

is smart upon my preference of an incommensurable value of [pi] to 3-1/5,
or some such simple substitute. While,

 "Gus! Gus! at 'em a' round!"

ought to be the backing of the scientific world to the author of the
_Budget of Paradoxes_.

The whole collection commenced existence in the head of a powerful
mathematician during some sleepless nights. Seeing how large a number was
practicable, he amused himself by inventing a digested plan of finding
more.

Is there any one whose name cannot be twisted into either praise or satire?
I have had given to me,

 "Thomas Babington Macaulay
   Mouths big: a Cantab anomaly."



NEWTON'S DE MUNDI SYSTEMATE LIBER.

    A treatise of the system of the world. By Sir Isaac Newton. Translated
    into English. London, 1728, 8vo.

I think I have a right to one little paradox of my own: I greatly doubt
that Newton wrote this book. Castiglione,[290] in his _Newtoni
Opuscula_,[291] gives it in the Latin which appeared in 1731,[292] not for
the first time; he says _Angli omnes Newtono tribuunt_.[293] It appeared
just after Newton's death, without the name of any editor, or any allusion
to Newton's {140} recent departure, purporting to be that popular treatise
which Newton, at the beginning of the third book of the _Principia_, says
he wrote, intending it to be the third book. It is very possible that some
observant turnpenny might construct such a treatise as this from the third
book, that it might be ready for publication the moment Newton could not
disown it. It has been treated with singular silence: the name of the
editor has never been given. Rigaud[294] mentions it without a word: I
cannot find it in Brewster's _Newton_, nor in the _Biographia Britannica_.
There is no copy in the Catalogue of the Royal Society's Library, either in
English or Latin, except in Castiglione. I am open to correction; but I
think nothing from Newton's acknowledged works will prove--as laid down in
the suspected work--that he took Numa's temple of Vesta, with a central
fire, to be intended to symbolize the sun as the center of our system, in
the Copernican sense.[295]

Mr. Edleston[296] gives an account of the _lectures_ "de motu corporum,"
and gives the corresponding pages of the _Latin_ "De Systemate Mundi" of
1731. But no one mentions the _English_ of 1728. This English seems to
agree with the Latin; but there is a mystery about it. The preface says,
"That this work as here published is genuine will so clearly appear by the
intrinsic marks it bears, that it will be but losing words and the reader's
time to take pains in giving him any other satisfaction." Surely fewer
words would have been lost if the prefator had said at once that the work
was from the manuscript preserved at Cambridge. Perhaps it was a mangled
copy clandestinely taken and interpreted. {141}



A BACONIAN CONTROVERSY.

    Lord Bacon not the author of "The Christian Paradoxes," being a reprint
    of "Memorials of Godliness and Christianity," by Herbert Palmer,
    B.D.[297] With Introduction, Memoir, and Notes, by the Rev. Alexander
    B. Grosart,[298] Kenross. (Private circulation, 1864).

I insert the above in this place on account of a slight connection with the
last. Bacon's Paradoxes,--so attributed--were first published as his in
some asserted "Remains," 1648.[299] They were admitted into his works in
1730, and remain there to this day. The title is "The Character of a
believing Christian, set forth in paradoxes and seeming contradictions."
The following is a specimen:

"He believes three to be one and one to be three; a father not to be older
than his son; a son to be equal with his father; and one proceeding from
both to be equal with both: he believes three persons in one nature, and
two natures in one person.... He believes the God of all grace to have been
angry with one that never offended Him; and that God that hates sin to be
reconciled to himself though sinning continually, and never making or being
able to make Him any satisfaction. He believes a most just God to have
punished a most just person, and to have justified himself, though a most
ungodly sinner. He believes himself freely pardoned, and yet a sufficient
satisfaction was made for him."

Who can doubt that if Bacon had written this it must have been wrong? Many
writers, especially on the {142} Continent, have taken him as sneering at
(Athanasian) Christianity right and left. Many Englishmen have taken him to
be quite in earnest, and to have produced a body of edifying doctrine. More
than a century ago the Paradoxes were published as a penny tract; and,
again, at the same price, in the _Penny Sunday Reader_, vol. vi, No. 148, a
few passages were omitted, as _too strong_. But all did not agree: in my
copy of Peter Shaw's [300] edition (vol. ii, p. 283) the Paradoxes have
been cut out by the binder, who has left the backs of the leaves. I never
had the curiosity to see whether other copies of the edition have been
served in the same way. The Religious Tract Society republished them
recently in _Selections from the Writings of Lord Bacon_, (no date; bad
plan; about 1863, I suppose). No omissions were made, so far as I find.

I never believed that Bacon wrote this paper; it has neither his _sparkle_
nor his idiom. I stated my doubts even before I heard that Mr. Spedding,
one of Bacon's editors, was of the same mind. (_Athenæum_, July 16, 1864).
I was little moved by the wide consent of orthodox men: for I knew how
Bacon, Milton, Newton, Locke, etc., were always claimed as orthodox until
almost the present day. Of this there is a remarkable instance.



LOCKE AND SOCINIANISM.

Among the books which in my younger day were in some orthodox publication
lists--I think in the list of the Christian Knowledge Society, but I am not
sure--was Locke's [301] "Reasonableness of Christianity." It seems to have
come down from the eighteenth century, when the battle was belief in Christ
against unbelief, _simpliciter_, as the {143} logicians say. Now, if ever
there was a Socinian[302] book in the world, it is this work of Locke.
"These two," says Locke, "faith and repentance, i.e., believing Jesus to be
the Messiah, and a good life, are the indispensable conditions of the new
covenant, to be performed by all those who would obtain eternal life." All
the book is amplification of this doctrine. Locke, in this and many other
things, followed Hobbes, whose doctrine, in the Leviathan, is _fidem,
quanta ad salutem necessaria est, contineri in hoc articulo, Jesus est
Christus_.[303] For this Hobbes was called an atheist, which {144} many
still believe him to have been: some of his contemporaries called him,
rightly, a Socinian. Locke was known for a Socinian as soon as his work
appeared: Dr. John Edwards,[304] his assailant, says he is "Socinianized
all over." Locke, in his reply, says "there is not one word of Socinianism
in it:" and he was right: the positive Socinian doctrine has _not one word
of Socinianism in it_; Socinianism consists in omissions. Locke and Hobbes
did not dare _deny_ the Trinity: for such a thing Hobbes might have been
roasted, and Locke might have been strangled. Accordingly, the well-known
way of teaching Unitarian doctrine was the collection of the asserted
essentials of Christianity, without naming the Trinity, etc. This is the
plan Newton followed, in the papers which have at last been published.[305]

So I, for one, thought little about the general tendency of orthodox
writers to claim Bacon by means of the Paradoxes. I knew that, in his
"Confession of Faith"[306] he is a Trinitarian of a heterodox stamp. His
second Person takes human nature before he took flesh, not for redemption,
but as a condition precedent of creation. "God is so holy, pure, and
jealous, that it is impossible for him to be pleased in any creature,
though the work of his own hands.... [Gen. i. 10, 12, 18, 21, 25, 31,
freely rendered]. But--purposing to become a Creator, and to communicate to
his creatures, he ordained in his eternal counsel that one person of the
Godhead should be united to one nature, and to one particular of his
creatures; that so, in the person of the Mediator, the true ladder might be
fixed, whereby God might {145} descend to his creatures and his creatures
might ascend to God...."

This is republished by the Religious Tract Society, and seems to suit their
theology, for they confess to having omitted some things of which they
disapprove.

In 1864, Mr. Grosart published his discovery that the Paradoxes are by
Herbert Palmer; that they were first published surreptitiously, and
immediately afterwards by himself, both in 1645; that the "Remains" of
Bacon did not appear until 1648; that from 1645 to 1708, thirteen editions
of the "Memorials" were published, all containing the Paradoxes. In spite
of this, the Paradoxes were introduced into Bacon's works in 1730, where
they have remained.

Herbert Palmer was of good descent, and educated as a Puritan. He was an
accomplished man, one of the few of his day who could speak French as well
as English. He went into the Church, and was beneficed by Laud,[307] in
spite of his puritanism; he sat in the Assembly of Divines, and was finally
President of Queens' College, Cambridge, in which post he died, August 13,
1647, in the 46th year of his age.

Mr. Grosart says, speaking of Bacon's "Remains," "All who have had occasion
to examine our early literature are aware that it was a common trick to
issue imperfect, false, and unauthorized writings under any recently
deceased name that might be expected to take. The Puritans, down to John
Bunyan, were perpetually expostulating and protesting against such
procedure." I have met with instances of all this; but I did not know that
there was so much of it: a good collection would be very useful. The work
of 1728, attributed to Newton, is likely enough to be one of the class.

{146}



    Demonstration de l'immobilitez de la Terre.... Par M. de la
    Jonchere,[308] Ingénieur Français. Londres, 1728, 8vo.

A synopsis which is of a line of argument belonging to the beginning of the
preceding century.



TWO FORGOTTEN CIRCLE SQUARERS.

    The Circle squared; together with the Ellipsis and several reflections
    on it. The finding two geometrical mean proportionals, or doubling the
    cube geometrically. By Richard Locke[309].... London, no date, probably
    about 1730, 8vo.

According to Mr. Locke, the circumference is three diameters, three-fourths
the difference of the diameter and the side of the inscribed equilateral
triangle, and three-fourths the difference between seven-eighths of the
diameter and the side of the same triangle. This gives, he says, 3.18897.
There is an addition to this tract, being an appendix to a book on the
longitude.



    The Circle squar'd. By Thos. Baxter, Crathorn, Cleaveland, Yorkshire.
    London, 1732, 8vo.

Here [pi] = 3.0625. No proof is offered.[310]



    The longitude discovered by the Eclipses, Occultations, and
    Conjunctions of Jupiter's planets. By William Whiston. London, 1738.

This tract has, in some copies, the celebrated preface containing the
account of Newton's appearance before the Parliamentary Committee on the
longitude question, in 1714 {147} (Brewster, ii. 257-266). This "historical
preface," is an insertion and is dated April 28, 1741, with four additional
pages dated August 10, 1741. The short "preface" is by the publisher, John
Whiston,[311] the author's son.



THE STEAMSHIP SUGGESTED.

    A description and draught of a new-invented machine for carrying
    vessels or ships out of, or into any harbour, port, or river, against
    wind and tide, or in a calm. For which, His Majesty has granted letters
    patent, for the sole benefit of the author, for the space of fourteen
    years. By Jonathan Hulls.[312] London: printed for the author, 1737.
    Price sixpence (folding plate and pp. 48, beginning from title).

(I ought to have entered this tract in its place. It is so rare that its
existence was once doubted. It is the earliest description of steam-power
applied to navigation. The plate shows a barge, with smoking funnel, and
paddles at the stem, towing a ship of war. The engine, as described, is
Newcomen's.[313]

In 1855, John Sheepshanks,[314] so well known as a friend of Art and a
public donor, reprinted this tract, in fac-simile, from his own copy;
twenty-seven copies of the original 12mo size, and twelve on old paper,
small 4to. I have an original copy, wanting the plate, and with "Price
sixpence" carefully erased, to the honor of the book.[315]

{148}

It is not known whether Hulls actually constructed a boat.[316] In all
probability his tract suggested to Symington, as Symington[317] did to
Fulton.)



THE NEWTONIANS ATTACKED.

    Le vrai système de physique générale de M. Isaac Newton exposé et
    analysé en parallèle avec celui de Descartes. By Louis Castel[318]
    [Jesuit and F.R.S.] Paris, 1743, 4to.

This is an elaborate correction of Newton's followers, and of Newton
himself, who it seems did not give his own views with perfect fidelity.
Father Castel, for instance, assures us that Newton placed the sun _at
rest_ in the center of the system. Newton left the sun to arrange that
matter with the planets and the rest of the universe. In this volume of 500
pages there is right and wrong, both clever.



    A dissertation on the Æther of Sir Isaac Newton. By Bryan
    Robinson,[319] M.D. Dublin, 1743, 8vo.[320]

{149}

A mathematical work professing to prove that the assumed ether causes
gravitation.



MATHEMATICAL THEOLOGY.

    Mathematical principles of theology, or the existence of God
    geometrically demonstrated. By Richard Jack, teacher of Mathematics.
    London, 1747, 8vo.[321]

Propositions arranged after the manner of Euclid, with beings represented
by circles and squares. But these circles and squares are logical symbols,
not geometrical ones. I brought this book forward to the Royal Commission
on the British Museum as an instance of the absurdity of attempting a
_classed_ catalogue from the _titles_ of books. The title of this book
sends it either to theology or geometry: when, in fact, it is a logical
vagary. Some of the houses which Jack built were destroyed by the fortune
of war in 1745, at Edinburgh: who will say the rebels did no good whatever?
I suspect that Jack copied the ideas of J.B. Morinus, "Quod Deus sit,"
Paris, 1636,[322] 4to, containing an attempt of the same kind, but not
stultified with diagrams.



TWO MODEL INDORSEMENTS.

    Dissertation, découverte, et démonstrations de la quadrature
    mathématique du cercle. Par M. de Fauré, géomètre. [_s. l._, probably
    Geneva] 1747, 8vo.

    Analyse de la Quadrature du Cercle. Par M. de Fauré, Gentilhomme
    Suisse. Hague, 1749,[323] 4to.

According to this octavo geometer and quarto gentleman, a diameter of 81
gives a circumference of 256. There is an amusing circumstance about the
quarto which has been overlooked, if indeed the book has ever been {150}
examined. John Bernoulli (the one of the day)[324] and Koenig[325] have
both given an attestation: my mathematical readers may stare as they
please, such is the fact. But, on examination, there will be reason to
think the two sly Swiss played their countryman the same trick as the
medical man played Miss Pickle, in the novel of that name. The lady only
wanted to get his authority against sousing her little nephew, and said,
"Pray, doctor, is it not both dangerous and cruel to be the means of
letting a poor tender infant perish by sousing it in water as cold as
ice?"--"Downright murder, I affirm," said the doctor; and certified
accordingly. De Fauré had built a tremendous scaffolding of equations,
quite out of place, and feeling cock-sure that his solutions, if correct,
would square the circle, applied to Bernoulli and Koenig--who after his
tract of two years before, must have known what he was at--for their
approbation of the solutions. And he got it, as follows, well guarded:

    "Suivant les suppositions posées dans ce Mémoire, il est si évident que
    t doit être = 34, y = 1, et z = 1, que cela n'a besoin ni de preuve ni
    d'autorité pour être reconnu par tout le monde.[326]

    "à Basle le 7e Mai 1749. JEAN BERNOULLI."

    "Je souscris au jugement de Mr. Bernoulli, en conséquence de ces
    suppositions.[327]

    "à la Haye le 21 Juin 1749. S. KOENIG."

On which de Fauré remarks with triumph--as I have no doubt it was intended
he should do--"il conste clairement par ma présente Analyse et
Démonstration, qu'ils y ont déja {151} reconnu et approuvé parfaitement que
la quadrature du cercle est mathématiquement démontrée."[328] It should
seem that it is easier to square the circle than to get round a
mathematician.



    An attempt to demonstrate that all the Phenomena in Nature may be
    explained by two simple active principles, Attraction and Repulsion,
    wherein the attraction of Cohesion, Gravity and Magnetism are shown to
    be one the same. By Gowin Knight. London, 1748, 4to.

Dr. Knight[329] was Mr. Panizzi's[330] archetype, the first Principal
Librarian of the British Museum. He was celebrated for his magnetical
experiments. This work was long neglected; but is now recognized as of
remarkable resemblance to modern speculations.



THOMAS WRIGHT OF DURHAM.

    An original theory or Hypothesis of the Universe. By Thomas Wright[331]
    of Durham. London, 4to, 1750.

Wright is a speculator whose thoughts are now part of our current
astronomy. He took that view--or most of it--of the milky way which
afterwards suggested itself to William Herschel. I have given an account of
him and his work in the _Philosophical Magazine_ for April, 1848.

Wright was mathematical instrument maker to the King, {152} and kept a shop
in Fleet Street. Is the celebrated business of Troughton & Simms, also in
Fleet Street, a lineal descendant of that of Wright? It is likely enough,
more likely that that--as I find him reported to have affirmed--Prester
John was the descendant of Solomon and the Queen of Sheba. Having settled
it thus, it struck me that I might apply to Mr. Simms, and he informs me
that it is as I thought, the line of descent being Wright, Cole, John
Troughton, Edward Troughton,[332] Troughton & Simms.[333]



BISHOP HORNE ON NEWTON.

    The theology and philosophy in Cicero's _Somnium Scipionis_ explained.
    Or, a brief attempt to demonstrate, that the Newtonian system is
    perfectly agreeable to the notions of the wisest ancients: and that
    mathematical principles are the only sure ones. [By Bishop Horne,[334]
    at the age of nineteen.] London, 1751, 8vo.

This tract, which was not printed in the collected works, and is now
excessively rare, is mentioned in _Notes and Queries_, 1st S., v, 490, 573;
2d S., ix, 15. The boyish satire on Newton is amusing. Speaking of old
Benjamin Martin,[335] he goes on as follows:

{153}

"But the most elegant account of the matter [attraction] is by that
hominiform animal, Mr. Benjamin Martin, who having attended Dr.
Desaguliers'[336] fine, raree, gallanty shew for some years [Desaguliers
was one of the first who gave public experimental lectures, before the
saucy boy was born] in the capacity of a turnspit, has, it seems, taken it
into his head to set up for a philosopher."

Thus is preserved the fact, unknown to his biographers, that Benj. Martin
was an assistant to Desaguliers in his lectures. Hutton[337] says of him,
that "he was well skilled in the whole circle of the mathematical and
philosophical sciences, and wrote useful books on every one of them": this
is quite true; and even at this day he is read by twenty where Horne is
read by one; see the stalls, _passim_. All that I say of him, indeed my
knowledge of the tract, is due to this contemptuous mention of a more
durable man than himself. My assistant secretary at the Astronomical
Society, the late Mr. Epps,[338] bought the copy at a stall because his eye
was caught by the notice of "Old Ben Martin," of whom he was a great
reader. Old Ben could not be a Fellow of the Royal Society, because he kept
a shop: even though the shop sold nothing but philosophical instruments.
Thomas Wright, similarly situated as to shop and goods, never was a Fellow.
The Society of our day has greatly degenerated: those of the old time would
be pleased, no doubt, that the glories of their day {154} should be
commemorated. In the early days of the Society, there was a similar
difficulty about Graunt, the author of the celebrated work on mortality.
But their royal patron, "who never said a foolish thing," sent them a sharp
message, and charged them if they found any more such tradesmen, they
should "elect them without more ado."

Horne's first pamphlet was published when he was but twenty-one years old.
Two years afterwards, being then a Fellow of his college, and having seen
more of the world, he seems to have felt that his manner was a little too
pert. He endeavored, it is said, to suppress his first tract: and copies
are certainly of extreme rarity. He published the following as his maturer
view:

    A fair, candid, and impartial state of the case between Sir Isaac
    Newton and Mr. Hutchinson.[339] In which is shown how far a system of
    physics is capable of mathematical demonstration; how far Sir Isaac's,
    as such a system, has that demonstration; and consequently, what regard
    Mr. Hutchinson's claim may deserve to have paid to it. By George Horne,
    M.A. Oxford, 1753, 8vo.

It must be remembered that the successors of Newton were very apt to
declare that Newton had demonstrated attraction as a _physical_ cause: he
had taken reasonable pains to show that he did not pretend to this. If any
one had said to Newton, I hold that every particle of matter is a
responsible being of vast intellect, ordered by the Creator to move as it
would do if every other particle attracted it, and gifted with power to
make its way in true accordance with that law, as easily as a lady picks
her way across the street; what have you to say against it?--Newton must
have replied, Sir! if you really undertake to maintain this as
_demonstrable_, your soul had better borrow a little power {155} from the
particles of which your body is made: if you merely ask me to refute it, I
tell you that I neither can nor need do it; for whether attraction comes in
this way or in any other, _it comes_, and that is all I have to do with it.

The reader should remember that the word attraction, as used by Newton and
the best of his followers, only meant a _drawing towards_, without any
implication as to the cause. Thus whether they said that matter attracts
matter, or that young lady attracts young gentleman, they were using one
word in one sense. Newton found that the law of the first is the inverse
square of the distance: I am not aware that the law of the second has been
discovered; if there be any chance, we shall see it at the year 1856 in
this list.

In this point young Horne made a hit. He justly censures those who fixed
upon Newton a more positive knowledge of what attraction is than he
pretended to have. "He has owned over and over he did not know what he
meant by it--it might be this, or it might be that, or it might be
anything, or it might be nothing." With the exception of the _nothing_
clause, this is true, though Newton might have answered Horne by "Thou hast
said it."

(I thought everybody knew the meaning of "Thou hast said it": but I was
mistaken. In three of the evangelists [Greek: Su legeis] is the answer to
"Art thou a king?" The force of this answer, as always understood, is "That
is your way of putting it." The Puritans, who lived in Bible phrases, so
understood it: and Walter Scott, who caught all peculiarities of language
with great effect, makes a marked instance, "Were you armed?--I was not--I
went in my calling, as a preacher of God's word, to encourage them that
drew the sword in His cause. In other words, to aid and abet the rebels,
said the Duke. _Thou hast spoken it_, replied the prisoner.")

Again, Horne quotes Rowning[340] as follows:

{156}

"Mr. Rowning, pt. 2, p. 5 in a note, has a very pretty conceit upon this
same subject of attraction, about every particle of a fluid being
intrenched in three spheres of attraction and repulsion, one within
another, 'the innermost of which (he says) is a sphere of repulsion, which
keeps them from approaching into contact; the next, a sphere of attraction,
diffused around this of repulsion, by which the particles are disposed to
run together into drops; and the outermost of all, a sphere of repulsion,
whereby they repel each other, when removed out of the attraction.' So that
between the _urgings_, and _solicitations_, of one and t'other, a poor
unhappy particle must ever be at his wit's end, not knowing which way to
turn, or whom to obey first."

Rowning has here started the notion which Boscovich[341] afterwards
developed.

I may add to what precedes that it cannot be settled that, as Granger[342]
says, Desaguliers was the first who gave experimental lectures in London.
William Whiston gave some, and Francis Hauksbee[343] made the experiments.
The prospectus, as we should now call it, is extant, a quarto tract of
plates and descriptions, without date. Whiston, in his life, {157} gives
1714 as the first date of publication, and therefore, no doubt, of the
lectures. Desaguliers removed to London soon after 1712, and commenced his
lectures soon after that. It will be rather a nice point to settle which
lectured first; probabilities seem to go in favor of Whiston.



FALLACIES IN A THEORY OF ANNUITIES.

    An Essay to ascertain the value of leases, and annuities for years and
    lives. By W[eyman] L[ee]. London, 1737, 8vo.

    A valuation of Annuities and Leases certain, for a single life. By
    Weyman Lee, Esq. of the Inner Temple. London, 1751, 8vo. Third edition,
    1773.

Every branch of exact science has its paradoxer. The world at large cannot
tell with certainty who is right in such questions as squaring the circle,
etc. Mr. Weyman Lee[344] was the assailant of what all who had studied
called demonstration in the question of annuities. He can be exposed to the
world: for his error arose out of his not being able to see that the whole
is the sum of all its parts.

By an annuity, say of £100, now bought, is meant that the buyer is to have
for his money £100 in a year, if he be then alive, £100 at the end of two
years, if then alive, and so on. It is clear that he would buy a life
annuity if he should buy the first £100 in one office, the second in
another, and so on. All the difference between buying the whole from one
office and buying all the separate contingent payments at different
offices, is immaterial to calculation. Mr. Lee would have agreed with the
rest of the world about the payments to be made to the several different
offices, in consideration of their several contracts: but he differed from
every one else about the sum to be paid to _one_ office. He contended that
the way to value an annuity is to find out the term of years which the
individual has an even chance of surviving, and to charge for the life
annuity the value of an annuity certain for that term.

{158}

It is very common to say that Lee took the average life, or expectation, as
it is wrongly called, for his term: and this I have done myself, taking the
common story. Having exposed the absurdity of this second supposition,
taking it for Lee's, in my _Formal Logic_,[345] I will now do the same with
the first.

A mathematical truth is true in its extreme cases. Lee's principle is that
an annuity on a life is the annuity made certain for the term within which
it is an even chance the life drops. If, then, of a thousand persons, 500
be sure to die within a year, and the other 500 be immortal, Lee's price of
an annuity to any one of these persons is the present value of one payment:
for one year is the term which each one has an even chance of surviving and
not surviving. But the true value is obviously half that of a perpetual
annuity: so that at 5 percent Lee's rule would give less than the tenth of
the true value. It must be said for the poor circle-squarers, that they
never err so much as this.

Lee would have said, if alive, that I have put an _extreme case_: but any
_universal_ truth is true in its extreme cases. It is not fair to bring
forward an extreme case against a person who is speaking as of usual
occurrences: but it is quite fair when, as frequently happens, the proposer
insists upon a perfectly general acceptance of his assertion. And yet many
who go the whole hog protest against being tickled with the tail. Counsel
in court are good instances: they are paradoxers by trade. June 13, 1849,
at Hertford, there was an action about a ship, insured against a _total_
loss: some planks were saved, and the underwriters refused to pay. Mr. Z.
(for deft.) "There can be no degrees of totality; and some timbers were
saved."--L. C. B. "Then if the vessel were burned to the water's edge, and
some rope saved in the boat, there would be no total loss."--Mr. Z. "This
is putting a very extreme case."--L. C. B. "The argument {159} would go
that length." What would _Judge_ Z.--as he now is--say to the extreme case
beginning somewhere between six planks and a bit of rope?



MONTUCLA'S WORK ON THE QUADRATURE.

    Histoire des recherches sur la quadrature du cercle ... avec une
    addition concernant les problèmes de la duplication du cube et de la
    trisection de l'angle. Paris, 1754, 12mo. [By Montucla.]

This is _the_ history of the subject.[346] It was a little episode to the
great history of mathematics by Montucla, of which the first edition
appeared in 1758. There was much addition at the end of the fourth volume
of the second edition; this is clearly by Montucla, though the bulk of the
volume is put together, with help from Montucla's papers, by Lalande.[347]
There is also a second edition of the history of the quadrature, Paris,
1831, 8vo, edited, I think, by Lacroix; of which it is the great fault that
it makes hardly any use of the additional matter just mentioned.

Montucla is an admirable historian when he is writing from his own direct
knowledge: it is a sad pity that he did not tell us when he was depending
on others. We are not to trust a quarter of his book, and we must read many
other books to know which quarter. The fault is common enough, but
Montucla's good three-quarters is so good that the fault is greater in him
than in most others: I mean the fault of not acknowledging; for an
historian cannot read everything. But it must be said that mankind give
little encouragement to candor on this point. Hallam, in his {160} _History
of Literature_, states with his own usual instinct of honesty every case in
which he depends upon others: Montucla does not. And what is the
consequence?--Montucla is trusted, and believed in, and cried up in the
bulk; while the smallest talker can lament that Hallam should be so unequal
and apt to depend on others, without remembering to mention that Hallam
himself gives the information. As to a universal history of any great
subject being written entirely upon primary knowledge, it is a thing of
which the possibility is not yet proved by an example. Delambre attempted
it with astronomy, and was removed by death before it was finished,[348] to
say nothing of the gaps he left.

Montucla was nothing of a bibliographer, and his descriptions of books in
the first edition were insufficient. The Abbé Rive[349] fell foul of him,
and as the phrase is, gave it him. Montucla took it with great good humor,
tried to mend, and, in his second edition, wished his critic had lived to
see the _vernis de bibliographe_ which he had given himself.

I have seen Montucla set down as an _esprit fort_, more than once: wrongly,
I think. When he mentions Barrow's[350] address to the Almighty, he adds,
"On voit, au reste, par là, que Barrow étoit un pauvre philosophe; car il
croyait en l'immortalité de l'âme, et en une Divinité autre que la nature
{161} universelle."[351] This is irony, not an expression of opinion. In
the book of mathematical recreations which Montucla constructed upon that
of Ozanam,[352] and Ozanam upon that of Van Etten,[353] now best known in
England by Hutton's similar treatment of Montucla, there is an amusing
chapter on the quadrators. Montucla refers to his own anonymous book of
1754 as a curious book published by Jombert.[354] He seems to have been a
little ashamed of writing about circle-squarers: what a slap on the face
for an unborn Budgeteer!

Montucla says, speaking of France, that he finds three notions prevalent
among the cyclometers: (1) that there is a large reward offered for
success; (2) that the longitude problem depends on that success; (3) that
the solution is the great end and object of geometry. The same three {162}
notions are equally prevalent among the same class in England. No reward
has ever been offered by the government of either country. The longitude
problem in no way depends upon perfect solution; existing approximations
are sufficient to a point of accuracy far beyond what can be wanted.[355]
And geometry, content with what exists, has long passed on to other
matters. Sometimes a cyclometer persuades a skipper who has made land in
the wrong place that the astronomers are in fault, for using a wrong
measure of the circle; and the skipper thinks it a very comfortable
solution! And this is the utmost that the problem ever has to do with
longitude.



ANTINEWTONIANISMUS.

    Antinewtonianismus.[356] By Cælestino Cominale,[357] M.D. Naples, 1754
    and 1756, 2 vols. 4to.

The first volume upsets the theory of light; the second vacuum, vis
inertiæ, gravitation, and attraction. I confess I never attempted these big
Latin volumes, numbering 450 closely-printed quarto pages. The man who
slays Newton in a pamphlet is the man for me. But I will lend them to
anybody who will give security, himself in £500, and two sureties in £250
each, that he will read them through, and give a full abstract; and I will
not exact security for their return. I have never seen any mention of this
book: it has a printer, but not a publisher, as happens with so many
unrecorded books.

{163}



OFFICIAL BLOW TO CIRCLE SQUARERS.

1755. The French Academy of Sciences came to the determination not to
examine any more quadratures or kindred problems. This was the consequence,
no doubt, of the publication of Montucla's book: the time was well chosen;
for that book was a full justification of the resolution. The Royal Society
followed the same course, I believe, a few years afterwards. When our Board
of Longitude was in existence, most of its time was consumed in listening
to schemes, many of which included the quadrature of the circle. It is
certain that many quadrators have imagined the longitude problem to be
connected with theirs: and no doubt the notion of a reward offered by
Government for a true quadrature is a result of the reward offered for the
longitude. Let it also be noted that this longitude reward was not a
premium upon excogitation of a mysterious difficulty. The legislature was
made to know that the rational hopes of the problem were centered in the
improvement of the lunar tables and the improvement of chronometers. To
these objects alone, and by name, the offer was directed: several persons
gained rewards for both; and the offer was finally repealed.



AN INTERESTING HOAX.

    Fundamentalis Figura Geometrica, primas tantum lineas circuli
    quadraturæ possibilitatis ostendens. By Niels Erichsen (Nicolaus
    Ericius), shipbuilder, of Copenhagen. Copenhagen, 1755, 12mo.

This was a gift from my oldest friend who was not a relative, Dr. Samuel
Maitland of the "Dark Ages."[358] He found it among his books, and could
not imagine how he came by it: I could have told him. He once collected
interpretations of the Apocalypse: and auction lots of such {164} books
often contain quadratures. The wonder is he never found more than one.

The quadrature is not worth notice. Erichsen is the only squarer I have met
with who has distinctly asserted the particulars of that reward which has
been so frequently thought to have been offered in England. He says that in
1747 the Royal Society on the 2d of June, offered to give a large reward
for the quadrature of the circle and a true explanation of magnetism, in
addition to £30,000 previously promised for the same. I need hardly say
that the Royal Society had not £30,000 at that time, and would not, if it
had had such a sum, have spent it on the circle, nor on magnetic theory;
nor would it have coupled the two things. On this book, see _Notes and
Queries_, 1st S., xii, 306. Perhaps Erichsen meant that the £30,000 had
been promised by the Government, and the addition by the Royal Society.

October 8, 1866. I receive a letter from a cyclometer who understands that
a reward is offered to any one who will square the circle, and that all
competitors are to send their plans to me. The hoaxers have not yet failed
out of the land.



TWO JESUIT CONTRIBUTIONS.

    Theoria Philosophiæ Naturalis redacta ad unicam legem virium in natura
    existentium. Editio _Veneta_ prima. By Roger Joseph Boscovich. Venice,
    1763, 4to.

The first edition is said to be of Vienna, 1758.[359] This is a celebrated
work on the molecular theory of matter, grounded on the hypothesis of
spheres of alternate attraction and repulsion. Boscovich was a Jesuit of
varied pursuit. During his measurement of a degree of the meridian, while
on horseback or waiting for his observations, he composed a Latin poem of
about five thousand verses on eclipses, {165} with notes, which he
dedicated to the Royal Society: _De Solis et Lunæ defectibus_,[360] London,
Millar and Dodsley, 1760, 4to.



    Traité de paix entre Des Cartes et Newton, _précédé_ des vies
    littéraires de ces deux chefs de la physique moderne.... By Aimé Henri
    Paulian.[361] Avignon, 1763, 12mo.

I have had these books for many years without feeling the least desire to
see how a lettered Jesuit would atone Descartes and Newton. On looking at
my two volumes, I find that one contains nothing but the literary life of
Descartes; the other nothing but the literary life of Newton. The preface
indicates more: and Watt mentions _three_ volumes.[362] I dare say the
first two contain all that is valuable. On looking more attentively at the
two volumes, I find them both readable and instructive; the account of
Newton is far above that of Voltaire, but not so popular. But he should not
have said that Newton's family came from Newton in Ireland. Sir Rowland
Hill gives fourteen _Newtons_ in Ireland;[363] twice the number of the
cities that contended for the birth of Homer may now contend for the origin
of Newton, on the word of Father Paulian.



    Philosophical Essays, in three parts. By R. Lovett, Lay Clerk of the
    Cathedral Church of Worcester. Worcester, 1766, 8vo.

    The Electrical Philosopher: containing a new system of physics {166}
    founded upon the principle of an universal Plenum of elementary
    fire.... By R. Lovett, Worcester, 1774, 8vo.

Mr. Lovett[364] was one of those ether philosophers who bring in elastic
fluid as an explanation by imposition of words, without deducing any one
phenomenon from what we know of it. And yet he says that attraction has
received no support from geometry; though geometry, applied to a particular
law of attraction, had shown how to predict the motions of the bodies of
the solar system. He, and many of his stamp, have not the least idea of the
confirmation of a theory by accordance of deduced results with observation
posterior to the theory.



BAILLY'S EXAGGERATED VIEW OF ASTRONOMY.

    Lettres sur l'Atlantide de Platon, et sur l'ancien Histoire de l'Asie,
    pour servir de suite aux lettres sur l'origine des Sciences, adressées
    à M. de Voltaire, par M. Bailly.[365] London and Paris, 1779, 8vo.

I might enter here all Bailly's histories of astronomy.[366] The paradox
which runs through them all more or less, is the doctrine that astronomy is
of immense antiquity, coming from some forgotten source, probably the
drowned island of Plato, peopled by a race whom Bailly makes, as has {167}
been said, to teach us everything except their existence and their name.
These books, the first scientific histories which belong to readable
literature, made a great impression by power of style: Delambre created a
strong reaction, of injurious amount, in favor of history founded on
contemporary documents, which early astronomy cannot furnish. These letters
are addressed to Voltaire, and continue the discussion. There is one letter
of Voltaire, being the fourth, dated Feb. 27, 1777, and signed "le vieux
malade de Ferney, V. puer centum annorum."[367] Then begin Bailly's
letters, from January 16 to May 12, 1778. From some ambiguous expressions
in the Preface, it would seem that these are fictitious letters, supposed
to be addressed to Voltaire at their dates. Voltaire went to Paris February
10, 1778, and died there May 30. Nearly all this interval was his closing
scene, and it is very unlikely that Bailly would have troubled him with
these letters.[368]



    An inquiry into the cause of motion, or a general theory of physics. By
    S. Miller. London, 1781, 4to

Newton all wrong: matter consists of two kinds of particles, one inert, the
other elastic and capable of expanding themselves _ad infinitum_.



SAINT-MARTIN ON ERRORS AND TRUTH.

    Des Erreurs et de la Vérité, ou les hommes rappelés au principe
    universel de la science; ouvrage dans lequel, en faisant remarquer aux
    observateurs l'incertitude de leurs recherches, et leurs méprises
    continuelles, on leur indique la route qu'ils auroient dû suivre, pour
    acquérir l'évidence physique sur l'origine du bien et du mal, sur
    l'homme, sur la nature matérielle, et la nature sacrée; sur la base des
    gouvernements {168} politiques, sur l'autorité des souverains, sur la
    justice civile et criminelle, sur les sciences, les langues, et les
    arts. Par un Ph.... Inc.... A Edimbourg. 1782.[369] Two vols. 8vo.

This is the famous work of Louis Claude de Saint-Martin[370] (1743-1803),
for whose other works, vagaries included, the reader must look elsewhere:
among other things, he was a translator of Jacob Behmen.[371] The title
promises much, and the writer has smart thoughts now and then; but the
whole is the wearisome omniscience of the author's day and country, which
no reader of our time can tolerate. Not that we dislike omniscience; but we
have it of our own country, both home-made and imported; and fashions vary.
But surely there can be but one omniscience? Must a man have but one wife?
Nay, may not a man have a new wife while the old one is living? There was a
famous instrumental professor forty years ago, who presented a friend to
Madame ----. The friend started, and looked surprised; for, not many weeks
before, he had been presented to another lady, with the same title, at
Paris. The musician observed his surprise, and quietly said, "Celle-ci est
Madame ---- de Londres." In like manner we have a London omniscience now
current, which would make any one start who only knew the old French
article.

The book was printed at Lyons, but it was a trick of French authors to
pretend to be afraid of prosecution: it {169} made a book look wicked-like
to have a feigned place of printing, and stimulated readers. A Government
which had undergone Voltaire would never have drawn its sword upon quiet
Saint-Martin. To make himself look still worse, he was only ph[ilosophe]
Inc...., which is generally read _Inconnu_[372] but sometimes _Incrédule_;
[373] most likely the ambiguity was intended. There is an awful paradox
about the book, which explains, in part, its leaden sameness. It is all
about _l'homme_, _l'homme_, _l'homme_,[374] except as much as treats of
_les hommes_, _les hommes_, _les hommes_;[375] but not one single man is
mentioned by name in its 500 pages. It reminds one of

 "Water, water everywhere,
  And not a drop to drink."

Not one opinion of any other man is referred to, in the way of agreement or
of opposition. Not even a town is mentioned: there is nothing which brings
a capital letter into the middle of a sentence, except, by the rarest
accident, such a personification as _Justice_. A likely book to want an
_Edimbourg_ godfather!

Saint-Martin is great in mathematics. The number _four_ essentially belongs
to straight lines, and _nine_ to curves. The object of a straight line is
to perpetuate _ad infinitum_ the production of a point from which it
emanates. A circle [circle] bounds the production of all its radii, tends
to destroy them, and is in some sort their enemy. How is it possible that
things so distinct should not be distinguished in their _number_ as well as
in their action? If this important observation had been made earlier,
immense trouble would have been saved to the mathematicians, who would have
been prevented from searching for a common measure to lines which have
nothing in common. But, though all straight lines have the number _four_,
it must not be supposed that they are all equal, for a line is the result
of its law and {170} its number; but though both are the same for all lines
of a sort, they act differently, as to force, energy, and duration, in
different individuals; which explains all differences of length, etc. I
congratulate the reader who understands this; and I do not pity the one who
does not.

Saint-Martin and his works are now as completely forgotten as if they had
never been born, except so far as this, that some one may take up one of
the works as of heretical character, and lay it down in disappointment,
with the reflection that it is as dull as orthodoxy. For a person who was
once in some vogue, it would be difficult to pick out a more fossil writer,
from Aa to Zypoeus, except,--though it is unusual for (,--) to represent an
interval of more than a year--his unknown opponent. This opponent, in the
very year of the _Des Erreurs_ ... published a book in two parts with the
same fictitious place of printing;

    Tableau Naturel des Rapports qui existent entre Dieu, l'Homme, et
    l'Univers. A Edimbourg, 1782, 8vo.[376]

There is a motto from the _Des Erreurs_ itself, "Expliquer les choses par
l'homme, et non l'homme par les choses. _Des Erreurs et de la Vérité_, par
un PH.... INC...., p. 9."[377] This work is set down in various catalogues
and biographies as written by the PH.... INC.... himself. But it is not
usual for a writer to publish two works in the same year, one of which
takes a motto from the other. And the second work is profuse in capitals
and italics, and uses Hebrew learning: its style differs much from the
first work. The first work sets out from man, and has nothing to do with
God: the second is religious and raps the knuckles of the first as follows:
"Si nous voulons nous préserver de toutes {171} les illusions, et surtout
des amorces de l'orgueil par lesquelles l'homme est si souvent séduit, ne
prenons jamais les hommes, mais toujours _Dieu_ pour notre terme de
comparaison."[378] The first uses _four_ and _nine_ in various ways, of
which I have quoted one: the second says, "Et ici se trouve déjà une
explication des nombres _quatre_ et _neuf_, qui ont peu embarrassé dans
l'ouvrage déjà cité. L'homme s'est égaré en allant de _quatre_ à
_neuf_...."[379] The work cited is the _Erreurs_, etc., and the citation is
in the motto, which is the text of the opposition sermon.



A FORERUNNER OF THE METRIC SYSTEM.

    Method to discover the difference of the earth's diameters; proving its
    true ratio to be not less variable than as 45 is to 46, and shortest in
    its pole's axis 174 miles.... likewise a method for fixing an universal
    standard for weights and measures. By Thomas Williams.[380] London,
    1788, 8vo.

Mr. Williams was a paradoxer in his day, and proposed what was, no doubt,
laughed at by some. He proposed the sort of plan which the
French--independently of course--carried into effect a few years after. He
would have the 52d degree of latitude divided into 100,000 parts and each
part a geographical yard. The geographical ton was to be the cube of a
geographical yard filled with sea-water taken some leagues from land. All
multiples and sub-divisions were to be decimal.

I was beginning to look up those who had made similar proposals, when a
learned article on the proposal of a {172} metrical system came under my
eye in the _Times_ of Sept. 15, 1863. The author cites Mouton,[381] who
would have the minute of a degree divided into 10,000 _virgulæ_; James
Cassini,[382] whose foot was to be six thousandths of a minute; and
Paucton,[383] whose foot was the 400,000th of a degree. I have verified the
first and third statements; surely the second ought to be the
_six-thousandth_.



    An inquiry into the Copernican system ... wherein it is proved, in the
    clearest manner, that the earth has only her diurnal motion ... with an
    attempt to point out the only true way whereby mankind can receive any
    real benefit from the study of the heavenly bodies. By John
    Cunningham.[384] London, 1789, 8vo.

The "true way" appears to be the treatment of heaven and earth as
emblematical of the Trinity.



    Cosmology. An inquiry into the cause of what is called gravitation or
    attraction, in which the motions of the heavenly bodies, and the
    preservation and operations of all nature, are deduced from an
    universal principle of efflux and reflux. By T. Vivian,[385] vicar of
    Cornwood, Devon. Bath, 1792, 12mo.

{173}

Attraction, an influx of matter to the sun; centrifugal force, the solar
rays; cohesion, the pressure of the atmosphere. The confusion about
centrifugal _force_, so called, as demanding an external agent, is very
common.



THOMAS PAINE'S RIGHTS OF MAN.

    The rights of MAN, being an answer to Mr. Burke's attack on the French
    Revolution.[386] By Thomas Paine.[387] In two parts. 1791-1792. 8vo.
    (Various editions.)[388]

    A vindication of the rights of WOMAN, with strictures on political and
    moral subjects. By Mary Wollstonecraft.[389] 1792. 8vo.

    A sketch of the rights of BOYS and GIRLS. By Launcelot Light, of
    Westminster School; and Lætitia Lookabout, of Queen's Square,
    Bloomsbury. [By the Rev. Samuel Parr,[390] LL.D.] 1792. 8vo. (pp.64).

When did we three meet before? The first work has sunk into oblivion: had
it merited its title, it might have {174} lived. It is what the French call
a _pièce de circonstance_; it belongs in time to the French Revolution, and
in matter to Burke's opinion of that movement. Those who only know its name
think it was really an attempt to write a philosophical treatise on what we
now call socialism. Silly government prosecutions gave it what it never
could have got for itself.

Mary Wollstonecraft seldom has her name spelled right. I suppose the O! O!
character she got made her W_oo_lstonecraft. Watt gives double insinuation,
for his cross-reference sends us to G_oo_dwin.[391] No doubt the title of
the book was an act of discipleship to Paine's _Rights of Man_; but this
title is very badly chosen. The book was marred by it, especially when the
authoress and her husband assumed the right of dispensing with legal
sanction until the approach of offspring brought them to a sense of their
child's interest.[392] Not a hint of such a claim is found in the book,
which is mostly about female education. The right claimed for woman is to
have the education of a rational human being, and not to be considered as
nothing but woman throughout youthful training. The maxims of Mary
Wollstonecraft are now, though not derived from her, largely followed in
the education of girls, especially in home education: just as many of the
political principles of Tom Paine, again not derived from him, are the
guides of our actual legislation. I remember, forty years ago, an old lady
used to declare that she disliked girls from the age of sixteen to
five-and-twenty. "They are full," said she, "of _femalities_." She spoke of
their behavior to women as well as to men. She {175} would have been
shocked to know that she was a follower of Mary Wollstonecraft, and had
packed half her book into one sentence.

The third work is a satirical attack on Mary Wollstonecraft and Tom Paine.
The details of the attack would convince any one that neither has anything
which would now excite reprobation. It is utterly unworthy of Dr. Parr, and
has quite disappeared from lists of his works, if it were ever there. That
it was written by him I take to be evident, as follows. Nichols,[393] who
could not fail to know, says (_Anecd._, vol. ix, p. 120): "This is a
playful essay by a first-rate scholar, who is elsewhere noticed in this
volume, but whose name I shall not bring forward on so trifling an
occasion." Who the scholar was is made obvious by Master Launcelot being
made to talk of Bellendenus.[394] Further, the same boy is made to say,
"Let Dr. Parr lay his hand upon his heart, if his conscience will let him,
and ask himself how many thousands of wagon-loads of this article [birch]
he has cruelly misapplied." How could this apply to Parr, with his handful
of private pupils,[395] and no reputation for severity? Any one except
himself would have called on the head-master of Westminster or Eton. I
doubt whether the name of Parr could be connected with the rod by anything
in print, except the above and an anecdote of his pupil, Tom Sheridan.[396]
The Doctor had dressed for a dinner visit, and {176} was ready a quarter of
an hour too soon to set off. "Tom," said he, "I think I had better whip you
now; you are sure to do something while I am out."--"I wish you would,
sir!" said the boy; "it would be a letter of licence for the whole
evening." The Doctor saw the force of the retort: my two tutelaries will
see it by this time. They paid in advance; and I have given liberal
interpretation to the order.

The following story of Dr. Parr was told me and others, about 1829, by the
late Leonard Horner,[397] who knew him intimately. Parr was staying in a
house full of company, I think in the north of England. Some gentlemen from
America were among the guests, and after dinner they disputed some of
Parr's assertions or arguments. So the Doctor broke out with "Do you know
what country you come from? You come from the place to which we used to
send our thieves!" This made the host angry, and he gave Parr such a severe
rebuke as sent him from the room in ill-humor. The rest walked on the lawn,
amusing the Americans with sketches of the Doctor. There was a dark cloud
overhead, and from that cloud presently came a voice which called _Tham_
(Parr-lisp for _Sam_). The company were astonished for a moment, but
thought the Doctor was calling his servant in the house, and that the
apparent direction was an illusion arising out of inattention. But
presently the sound was repeated, certainly from the cloud,

    "And nearer, clearer, deadlier than before."

There was now a little alarm: where could the Doctor have got to? They ran
to his bedroom, and there they discovered a sufficient rather than
satisfactory explanation. The Doctor had taken his pipe into his bedroom,
and had seated himself, in sulky mood, upon the higher bar of a large and
deep old-fashioned grate with a high mantelshelf. Here he had {177} tumbled
backwards, and doubled himself up between the bars and the back of the
grate. He was fixed tight, and when he called for help, he could only throw
his voice up the chimney. The echo from the cloud was the warning which
brought his friends to the rescue.



ATTACKS ON RELIGIOUS CUSTOMS.

Days of political paradox were coming, at which we now stare. Cobbett[398]
said, about 1830, in earnest, that in the country every man who did not
take off his hat to the clergyman was suspected, and ran a fair chance of
having something brought against him. I heard this assertion canvassed,
when it was made, in a party of elderly persons. The Radicals backed it,
the old Tories rather denied it, but in a way which satisfied me they ought
to have denied it less if they could not deny it more. But it must be said
that the Governments stopped far short of what their partisans would have
had them do. All who know Robert Robinson's[399] very quiet assault on
church-made festivals in his _History and Mystery of Good Friday_
(1777)[400] will hear or remember with surprise that the _British Critic_
pronounced it a direct, unprovoked, and malicious libel on the most {178}
sacred institutions of the national Church. It was reprinted again and
again: in 1811 it was in a cheap form at 6s. 6d. a hundred. When the
Jacobin day came, the State was really in a fright: people thought twice
before they published what would now be quite disregarded. I examined a
quantity of letters addressed to George Dyer[401] (Charles Lamb's G.D.) and
what between the autographs of Thelwall, Hardy, Horne Tooke, and all the
rebels,[402] put together a packet which produced five guineas, or
thereabouts, for the widow. Among them were the following verses, sent by
the author--who would not put his name, even in a private letter, for fear
of accidents--for consultation whether they could safely be sent to an
editor: and they were _not_ sent. The occasion was the public thanksgiving
at St. Paul's for the naval victories, December 19, 1797.

 "God bless me! what a thing!
  Have you heard that the King
    Goes to St. Paul's?
  {179}
  Good Lord! and when he's there,
  He'll roll his eyes in prayer,
  To make poor Johnny stare
    At this fine thing.

 "No doubt the plan is wise
  To blind poor Johnny's eyes
    By this grand show;
  For should he once suppose
  That he's led by the nose,
  Down the whole fabric goes,
    Church, lords, and king.

 "As he shouts Duncan's[403] praise,
  Mind how supplies they'll raise
    In wondrous haste.
  For while upon the sea
  We gain one victory,
  John still a dupe will be
    And taxes pay.

 "Till from his little store
  Three-fourths or even more
    Goes to the Crown.
  Ah, John! you little think
  How fast we downward sink
  And touch the fatal brink
    At which we're slaves."

I would have indicted the author for not making his thirds and sevenths
rhyme. As to the rhythm, it is not much better than what the French sang in
the Calais theater when the Duke of Clarence[404] took over Louis XVIII in
1814.

 "God save noble Clarence,
  Who brings our king to France;
    God save Clarence!
  He maintains the glory
  Of the British navy,
    etc., etc."

{180} Perhaps had this been published, the Government would have assailed
it as a libel on the church service. They got into the way of defending
themselves by making libels on the Church, of what were libels, if on
anything, on the rulers of the State; until the celebrated trials of Hone
settled the point for ever, and established that juries will not convict
for one offence, even though it have been committed, when they know the
prosecution is directed at another offence and another intent.



HONE'S FAMOUS TRIALS.

The results of Hone's trials (William Hone, 1779-1842) are among the
important constitutional victories of our century. He published parodies on
the Creeds, the Lord's Prayer, the Catechism, etc., with intent to bring
the Ministry into contempt: everybody knew that was his _purpose_. The
Government indicted him for impious, profane, blasphemous intent, but not
for seditious intent. They hoped to wear him out by proceeding day by day.
December 18, 1817, they hid themselves under the Lord's Prayer, the Creed,
and the Commandments; December 19, under the Litany; December 20, under the
Athanasian Creed, an odd place for shelter when they could not find it in
the previous places. Hone defended himself for six, seven, and eight hours
on the several days: and the jury acquitted him in 15, 105, and 20 minutes.
In the second trial the offense was laid both as profanity and as sedition,
which seems to have made the jury hesitate. And they probably came to think
that the second count was false pretence: but the length of their
deliberation is a satisfactory addition to the value of the whole. In the
first trial the Attorney-General (Shepherd) had the impudence to say that
the libel had nothing of a political tendency about it, but was _avowedly_
set off against the religion and worship of the Church of England. The
whole {181} is political in every sentence; neither more nor less political
than the following, which is part of the parody on the Catechism: "What is
thy duty towards the Minister? My duty towards the Minister is, to trust
him as much as I can; to honor him with all my words, with all my bows,
with all my scrapes, and with all my cringes; to flatter him; to give him
thanks; to give up my whole soul to him; to idolize his name, and obey his
word, and serve him blindly all the days of his political life." And the
parody on the Creed begins, "I believe in George, the Regent almighty,
maker of new streets and Knights of the Bath." This is what the
Attorney-General said had nothing of a political tendency about it. But
this was _on the first trial_: Hone was not known. The first day's trial
was under Justice Abbott (afterwards C. J. Tenterden).[405] It was
perfectly understood, when Chief Justice Ellenborough[406] appeared in
Court on the second day, that he was very angry at the first result, and
put his junior aside to try his own rougher dealing. But Hone tamed the
lion. An eye-witness told me that when he implored of Hone not to detail
his own father Bishop Law's[407] views on the Athanasian Creed, which
humble petition Hone kindly granted, he held by the desk for support. And
the same when--which is not reported--the Attorney-General appealed to the
Court for protection against a {182} stinging attack which Hone made on the
Bar: he _held on_, and said, "Mr. Attorney, what _can_ I do!" I was a boy
of twelve years old, but so strong was the feeling of exultation at the
verdicts that boys at school were not prohibited from seeing the parodies,
which would have been held at any other time quite unfit to meet their
eyes. I was not able to comprehend all about the Lord Chief Justice until I
read and heard again in after years. In the meantime, Joe Miller had given
me the story of the leopard which was sent home on board a ship of war, and
was in two days made as docile as a cat by the sailors.[408] "You have got
that fellow well under," said an officer. "Lord bless your Honor!" said
Jack, "if the Emperor of Marocky would send us a cock rhinoceros, we'd
bring him to his bearings in no time!" When I came to the subject again, it
pleased me to entertain the question whether, if the Emperor had sent a
cock rhinoceros to preside on the third day in the King's Bench, Hone would
have mastered _him_: I forget how I settled it. There grew up a story that
Hone caused Lord Ellenborough's death, but this could not have been true.
Lord Ellenborough resigned his seat in a few months, and died just a year
after the trials; but sixty-eight years may have had more to do with it
than his defeat.

A large subscription was raised for Hone, headed by the Duke of
Bedford[409] for £105. Many of the leading anti-ministerialists joined: but
there were many of the other side who avowed their disapprobation of the
false pretense. Many could not venture their names. In the list I find:
{183} A member of the House of Lords, an enemy to persecution, and
especially to religious persecution employed for political purposes--No
parodist, but an enemy to persecution--A juryman on the third day's
trial--Ellen Borough--My name would ruin me--Oh! minions of Pitt--Oil for
the Hone--The Ghosts of Jeffries[410] and Sir William Roy [Ghosts of
Jeffries in abundance]--A conscientious Jury and a conscientious Attorney,
£1 6s. 8d.--To Mr. Hone, for defending in his own person the freedom of the
press, attacked for a political object, under the old pretense of
supporting Religion--A cut at corruption--An Earldom for myself and a
translation for my brother--One who disapproves of parodies, but abhors
persecution--From a schoolboy who wishes Mr. Hone to have a very grand
subscription--"For delicacy's sake forbear," and "Felix trembled"--"I will
go myself to-morrow"--Judge Jeffries' works rebound in calf by Law--Keep us
from Law, and from the Shepherd's paw--I must not give you my name, but God
bless you!--As much like Judge Jeffries as the present times will
permit--May Jeffries' fame and Jeffries' fate on every modern Jeffries
wait--No parodist, but an admirer of the man who has proved the fallacy of
the Lawyer's Law, that when a man is his own advocate he has a fool for his
client--A Mussulman who thinks it would not be an impious libel to parody
the Koran--May the suspenders of the Habeas Corpus Act be speedily
suspended--Three times twelve for thrice-tried Hone, who cleared the cases
himself alone, and won three heats by twelve to one, £1 16s.--A
conscientious attorney, £1 6s. 8d.--Rev. T. B. Morris, rector of
Shelfanger, who disapproves of the parodies, but abhors the making an
affected zeal for religion the pretext for political persecution--A Lawyer
opposed in principle to {184} Law--For the Hone that set the razor that
shaved the rats--Rev. Dr. Samuel Parr, who most seriously disapproves of
all parodies upon the hallowed language of Scripture and the contents of
the Prayer-book, but acquits Mr. Hone of intentional impiety, admires his
talents and fortitude, and applauds the good sense and integrity of his
juries--Religion without hypocrisy, and Law without impartiality--O Law! O
Law! O Law!

These are specimens of a great many allusive mottoes. The subscription was
very large, and would have bought a handsome annuity, but Hone employed it
in the bookselling trade, and did not thrive. His _Everyday Book_[411] and
his _Apocryphal New Testament_,[412] are useful books. On an annuity he
would have thriven as an antiquarian writer and collector. It is well that
the attack upon the right to ridicule Ministers roused a dormant power
which was equal to the occasion. Hone declared, on his honor, that he had
never addressed a meeting in his life, nor spoken a word before more than
twelve persons. Had he--which however could not then be done--employed
counsel and had a _guilty defense_ made for him, he would very likely have
been convicted, and the work would have been left to be done by another. No
question that the parodies disgusted all who reverenced Christianity, and
who could not separate the serious and the ludicrous, and prevent their
existence in combination.

My extracts, etc., are from the nineteenth, seventeenth, and sixteenth
editions of the three trials, which seem to have been contemporaneous (all
in 1818) as they are made up into one book, with additional title over all,
and the motto "Thrice the brindled cat hath mew'd." They are published by
Hone himself, who I should have said was a publisher {185} as well as was
to be. And though the trials only ended Dec. 20, 1817, the preface attached
to this common title is dated Jan. 23, 1818.[413]

The spirit which was roused against the false dealing of the Government,
i.e., the pretense of prosecuting for impiety when all the world knew the
real offense was, if anything, sedition--was not got up at the moment:
there had been previous exhibitions of it. For example, in the spring of
1818 Mr. Russell, a little printer in Birmingham, was indicted for
publishing the Political Litany[414] on which Hone was afterwards tried. He
took his witnesses to the summer Warwick assizes, and was told that the
indictment had been removed by certiorari into the King's Bench. He had
notice of trial for the spring assizes at Warwick: he took his witnesses
there, and the trial was postponed by the Crown. He then had notice for the
summer assizes at Warwick; and so on. The policy seems to have been to wear
out the obnoxious parties, either by delays or by heaping on trials. The
Government was odious, and knew it could _not_ get verdicts against
ridicule, and _could_ get verdicts against impiety. No difficulty was found
in convicting the sellers of Paine's works, and the like. When Hone was
held to bail it was seen that a crisis was at hand. All parties in politics
furnished him with parodies in proof of religious persons having made
instruments of them. The parodies by Addison and Luther were contributed by
a Tory lawyer, who was afterwards a judge.

Hone had published, in 1817, tracts of purely political ridicule: _Official
Account of the Noble Lord's Bite,_[415] _Trial of the Dog for Biting the
Noble Lord_, etc. These were not touched. After the trials, it is manifest
that Hone was {186} to be unassailed, do what he might. _The Political
House that Jack built_, in 1819; _The Man in the Moon_, 1820; _The Queen's
Matrimonial Ladder_, _Non mi ricordo_, _The R--l Fowls_, 1820; _The
Political Showman at Home_, with plates by G. Cruickshank,[416] 1821 [he
did all the plates]; _The Spirit of Despotism_, 1821--would have been
legitimate marks for prosecution in previous years. The biting caricature
of several of these works are remembered to this day. _The Spirit of
Despotism_ was a tract of 1795, of which a few copies had been privately
circulated with great secrecy. Hone reprinted it, and prefixed the
following address to "Robert Stewart, _alias_ Lord Castlereagh"[417]: "It
appears to me that if, unhappily, your counsels are allowed much longer to
prevail in the Brunswick Cabinet, they will bring on a crisis, in which the
king may be dethroned or the people enslaved. Experience has shown that the
people will not be enslaved--the alternative is the affair of your
employers." Hone might say this without notice.

In 1819 Mr. Murray[418] published Lord Byron's _Don Juan_,[419] and Hone
followed it with _Don John, or Don Juan Unmasked_, a little account of what
the publisher to the Admiralty was allowed to issue without prosecution.
The parody on the Commandments was a case very much in point: and Hone
makes a stinging allusion to the use of the "_unutterable Name_, with a
profane levity unsurpassed by {187} any other two lines in the English
language." The lines are

 "'Tis strange--the Hebrew noun which means 'I am,'
  The English always use to govern d----n."

Hone ends with: "Lord Byron's dedication of 'Don Juan' to Lord Castlereagh
was suppressed by Mr. Murray from delicacy to Ministers. Q. Why did not Mr.
Murray suppress Lord Byron's _parody_ on the Ten Commandments? _A._ Because
it contains nothing in ridicule of Ministers, and therefore nothing that
_they_ could suppose would lead to the displeasure of Almighty God."

The little matters on which I have dwelt will never appear in history from
their political importance, except in a few words of result. As a mode of
thought, silly evasions of all kinds belong to such a work as the present.
Ignorance, which seats itself in the chair of knowledge, is a mother of
revolutions in politics, and of unread pamphlets in circle-squaring. From
1815 to 1830 the question of revolution or no revolution lurked in all our
English discussions. The high classes must govern; the high classes shall
not govern; and thereupon issue was to be joined. In 1828-33 the question
came to issue; and it was, Revolution with or without civil war; choose.
The choice was wisely made; and the Reform Bill started a new system so
well dovetailed into the old that the joinings are hardly visible. And now,
in 1867, the thing is repeated with a marked subsidence of symptoms; and
the party which has taken the place of the extinct Tories is carrying
through Parliament a wider extension of the franchise than their opponents
would have ventured. Napoleon used to say that a decided nose was a sign of
power: on which it has been remarked that he had good reason to say so
before the play was done. And so had our country; it was saved from a
religious war, and from a civil war, by the power of that nose over its
colleagues. {188}



THOMAS TAYLOR, THE PLATONIST.

    The Commentaries of Proclus.[420] Translated by Thomas Taylor.[421]
    London, 1792, 2 vols. 4to.[422]

The reputation of "the Platonist" begins to grow, and will continue to
grow. The most authentic account is in the _Penny Cyclopædia_, written by
one of the few persons who knew him well, and one of the fewer who possess
all his works. At page lvi of the Introduction is Taylor's notion of the
way to find the circumference. It is not geometrical, for it proceeds on
the motion of a point: the words "on account of the simplicity of the
impulsive motion, such a line must be either straight or circular" will
suffice to show how Platonic it is. Taylor certainly professed a kind of
heathenism. D'lsraeli said, "Mr. T. Taylor, the Platonic philosopher and
the modern Plethon,[423] consonant to that philosophy, professes
polytheism." Taylor printed this in large type, in a page by itself after
the dedication, without any disavowal. I have seen the following, Greek and
translation both, in his handwriting: "[Greek: Pas agathos hêi agathos
ethnikos; kai pas christianos hêi christianos kakos.] Every good man, so
far as he is a good man, is a heathen; and every Christian, so far as he is
a Christian, is a bad man." Whether Taylor had in his head the Christian of
the New Testament, or whether he drew from those members of the "religious
world" who make manifest the religious flesh and the religious devil, {189}
cannot be decided by us, and perhaps was not known to himself. If a
heathen, he was a virtuous one.



A NEW ERA IN FICTION.

(1795.) This is the date of a very remarkable paradox. The religious
world--to use a name claimed by a doctrinal sect--had long set its face
against amusing literature, and all works of imagination. Bunyan, Milton,
and a few others were irresistible; but a long face was pulled at every
attempt to produce something readable for poor people and _poor children_.
In 1795, a benevolent association began to circulate the works of a lady
who had been herself a dramatist, and had nourished a pleasant vein of
satire in the society of Garrick and his friends; all which is carefully
suppressed in some biographies. Hannah More's[424] _Cheap Repository
Tracts_,[425] which were bought by millions of copies, destroyed the
vicious publications with which the hawkers deluged the country, by the
simple process of furnishing the hawkers with something more saleable.

_Dramatic fiction_, in which the _characters_ are drawn by themselves, was,
at the middle of the last century, the monopoly of writers who required
indecorum, such as Fielding and Smollett. All, or nearly all, which could
be permitted to the young, was dry narrative, written by people who could
not make their personages _talk character_; they all spoke {190} alike. The
author of the _Rambler_[426] is ridiculed, because his young ladies talk
Johnsonese; but the satirists forget that all the presentable novel-writers
were equally incompetent; even the author of _Zeluco_ (1789)[427] is the
strongest possible case in point.

Dr. Moore,[428] the father of the hero of Corunna,[429] with good narrative
power, some sly humor, and much observation of character, would have been,
in our day, a writer of the _Peacock_[430] family. Nevertheless, to one who
is accustomed to our style of things, it is comic to read the dialogue of a
jealous husband, a suspected wife, a faithless maid-servant, a tool of a
nurse, a wrong-headed pomposity of a priest, and a sensible physician, all
talking Dr. Moore through their masks. Certainly an Irish soldier does say
"by Jasus," and a cockney footman "this here" and "that there"; and this
and the like is all the painting of characters which is effected out of the
mouths of the bearers by a narrator of great power. I suspect that some
novelists repressed their power under a rule that a narrative should
narrate, and that the dramatic should be confined to the drama.

I make no exception in favor of Miss Burney;[431] though she was the
forerunner of a new era. Suppose a country {191} in which dress is always
of one color; suppose an importer who brings in cargoes of blue stuff, red
stuff, green stuff, etc., and exhibits dresses of these several colors,
that person is the similitude of Miss Burney. It would be a delightful
change from a universal dull brown, to see one person all red, another all
blue, etc.; but the real inventor of pleasant dress would be the one who
could mix his colors and keep down the bright and gaudy. Miss Burney's
introduction was so charming, by contrast, that she nailed such men as
Johnson, Burke, Garrick, etc., to her books. But when a person who has read
them with keen pleasure in boyhood, as I did, comes back to them after a
long period, during which he has made acquaintance with the great novelists
of our century, three-quarters of the pleasure is replaced by wonder that
he had not seen he was at a puppet-show, not at a drama. Take some
_labeled_ characters out of our humorists, let them be put together into
one piece, to speak only as labeled: let there be a Dominie with nothing
but "Prodigious!" a Dick Swiveller with nothing but adapted quotations; a
Dr. Folliott with nothing but sneers at Lord Brougham;[432] and the whole
will pack up into one of Miss Burney's novels.

Maria Edgeworth,[433] Sydney Owenson (Lady Morgan),[434] Jane Austen,[435]
Walter Scott,[436] etc., are all of our century; as {192} are, I believe,
all the Minerva Press novels, as they were called, which show some of the
power in question. Perhaps dramatic talent found its best encouragement in
the drama itself. But I cannot ascertain that any such power was directed
at the multitude, whether educated or uneducated, with natural mixture of
character, under the restraints of decorum, until the use of it by two
religious writers of the school called "evangelical," Hannah More and
Rowland Hill.[437] The _Village Dialogues_, though not equal to the
_Repository Tracts_, are in many parts an approach, and perhaps a copy;
there is frequently humorous satire, in that most effective form,
self-display. They were published in 1800, and, partly at least, by the
Religious Tract Society, the lineal successor of the _Repository_
association, though knowing nothing about its predecessor. I think it right
to add that Rowland Hill here mentioned is not the regenerator of the Post
Office.[438] Some do not distinguish accurately; I have heard of more than
one who took me to have had a logical controversy with a diplomatist who
died some years before I was born.



THE RELIGIOUS TRACT SOCIETY.

A few years ago, an attempt was made by myself and others to collect some
information about the _Cheap Repository_ (see _Notes and Queries_, 3d
Series, vi. 241, 290, 353; _Christian Observer_, Dec. 1864, pp. 944-49). It
appeared that after the Religious Tract Society had existed more than fifty
years, a friend presented it with a copy of the original prospectus of the
_Repository_, a thing the existence of which was not known. In this
prospectus it is announced that from the plan "will be carefully excluded
whatever is enthusiastic, absurd, or superstitious." The "evangelical"
{193} party had, from the foundation of the Religious Tract Society,
regretted that the _Repository Tracts_ "did not contain a fuller statement
of the great evangelical principles"; while in the prospectus it is also
stated that "no cause of any particular party is intended to be served by
it, but general Christianity will be promoted upon practical principles."
This explains what has often been noticed, that the tracts contain a mild
form of "evangelical" doctrine, free from that more fervid dogmatism which
appears in the _Village Dialogues_; and such as H. More's friend, Bishop
Porteus[439]--a great promoter of the scheme--might approve. The Religious
Tract Society (in 1863) republished some of H. More's tracts, with
alterations, additions, and omissions _ad libitum_. This is an improper way
of dealing with the works of the dead; especially when the reprints are of
popular works. A small type addition to the preface contains: "Some
alterations and abridgements have been made to adapt them to the present
times and the aim of the Religious Tract Society." I think every publicity
ought to be given to the existence of such a practice; and I reprint what I
said on the subject in _Notes and Queries_.

Alterations in works which the Society republishes are a necessary part of
their plan, though such notes as they should judge to be corrective would
be the best way of proceeding. But the fact of alteration should be very
distinctly announced on the title of the work itself, not left to a little
bit of small type at the end of the preface, in the place where trade
advertisements, or directions to the binder, are often found. And the
places in which alteration has been made should be pointed out, either by
marks of omission, when omission is the alteration, or by putting the
altered sentences in brackets, when change has been made. May any one alter
the works of the dead at his own discretion? {194} We all know that readers
in general will take each sentence to be that of the author whose name is
on the title; so that a correcting republisher _makes use of his author's
name to teach his own variation_. The tortuous logic of "the trade," which
is content when "the world" is satisfied, is not easily answered, any more
than an eel is easily caught; but the Religious Tract Society may be
_convinced_ [in the old sense] in a sentence. On which course would they
feel most safe in giving their account to the God of truth? "In your own
conscience, now?"

I have tracked out a good many of the variations made by the Religious
Tract Society in the recently published volume of _Repository Tracts_. Most
of them are doctrinal insertions or amplifications, to the matter of which
Hannah More would not have objected--all that can be brought against them
is the want of notice. But I have found two which the respect I have for
the Religious Tract Society, in spite of much difference on various points,
must not prevent my designating as paltry. In the story of Mary Wood, a
kind-hearted clergyman converses with the poor girl who has ruined herself
by lying. In the original, he "assisted her in the great work of
repentance;" in the reprint it is to be shown in some detail how he did
this. He is to begin by pointing out that "the heart is deceitful above all
things and desperately wicked." Now the clergyman's name is _Heartwell_: so
to prevent his name from contradicting his doctrine, he is actually cut
down to _Harwell_. Hannah Moore meant this good man for one of those
described in Acts xv. 8, 9, and his name was appropriate.

Again, Mr. Flatterwell, in persuasion of Parley the porter to let him into
the castle, declares that the worst he will do is to "play an innocent game
of cards just to keep you awake, or sing a cheerful song with the maids."
Oh fie! Miss Hannah More! and you a single lady too, and a contemporary of
the virtuous Bowdler![440] Though Flatterwell be an {195} allegory of the
devil, this is really too indecorous, even for him. Out with the three last
words! and out it is.

The Society cuts a poor figure before a literary tribunal. Nothing was
wanted except an admission that the remarks made by me were unanswerable,
and this was immediately furnished by the Secretary (_N. and Q._, 3d S.,
vi. 290). In a reply of which six parts out of seven are a very amplified
statement that the Society did not intend to reprint _all_ Hannah More's
tracts, the remaining seventh is as follows:

"I am not careful [perhaps this should be _careful not_] to notice
Professor De Morgan's objections to the changes in 'Mary Wood' or 'Parley
the Porter,' but would merely reiterate that the tracts were neither
designed nor announced to be 'reprints' of the originals [design is only
known to the designers; as to announcement, the title is ''Tis all for the
best, The Shepherd of Salisbury Plain, and other narratives by Hannah
More']; and much less [this must be _careful not_; further removed from
answer than _not careful_] can I occupy your space by a treatise on the
Professor's question: 'May any one alter the works of the dead at his own
discretion?'"

To which I say: Thanks for help!

I predict that Hannah More's _Cheap Repository Tracts_ will somewhat
resemble the _Pilgrim's Progress_ in their fate. Written for the cottage,
and long remaining in their original position, they will become classical
works of their kind. Most assuredly this will happen if my assertion cannot
be upset, namely, that they contain the first specimens of fiction
addressed to the world at large, and widely circulated, in which
dramatic--as distinguished from puppet--power is shown, and without
indecorum.

{196}

According to some statements I have seen, but which I have not verified,
other publishing bodies, such as the Christian Knowledge Society, have
taken the same liberty with the names of the dead as the Religious Tract
Society. If it be so, the impropriety is the work of the smaller spirits
who have not been sufficiently overlooked. There must be an overwhelming
majority in the higher councils to feel that, whenever _altered_ works are
published, _the fact of alteration should be made as prominent as the name
of the author_. Everything short of this is suppression of truth, and will
ultimately destroy the credit of the Society. Equally necessary is it that
the alterations should be noted. When it comes to be known that the author
before him is altered, he knows not where nor how nor by whom, the lowest
reader will lose his interest.



A TRIBUTE TO WILLIAM FREND.

    The principles of Algebra. By William Frend.[441] London, 1796, 8vo.
    Second Part, 1799.

This Algebra, says Dr. Peacock,[442] shows "great distrust {197} of the
results of algebraical science which were in existence at the time when it
was written." Truly it does; for, as Dr. Peacock had shown by full
citation, it makes war of extermination upon all that distinguishes algebra
from arithmetic. Robert Simson[443] and Baron Maseres[444] were Mr. Frend's
predecessors in this opinion.

The genuine respect which I entertained for my father-in-law did not
prevent my canvassing with perfect freedom his anti-algebraical and
anti-Newtonian opinions, in a long obituary memoir read at the Astronomical
Society in February 1842, which was written by me. It was copied into the
_Athenæum_ of March 19. It must be said that if the manner in which algebra
_was_ presented to the learner had been true algebra, he would have been
right: and if he had confined himself to protesting against the imposition
of attraction as a fundamental part of the existence of matter, he would
have been in unity with a great many, including Newton himself. I wish he
had preferred amendment to rejection when he was a college tutor: he wrote
and spoke English with a clearness which is seldom equaled.

His anti-Newtonian discussions are confined to the preliminary chapters of
his _Evening Amusements_,[445] a series of astronomical lessons in nineteen
volumes, following the moon through a period of the golden numbers.

There is a mistake about him which can never be destroyed. It is constantly
said that, at his celebrated trial in 1792, for sedition and opposition to
the Liturgy, etc., he was _expelled_ from the University. He was
_banished_. People cannot see the difference; but it made all the
difference to {198} Mr. Frend. He held his fellowship and its profits till
his marriage in 1808, and was a member of the University and of its Senate
till his death in 1841, as any Cambridge Calendar up to 1841 will show.
That they would have expelled him if they could, is perfectly true; and
there is a funny story--also perfectly true--about their first proceedings
being under a statute which would have given the power, had it not been
discovered during the proceedings that the statute did not exist. It had
come so near to existence as to be entered into the Vice-Chancellor's book
for his signature, which it wanted, as was not seen till Mr. Frend exposed
it: in fact, the statute had never actually passed.

There is an absurd mistake in Gunning's[446] _Reminiscences of Cambridge_.
In quoting a passage of Mr. Frend's pamphlet, which was very obnoxious to
the existing Government, it is printed that the poor market-women
complained that they were to be _scotched_ a quarter of their wages by
taxation; and attention is called to the word by its being three times
printed in italics. In the pamphlet it is "sconced"; that very common old
word for fined or mulcted.

Lord Lyndhurst,[447] who has [1863] just passed away under a load of years
and honors, was Mr. Frend's private pupil at Cambridge. At the time of the
celebrated trial, he and two others amused themselves, and vented the
feeling which was very strong among the undergraduates, by chalking the
walls of Cambridge with "Frend for ever!" While thus engaged in what, using
the term legally, we are probably to call his first publication, he and his
friends were surprised by the proctors. Flight and chase followed of
course: Copley and one of the others, Serjeant Rough,[448] escaped: the
{199} third, whose name I forget, but who afterwards, I have been told was
a bishop,[449] being lame, was captured and impositioned. Looking at the
Cambridge Calendar to verify the fact that Copley was an undergraduate at
the time, I find that there are but two other men in the list of honors of
his year whose names are now widely remembered. And they were both
celebrated schoolmasters; Butler[450] of Harrow, and Tate[451] of Richmond.

But Mr. Frend had another noted pupil. I once had a conversation with a
very remarkable man, who was generally called "Place,[452] the tailor," but
who was politician, political economist, etc., etc. He sat in the room
above his shop--he was then a thriving master tailor at Charing
Cross--surrounded by books enough for nine, to shame a proverb. The blue
books alone, cut up into strips, would have measured Great Britain for
oh-no-we-never-mention-'ems, the Highlands included. I cannot find a
biography of this worthy and able man. I happened to mention William Frend,
and he said, "Ah! my old master, as I always call him. Many and many a
time, and year after year, did he come in every {200} now and then to give
me instruction, while I was sitting on the board, working for my living,
you know."

Place, who really was a sound economist, is joined with Cobbett, because
they were together at one time, and because he was, in 1800, etc., a great
Radical. But for Cobbett he had a great contempt. He told me the following
story. He and others were advising with Cobbett about the defense he was to
make on a trial for seditious libel which was coming on. Said Place, "You
must put in the letters you have received from Ministers, members of the
Commons from the Speaker downwards, etc., about your Register, and their
wish to have subjects noted. You must then ask the jury whether a person so
addressed must be considered as a common sower of sedition, etc. You will
be acquitted; nay, if your intention should get about, very likely they
will manage to stop proceedings." Cobbett was too much disturbed to listen;
he walked about the room ejaculating "D---- the prison!" and the like. He
had not the sense to follow the advice, and was convicted.

Cobbett, to go on with the chain, was a political acrobat, ready for any
kind of posture. A friend of mine gave me several times an account of a
mission to him. A Tory member--those who know the old Tory world may look
for his initials in initials of two consecutive words of "Pay his money
with interest"--who was, of course, a political opponent, thought Cobbett
had been hardly used, and determined to subscribe handsomely towards the
expenses he was incurring as a candidate. My friend was commissioned to
hand over the money--a bag of sovereigns, that notes might not be traced.
He went into Cobbett's committee-room, told the patriot his errand, and put
the money on the table. "And to whom, sir, am I indebted?" said Cobbett.
"The donor," was the answer, "is Mr. Andrew Theophilus Smith," or some such
unlikely pair of baptismals. "Ah!" said Cobbett, "I have known Mr. A. T. S.
a long time! he was always a true friend of his country!" {201}

To return to Place. He is a noted instance of the advantage of our jury
system, which never asks a man's politics, etc. The late King of Hanover,
when Duke of Cumberland, being unpopular, was brought under unjust
suspicions by the suicide of his valet: he must have seduced the wife and
murdered the husband. The charges were as absurd as those brought against
the Englishman in the Frenchman's attempt at satirical verses upon him:

 "The Englishman is a very bad man;
  He drink the beer and he steal the can:
  He kiss the wife and he beat the man;
  And the Englishman is a very G---- d----."

The charges were revived in a much later day, and the defense might have
given some trouble. But Place, who had been the foreman at the inquest,
came forward, and settled the question in a few lines. Every one knew that
the old Radical was quite free of all disposition to suppress truth from
wish to curry favor with royalty.

John Speed,[453] the author of the _English History_,[454] (1632) which
Bishop Nicolson[455] calls the best chronicle extant, was a man, like
Place, of no education, but what he gave himself. The bishop says he would
have done better if he had a better training: but what, he adds, could have
been expected from a tailor! This Speed was, as well as Place. But he was
{202} released from manual labor by Sir Fulk Grevil,[456] who enabled him
to study.



A STORY ON SIMSON.

I have elsewhere noticed that those who oppose the mysteries of algebra do
not ridicule them; this I want the cyclometers to do. Of the three who
wrote against the great point, the negative quantity, and the uses of 0
which are connected with it, only one could fire a squib. That Robert
Simson[457] should do such a thing will be judged impossible by all who
admit tradition. I do not vouch for the following; I give it as a proof of
the impression which prevailed about him:

He used to sit at his open window on the ground floor, as deep in geometry
as a Robert Simson ought to be. Here he would be accosted by beggars, to
whom he generally gave a trifle, he roused himself to hear a few words of
the story, made his donation, and instantly dropped down into his depths.
Some wags one day stopped a mendicant who was on his way to the window with
"Now, my man, do as we tell you, and you will get something from that
gentleman, and a shilling from us besides. You will go and say you are in
distress, he will ask you who you are, and you will say you are Robert
Simson, son of John Simson of Kirktonhill." The man did as he was told;
Simson quietly gave him a coin, and dropped off. The wags watched a little,
and saw him rouse himself again, and exclaim "Robert Simson, son of John
Simson of Kirktonhill! why, that is myself. That man must be an impostor."
Lord Brougham tells the same story, with some difference of details.

{203}



BARON MASERES.

Baron Maseres[458] was, as a writer, dry; those who knew his writings will
feel that he seldom could have taken in a joke or issued a pun. Maseres was
the fourth wrangler of 1752, and first Chancellor's medallist (or highest
in classics); his second was Porteus[459] (afterward Bishop of London).
Waring[460] came five years after him: he could not get Maseres through the
second page of his first book on algebra; a negative quantity stood like a
lion in the way. In 1758 he published his _Dissertation on the Use of the
Negative Sign_,[461] 4to. There are some who care little about + and -, who
would give it house-room for the sake of the four words "Printed by Samuel
Richardson."

Maseres speaks as follows: "A single quantity can never be marked with
either of those signs, or considered as either affirmative or negative; for
if any single quantity, as b, is marked either with the sign + or with the
sign - without assigning some other quantity, as a, to which it is to be
added, or from which it is to be subtracted, the mark will have no meaning
or signification: thus if it be said that the square of -5, or the product
of -5 into -5, is equal to +25, such an assertion must either signify no
more than that 5 times 5 is equal to 25 without any regard to the signs, or
it must be mere nonsense and unintelligible jargon. I speak according to
the foregoing definition, by which the affirmativeness or negativeness of
any quantity implies a relation to another quantity of the same kind to
which it {204} is added, or from which it is subtracted; for it may perhaps
be very clear and intelligible to those who have formed to themselves some
other idea of affirmative and negative quantities different from that above
defined."

Nothing can be more correct, or more identically logical: +5 and -5,
standing alone, are jargon if +5 and -5 are to be understood as without
reference to another quantity. But those who have "formed to themselves
some other idea" see meaning enough. The great difficulty of the opponents
of algebra lay in want of power or will to see extension of terms. Maseres
is right when he implies that extension, accompanied by its refusal, makes
jargon. One of my paradoxers was present at a meeting of the Royal Society
(in 1864, I think) and asked permission to make some remarks upon a paper.
He rambled into other things, and, naming me, said that I had written a
book in which two sides of a triangle are pronounced _equal_ to the
third.[462] So they are, in the sense in which the word is used in complete
algebra; in which A + B = C makes A, B, C, three sides of a triangle, and
declares that going over A and B, one after the other, is equivalent, in
change of place, to going over C at once. My critic, who might, if he
pleased, have objected to extension, insisted upon reading me in unextended
meaning.

On the other hand, it must be said that those who wrote on the other idea
wrote very obscurely about it and justified Des Cartes (_De Methodo_)[463]
when he said: "Algebram vero, ut solet doceri, animadverti certis regulis
et numerandi formulis ita esse contentam, ut videatur potius ars quædam
confusa, cujus usu ingenium quodam modo turbatur et obscuratur, quam
scientia qua excolatur et perspicacius {205} reddatur."[464] Maseres wrote
this sentence on the title of his own work, now before me; he would have
made it his motto if he had found it earlier.

There is, I believe, in Cobbett's _Annual Register_,[465] an account of an
interview between Maseres and Cobbett when in prison.

The conversation of Maseres was lively, and full of serious anecdote: but
only one attempt at humorous satire is recorded of him; it is an
instructive one. He was born in 1731 (Dec. 15), and his father was a
refugee. French was the language of the house, with the pronunciation of
the time of Louis XIV. He lived until 1824 (May 19), and saw the race of
refugees who were driven out by the first Revolution. Their pronunciation
differed greatly from his own; and he used to amuse himself by mimicking
them. Those who heard him and them had the two schools of pronunciation
before them at once; a thing which seldom happens. It might even yet be
worth while to examine the Canadian pronunciation.

Maseres went as Attorney-General to Quebec; and was appointed Cursitor
Baron of our Exchequer in 1773. There is a curious story about his mission
to Canada, which I have heard as good tradition, but have never seen in
print. The reader shall have it as cheap as I; and I confess I rather
believe it. Maseres was inveterately honest; he could not, at the bar, bear
to see his own client victorious, when he knew his cause was a bad one. On
a certain occasion he was in a cause which he knew would go against him if
a certain case were quoted. Neither the judge nor the opposite counsel
seemed to remember this case, and Maseres could not help dropping an
allusion which brought it out. {206} His business as a barrister fell off,
of course. Some time after, Mr. Pitt (Chatham) wanted a lawyer to send to
Canada on a private mission, and wanted a _very honest man_. Some one
mentioned Maseres, and told the above story: Pitt saw that he had got the
man he wanted. The mission was satisfactorily performed, and Maseres
remained as Attorney-General.

The _Doctrine of Life Annuities_[466] (4to, 726 pages, 1783) is a strange
paradox. Its size, the heavy dissertations on the national debt, and the
depth of algebra supposed known, put it out of the question as an
elementary work, and it is unfitted for the higher student by its elaborate
attempt at elementary character, shown in its rejection of forms derived
from chances in favor of _the average_, and its exhibition of the separate
values of the years of an annuity, as arithmetical illustrations. It is a
climax of unsaleability, unreadability, and inutility. For intrinsic
nullity of interest, and dilution of little matter with much ink, I can
compare this book to nothing but that of Claude de St. Martin, elsewhere
mentioned, or the lectures _On the Nature and Properties of Logarithms_, by
James Little,[467] Dublin, 1830, 8vo. (254 heavy pages of many words and
few symbols), a wonderful weight of weariness.

The stock of this work on annuities, very little diminished, was given by
the author to William Frend, who paid warehouse room for it until about
1835, when he consulted me as to its disposal. As no publisher could be
found who would take it as a gift, for any purpose of sale, it was
consigned, all but a few copies, to a buyer of waste paper.

Baron Maseres's republications are well known: the _Scriptores
Logarithmici_[468] is a set of valuable reprints, mixed {207} with much
which might better have entered into another collection. It is not so well
known that there is a volume of optical reprints, _Scriptores Optici_,
London, 1823, 4to, edited for the veteran of ninety-two by Mr. Babbage[469]
at twenty-nine. This excellent volume contains James Gregory, Des Cartes,
Halley, Barrow, and the optical writings of Huyghens, the _Principia_ of
the undulatory theory. It also contains, by the sort of whim in which such
men as Maseres, myself, and some others are apt to indulge, a reprint of
"The great new Art of weighing Vanity,"[470] by M. Patrick Mathers,
Arch-Bedel to the University of St. Andrews, Glasgow, 1672. Professor
Sinclair,[471] of Glasgow, a good man at clearing mines of the water which
they did not want, and furnishing cities with water which they did want,
seems to have written absurdly about hydrostatics, and to have attacked a
certain Sanders,[472] M.A. So Sanders, assisted by James Gregory, published
a heavy bit of jocosity about him. This story of the authorship rested on a
note made in his {208} copy by Robert Gray, M.D.; but it has since been
fully confirmed by a letter of James Gregory to Collins, in the
Macclesfield Correspondence. "There is one Master Sinclair, who did write
the _Ars Magna et Nova_,[473] a pitiful ignorant fellow, who hath lately
written horrid nonsense in the hydrostatics, and hath abused a master in
the University, one Mr. Sanders, in print. This Mr. Sanders ... is resolved
to cause the Bedel of the University to write against him.... We resolve to
make excellent sport with him."

On this I make two remarks: First, I have learned from experience that old
notes, made in books by their possessors, are statements of high authority:
they are almost always confirmed. I do not receive them without hesitation;
but I believe that of all the statements about books which rest on one
authority, there is a larger percentage of truth in the written word than
in the printed word. Secondly, I mourn to think that when the New Zealander
picks up his old copy of this book, and reads it by the associations of his
own day, he may, in spite of the many assurances I have received that my
_Athenæum Budget_ was amusing, feel me to be as heavy as I feel James
Gregory and Sanders. But he will see that I knew what was coming, which
Gregory did not.



MR. FREND'S BURLESQUE.

It was left for Mr. Frend to prove that an impugner of algebra could
attempt ridicule. He was, in 1803, editor of a periodical _The Gentleman's
Monthly Miscellany_, which lasted a few months.[474] To this, among other
things, he contributed the following, in burlesque of the use made of 0, to
which he objected.[475] The imitation of Rabelais, a writer {209} in whom
he delighted, is good: to those who have never dipped, it may give such a
notion as they would not easily get elsewhere. The point of the satire is
not so good. But in truth it is not easy to make pungent scoffs upon what
is common sense to all mankind. Who can laugh with effect at six times
nothing is nothing, as false or unintelligible? In an article intended for
that undistinguishing know-0 the "general reader," there would have been no
force of satire, if _division_ by 0 had been separated from multiplication
by the same.

I have followed the above by another squib, by the same author, on the
English language. The satire is covertly aimed at theological phraseology;
and any one who watches this subject will see that it is a very just
observation that the Greek words are not boiled enough.

PANTAGRUEL'S DECISION _of the_ QUESTION _about_ NOTHING.

"Pantagruel determined to have a snug afternoon with Epistemon and Panurge.
Dinner was ordered to be set in a small parlor, and a particular batch of
Hermitage with some choice Burgundy to be drawn from a remote corner of the
cellar upon the occasion. By way of lunch, about an hour before dinner,
Pantagruel was composing his stomach with German sausages, reindeer's
tongues, oysters, brawn, and half a dozen different sorts of English beer
just come into fashion, when a most thundering knocking was heard at the
great gate, and from the noise they expected it to announce the arrival at
least of the First Consul, or king Gargantua. Panurge was sent to
reconnoiter, and after a quarter of an hour's absence, returned with the
news that the University of Pontemaca was waiting his highness's leisure in
the great hall, to propound a question which {210} had turned the brains of
thirty-nine students, and had flung twenty-seven more into a high fever.
With all my heart, says Pantagruel, and swallowed down three quarts of
Burton ale; but remember, it wants but an hour of dinner time, and the
question must be asked in as few words as possible; for I cannot deprive
myself of the pleasure I expected to enjoy in the company of my good
friends for a set of mad-headed masters. I wish brother John was here to
settle these matters with the black gentry.

"Having said or rather growled this, he proceeded to the hall of ceremony,
and mounted his throne; Epistemon and Panurge standing on each side, but
two steps below him. Then advanced to the throne the three beadles of the
University of Pontemaca with their silver staves on their shoulders, and
velvet caps on their heads, and they were followed by three times three
doctors, and thrice three times three masters of art; for everything was
done in Pontemaca by the number three, and on this account the address was
written on parchment, one foot in breadth, and thrice three times thrice
three feet in length. The beadles struck the ground with their heads and
their staves three times in approaching the throne; the doctors struck the
ground with their heads thrice three times, and the masters did the same
thrice each time, beating the ground with their heads thrice three times.
This was the accustomed form of approaching the throne, time out of mind,
and it was said to be emblematic of the usual prostration of science to the
throne of greatness.

"The mathematical professor, after having spit, and hawked, and cleared his
throat, and blown his nose on a handkerchief lent to him, for he had
forgotten to bring his own, began to read the address. In this he was
assisted by three masters of arts, one of whom, with a silver pen, pointed
out the stops; the second with a small stick rapped his knuckles when he
was to raise or lower his voice; and a third pulled his hair behind when he
was to look Pantagruel in the face. Pantagruel began to chafe like a lion:
{211} he turned first on one side, then on the other: he listened and
groaned, and groaned and listened, and was in the utmost cogitabundity of
cogitation. His countenance began to brighten, when, at the end of an hour,
the reader stammered out these words:

"'It has therefore been most clearly proved that as all matter may be
divided into parts infinitely smaller than the infinitely smallest part of
the infinitesimal of nothing, so nothing has all the properties of
something, and may become, by just and lawful right, susceptible of
addition, subtraction, multiplication, division, squaring, and cubing: that
it is to all intents and purposes as good as anything that has been, is, or
can be taught in the nine universities of the land, and to deprive it of
its rights is a most cruel innovation and usurpation, tending to destroy
all just subordination in the world, making all universities superfluous,
leveling vice-chancellors, doctors, and proctors, masters, bachelors, and
scholars, to the mean and contemptible state of butchers and
tallow-chandlers, bricklayers and chimney-sweepers, who, if it were not for
these learned mysteries, might think that they knew as much as their
betters. Every one then, who has the good of science at heart, must pray
for the interference of his highness to put a stop to all the disputes
about nothing, and by his decision to convince all gainsayers that the
science of nothing is taught in the best manner in the universities, to the
great edification and improvement of all the youth in the land.'

"Here Pantagruel whispered in the ear of Panurge, who nodded to Epistemon,
and they two left the assembly, and did not return for an hour, till the
orator had finished his task. The three beadles had thrice struck the
ground with their heads and staves, the doctors had finished their
compliments, and the masters were making their twenty-seven prostrations.
Epistemon and Panurge went up to Pantagruel, whom they found fast asleep
and snoring; nor could he be roused but by as many tugs as there had been
{212} bowings from the corps of learning. At last he opened his eyes, gave
a good stretch, made half a dozen yawns, and called for a stoup of wine. I
thank you, my masters, says he; so sound a nap I have not had since I came
from the island of Priestfolly. Have you dined, my masters? They answered
the question by as many bows as at entrance; but his highness left them to
the care of Panurge, and retired to the little parlor with Epistemon, where
they burst into a fit of laughter, declaring that this learned Baragouin
about nothing was just as intelligible as the lawyer's Galimathias. Panurge
conducted the learned body into a large saloon, and each in his way hearing
a clattering of plates and glasses, congratulated himself on his
approaching good cheer. There they were left by Panurge, who took his chair
by Pantagruel just as the soup was removed, but he made up for the want of
that part of his dinner by a pint of champagne. The learning of the
university had whetted their appetites; what they each ate it is needless
to recite; good wine, good stories, and hearty laughs went round, and three
hours elapsed before one soul of them recollected the hungry students of
Pontemaca.

"Epistemon reminded them of the business in hand, and orders were given for
a fresh dozen of hermitage to be put upon table, and the royal attendants
to get ready. As soon as the dozen bottles were emptied, Pantagruel rose
from table, the royal trumpets sounded, and he was accompanied by the great
officers of his court into the large dining hall, where was a table with
forty-two covers. Pantagruel sat at the head, Epistemon at the bottom, and
Panurge in the middle, opposite an immense silver tureen, which would hold
fifty gallons of soup. The wise men of Pontemaca then took their seats
according to seniority. Every countenance glistened with delight; the music
struck up; the dishes were uncovered. Panurge had enough to do to handle
the immense silver ladle: Pantagruel and Epistemon had no time for eating,
they were fully employed in carving. The bill {213} of fare announced the
names of a hundred different dishes. From Panurge's ladle came into the
soup plate as much as he took every time out of the tureen; and as it was
the rule of the court that every one should appear to eat, as long as he
sat at table, there was the clattering of nine and thirty spoons against
the silver soup-plates for a quarter of an hour. They were then removed,
and knives and forks were in motion for half an hour. Glasses were
continually handed round in the mean time, and then everything was removed,
except the great tureen of soup. The second course was now served up, in
dispatching which half an hour was consumed; and at the conclusion the wise
men of Pontemaca had just as much in their stomachs as Pantagruel in his
head from their address: for nothing was cooked up for them in every
possible shape that Panurge could devise.

"Wine-glasses, large decanters, fruit dishes, and plates were now set on.
Pantagruel and Epistemon alternately gave bumper toasts: the University of
Pontemaca, the eye of the world, the mother of taste and good sense and
universal learning, the patroness of utility, and the second only to
Pantagruel in wisdom and virtue (for these were her titles), was drank
standing with thrice three times three, and huzzas and clattering of
glasses; but to such wine the wise men of Pontemaca had not been
accustomed; and though Pantagruel did not suffer one to rise from table
till the eighty-first glass had been emptied, not even the weakest headed
master of arts felt his head in the least indisposed. The decanters indeed
were often removed, but they were brought back replenished, filled always
with nothing.

"Silence was now proclaimed, and in a trice Panurge leaped into the large
silver tureen. Thence he made his bows to Pantagruel and the whole company,
and commenced an oration of signs, which lasted an hour and a half, and in
which he went over all the matter contained in the Pontemaca address; and
though the wise men looked very serious during the whole time, Pantagruel
himself and his whole {214} court could not help indulging in repeated
bursts of laughter. It was universally acknowledged that he excelled
himself, and that the arguments by which he beat the English masters of
arts at Paris were nothing to the exquisite selection of attitudes which he
this day assumed. The greatest shouts of applause were excited when he was
running thrice round the tureen on its rim, with his left hand holding his
nose, and the other exercising itself nine and thirty times on his back. In
this attitude he concluded with his back to the professor of mathematics;
and at the instant he gave his last flap, by a sudden jump, and turning
heels over head in the air, he presented himself face to face to the
professor, and standing on his left leg, with his left hand holding his
nose, he presented to him, in a white satin bag, Pantagruel's royal decree.
Then advancing his right leg, he fixed it on the professor's head, and
after three turns, in which he clapped his sides with both hands thrice
three times, down he leaped, and Pantagruel, Epistemon, and himself took
their leaves of the wise men of Pontemaca.

"The wise men now retired, and by royal orders were accompanied by a guard,
and according to the etiquette of the court, no one having a royal order
could stop at any public house till it was delivered. The procession
arrived at Pontemaca at nine o'clock the next morning, and the sound of
bells from every church and college announced their arrival. The
congregation was assembled; the royal decree was saluted in the same manner
as if his highness had been there in person; and after the proper
ceremonies had been performed, the satin bag was opened exactly at twelve
o'clock. A finely emblazoned roll was drawn forth, and the public orator
read to the gaping assembly the following words:

"'They who can make something out of nothing shall have nothing to eat at
the court of--PANTAGRUEL.'" {215}

ORIGIN _of the_ ENGLISH LANGUAGE, _related by a_ SWEDE.

"Some months ago in a party in Holland, consisting of natives of various
countries, the merit of their respective languages became a topic of
conversation. A Swede, who had been a great traveler, and could converse in
most of the modern languages of Europe, laughed very heartily at an
Englishman, who had ventured to speak in praise of the tongue of his dear
country. I never had any trouble, says he, in learning English. To my very
great surprise, the moment I sat foot on shore at Gravesend, I found out,
that I could understand, with very little trouble, every word that was
said. It was a mere jargon, made up of German, French, and Italian, with
now and then a word from the Spanish, Latin or Greek. I had only to bring
my mouth to their mode of speaking, which was done with ease in less than a
week, and I was everywhere taken for a true-born Englishman; a privilege by
the way of no small importance in a country, where each man, God knows why,
thinks his foggy island superior to any other part of the world: and though
his door is never free from some dun or other coming for a tax, and if he
steps out of it he is sure to be knocked down or to have his pocket picked,
yet he has the insolence to think every foreigner a miserable slave, and
his country the seat of everything wretched. They may talk of liberty as
they please, but Spain or Turkey for my money: barring the bowstring and
the inquisition, they are the most comfortable countries under heaven, and
you need not be afraid of either, if you do not talk of religion and
politics. I do not see much difference too in this respect in England, for
when I was there, one of their most eminent men for learning was put in
prison for a couple of years, and got his death for translating one of
Æsop's fables into English, which every child in Spain and Turkey is
taught, as soon as he comes out of his leading strings. Here all the
company unanimously cried out against the Swede, that it was {216}
impossible: for in England, the land of liberty, the only thing its worst
enemies could say against it, was, that they paid for their liberty a much
greater price than it was worth.--Every man there had a fair trial
according to laws, which everybody could understand; and the judges were
cool, patient, discerning men, who never took the part of the crown against
the prisoner, but gave him every assistance possible for his defense.

"The Swede was borne down, but not convinced; and he seemed determined to
spit out all his venom. Well, says he, at any rate you will not deny that
the English have not got a language of their own, and that they came by it
in a very odd way. Of this at least I am certain, for the whole history was
related to me by a witch in Lapland, whilst I was bargaining for a wind.
Here the company were all in unison again for the story.

"In ancient times, said the old hag, the English occupied a spot in
Tartary, where they lived sulkily by themselves, unknowing and unknown. By
a great convulsion that took place in China, the inhabitants of that and
the adjoining parts of Tartary were driven from their seats, and after
various wanderings took up their abode in Germany. During this time nobody
could understand the English, for they did not talk, but hissed like so
many snakes. The poor people felt uneasy under this circumstance, and in
one of their parliaments, or rather hissing meetings, it was determined to
seek a remedy: and an embassy was sent to some of our sisterhood then
living on Mount Hecla. They were put to a nonplus, and summoned the Devil
to their relief. To him the English presented their petitions, and
explained their sad case; and he, upon certain conditions, promised to
befriend them, and to give them a language. The poor Devil was little aware
of what he had promised; but he is, as all the world knows, a man of too
much honor to break his word. Up and down the world then he went in quest
of this new language: visited all the universities, and all {217} the
schools, and all the courts of law, and all the play-houses, and all the
prisons; never was poor devil so fagged. It would have made your heart
bleed to see him. Thrice did he go round the earth in every parallel of
latitude; and at last, wearied and jaded out, back came he to Hecla in
despair, and would have thrown himself into the volcano, if he had been
made of combustible materials. Luckily at that time our sisters were
engaged in settling the balance of Europe; and whilst they were looking
over projects, and counter-projects, and ultimatums, and post ultimatums,
the poor Devil, unable to assist them was groaning in a corner and
ruminating over his sad condition.

"On a sudden, a hellish joy overspread his countenance; up he jumped, and,
like Archimedes of old, ran like a madman amongst the throng, turning over
tables, and papers, and witches, roaring out for a full hour together
nothing else but 'tis found, 'tis found! Away were sent the sisterhood in
every direction, some to traverse all the corners of the earth, and others
to prepare a larger caldron than had ever yet been set upon Hecla. The
affairs of Europe were at a stand: its balance was thrown aside; prime
ministers and ambassadors were everywhere in the utmost confusion; and, by
the way, they have never been able to find the balance since that time, and
all the fine speeches upon the subject, with which your newspapers are
every now and then filled, are all mere hocus-pocus and rhodomontade.
However, the caldron was soon set on, and the air was darkened by witches
riding on broomsticks, bringing a couple of folios under each arm, and
across each shoulder. I remember the time exactly: it was just as the
council of Nice had broken up, so that they got books and papers there dog
cheap; but it was a bad thing for the poor English, as these were the worst
materials that entered into the caldron. Besides, as the Devil wanted some
amusement, and had not seen an account of the transactions of this famous
council, he had all the books brought from it laid before him, and split
his sides almost {218} with laughing, whilst he was reading the speeches
and decrees of so many of his old friends and acquaintances. All this while
the witches were depositing their loads in the great caldron. There were
books from the Dalai Lama, and from China: there were books from the
Hindoos, and tallies from the Caffres: there were paintings from Mexico,
and rocks of hieroglyphics from Egypt: the last country supplied besides
the swathings of two thousand mummies, and four-fifths of the famed library
of Alexandria. Bubble! bubble! toil and trouble! never was a day of more
labor and anxiety; and if our good master had but flung in the Greek books
at the proper time, they would have made a complete job of it. He was a
little too impatient: as the caldron frothed up, he skimmed it off with a
great ladle, and filled some thousands of our wind-bags with the froth,
which the English with great joy carried back to their own country. These
bags were sent to every district: the chiefs first took their fill, and
then the common people; hence they now speak a language which no foreigner
can understand, unless he has learned half a dozen other languages; and the
poor people, not one in ten, understand a third part of what is said to
them. The hissing, however, they have not entirely got rid of, and every
seven years, when the Devil, according to agreement, pays them a visit,
they entertain him at their common halls and county meetings with their
original language.

"The good-natured old hag told me several other circumstances, relative to
this curious transaction, which, as there is an Englishman in company, it
will be prudent to pass over in silence: but I cannot help mentioning one
thing which she told me as a very great secret. You know, says she to me,
that the English have more religions among them than any other nation in
Europe, and that there is more teaching and sermonizing with them than in
any other country. The fact is this; it matters not who gets up to teach
them, the hard words of the Greek were not sufficiently {219} boiled, and
whenever they get into a sentence, the poor people's brains are turned, and
they know no more what the preacher is talking about, than if he harangued
them in Arabic. Take my word for it if you please; but if not, when you get
to England, desire the bettermost sort of people that you are acquainted
with to read to you an act of parliament, which of course is written in the
clearest and plainest style in which anything can be written, and you will
find that not one in ten will be able to make tolerable sense of it. The
language would have been an excellent language, if it had not been for the
council of Nice, and the words had been well boiled.

"Here the company burst out into a fit of laughter. The Englishman got up
and shook hands with the Swede: _si non è vero_, said he, _è ben
trovato_.[476] But, however I may laugh at it here, I would not advise you
to tell this story on the other side of the water. So here's a bumper to
Old England for ever, and God save the king."



ON YOUTHFUL PRODIGIES.

The accounts given of extraordinary children and adolescents frequently
defy credence.[477] I will give two well-attested instances.

The celebrated mathematician Alexis Claude Clairault (now Clairaut)[478]
was certainly born in May, 1713. His treatise on curves of double curvature
(printed in 1731)[479] received {220} the approbation of the Academy of
Sciences, August 23, 1729. Fontenelle, in his certificate of this, calls
the author sixteen years of age, and does not strive to exaggerate the
wonder, as he might have done, by reminding his readers that this work, of
original and sustained mathematical investigation, must have been coming
from the pen at the ages of fourteen and fifteen. The truth was, as
attested by De Molières,[480] Clairaut had given public proofs of his power
at twelve years old. His age being thus publicly certified, all doubt is
removed: say he had been--though great wonder would still have been
left--twenty-one instead of sixteen, his appearance, and the remembrances
of his friends, schoolfellows, etc., would have made it utterly hopeless to
knock off five years of that age while he was on view in Paris as a young
lion. De Molières, who examined the work officially for the _Garde des
Sceaux_, is transported beyond the bounds of official gravity, and says
that it "ne mérite pas seulement d'être imprimé, mais d'être admiré comme
un prodige d'imagination, de conception, et de capacité."[481]

That Blaise Pascal was born in June, 1623, is perfectly well established
and uncontested.[482] That he wrote his conic sections at the age of
sixteen might be difficult to establish, though tolerably well attested, if
it were not for {221} one circumstance, for the book was not published. The
celebrated theorem, "Pascal's hexagram,"[483] makes all the rest come very
easy. Now Curabelle,[484] in a work published in 1644, sneers at
Desargues,[485] whom he quotes, for having, in 1642, deferred a discussion
until "cette grande proposition nommée le Pascale verra le jour."[486] That
is, by the time Pascal was nineteen, the _hexagram_ was circulating under a
name derived from the author. The common story about Pascal, given by his
sister,[487] is an absurdity which no doubt has prejudiced many against
tales of early proficiency. He is made, when quite a boy, to invent
geometry _in the order of Euclid's propositions_: as if that order were
natural sequence of investigation. The hexagram at ten years old would be a
hundred times less unlikely.

The instances named are painfully astonishing: I give one which has fallen
out of sight, because it will preserve an imperfect biography. John
Wilson[488] is Wilson of that {222} Ilk, that is, of "Wilson's Theorem." It
is this: if _p_ be a prime number, the product of all the numbers up to
_p_-1, increased by 1, is divisible without remainder by _p_. All
mathematicians know this as Wilson's theorem, but few know who Wilson was.
He was born August 6, 1741, at the Howe in Applethwaite, and he was heir to
a small estate at Troutbeck in Westmoreland. He was sent to Peterhouse, at
Cambridge, and while an undergraduate was considered stronger in algebra
than any one in the University, except Professor Waring, one of the most
powerful algebraists of the century.[489] He was the senior wrangler of
1761, and was then for some time a private tutor. When Paley,[490] then in
his third year, determined to make a push for the senior wranglership,
which he got, Wilson was recommended to him as a tutor. Both were ardent in
their work, except that sometimes Paley, when he came for his lesson, would
find "Gone a fishing" written on his tutor's outer door: which was insult
added to injury, for Paley was very fond of fishing. Wilson soon left
Cambridge, and went to the bar. He practised on the northern circuit with
great success; and, one day, while passing his vacation on his little
property at Troutbeck, he received information, to his great surprise, that
Lord Thurlow,[491] with whom he had {223} no acquaintance, had recommended
him to be a Judge of the Court of Common Pleas. He died, Oct. 18, 1793,
with a very high reputation as a lawyer and a Judge. These facts are partly
from Meadley's _Life of Paley_,[492] no doubt from Paley himself, partly
from the _Gentleman's Magazine_, and from an epitaph written by Bishop
Watson.[493] Wilson did not publish anything: the theorem by which he has
cut his name in the theory of numbers was communicated to Waring, by whom
it was published. He married, in 1788, a daughter of Serjeant Adair,[494]
and left issue. _Had a family_, many will say: but a man and his wife are a
family, even without children. An actuary may be allowed to be accurate in
this matter, of which I was reminded by what an actuary wrote of another
actuary. William Morgan,[495] in the life of his uncle Dr. Richard
Price,[496] says that the Doctor and his {224} wife were "never blessed
with an addition to their family." I never met with such accuracy
elsewhere. Of William Morgan I add that my surname and pursuits have
sometimes, to my credit be it said, made a confusion between him and me.
Dates are nothing to the mistaken; the last three years of Morgan's life
were the first three years of my actuary-life (1830-33). The mistake was to
my advantage as well as to my credit. I owe to it the acquaintance of one
of the noblest of the human race, I mean Elizabeth Fry,[497] who came to me
for advice about a philanthropic design, which involved life questions,
under a general impression that some Morgan had attended to such
things.[498]

{225}



NEWTON AGAIN OVERTHROWN.

    A treatise on the sublime science of heliography, satisfactorily
    demonstrating our great orb of light, the sun, to be absolutely no
    other than a body of ice! Overturning all the received systems of the
    universe hitherto extant; proving the celebrated and indefatigable Sir
    Isaac Newton, in his theory of the solar system, to be as far distant
    from the truth, as many of the heathen authors of Greece and Rome. By
    Charles Palmer,[499] Gent. London, 1798, 8vo.

Mr. Palmer burned some tobacco with a burning glass, saw that a lens of ice
would do as well, and then says:

"If we admit that the sun could be removed, and a terrestrial body of ice
placed in its stead, it would produce the same effect. The sun is a
crystaline body receiving the radiance of God, and operates on this earth
in a similar manner as the light of the sun does when applied to a convex
mirror or glass."

Nov. 10, 1801. The Rev. Thomas Cormouls,[500] minister of Tettenhall,
addressed a letter to Sir Wm. Herschel, from which I extract the following:

"Here it may be asked, then, how came the doctrines of Newton to solve all
astronomic Phenomina, and all problems concerning the same, both _a parte
ante_ and _a parte post_.[501] It is answered that he certainly wrought the
principles he made use of into strickt analogy with the real Phenomina of
the heavens, and that the rules and results arizing from them {226} agree
with them and resolve accurately all questions concerning them. Though they
are not fact and true, or nature, but analogous to it, in the manner of the
artificial numbers of logarithms, sines, &c. A very important question
arises here, Did Newton mean to impose upon the world? By no means: he
received and used the doctrines reddy formed; he did a little extend and
contract his principles when wanted, and commit a few oversights of
consequences. But when he was very much advanced in life, he suspected the
fundamental nullity of them: but I have from a certain anecdote strong
ground to believe that he knew it before his decease and intended to have
retracted his error. But, however, somebody did deceive, if not wilfully,
negligently at least. That was a man to whom the world has great
obligations too. It was no less a philosopher than Galileo."

That Newton wanted to retract before his death, is a notion not uncommon
among paradoxers. Nevertheless, there is no retraction in the third edition
of the _Principia_, published when Newton was eighty-four years old! The
moral of the above is, that a gentleman who prefers instructing William
Herschel to learning how to spell, may find a proper niche in a proper
place, for warning to others. It seems that gravitation is not truth, but
only the logarithm of it.



BISHOPS AS PARADOXERS.

    The mathematical and philosophical works of the Right Rev. John
    Wilkins[502].... In two volumes. London, 1802, 8vo.

This work, or at least part of the edition--all for aught I know--is
printed on wood; that is, on paper made from wood-pulp. It has a rough
surface; and when held before a candle is of very unequal transparency.
There is in it a reprint of the works on the earth and moon. The discourse
on the possibility of going to the moon, in this and the edition of 1640,
is incorporated: but from the account in the {227} life prefixed, and a
mention by D'Israeli, I should suppose that it had originally a separate
title-page, and some circulation as a separate tract. Wilkins treats this
subject half seriously, half jocosely; he has evidently not quite made up
his mind. He is clear that "arts are not yet come to their solstice," and
that posterity will bring hidden things to light. As to the difficulty of
carrying food, he thinks, scoffing Puritan that he is, the Papists may be
trained to fast the voyage, or may find the bread of their Eucharist "serve
well enough for their _viaticum_."[503] He also puts the case that the
story of Domingo Gonsales may be realized, namely, that wild geese find
their way to the moon. It will be remembered--to use the usual substitute
for, It has been forgotten--that the posthumous work of Bishop Francis
Godwin[504] of Llandaff was published in 1638, the very year of Wilkins's
first edition, in time for him to mention it at the end. Godwin makes
Domingo Gonsales get to the moon in a chariot drawn by wild geese, and, as
old books would say, discourses fully on that head. It is not a little
amusing that Wilkins should have been seriously accused of plagiarizing
Godwin, Wilkins writing in earnest, or nearly so, and Godwin writing
fiction. It may serve to show philosophers how very near pure speculation
comes to fable. From the sublime to the ridiculous is but a step: which is
the sublime, and which the ridiculous, every one must settle for himself.
With me, good fiction is the sublime, and bad speculation the ridiculous.
The number of bishops in my list is small. I might, had I possessed the
book, have opened the list of quadrators with an Archbishop of Canterbury,
or at least with a divine who was not wholly not archbishop. Thomas
Bradwardine[505] (Bragvardinus, Bragadinus) was elected in {228} 1348; the
Pope put in another, who died unconsecrated; and Bradwardine was again
elected in 1349, and lived five weeks longer, dying, I suppose, unconfirmed
and unconsecrated.[506] Leland says he held the see a year, _unus tantum
annulus_,[507] which seems to be a confusion: the whole business, from the
first election, took about a year. He squared the circle, and his
performance was printed at Paris in 1494. I have never seen it, nor any
work of the author, except a tract on proportion.

As Bradwardine's works are very scarce indeed, I give two titles from one
of the Libri catalogues.

    "ARITHMETIC. BRAUARDINI (Thomæ) Arithmetica speculativa revisa et
    correcta a Petro Sanchez Ciruelo Aragonesi, black letter, _elegant
    woodcut title-page_, VERY RARE, _folio. Parisiis, per Thomam Anguelast
    (pro Olivier Senant), s. a. circa 1510_.[508]

"This book, by Thomas Bradwardine, Archbishop of Canterbury must be
exceedingly scarce as it has escaped the notice of Professor De Morgan,
who, in his _Arithmetical Books_, speaks of a treatise of the same author
on proportions,[509] printed at Vienna in 1515, but does not mention the
present work.

{229}

    "Bradwardine (Archbp. T.). Brauardini (Thomæ) Geometria speculativa,
    com Tractato de Quadratura Circuli bene revisa a Petro Sanchez Ciruelo,
    SCARCE, _folio. Parisiis, J. Petit_, 1511.[510]

"In this work we find the _polygones étoilés_,[511] see Chasles (_Aperçu_,
pp. 480, 487, 521, 523, &c.) on the merit of the discoveries of this
English mathematician, who was Archbishop of Canterbury in the XIVth
Century (_tempore_ Edward III. A.D. 1349); and who applied geometry to
theology. M. Chasles says that the present work of Bradwardine contains
'Une théorie nouvelle qui doit faire honneur au XIVe Siècle.'"[512]

The titles do not make it quite sure that Bradwardine is the quadrator; it
may be Peter Sanchez after all.[513]



THE QUESTION OF PARALLELS.

    Nouvelle théorie des parallèles. Par Adolphe Kircher[514] [so signed at
    the end of the appendix]. Paris, 1803, 8vo.

An alleged emendation of Legendre.[515] The author refers {230} to attempts
by Hoffman,[516] 1801, by Hauff,[517] 1799, and to a work of Karsten,[518]
or at least a theory of Karsten, contained in "Tentamen novæ parallelarum
theoriæ notione situs fundatæ; auctore G. C. Schwal,[519] Stuttgardæ, 1801,
en 8 volumes." Surely this is a misprint; _eight_ volumes on the theory of
parallels? If there be such a work, I trust I and it may never meet, though
ever so far produced.

{231}



    Soluzione ... della quadratura del Circolo. By Gaetano Rossi.[520]
    London, 1804, 8vo.

The three remarkable points of this book are, that the household of the
Prince of Wales took ten copies, Signora Grassini[521] sixteen, and that
the circumference is 3-1/5 diameters. That is, the appetite of Grassini for
quadrature exceeded that of the whole household (_loggia_) of the Prince of
Wales in the ratio in which the semi-circumference exceeds the diameter.
And these are the first two in the list of subscribers. Did the author see
this theorem?



A PATRIOTIC PARADOX.

    Britain independent of commerce; or proofs, deduced from an
    investigation into the true cause of the wealth of nations, that our
    riches, prosperity, and power are derived from sources inherent in
    ourselves, and would not be affected, even though our commerce were
    annihilated. By Wm. Spence.[522] 4th edition, 1808, 8vo.

A patriotic paradox, being in alleviation of the Commerce panic which the
measures of Napoleon I.--who _felt_ our Commerce, while Mr. Spence only
_saw_ it--had awakened. In this very month (August, 1866), the Pres. Brit.
Assoc. has applied a similar salve to the coal panic; it is fit that
science, which rubbed the sore, should find a plaster. We ought to have an
iron panic and a timber panic; and {232} a solemn embassy to the Americans,
to beg them not to whittle, would be desirable. There was a gold panic
beginning, before the new fields were discovered. For myself, I am the
unknown and unpitied victim of a chronic gutta-percha panic: I never could
get on without it; to me, gutta percha and Rowland Hill are the great
discoveries of our day; and not unconnected either, gutta percha being to
the submarine post what Rowland Hill is to the superterrene. I should be
sorry to lose cow-choke--I gave up trying to spell it many years ago--but
if gutta percha go, I go too. I think, that perhaps when, five hundred
years hence, the people say to the Brit. Assoc. (if it then exist) "Pray
gentlemen, is it not time for the coal to be exhausted?" they will be
answered out of Molière (who will certainly then exist): "_Cela était
autrefois ainsi, mais nous avons changé tout cela._"[523] A great many
people think that if the coal be used up, it will be announced some
unexpected morning by all the yards being shut up and written notice
outside, "Coal all gone!" just like the "Please, ma'am, there ain't no more
sugar," with which the maid servant damps her mistress just at
breakfast-time. But these persons should be informed that there is every
reason to think that there will be time, as the city gentleman said, to
_venienti_ the _occurrite morbo_.[524]



SOME SCIENTIFIC PARADOXES.

    An appeal to the republic of letters in behalf of injured science, from
    the opinions and proceedings of some modern authors of elements of
    geometry. By George Douglas.[525] Edinburgh, 1810, 8vo.

Mr. Douglas was the author of a very good set of {233} mathematical tables,
and of other works. He criticizes Simson,[526] Playfair,[527] and
others,--sometimes, I think, very justly. There is a curious phrase which
occurs more than once. When he wants to say that something or other was
done before Simson or another was born, he says "before he existed, at
least as an author." He seems to reserve the possibility of Simson's
_pre-existence_, but at the same time to assume that he never wrote
anything in his previous state. Tell me that Simson pre-existed in any
other way than as editor of some pre-existent Euclid? Tell Apella![528]

1810. In this year Jean Wood, Professor of Mathematics in the University of
Virginia (Richmond),[529] addressed a printed circular to "Dr. Herschel,
Astronomer, Greenwich Observatory." No mistake was more common than the
natural one of imagining that the _Private Astronomer_ of the king was the
_Astronomer Royal_. The letter was on the {234} difference of velocities of
the two sides of the earth, arising from the composition of the rotation
and the orbital motion. The _paradox_ is a fair one, and deserving of
investigation; but, perhaps it would not be easy to deduce from it tides,
trade-winds, aerolithes, &c., as Mr. Wood thought he had done in a work
from which he gives an extract, and which he describes as published. The
composition of rotations, &c., is not for the world at large: the paradox
of the non-rotation of the moon about her axis is an instance. How many
persons know that when a wheel rolls on the ground, the lowest point is
moving upwards, the highest point forwards, and the intermediate points in
all degrees of betwixt and between? This is too short an explanation, with
some good difficulties.



    The Elements of Geometry. In 2 vols. [By the Rev. J. Dobson,[530] B.D.]
    Cambridge, 1815. 4to.

Of this unpunctuating paradoxer I shall give an account in his own way: he
would not stop for any one; why should I stop for him? It is worth while to
try how unpunctuated sentences will read.

The reverend J Dobson BD late fellow of saint Johns college Cambridge was
rector of Brandesburton in Yorkshire he was seventh wrangler in 1798 and
died in 1847 he was of that sort of eccentricity which permits account of
his private life if we may not rather say that in such cases private life
becomes public there is a tradition that he was called Death Dobson on
account of his head and aspect of countenance being not very unlike the
ordinary pictures of a human skull his mode of life is reported to have
been very singular whenever he visited Cambridge he was never known to go
twice to the same inn he never would sleep at the rectory with another
person in the house some ancient charwoman used to attend to the house but
never slept in it he has been known in the time of coach travelling to have
{235} deferred his return to Yorkshire on account of his disinclination to
travel with a lady in the coach he continued his mathematical studies until
his death and till his executors sold the type all his tracts to the number
of five were kept in type at the university press none of these tracts had
any stops except full stops at the end of paragraphs only neither had they
capitals except one at the beginning of a paragraph so that a full stop was
generally followed by some white as there is not a single proper name in
the whole of the book I have I am not able to say whether he would have
used capitals before proper names I have inserted them as usual for which I
hope his spirit will forgive me if I be wrong he also published the
elements of geometry in two volumes quarto Cambridge 1815 this book had
also no stops except when a comma was wanted between letters as in the
straight lines AB, BC I should also say that though the title is
unpunctuated in the author's part it seems the publishers would not stand
it in their imprint this imprint is punctuated as usual and Deighton and
Sons to prove the completeness of their allegiance have managed that comma
semicolon and period shall all appear in it why could they not have
contrived interrogation and exclamation this is a good precedent to
establish the separate right of the publisher over the imprint it is said
that only twenty of the tracts were printed and very few indeed of the book
on geometry it is doubtful whether any were sold there is a copy of the
geometry in the university library at Cambridge and I have one myself the
matter of the geometry differs entirely from Euclid and is so fearfully
prolix that I am sure no mortal except the author ever read it the man went
on without stops and without stop save for a period at the end of a
paragraph this is the unpunctuated account of the unpunctuating geometer
_suum cuique tribuito_[531] Mrs Thrale[532] would have been amused {236} at
a Dobson who managed to come to a full stop without either of the three
warnings.

I do not find any difficulty in reading Dobson's geometry; and I have read
more of it to try reading without stops than I should have done had it been
printed in the usual way. Those who dip into the middle of my paragraph may
be surprised for a moment to see "on account of his disinclination to
travel with a lady in the coach he continued his mathematical studies until
his death and [further, of course] until his executors sold the type." But
a person reading straight through would hardly take it so. I should add
that, in order to give a fair trial, I did not compose as I wrote, but
copied the words of the correspondent who gave me the facts, so far as they
went.



A RELIGIOUS PARADOX.

    _Philosophia Sacra, or the principles of natural Philosophy. Extracted
    from Divine Revelation._ By the Rev. Samuel Pike.[533] Edited by the
    Rev. Samuel Kittle.[534] Edinburgh, 1815, 8vo.

This is a work of modified Hutchinsonianism, which I have seen cited by
several. Though rather dark on the subject, it seems not to contradict the
motion of the earth, or the doctrine of gravitation. Mr. Kittle gives a
list of some Hutchinsonians,--as Bishop Horne;[535] Dr. Stukeley;[536] the
Rev. {237} W. Jones,[537] author of _Physiological Disquisitions_; Mr.
Spearman,[538] author of _Letters on the Septuagint_ and editor of
Hutchinson; Mr. Barker,[539] author of _Reflexions on Learning_; Dr.
Catcott,[540] author of a work on the creation, &c.; Dr. Robertson,[541]
author of a _Treatise on the Hebrew Language_; _Dr. Holloway_,[542] author
of _Originals, Physical and Theological_; Dr. Walter Hodges,[543] author of
a work on _Elohim_; Lord President Forbes (_ob._ 1747).[544]

The Rev. William Jones, above mentioned (1726-1800), the friend and
biographer of Bishop Horne and his stout {238} defender, is best known as
William Jones of Nayland, who (1757)[545] published the _Catholic Doctrine
of the Trinity_; he was also strong for the Hutchinsonian physical trinity
of fire, light, and spirit. This well-known work was generally recommended,
as the defence of the orthodox system, to those who could not go into the
learning of the subject. There is now a work more suited to our time: _The
Rock of Ages_, by the Rev. E. H. Bickersteth,[546] now published by the
Religious Tract Society, without date, answered by the Rev. Dr.
Sadler,[547] in a work (1859) entitled _Gloria Patri_, in which, says Mr.
Bickersteth, "the author has not even attempted to grapple with my main
propositions." I have read largely on the controversy, and I think I know
what this means. Moreover, when I see the note "There are two other
passages to which Unitarians sometimes refer, but the deduction they draw
from them is, in each case, refuted by the context"--I think I see why the
two texts are not named. Nevertheless, the author is a little more disposed
to yield to criticism than his foregoers; he does not insist on texts and
readings which the greatest editors have rejected. And he writes with
courtesy, both direct and oblique, towards his antagonists; which, on his
side of this subject, is like letting in fresh air. So that I suspect the
two books will together make a tolerably good introduction to the subject
for those who cannot go deep. Mr. Bickersteth's book is well arranged and
indexed, which is a point of superiority to Jones of Nayland. There is a
point which I should gravely recommend to writers on the orthodox side. The
Unitarians in {239} England have frequently contended that the method of
proving the divinity of Jesus Christ from the New Testament would equally
prove the divinity of Moses. I have not fallen in the way of any orthodox
answers specially directed at the repeated tracts written by Unitarians in
proof of their assertion. If there be any, they should be more known; if
there be none, some should be written. Which ever side may be right, the
treatment of this point would be indeed coming to close quarters. The
heterodox assertion was first supported, it is said, by John Bidle or
Biddle (1615-1662) of Magdalen College, Oxford, the earliest of the English
Unitarian writers, previously known by a translation of part of Virgil and
part of Juvenal.[548] But I cannot find that he wrote on it.[549] It is the
subject of "[Greek: haireseôn anastasis], or a new way of deciding old
controversies. By Basanistes. Third edition, enlarged," London, 1815,
8vo.[550] It is the appendix to the amusing, "Six more letters to Granville
Sharp, Esq., ... By Gregory Blunt, Esq." London, 8vo., 1803.[551] This much
I can confidently say, that the study of these tracts would prevent
orthodox writers from some curious slips, which are slips obvious to all
sides of opinion. The lower defenders of orthodoxy frequently vex the
spirits of the higher ones.

Since writing the above I have procured Dr. Sadler's answer. I thought I
knew what the challenger meant when he said the respondent had not grappled
with his main {240} propositions. I should say that he is clung on to from
beginning to end. But perhaps Mr. B. has his own meaning of logical terms,
such as "proposition": he certainly has his own meaning of "cumulative." He
says his evidence is cumulative; not a catena, the strength of which is in
its weakest part, but distinct and independent lines, each of which
corroborates the other. This is the very opposite of _cumulative_: it is
_distributive_. When different arguments are each necessary to a
conclusion, the evidence is _cumulative_; when any one will do, even though
they strengthen each other, it is _distributive_. The word "cumulative" is
a synonym of the law word "constructive"; a whole which will do made out of
parts which separately will not. Lord Strafford [552] opens his defence
with the use of both words: "They have invented a kind of _accumulated_ or
_constructive_ evidence; by which many actions, either totally innocent in
themselves, or criminal in a much inferior degree, shall, when united,
_amount_ to treason." The conclusion is, that Mr. B. is a Cambridge man;
the Oxford men do not confuse the elementary terms of logic. O dear old
Cambridge! when the New Zealander comes let him find among the relics of
your later sons some proof of attention to the elementary laws of thought.
A little-go of logic, please!

Mr. B., though apparently not a Hutchinsonian, has a nibble at a physical
Trinity. "If, as we gaze on the sun shining in the firmament, we see any
faint adumbration of the doctrine of the Trinity in the fontal orb, the
light ever generated, and the heat proceeding from the sun and its
beams--threefold and yet one, the sun, its light, and its {241} heat,--that
luminous globe, and the radiance ever flowing from it, are both evident to
the eye; but the vital warmth is felt, not seen, and is only manifested in
the life it transfuses through creation. The proof of its real existence is
self-demonstrating."

We shall see how Revilo[553] illustrates orthodoxy by mathematics. It was
my duty to have found one of the many illustrations from physics; but
perhaps I should have forgotten it if this instance had not come in my way.
It is very bad physics. The sun, apart from its light, evident to the eye!
Heat more self-demonstrating than light, because _felt_! Heat only
manifested by the life it diffuses! Light implied not necessary to life!
But the theology is worse than Sabellianism[554]. To adumbrate--i.e., make
a picture of--the orthodox doctrine, the sun must be heavenly body, the
light heavenly body, the heat heavenly body; and yet, not three heavenly
bodies, but one heavenly body. The truth is, that this illustration and
many others most strikingly illustrate the Trinity of fundamental doctrine
held by the Unitarians, in all its differences from the Trinity of persons
held by the Orthodox. Be right which may, the right or wrong of the
Unitarians shines out in the comparison. Dr. Sadler confirms me--by which I
mean that I wrote the above before I saw what he says--in the following
words: "The sun is one object with two _properties_, and these properties
have a parallel not in the second and third persons of the Trinity, but in
the attributes of Deity."

The letting light alone, as self-evident, and making heat
self-demonstrating, because felt--i.e., perceptible now and then--has the
character of the Irishman's astronomy:

{242}

 "Long life to the moon, for a dear noble cratur,
  Which serves us for lamplight all night in the dark,
  While the sun only shines in the day, which by natur,
  Wants no light at all, as ye all may remark."



SIR RICHARD PHILLIPS.

_Sir Richard Phillips_[555] (born 1768) was conspicuous in 1793, when he
was sentenced to a year's imprisonment[556] for selling Paine's _Rights of
Man_; and again when, in 1807[557], he was knighted as Sheriff of London.
As a bookseller, he was able to enforce his opinions in more ways than
others. For instance, in James Mitchell's[558] _Dictionary of the
Mathematical and Physical Sciences_, 1823, 12mo, which, though he was not
technically a publisher, was printed for him--a book I should recommend to
the collector of works of reference--there is a temperate description of
his doctrines, which one may almost swear was one of his conditions
previous to undertaking the work. Phillips himself was not only an
anti-Newtonian, but carried to a fearful excess the notion that statesmen
and Newtonians were in league to deceive the world. He saw this plot in
Mrs. Airy's[559] pension, and in Mrs. Somerville's[560]. In 1836, he {243}
did me the honor to attempt my conversion. In his first letter he says:

"Sir Richard Phillips has an inveterate abhorrence of all the pretended
wisdom of philosophy derived from the monks and doctors of the middle ages,
and not less of those of higher name who merely sought to make the monkish
philosophy more plausible, or so to disguise it as to mystify the mob of
small thinkers."

So little did his writings show any knowledge of antiquity, that I strongly
suspect, if required to name one of the monkish doctors, he would have
answered--Aristotle. These schoolmen, and the "philosophical trinity of
gravitating force, projectile force, and void space," were the bogies of
his life.

I think he began to publish speculations in the _Monthly Magazine_ (of
which he was editor) in July 1817: these he republished separately in 1818.
In the Preface, perhaps judging the feelings of others by his own, he says
that he "fully expects to be vilified, reviled, and anathematized, for many
years to come." Poor man! he was let alone. He appeals with confidence to
the "impartial decision of posterity"; but posterity does not appoint a
hearing for one per cent. of the appeals which are made; and it is much to
be feared that an article in such a work of reference as this will furnish
nearly all her materials fifty years hence. The following, addressed to M.
Arago,[561] in 1835, will give posterity as good a notion as she will
probably need:

"Even the present year has afforded EVER-MEMORABLE examples, paralleled
only by that of the Romish Conclave which persecuted Galileo. Policy has
adopted that maxim of Machiavel which teaches that it is _more prudent_ to
_reward_ {244} partisans than to _persecute_ opponents. Hence, a bigotted
party had influence enough with the late short-lived administration [I
think he is wrong as to the administration] of Wellington, Peel, &c., to
confer munificent royal pensions on three writers whose sole distinction
was their advocacy of the Newtonian philosophy. A Cambridge professor last
year published an elaborate volume in illustration of _Gravitation_, and on
him has been conferred a pension of 300l. per annum. A lady has written a
light popular view of the Newtonian Dogmas, and she has been complimented
by a pension of 200l. per annum. And another writer, who has recently
published a volume to prove that the only true philosophy is that of Moses,
has been endowed with a pension of 200l. per annum. Neither of them were
needy persons, and the political and ecclesiastical bearing of the whole
was indicated by another pension of 300l. bestowed on a political writer,
the advocate of all abuses and prejudices. Whether the conduct of the
Romish Conclave was more base for visiting with legal penalties the
promulgation of the doctrines that the Earth turns on its axis and revolves
around the Sun; or that of the British Court, for its craft in conferring
pensions on the opponents of the plain corollary, that all the motions of
the Earth are 'part and parcel' of these great motions, and those again and
all like them consecutive displays of still greater motions in equality of
action and reaction, is A QUESTION which must be reserved for the casuists
of other generations.... I cannot expect that on a sudden you and your
friends will come to my conclusion, that the present philosophy of the
Schools and Universities of Europe, based on faith in witchcraft, magic,
&c., is a system of execrable nonsense, _by which quacks live on the faith
of fools_; but I desire a free and fair examination of my Aphorisms, and if
a few are admitted to be true, merely as courteous concessions to
arithmetic, my purpose will be effected, for men will thus be led to think;
and if they think, then the fabric {245} of false assumptions, and
degrading superstitions will soon tumble in ruins."

This for posterity. For the present time I ground the fame of Sir R.
Phillips on his having squared the circle without knowing it, or intending
to do it. In the _Protest_ presently noted he discovered that "the force
taken as 1 is equal to the sum of all its fractions ... thus 1 = 1/4 + 1/9
+ 1/16 + 1/25, &c., carried to infinity." This the mathematician instantly
sees is equivalent to the theorem that the circumference of any circle is
double of the diagonal of the cube on its diameter.[562]

I have examined the following works of Sir R. Phillips, and heard of many
others:

    Essays on the proximate mechanical causes of the general phenomena of
    the Universe, 1818, 12mo.[563]

    Protest against the prevailing principles of natural philosophy, with
    the development of a common sense system (no date, 8vo, pp. 16).[564]

    Four dialogues between an Oxford Tutor and a disciple of the
    common-sense philosophy, relative to the proximate causes of material
    phenomena. 8vo, 1824.

    A century of original aphorisms on the proximate causes of the
    phenomena of nature, 1835, 12mo.

Sir Richard Phillips had four valuable qualities; honesty, zeal, ability,
and courage. He applied them all to teaching {246} matters about which he
knew nothing; and gained himself an uncomfortable life and a ridiculous
memory.



    Astronomy made plain; or only way the true perpendicular distance of
    the Sun, Moon, or Stars, from this earth, can be obtained. By Wm.
    Wood.[565] Chatham, 1819, 12mo.

If this theory be true, it will follow, of course, that this earth is the
only one God made, and that it does not whirl round the sun, but _vice
versa_, the sun round it.



WHATELY'S FAMOUS PARADOX.

    Historic doubts relative to Napoleon Buonaparte. London, 1819, 8vo.

This tract has since been acknowledged by Archbishop Whately[566] and
reprinted. It is certainly a paradox: but differs from most of those in my
list as being a joke, and a satire upon the reasoning of those who cannot
receive narrative, no matter what the evidence, which is to them utterly
improbable _a priori_. But had it been serious earnest, it would not have
been so absurd as many of those which I have brought forward. The next on
the list is not a joke.

The idea of the satire is not new. Dr. King,[567] in the dispute on the
genuineness of Phalaris, proved with humor that Bentley did not write his
own dissertation. An attempt has lately been made, for the honor of Moses,
to prove, {247} without humor, that Bishop Colenso did not write his own
book. This is intolerable: anybody who tries to use such a weapon without
banter, plenty and good, and of form suited to the subject, should get the
drubbing which the poor man got in the Oriental tale for striking the
dervishes with the wrong hand.

The excellent and distinguished author of this tract has ceased to live. I
call him the Paley of our day: with more learning and more purpose than his
predecessor; but perhaps they might have changed places if they had changed
centuries. The clever satire above named is not the only work which he
published without his name. The following was attributed to him, I believe
rightly: "Considerations on the Law of Libel, as relating to Publications
on the subject of Religion, by John Search." London, 1833, 8vo. This tract
excited little attention: for those who should have answered, could not.
Moreover, it wanted a prosecution to call attention to it: the fear of
calling such attention may have prevented prosecutions. Those who have read
it will have seen why.

The theological review elsewhere mentioned attributes the pamphlet of John
Search on blasphemous libel to Lord Brougham. This is quite absurd: the
writer states points of law on credence where the judge must have spoken
with authority. Besides which, a hundred points of style are decisive
between the two. I think any one who knows Whately's writing will soon
arrive at my conclusion. Lord Brougham himself informs me that he has no
knowledge whatever of the pamphlet.

It is stated in _Notes and Queries_ (3 S. xi. 511) that Search was answered
by the Bishop of Ferns[568] as S. N., with {248} a rejoinder by Blanco
White.[569] These circumstances increase the probability that Whately was
written against and for.



    VOLTAIRE A CHRISTIAN.

    Voltaire Chrétien; preuves tirées de ses ouvrages. Paris, 1820, 12mo.

If Voltaire have not succeeded in proving himself a strong theist and a
strong anti-revelationist, who is to succeed in proving himself one thing
or the other in any matter whatsoever? By occasional confusion between
theism and Christianity; by taking advantage of the formal phrases of
adhesion to the Roman Church, which very often occur, and are often the
happiest bits of irony in an ironical production; by citations of his
morality, which is decidedly Christian, though often attributed to
Brahmins; and so on--the author makes a fair case for his paradox, in the
eyes of those who know no more than he tells them. If he had said that
Voltaire was a better Christian than himself knew of, towards all mankind
except men of letters, I for one should have agreed with him.

_Christian!_ the word has degenerated into a synonym of _man_, in what are
called Christian countries. So we have the parrot who "swore for all the
world like a Christian," and the two dogs who "hated each other just like
Christians." When the Irish duellist of the last century, whose name may be
spared in consideration of its historic fame {249} and the worthy people
who bear it, was (June 12, 1786) about to take the consequence of his last
brutal murder, the rope broke, and the criminal got up, and exclaimed, "By
---- Mr. Sheriff, you ought to be ashamed of yourself! this rope is not
strong enough to hang a dog, far less a Christian!" But such things as this
are far from the worst depravations. As to a word so defiled by usage, it
is well to know that there is a way of escape from it, without renouncing
the New Testament. I suppose any one may assume for himself what I have
sometimes heard contended for, that no New Testament word is to be used in
religion in any sense except that of the New Testament. This granted, the
question is settled. The word _Christian_, which occurs three times, is
never recognized as anything but a term of contempt from those without the
pale to those within. Thus, Herod Agrippa, who was deep in Jewish
literature, and a correspondent of Josephus, says to Paul (Acts xxvi. 28),
"Almost thou persuadest me to be (what I and other followers of the state
religion despise under the name) a Christian." Again (Acts xi. 26), "The
disciples (as they called _themselves_) were called (by the surrounding
heathens) Christians first in Antioch." Thirdly (1 Peter iv. 16), "Let none
of you suffer as a _murderer_.... But if as a _Christian_ (as the heathen
call it by whom the suffering comes), let him not be ashamed." That is to
say, no _disciple_ ever called _himself_ a Christian, or applied the name,
as from himself, to another disciple, from one end of the New Testament to
the other; and no disciple need apply that name to himself in our day, if
he dislike the associations with which the conduct of Christians has
clothed it.



WRONSKI ON THE LONGITUDE PROBLEM.

    Address of M. Hoene Wronski to the British Board of Longitude, upon the
    actual state of the mathematics, their reform, {250} and upon the new
    celestial mechanics, giving the definitive solution of the problem of
    longitude.[570] London, 1820, 8vo.

M. Wronski[571] was the author of seven quartos on mathematics, showing
very great power of generalization. He was also deep in the transcendental
philosophy,[572] and had the Absolute at his fingers' ends. All this
knowledge was rendered useless by a persuasion that he had greatly advanced
beyond the whole world, with many hints that the Absolute would not be
forthcoming, unless prepaid. He was a man of the widest extremes. At one
time he desired people to see all possible mathematics in

  F_x_ = A_{0}[Omega]_{0} + A_{1}[Omega]_{1} + A_{2}[Omega]_{2} +
      A_{3}[Omega]_{3} + &c.

which he did not explain, though there is meaning to it in the quartos. At
another time he was proposing the general solution of the[573] fifth degree
by help of 625 independent equations of one form and 125 of another. The
first separate memoir from any Transactions that I ever possessed was given
to me when at Cambridge; the refutation (1819) of this asserted solution,
presented to the Academy of Lisbon by Evangelista Torriano. I cannot say I
read it. The tract above is an attack on modern mathematicians in general,
and on the Board of Longitude, and Dr. Young.[574]

{251}



DR. MILNER'S PARADOXES.

1820. In this year died Dr. Isaac Milner,[575] President of Queens'
College, Cambridge, one of the class of rational paradoxers. Under this
name I include all who, in private life, and in matters which concern
themselves, take their own course, and suit their own notions, no matter
what other people may think of them. These men will put things to uses they
were never intended for, to the great distress and disgust of their
gregarious friends. I am one of the class, and I could write a little book
of cases in which I have incurred absolute reproach for not "doing as other
people do." I will name two of my atrocities: I took one of those
butter-dishes which have for a top a dome with holes in it, which is turned
inward, out of reach of accident, when not in use. Turning the dome
inwards, I filled the dish with water, and put a sponge in the dome: the
holes let it fill with water, and I had a penwiper, always moist, and worth
its price five times over. "Why! what do you mean? It was made to hold
butter. You are always at some queer thing or other!" I bought a leaden
comb, intended to dye the hair, it being supposed that the application of
lead will have this effect. I did not try: but I divided the comb into two,
separated the part of closed prongs from the other; and thus I had two
ruling machines. The lead marks paper, and by drawing the end of one of the
machines along a ruler, I could rule twenty lines at a time, quite fit to
write on. I thought I should have killed a friend to whom I explained it:
he could not for the life of him understand how leaden _lines_ on paper
would dye the hair.

But Dr. Milner went beyond me. He wanted a seat suited to his shape, and he
defied opinion to a fearful point. {252} He spread a thick block of putty
over a wooden chair and sat in it until it had taken a ceroplast copy of
the proper seat. This he gave to a carpenter to be imitated in wood. One of
the few now living who knew him--my friend, General Perronet
Thompson[576]--answers for the wood, which was shown him by Milner himself;
but he does not vouch for the material being putty, which was in the story
told me at Cambridge; William Frend[577] also remembered it. Perhaps the
Doctor took off his great seal in green wax, like the Crown; but some soft
material he certainly adopted; and very comfortable he found the wooden
copy.

[Illustration]

The same gentleman vouches for Milner's lamp: but this had visible
_science_ in it; the vulgar see no science in the construction of the
chair. A hollow semi-cylinder, but not with a circular curve, revolved on
pivots. The curve was calculated on the law that, whatever quantity of oil
might be in the lamp, the position of equilibrium just brought the oil up
to the edge of the cylinder, at which a bit of wick was placed. As the wick
exhausted the oil, the cylinder slowly revolved about the pivots so as to
keep the oil always touching the wick.

Great discoveries are always laughed at; but it is very often not the laugh
of incredulity; it is a mode of distorting the sense of inferiority into a
sense of superiority, or a mimicry of superiority interposed between the
laugher and his feeling of inferiority. Two persons in conversation {253}
agreed that it was often a nuisance not to be able to lay hands on a bit of
paper to mark the place in a book, every bit of paper on the table was sure
to contain something not to be spared. I very quietly said that I always
had a stock of bookmarkers ready cut, with a proper place for them: my
readers owe many of my anecdotes to this absurd practice. My two
colloquials burst into a fit of laughter; about what? Incredulity was out
of the question; and there could be nothing foolish in my taking measures
to avoid what they knew was an inconvenience. I was in this matter
obviously their superior, and so they laughed at me. Much more candid was
the Royal Duke of the last century, who was noted for slow ideas. "The rain
comes into my mouth," said he, while riding. "Had not your Royal Highness
better shut your mouth?" said the equerry. The Prince did so, and ought, by
rule, to have laughed heartily at his adviser; instead of this, he said
quietly, "It doesn't come in now."



HERBART'S MATHEMATICAL PSYCHOLOGY.

    De Attentionis mensura causisque primariis. By J. F. Herbart.[578]
    Koenigsberg, 1822, 4to.

{254}

This celebrated philosopher maintained that mathematics ought to be applied
to psychology, in a separate tract, published also in 1822: the one above
seems, therefore, to be his challenge on the subject. It is on _attention_,
and I think it will hardly support Herbart's thesis. As a specimen of his
formula, let _t_ be the time elapsed since the consideration began, [beta]
the whole perceptive intensity of the individual, [phi] the whole of his
mental force, and _z_ the force given to a notion by attention during the
time _t_. Then,

z = [phi] (1 - [epsilon]^{-[beta]t})

Now for a test. There is a _jactura_, _v_, the meaning of which I do not
comprehend. If there be anything in it, my mathematical readers ought to
interpret it from the formula

_v_ = [pi][phi][beta]/(1 - [beta])[epsilon]^{-[beta]t} + C[epsilon]^{-t}

and to this task I leave them, wishing them better luck than mine. The time
may come when other manifestations of mind, besides _belief_, shall be
submitted to calculation: at that time, should it arrive, a final decision
may be passed upon Herbart.



ON THE WHIZGIG.

    The theory of the Whizgig considered; in as much as it mechanically
    exemplifies the three working properties of nature; which are now set
    forth under the guise of this toy, for children of all ages. London,
    1822, 12mo (pp. 24, B. McMillan, Bow Street, Covent Garden).

The toy called the _whizgig_ will be remembered by many. The writer is a
follower of Jacob Behmen,[579] William Law,[580] {255} Richard Clarke,[581]
and Eugenius Philalethes.[582] Jacob Behmen first announced the three
working properties of nature, which Newton stole, as described in the
_Gentleman's Magazine_, July, 1782, p. 329. These laws are illustrated in
the whizgig. There is the harsh astringent, attractive compression; the
bitter compunction, repulsive expansion; and the stinging anguish, duplex
motion. The author hints that he has written other works, to which he gives
no clue. I have heard that Behmen was pillaged by Newton, and
Swedenborg[583] by Laplace,[584] and Pythagoras by Copernicus,[585] and
Epicurus by Dalton,[586] &c. I do not think this mention will revive
Behmen; but it may the whizgig, a very pretty toy, and philosophical
withal, for few of those who used it could explain it.

{256}



SOME MYTHOLOGICAL PARADOXES.

    A Grammar of infinite forms; or the mathematical elements of ancient
    philosophy and mythology. By Wm. Howison.[587] Edinburgh, 1823, 8vo.

A curius combination of geometry and mythology. Perseus, for instance, is
treated under the head, "the evolution of diminishing hyperbolic branches."



    The Mythological Astronomy of the Ancients; part the second: or the key
    of Urania, the words of which will unlock all the mysteries of
    antiquity. Norwich, 1823, 12mo.

    A Companion to the Mythological Astronomy, &c., containing remarks on
    recent publications.... Norwich, 1824, 12mo.

    A new Theory of the Earth and of planetary motion; in which it is
    demonstrated that the Sun is vicegerent of his own system. Norwich,
    1825, 12mo.

    The analyzation of the writings of the Jews, so far as they are found
    to have any connection with the sublime science of astronomy. [This is
    pp. 97-180 of some other work, being all I have seen.]

These works are all by Sampson Arnold Mackey,[588] for whom see _Notes and
Queries_, 1st S. viii. 468, 565, ix. 89, 179. Had it not been for actual
quotations given by one correspondent only (1st S. viii. 565), that journal
would have handed him down as a man of some real learning. An extraordinary
man he certainly was: it is not one illiterate shoemaker in a thousand who
could work upon such a singular mass of Sanskrit and Greek words, without
showing {257} evidence of being able to read a line in any language but his
own, or to spell that correctly. He was an uneducated Godfrey Higgins.[589]
A few extracts will put this in a strong light: one for history of science,
one for astronomy, and one for philology:

"Sir Isaac Newton was of opinion that 'the atmosphere of the earth was the
sensory of God; by which he was enabled to see quite round the earth:'
which proves that Sir Isaac had no idea that God could see through the
earth.

"Sir Richard [Phillips] has given the most rational explanation of the
cause of the earth's elliptical orbit that I have ever seen in print. It is
because the earth presents its watery hemisphere to the sun at one time and
that of solid land the other; but why has he made his Oxonian astonished at
the coincidence? It is what I taught in my attic twelve years before.

"Again, admitting that the Eloim were powerful and intelligent beings that
managed these things, we would accuse _them_ of being the authors of all
the sufferings of Chrisna. And as they and the constellation of Leo were
below the horizon, and consequently cut off from the end of the zodiac,
there were but eleven constellations of the zodiac to be seen; the three at
the end were wanted, but those three would be accused of bringing Chrisna
into the troubles which at last ended in his death. All this would be
expressed in the Eastern language by saying that Chrisna was persecuted by
those Judoth Ishcarioth!!!!! [the five notes of exclamation are the
author's]. But the astronomy of those distant ages, when the sun was at the
south pole in winter, would leave five of those Decans cut off from our
view, in the latitude of twenty-eight degrees; hence Chrisna died of {258}
wounds from five Decans, but the whole five may be included in Judoth
Ishcarioth! for the phrase means 'the men that are wanted at the extreme
parts.' Ishcarioth is a compound of _ish_, a man, and _carat_ wanted or
taken away, and oth the plural termination, more ancient than _im_...."

I might show at length how Michael is the sun, and the D'-ev-'l in French
Di-ob-al, also 'L-evi-ath-an--the evi being the radical part both of
d_evi_l and l_evi_athan--is the Nile, which the sun dried up for Moses to
pass: a battle celebrated by Jude. Also how _Moses_, the same name as
_Muses_, is from _mesha_, drawn out of the water, "and hence we called our
land which is saved from the water by the name of _marsh_." But it will be
of more use to collect the character of S. A. M. from such correspondents
of _Notes and Queries_ as have written after superficial examination. Great
astronomical and philological attainments, much ability and learning; had
evidently read and studied deeply; remarkable for the originality of his
views upon the very abstruse subject of mythological astronomy, in which he
exhibited great sagacity. Certainly his views were _original_; but their
sagacity, if it be allowable to copy his own mode of etymologizing, is of
an _ori-gin-ale_ cast, resembling that of a person who puts to his mouth
liquors both distilled and fermented.



A KANTESIAN JEWELER.

    Principles of the Kantesian, or transcendental philosophy. By Thomas
    Wirgman.[590] London, 1824, 8vo.

Mr. Wirgman's mind was somewhat attuned to psychology; but he was cracky
and vagarious. He had been a fashionable jeweler in St. James's Street, no
doubt the son or grandson of Wirgman at "the well-known toy-shop in {259}
St. James's Street," where Sam Johnson smartened himself with silver
buckles. (Boswell, _æt._ 69). He would not have the ridiculous large ones
in fashion; and he would give no more than a guinea a pair; such, says
Boswell, in Italics, were the _principles_ of the business: and I think
this may be the first place in which the philosophical word was brought
down from heaven to mix with men. However this may be, _my_ Wirgman sold
snuff-boxes, among other things, and fifty years ago a fashionable
snuff-boxer would be under inducement, if not positively obliged, to have a
stock with very objectionable pictures. So it happened that Wirgman--by
reason of a trifle too much candor--came under the notice of the
_Suppression_ Society, and ran considerable risk. Mr. Brougham was his
counsel; and managed to get him acquitted. Years and years after this, when
Mr. Brougham was deep in the formation of the London University (now
University College), Mr. Wirgman called on him. "What now?" said Mr. B.
with his most sarcastic look--a very perfect thing of its kind--"you're in
a scrape again, I suppose!" "No! indeed!" said W., "my present object is to
ask your interest for the chair of Moral Philosophy in the new University!"
He had taken up Kant!

Mr. Wirgman, an itinerant paradoxer, called on me in 1831: he came to
convert me. "I assure you," said he, "I am nothing but an old brute of a
jeweler;" and his eye and manner were of the extreme of jocosity, as good
in their way, as the satire of his former counsel. I mention him as one of
that class who go away quite satisfied that they have wrought conviction.
"Now," said he, "I'll make it clear to you! Suppose a number of gold-fishes
in a glass bowl,--you understand? Well! I come with my cigar and go puff,
puff, puff, over the bowl, until there is a little cloud of smoke: now,
tell me, what will the gold-fishes say to that?" "I should imagine," said
I, "That they would not know what to make of it." "By Jove! you're a
Kantian;" said he, and with this and the like, he left me, vowing that
{260} it was delightful to talk to so intelligent a person. The greatest
compliment Wirgman ever received was from James Mill, who used to say he
did not _understand_ Kant. That such a man as Mill should think this worth
saying is a feather in the cap of the jocose jeweler.

Some of my readers will stare at my supposing that Boswell may have been
the first down-bringer of the word _principles_ into common life; the best
answer will be a prior instance of the word as true vernacular; it has
never happened to me to notice one. Many words have very common uses which
are not old. Take the following from Nichols (_Anecd._ ix. 263): "Lord
Thurlow presents his best respects to Mr. and Mrs. Thicknesse, and assures
them that he knows of no cause to complain of any part of Mr. Thicknesse's
carriage; least of all the circumstance of sending the head to Ormond
Street." Surely Mr. T. had lent Lord T. a satisfactory carriage with a
movable head, and the above is a polite answer to inquiries. Not a bit of
it! _carriage_ is here _conduct_, and the _head_ is a _bust_. The vehicles
of the rich, at the time, were coaches, chariots, chaises, etc., never
carriages, which were rather _carts_. Gibbon has the word for
baggage-wagons. In Jane Austen's novels the word carriage is established.



WALSH'S DELUSIONS.

_John Walsh_,[591] of Cork (1786-1847). This discoverer has had the honor
of a biography from Professor Boole, who, at my request, collected
information about him on the scene of his labors. It is in the
_Philosophical Magazine_ for November, 1851, and will, I hope, be
transferred to some biographical collection where it may find a larger
class of readers. It is the best biography of a single hero of the kind
that I know. Mr. Walsh introduced himself to me, {261} as he did to many
others, in the anterowlandian days of the Post-office; his unpaid letters
were double, treble, &c. They contained his pamphlets, and cost their
weight in silver: all have the name of the author, and all are in octavo or
in quarto letter-form: most are in four pages, and all dated from Cork. I
have the following by me:

    The Geometric Base, 1825.--The theory of plane angles. 1827.--Three
    Letters to Dr. Francis Sadleir. 1838.--The invention of polar geometry.
    By Irelandus. 1839.--The theory of partial functions. Letter to Lord
    Brougham. 1839.--On the invention of polar geometry. 1839.--Letter to
    the Editor of the Edinburgh Review. 1840.--Irish Manufacture. A new
    method of tangents. 1841.--The normal diameter in curves. 1843.--Letter
    to Sir R. Peel. 1845.--[Hints that Government should compel the
    introduction of Walsh's Geometry into Universities.]--Solution of
    Equations of the higher orders. 1845.

Besides these, there is a _Metalogia_, and I know not how many others.

Mr. Boole,[592] who has taken the moral and social features of Walsh's
delusions from the commiserating point of view, which makes ridicule out of
place, has been obliged to treat Walsh as Scott's Alan Fairford treated his
client Peter Peebles; namely, keep the scarecrow out of court while the
case was argued. My plan requires me to bring him in: and when he comes in
at the door, pity and sympathy fly out at the window. Let the reader
remember that he was not an ignoramus in mathematics: he might have won his
spurs if he could have first served as an esquire. Though so illiterate
that even in Ireland he never picked up anything more Latin than
_Irelandus_, he was a very pretty mathematician spoiled in the making by
intense self-opinion.

This is part of a private letter to me at the back of a page of print: I
had never addressed a word to him:

{262}

"There are no limits in mathematics, and those that assert there are, are
infinite ruffians, ignorant, lying blackguards. There is no differential
calculus, no Taylor's theorem, no calculus of variations, &c. in
mathematics. There is no quackery whatever in mathematics; no % equal to
anything. What sheer ignorant blackguardism that!

"In mechanics the parallelogram of forces is quackery, and is dangerous;
for nothing is at rest, or in uniform, or in rectilinear motion, in the
universe. Variable motion is an essential property of matter. Laplace's
demonstration of the parallelogram of forces is a begging of the question;
and the attempts of them all to show that the difference of twenty minutes
between the sidereal and actual revolution of the earth round the sun
arises from the tugging of the Sun and Moon at the pot-belly of the earth,
without being sure even that the earth has a pot-belly at all, is perfect
quackery. The said difference arising from and demonstrating the revolution
of the Sun itself round some distant center."

In the letter to Lord Brougham we read as follows:

"I ask the Royal Society of London, I ask the Saxon crew of that crazy
hulk, where is the dogma of their philosophic god now?... When the Royal
Society of London, and the Academy of Sciences of Paris, shall have read
this memorandum, how will they appear? Like two cur dogs in the paws of the
noblest beast of the forest.... Just as this note was going to press, a
volume lately published by you was put into my hands, wherein you attempt
to defend the fluxions and _Principia_ of Newton. Man! what are you about?
You come forward now with your special pleading, and fraught with national
prejudice, to defend, like the philosopher Grassi,[593] the persecutor of
Galileo, principles {263} and reasoning which, unless you are actually
insane, or an ignorant quack in mathematics, you know are mathematically
false. What a moral lesson this for the students of the University of
London from its head! Man! demonstrate corollary 3, in this note, by the
lying dogma of Newton, or turn your thoughts to something you understand.

"WALSH IRELANDUS."

Mr. Walsh--honor to his memory--once had the consideration to save me
postage by addressing a pamphlet under cover to a Member of Parliament,
with an explanatory letter. In that letter he gives a candid opinion of
himself:

(1838.) "Mr. Walsh takes leave to send the enclosed corrected copy to Mr.
Hutton as one of the Council of the University of London, and to save
postage for the Professor of Mathematics there. He will find in it geometry
more deep and subtle, and at the same time more simple and elegant, than it
was ever contemplated human genius could invent."

He then proceeds to set forth that a certain "tomfoolery lemma," with its
"tomfoolery" superstructure, "never had existence outside the shallow
brains of its inventor," Euclid. He then proceeds thus:

"The same spirit that animated those philosophers who sent Galileo to the
Inquisition animates all the philosophers of the present day without
exception. If anything can free them from the yoke of error, it is the
[Walsh] problem of double tangence. But free them it will, how deeply
soever they may be sunk into mental slavery--and God knows that is deeply
enough; and they bear it with an admirable grace; for none bear slavery
with a better grace than tyrants. The lads must adopt my theory.... It will
be a sad reverse for all our great professors to be compelled to become
schoolboys in their gray years. But the sore scratch is to be compelled, as
they had before been compelled one thousand years ago, to have recourse to
Ireland for instruction." {264}

The following "Impromptu" is no doubt by Walsh himself: he was more of a
poet than of an astronomer:

   "Through ages unfriended,
    With sophistry blended,
  Deep science in Chaos had slept;
    Its limits were fettered,
    Its voters unlettered,
  Its students in movements but crept.
    Till, despite of great foes,
    Great WALSH first arose,
  And with logical might did unravel
    Those mazes of knowledge,
    Ne'er known in a college,
  Though sought for with unceasing travail.
    With cheers we now hail him,
    May success never fail him,
  In Polar Geometrical mining;
    Till his foes be as tamed
    As his works are far-famed
  For true philosophic refining."

Walsh's system is, that all mathematics and physics are wrong: there is
hardly one proposition in Euclid which is demonstrated. His example ought
to warn all who rely on their own evidence to their own success. He was
not, properly speaking, insane; he only spoke his mind more freely than
many others of his class. The poor fellow died in the Cork union, during
the famine. He had lived a happy life, contemplating his own perfections,
like Brahma on the lotus-leaf.[594]

{265}



GROWTH OF FREEDOM OF OPINION.

The year 1825 brings me to about the middle of my _Athenæum_ list: that is,
so far as mere number of names mentioned is concerned. Freedom of opinion,
beyond a doubt, is gaining ground, for good or for evil, according to what
the speaker happens to think: admission of authority is no longer made in
the old way. If we take soul-cure and body-cure, divinity and medicine, it
is manifest that a change has come over us. Time was when it was enough
that dose or dogma should be certified by "Il a été ordonné, Monsieur, il a
été ordonné,"[595] as the apothecary said when he wanted to operate upon
poor de Porceaugnac. Very much changed: but whether for good or for evil
does not now matter; the question is, whether contempt of _demonstration_
such as our paradoxers show has augmented with the rejection of _dogmatic
authority_. It ought to be just the other way: for the worship of reason is
the system on which, if we trust them, the deniers of guidance ground their
plan of life. The following attempt at an experiment on this point is the
best which I can make; and, so far as I know, the first that ever was made.

Say that my list of paradoxers divides in 1825: this of itself proves
nothing, because so many of the earlier books are lost, or not likely to be
come at. It would be a fearful rate of increase which would make the number
of paradoxes since 1825 equal to the whole number before that date. Let us
turn now to another collection of mine, arithmetical books, of which I have
published a list. The two collections are similarly circumstanced as to new
and old books; the paradoxes had no care given to the collection of either;
the arithmetical books equal care to both. The list of arithmetical books,
published in 1847, divides at 1735; the paradoxes, up to 1863, divide at
1825. If we take the process which is most against the distinction, and
allow every year {266} from 1847 to 1863 to add a year to 1735, we should
say that the arithmetical writers divide at 1751. This rough process may
serve, with sufficient certainty, to show that the proportion of paradoxes
to books of sober demonstration is on the increase; and probably, quite as
much as the proportion of heterodoxes to books of orthodox adherence. So
that divinity and medicine may say to geometry, Don't _you_ sneer: if
rationalism, homoeopathy, and their congeners are on the rise among us,
your enemies are increasing quite as fast. But geometry replies--Dear
friends, content yourselves with the rational inference that the rise of
heterodoxy within your pales is not conclusive against you, taken alone;
for it rises at the same time within mine. Store within your garners the
precious argument that you are not proved wrong by increase of dissent;
because there is increase of dissent against exact science. But do not
therefore _even_ yourselves to me: remember that you, Dame Divinity, have
inflicted every kind of penalty, from the stake to the stocks, in aid of
your reasoning; remember that you, Mother Medicine, have not many years ago
applied to Parliament for increase of forcible hindrance of
antipharmacopoeal drenches, pills, and powders. Who ever heard of my asking
the legislature to fine blundering circle-squarers? Remember that the D in
dogma is the D in decay; but the D in demonstration is the D in durability.



THE STATUS OF MEDICINE.

I have known a medical man--a young one--who was seriously of the opinion
that the country ought to be divided into medical parishes, with a
practitioner appointed to each, and a penalty for calling in any but the
incumbent curer. How should people know how to choose? The hair-dressers
once petitioned Parliament for an act to compel people to wear wigs. My own
opinion is of the opposite extreme, as in the following letter (_Examiner_,
April 5, 1856); which, to my surprise, I saw reprinted in a medical
journal, as a {267} plan not absolutely to be rejected. I am perfectly
satisfied that it would greatly promote true medical orthodoxy, the
predominance of well educated thinkers, and the development of their
desirable differences.



"SIR. The Medical Bill and the medical question generally is one on which
experience would teach, if people would be taught.

"The great soul question took three hundred years to settle: the little
body question might be settled in thirty years, if the decisions in the
former question were studied.

"Time was when the State believed, as honestly as ever it believed
anything, that it _might_, _could_, and _should_ find out the true doctrine
for the poor ignorant community; to which, like a worthy honest state, it
added _would_. Accordingly, by the assistance of the Church, which
undertook the physic, the surgery, and the pharmacy of sound doctrine all
by itself, it sent forth its legally qualified teachers into every parish,
and woe to the man who called in any other. They burnt that man, they
whipped him, they imprisoned him, they did everything but what was
Christian to him, all for his soul's health and the amendment of his
excesses.

"But men would not submit. To the argument that the State was a father to
the ignorant, they replied that it was at best the ignorant father of an
ignorant son, and that a blind man could find his way into a ditch without
another blind man to help him. And when the State said--But here we have
the Church, which knows all about it, the ignorant community declared that
it had a right to judge that question, and that it would judge it. It also
said that the Church was never one thing long, and that it progressed, on
the whole, rather more slowly than the ignorant community.

"The end of it was, in this country, that every one who chose taught all
who chose to let him teach, on condition only of an open and true
registration. The State was {268} allowed to patronize one particular
Church, so that no one need trouble himself to choose a pastor from the
mere necessity of choosing. But every church is allowed its colleges, its
studies, its diplomas; and every man is allowed his choice. There is no
proof that our souls are worse off than in the sixteenth century; and,
judging by fruits, there is much reason to hope they are better off.

"Now the little body question is a perfect parallel to the great soul
question in all its circumstances. The only things in which the parallel
fails are the following: Every one who believes in a future state sees that
the soul question is incomparably more important than the body question,
and every one can try the body question by experiment to a larger extent
than the soul question. The proverb, which always has a spark of truth at
the bottom, says that every man of forty is either a fool or a physician;
but did even the proverb maker ever dare to say that every man is at any
age either a fool or a fit teacher of religion?

"Common sense points out the following settlement of the medical question:
and to this it will come sooner or later.

"Let every man who chooses--subject to one common law of manslaughter for
all the _crass_ cases--doctor the bodies of all who choose to trust him,
and recover payment according to agreement in the courts of law. Provided
always that every person practising should be registered at a moderate fee
in a register to be republished every six months.

"Let the register give the name, address, and asserted qualification of
each candidate--as licentiate, or doctor, or what not, of this or that
college, hall, university, &c., home or foreign. Let it be competent to any
man to describe himself as qualified by study in public schools without a
diploma, or by private study, or even by intuition or divine inspiration,
if he please. But whatever he holds his qualification to be, that let him
declare. Let all qualification {269} which of its own nature admits of
proof be proved, as by the diploma or certificate, &c., leaving things
which cannot be proved, as asserted private study, intuition, inspiration,
&c., to work their own way.

"Let it be highly penal to assert to the patient any qualification which is
not in the register, and let the register be sold very cheap. Let the
registrar give each registered practitioner a copy of the register in his
own case; let any patient have the power to demand a sight of this copy;
and let no money for attendance be recoverable in any case in which there
has been false representation.

"Let any party in any suit have a right to produce what medical testimony
he pleases. Let the medical witness produce his register, and let his
evidence be for the jury, as is that of an engineer or a practitioner of
any art which is not attested by diplomas.

"Let any man who practises without venturing to put his name on the
register be liable to fine and imprisonment.

"The consequence would be that, as now, anybody who pleases might practise;
for the medical world is well aware that there is no power of preventing
what they call quacks from practising. But very different from what is now,
every man who practises would be obliged to tell the whole world what his
claim is, and would run a great risk if he dared to tell his patient in
private anything different from what he had told the whole world.

"The consequence would be that a real education in anatomy, physiology,
chemistry, surgery, and what is known of the thing called medicine, would
acquire more importance than it now has.

"It is curious to see how completely the medical man of the nineteenth
century squares with the priest of the sixteenth century. The clergy of all
sects are now better divines and better men than they ever were. They have
lost Bacon's reproach that they took a smaller measure of things than any
other educated men; and the physicians are now {270} in this particular the
rearguard of the learned world; though it may be true that the rear in our
day is further on in the march than the van of Bacon's day. Nor will they
ever recover the lost position until medicine is as free as religion.

"To this it must come. To this the public, which will decide for itself,
has determined it shall come. To this the public has, in fact, brought it,
but on a plan which it is not desirable to make permanent. We will be as
free to take care of our bodies as of our souls and of our goods. This is
the profession of all who sign as I do, and the practice of most of those
who would not like the name

"HETEROPATH."



    The motion of the Sun in the Ecliptic, proved to be uniform in a
    circular orbit ... with preliminary observations on the fallacy of the
    Solar System. By Bartholomew Prescott,[596] 1825, 8vo.

The author had published, in 1803, a _Defence of the Divine System_, which
I never saw; also, _On the inverted scheme of Copernicus_. The above work
is clever in its satire.



THE CHRISTIAN EVIDENCE SOCIETY.

    Manifesto of the Christian Evidence Society, established Nov. 12, 1824.
    Twenty-four plain questions to honest men.

These are two broadsides of August and November, 1826, signed by Robert
Taylor,[597] A.B., Orator of the Christian Evidence Society. This gentleman
was a clergyman, {271} and was convicted of blasphemy in 1827, for which he
suffered imprisonment, and got the name of the _Devil's Chaplain_. The
following are quotations:

"For the book of Revelation, there was no original Greek at all, but
_Erasmus_ wrote it himself in Switzerland, in the year 1516. Bishop
Marsh,[598] vol. i. p. 320."--"Is not God the author of your reason? Can he
then be the author of anything which is contrary to your reason? If reason
be a sufficient guide, why should God give you any other? if it be not a
sufficient guide, why has he given you _that_?"

I remember a votary of the Society being asked to substitute for _reason_
"the right leg," and for _guide_ "support," and to answer the two last
questions: he said there must be a quibble, but he did not see what. It is
pleasant to reflect that the _argumentum à carcere_[599] is obsolete. One
great defect of it was that it did not go far enough: there should have
been laws against subscriptions for blasphemers, against dealing at their
shops, and against rich widows marrying them.

Had I taken in theology, I must have entered books against Christianity. I
mention the above, and Paine's _Age of Reason_, simply because they are the
only English modern works that ever came in my way without my asking for
them. The three parts of the _Age of Reason_ were published in Paris 1793,
Paris 1795, and New York 1807. Carlile's[600] edition is of London, 1818,
8vo. It must be republished when the time comes, to show what stuff
governments and clergy were afraid of at the beginning of this century. I
should never have seen the book, if it {272} had not been prohibited: a
bookseller put it under my nose with a fearful look round him; and I could
do no less, in common curiosity, than buy a work which had been so
complimented by church and state. And when I had read it, I said in my mind
to church and state,--Confound you! you have taken me in worse than any
reviewer I ever met with. I forget what I gave for the book, but I ought to
have been able to claim compensation somewhere.



THE CABBALA.

    Cabbala Algebraica. Auctore Gul. Lud. Christmann.[601] Stuttgard, 1827,
    4to.

Eighty closely printed pages of an attempt to solve equations of every
degree, which has a process called by the author _cabbala_. An anonymous
correspondent spells _cabbala_ as follows, [Greek: chabball], and makes 666
out of its letters. This gentleman has sent me since my Budget commenced, a
little heap of satirical communications, each having a 666 or two; for
instance, alluding to my remarks on the spelling of _chemistry_, he finds
the fated number in [Greek: chimeia]. With these are challenges to explain
them, and hints about the end of the world. All these letters have
different fantastic seals; one of them with the legend "keep your
temper,"--another bearing "bank token five pence." The only signature is a
triangle with a little circle in it, which I interpret to mean that the
writer confesses himself to be the round man stuck in the three-cornered
hole, to be explained as in Sydney Smith's joke.

{273}

There is a kind of Cabbala Alphabetica which the investigators of the
numerals in words would do well to take up: it is the formation of
sentences which contain all the letters of the alphabet, and each only
once. No one has done it with _v_ and _j_ treated as consonants; but you
and I can do it. Dr. Whewell[602] and I amused ourselves, some years ago,
with attempts. He could not make sense, though he joined words: he gave me

  Phiz, styx, wrong, buck, flame, quid.

I gave him the following, which he agreed was "admirable sense": I
certainly think the words would never have come together except in this
way:

  I, quartz pyx, who fling muck beds.

I long thought that no human being could say this under any circumstances.
At last I happened to be reading a religious writer--as he thought
himself--who threw aspersions on his opponents thick and threefold. Heyday!
came into my head, this fellow flings muck beds; he must be a quartz pyx.
And then I remembered that a pyx is a sacred vessel, and quartz is a hard
stone, as hard as the heart of a religious foe-curser. So that the line is
the motto of the ferocious sectarian, who turns his religious vessels into
mudholders, for the benefit of those who will not see what he sees.

I can find no circumstances for the following, which I received from
another:

  Fritz! quick! land! hew gypsum box.

From other quarters I have the following:

  Dumpy quiz! whirl back fogs next.

This might be said in time of haze to the queer little figure in the Dutch
weather-toy, which comes out or goes in with the change in the atmosphere.
Again,

{274}

  Export my fund!  Quiz black whigs.

This Squire Western might have said, who was always afraid of the whigs
sending the sinking-fund over to Hanover. But the following is the best: it
is good advice to a young man, very well expressed under the circumstances:

  Get nymph; quiz sad brow; fix luck.

Which in more sober English would be, Marry; be cheerful; watch your
business. There is more edification, more religion in this than in all the
666-interpretations put together.

Such things would make excellent writing copies, for they secure attention
to every letter; _v_ and _j_ might be placed at the end.



ON GODFREY HIGGINS.

    The Celtic Druids. By Godfrey Higgins,[603] Esq. of Skellow Grange,
    near Doncaster. London, 1827, 4to.

    Anacalypsis, or an attempt to draw aside the veil of the Saitic Isis:
    or an inquiry into the origin of languages, nations, and religions. By
    Godfrey Higgins, &c..., London, 1836, 2 vols. 4to.

The first work had an additional preface and a new index in 1829. Possibly,
in future time, will be found bound up with copies of the second work two
sheets which Mr. Higgins circulated among his friends in 1831: the first a
"Recapitulation," the second "Book vi. ch. 1."

The system of these works is that--

"The Buddhists of Upper India (of whom the Phenician Canaanite,
Melchizedek, was a priest), who built the Pyramids, Stonehenge, Carnac, &c.
will be shown to have founded all the ancient mythologies of the world,
which, however varied and corrupted in recent times, were originally one,
and that one founded on principles sublime, beautiful, and true."

{275}

These works contain an immense quantity of learning, very honestly put
together. I presume the enormous number of facts, and the goodness of the
index, to be the reasons why the _Anacalypsis_ found a permanent place in
the _old_ reading-room of the British Museum, even before the change which
greatly increased the number of books left free to the reader in that room.

Mr. Higgins, whom I knew well in the last six years of his life, and
respected as a good, learned, and (in his own way) _pious_ man, was
thoroughly and completely the man of a system. He had that sort of mental
connection with his theory that made his statements of his authorities
trustworthy: for, besides perfect integrity, he had no bias towards
alteration of facts: he saw his system in the way the fact was presented to
him by his authority, be that what it might.

He was very sure of a fact which he got from any of his authorities:
nothing could shake him. Imagine a conversation between him and an Indian
officer who had paid long attention to Hindoo antiquities and their
remains: a third person was present, _ego qui scribo_. _G. H._ "You know
that in the temples of I-forget-who the Ceres is always sculptured
precisely as in Greece." _Col._ ----, "I really do not remember it, and I
have seen most of these temples." _G. H._ "It is so, I assure you,
especially at I-forget-where." _Col._ ----, "Well, I am sure! I was
encamped for six weeks at the gate of that very temple, and, except a
little shooting, had nothing to do but to examine its details, which I did,
day after day, and I found nothing of the kind." It was of no use at all.

Godfrey Higgins began life by exposing and conquering, at the expense of
two years of his studies, some shocking abuses which existed in the York
Lunatic Asylum. This was a proceeding which called much attention to the
treatment of the insane, and produced much good effect. He was very
resolute and energetic. The magistracy of his {276} time had such scruples
about using the severity of law to people of such station as well-to-do
farmers, &c.: they would allow a great deal of resistance, and endeavor to
mollify the rebels into obedience. A young farmer flatly refused to pay
under an order of affiliation made upon him by Godfrey Higgins. He was duly
warned; and persisted: he shortly found himself in gaol. He went there sure
to conquer the Justice, and the first thing he did was to demand to see his
lawyer. He was told, to his horror, that as soon as he had been cropped and
prison-dressed, he might see as many lawyers as he pleased, to be looked
at, laughed at, and advised that there was but one way out of the scrape.
Higgins was, in his speculations, a regular counterpart of Bailly; but the
celebrated Mayor of Paris had not his nerve. It was impossible to say, if
their characters had been changed, whether the unfortunate crisis in which
Bailly was not equal to the occasion would have led to very different
results if Higgins had been in his place: but assuredly constitutional
liberty would have had one chance more. There are two works of his by which
he was known, apart from his paradoxes. First, _An apology for the life and
character of the celebrated prophet of Arabia, called Mohamed, or the
Illustrious_. London, 8vo. 1829. The reader will look at this writing of
our English Buddhist with suspicious eye, but he will not be able to avoid
confessing that the Arabian prophet has some reparation to demand at the
hands of Christians. Next, _Horæ Sabaticæ; or an attempt to correct certain
superstitions and vulgar errors respecting the Sabbath_. Second edition,
with a large appendix. London, 12mo. 1833. This book was very heterodox at
the time, but it has furnished material for some of the clergy of our day.

I never could quite make out whether Godfrey Higgins took that system which
he traced to the Buddhists to have a Divine origin, or to be the result of
good men's meditations. Himself a strong theist, and believer in a future
{277} state, one would suppose that he would refer a _universal_ religion,
spread in different forms over the whole earth from one source, directly to
the universal Parent. And this I suspect he did, whether he knew it or not.
The external evidence is balanced. In his preface he says:

"I cannot help smiling when I consider that the priests have objected to
admit my former book, _The Celtic Druids_, into libraries, because it was
antichristian; and it has been attacked by Deists, because it was
superfluously religious. The learned Deist, the Rev. R. Taylor [already
mentioned], has designated me as the _religious_ Mr. Higgins."

The time will come when some profound historian of literature will make
himself much clearer on the point than I am.



ON POPE'S DIPPING NEEDLE.

    The triumphal Chariot of Friction: or a familiar elucidation of the
    origin of magnetic attraction, &c. &c. By William Pope.[604] London,
    1829, 4to.

Part of this work is on a dipping-needle of the author's construction. It
must have been under the impression that a book of naval magnetism was
proposed, that a great many officers, the Royal Naval Club, etc. lent their
names to the subscription list. How must they have been surprised to find,
right opposite to the list of subscribers, the plate presenting "the three
emphatic letters, J. A. O." And how much more when they saw it set forth
that if a square be inscribed in a circle, a circle within that, then a
square again, &c., it is impossible to have more than fourteen circles, let
the first circle be as large as you please. From this the seven attributes
of God are unfolded; and further, that all matter was _moral_, until
Lucifer _churned_ it into _physical_ "as far as the third circle in Deity":
this Lucifer, called Leviathan in Job, being thus the moving cause of {278}
chaos. I shall say no more, except that the friction of the air is the
cause of magnetism.



    Remarks on the Architecture, Sculpture, and Zodiac of Palmyra; with a
    Key to the Inscriptions. By B. Prescot.[605] London, 1830, 8vo.

Mr. Prescot gives the signs of the zodiac a Hebrew origin.



THE JACOTOT METHOD.

    Epitomé de mathématiques. Par F. Jacotot,[606] Avocat. 3ième edition,
    Paris, 1830, 8vo. (pp. 18).

    Méthode Jacotot. Choix de propositions mathématiques. Par P. Y.
    Séprés.[607] 2nde édition. Paris, 1830, 8vo. (pp. 82).

Of Jacotot's method, which had some vogue in Paris, the principle was _Tout
est dans tout_,[608] and the process _Apprendre quelque chose, et à y
rapporter tout le reste_.[609] The first tract has a proposition in conic
sections and its preliminaries: the second has twenty exercises, of which
the first is finding the greatest common measure of two numbers, and the
last is the motion of a point on a surface, acted on by given forces. This
is topped up with the problem of sound in a tube, and a slice of Laplace's
theory of the tides. All to be studied until known by heart, and all the
rest will come, or at least join on easily when it comes. There is much
truth in the assertion that new knowledge {279} hooks on easily to a little
of the old, thoroughly mastered. The day is coming when it will be found
out that crammed erudition, got up for examinations, does not cast out any
hooks for more.



    Lettre à MM. les Membres de l'Académie Royale des Sciences, contenant
    un développement de la réfutation du système de la gravitation
    universelle, qui leur a été présentée le 30 août, 1830. Par Félix
    Passot.[610] Paris, 1830, 8vo.

Works of this sort are less common in France than in England. In France
there is only the Academy of Sciences to go to: in England there is a
reading public out of the Royal Society, &c.



A DISCOURSE ON PROBABILITY.

About 1830 was published, in the _Library of Useful Knowledge_, the tract
on _Probability_, the joint work of the late Sir John Lubbock[611] and Mr.
Drinkwater (Bethune).[612] It is one of the best elementary openings of the
subject. A binder put my name on the outside (the work was anonymous) and
the consequence was that nothing could drive out of people's heads that it
was written by me. I do not know how many denials I have made, from a
passage in one of my own works to a letter in the _Times_: and I am not
sure that I have succeeded in establishing the truth, even now. I
accordingly note the fact once more. But as a book has no right here unless
it contain a paradox--or thing counter to general opinion or practice--I
will produce two small ones. Sir John Lubbock, with whom lay the executive
arrangement, had a strong objection to the last word in "Theory of
Probabilities," he maintained that the singular _probability_, should be
used; and I hold him quite right.

{280}

The second case was this: My friend Sir J. L., with a large cluster of
intellectual qualities, and another of social qualities, had one point of
character which I will not call bad and cannot call good; he never used a
slang expression. To such a length did he carry his dislike, that he could
not bear _head_ and _tail_, even in a work on games of chance: so he used
_obverse_ and _reverse_. I stared when I first saw this: but, to my
delight, I found that the force of circumstances beat him at last. He was
obliged to take an example from the race-course, and the name of one of the
horses was _Bessy Bedlam_! And he did not put her down as _Elizabeth
Bethlehem_, but forced himself to follow the jockeys.



    [Almanach Romain sur la Loterie Royale de France, ou les Etrennes
    nécessaires aux Actionnaires et Receveurs de la dite Loterie. Par M.
    Menut de St.-Mesmin. Paris, 1830. 12mo.

This book contains all the drawings of the French lottery (two or three,
each month) from 1758 to 1830. It is intended for those who thought they
could predict the future drawings from the past: and various sets of
_sympathetic_ numbers are given to help them. The principle is, that
anything which has not happened for a long time must be soon to come. At
_rouge et noir_, for example, when the red has won five times running,
sagacious gamblers stake on the black, for they think the turn which must
come at last is nearer than it was. So it is: but observation would have
shown that if a large number of those cases had been registered which show
a run of five for the red, the next game would just as often have made the
run into six as have turned in favor of the black. But the gambling
reasoner is incorrigible: if he would but take to squaring the circle, what
a load of misery would be saved. A writer of 1823, who appeared to be
thoroughly acquainted with the gambling of Paris and London, says that the
gamesters by {281} profession are haunted by a secret foreboding of their
future destruction, and seem as if they said to the banker at the table, as
the gladiators said to the emperor, _Morituri te salutant_.[613]

In the French lottery, five numbers out of ninety were drawn at a time. Any
person, in any part of the country, might stake any sum upon any event he
pleased, as that 27 should be drawn; that 42 and 81 should be drawn; that
42 and 81 should be drawn, and 42 first; and so on up to a _quine
déterminé_, if he chose, which is betting on five given numbers in a given
order. Thus, in July, 1821, one of the drawings was

  8   46   16   64   13.

A gambler had actually predicted the five numbers (but not their order),
and won 131,350 francs on a trifling stake. M. Menut seems to insinuate
that the hint what numbers to choose was given at his own office. Another
won 20,852 francs on the quaterne, 8, 16, 46, 64, in this very drawing.
These gains, of course, were widely advertised: of the multitudes who lost
nothing was said. The enormous number of those who played is proved to all
who have studied chances arithmetically by the numbers of simple quaternes
which were gained: in 1822, fourteen; in 1823, six; in 1824, sixteen; in
1825, nine, &c.

The paradoxes of what is called chance, or hazard, might themselves make a
small volume. All the world understands that there is a long run, a general
average; but great part of the world is surprised that this general average
should be computed and predicted. There are many remarkable cases of
verification; and one of them relates to the quadrature of the circle. I
give some account of this and another. Throw a penny time after time until
_head_ arrives, which it will do before long: let this be called a _set_.
Accordingly, H is the smallest set, TH the next smallest, then TTH, &c. For
abbreviation, let a set in which seven _tails_ {282} occur before _head_
turns up be T^{7}H. In an immense number of trials of sets, about half will
be H; about a quarter TH; about an eighth, T^{2}H. Buffon[614] tried 2,048
sets; and several have followed him. It will tend to illustrate the
principle if I give all the results; namely, that many trials will with
moral certainty show an approach--and the greater the greater the number of
trials--to that average which sober reasoning predicts. In the first column
is the most likely number of the theory: the next column gives Buffon's
result; the three next are results obtained from trial by correspondents of
mine. In each case the number of trials is 2,048.

  H         1,024    1,061    1,048    1,017    1,039
  TH          512      494      507      547      480
  T^{2}H      256      232      248      235      267
  T^{3}H      128      137       99      118      126
  T^{4}H       64       56       71       72       67
  T^{5}H       32       29       38       32       33
  T^{6}H       16       25       17       10       19
  T^{7}H        8        8        9        9       10
  T^{8}H        4        6        5        3        3
  T^{9}H        2                 3        2        4
  T^{10}H       1                 1        1
  T^{11}H                         0        1
  T^{12}H                         0        0
  T^{13}H       1                 1        0
  T^{14}H                         0        0
  T^{15}H                         1        1
  &c.                             0        0
            -----    -----    -----    -----    -----
            2,048    2,048    2,048    2,048    2,048

{283}

In very many trials, then, we may depend upon something like the predicted
average. Conversely, from many trials we may form a guess at what the
average will be. Thus, in Buffon's experiment the 2,048 first throws of the
sets gave _head_ in 1,061 cases: we have a right to infer that in the long
run something like 1,061 out of 2,048 is the proportion of heads, even
before we know the reasons for the equality of chance, which tell us that
1,024 out of 2,048 is the real truth. I now come to the way in which such
considerations have led to a mode in which mere pitch-and-toss has given a
more accurate approach to the quadrature of the circle than has been
reached by some of my paradoxers. What would my friend[615] in No. 14 have
said to this? The method is as follows: Suppose a planked floor of the
usual kind, with thin visible seams between the planks. Let there be a thin
straight rod, or wire, not so long as the breadth of the plank. This rod,
being tossed up at hazard, will either fall quite clear of the seams, or
will lay across one seam. Now Buffon, and after him Laplace, proved the
following: That in the long run the fraction of the whole number of trials
in which a seam is intersected will be the fraction which twice the length
of the rod is of the circumference of the circle having the breadth of a
plank for its diameter. In 1855 Mr. _Ambrose_ Smith, of Aberdeen, made
3,204 trials with a rod three-fifths of the distance between the planks:
there were 1,213 clear intersections, and 11 contacts on which it was
difficult to decide. Divide these contacts equally, and we have 1,218½ to
3,204 for the ratio of 6 to 5[pi], presuming that the greatness of the
number of trials gives something near to the final average, or result in
the long run: this gives [pi] = 3.1553. If all the 11 contacts had been
treated as intersections, the result would have been {284} [pi] = 3.1412,
exceedingly near. A pupil of mine made 600 trials with a rod of the length
between the seams, and got [pi] = 3.137.

This method will hardly be believed until it has been repeated so often
that "there never could have been any doubt about it."

The first experiment strongly illustrates a truth of the theory, well
confirmed by practice: whatever can happen will happen if we make trials
enough. Who would undertake to throw tail eight times running?
Nevertheless, in the 8,192 sets tail 8 times running occurred 17 times; 9
times running, 9 times; 10 times running, twice; 11 times and 13 times,
each once; and 15 times twice.]



ON CURIOSITIES OF [pi].

1830. The celebrated interminable fraction 3.14159..., which the
mathematician calls [pi], is the ratio of the circumference to the
diameter. But it is thousands of things besides. It is constantly turning
up in mathematics: and if arithmetic and algebra had been studied without
geometry, [pi] must have come in somehow, though at what stage or under
what name must have depended upon the casualties of algebraical invention.
This will readily be seen when it is stated that [pi] is nothing but four
times the series

  1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...

_ad infinitum_.[616] It would be wonderful if so simple a series {285} had
but one kind of occurrence. As it is, our trigonometry being founded on the
circle, [pi] first appears as the ratio stated. If, for instance, a deep
study of probable fluctuation from average had preceded, [pi] might have
emerged as a number perfectly indispensable in such problems as: What is
the chance of the number of aces lying between a million + x and a million
- x, when six million of throws are made with a die? I have not gone into
any detail of all those cases in which the paradoxer finds out, by his
unassisted acumen, that results of mathematical investigation _cannot be_:
in fact, this discovery is only an accompaniment, though a necessary one,
of his paradoxical statement of that which _must be_. Logicians are
beginning to see that the notion of _horse_ is inseparably connected with
that of _non-horse_: that the first without the second would be no notion
at all. And it is clear that the positive affirmation of that which
contradicts mathematical demonstration cannot but be accompanied by a
declaration, mostly overtly made, that demonstration is false. If the
mathematician were interested in punishing this indiscretion, he could make
his denier ridiculous by inventing asserted results which would completely
take him in.

More than thirty years ago I had a friend, now long gone, who was a
mathematician, but not of the higher branches: he was, _inter alia_,
thoroughly up in all that relates to mortality, life assurance, &c. One
day, explaining to him how it should be ascertained what the chance is of
the survivors of a large number of persons now alive lying between given
limits of number at the end of a certain time, I came, of course upon the
introduction of [pi], which I could only describe as the ratio of the
circumference of a circle to its diameter. "Oh, my dear friend! that must
be a delusion; what can the circle have to do with the numbers alive at the
end of a given time?"--"I cannot demonstrate it to you; but it is
demonstrated."--"Oh! stuff! I think you can prove anything with your
differential calculus: figment, {286} depend upon it." I said no more; but,
a few days afterwards, I went to him and very gravely told him that I had
discovered the law of human mortality in the Carlisle Table, of which he
thought very highly. I told him that the law was involved in this
circumstance. Take the table of expectation of life, choose any age, take
its expectation and make the nearest integer a new age, do the same with
that, and so on; begin at what age you like, you are sure to end at the
place where the age past is equal, or most nearly equal, to the expectation
to come. "You don't mean that this always happens?"--"Try it." He did try,
again and again; and found it as I said. "This is, indeed, a curious thing;
this _is_ a discovery." I might have sent him about trumpeting the law of
life: but I contented myself with informing him that the same thing would
happen with any table whatsoever in which the first column goes up and the
second goes down; and that if a proficient in the higher mathematics chose
to palm a figment upon him, he could do without the circle: _à corsaire,
corsaire et demi_,[617] the French proverb says. "Oh!" it was remarked, "I
see, this was Milne!"[618] It was _not_ Milne: I remember well showing the
formula to him some time afterwards. He raised no difficulty about [pi]; he
knew the forms of Laplace's results, and he was much interested. Besides,
Milne never said stuff! and figment! And he would not have been taken in:
he would have quietly tried it with the Northampton and all the other
tables, and would have got at the truth.

{287}



EUCLID WITHOUT AXIOMS.

    The first book of Euclid's Elements. With alterations and familiar
    notes. Being an attempt to get rid of axioms altogether; and to
    establish the theory of parallel lines, without the introduction of any
    principle not common to other parts of the elements. By a member of the
    University of Cambridge. Third edition. In usum serenissimæ filiolæ.
    London, 1830.

The author was Lieut. Col. (now General) Perronet Thompson,[619] the author
of the "Catechism on the Corn Laws." I reviewed the fourth edition--which
had the name of "Geometry without Axioms," 1833--in the quarterly _Journal
of Education_ for January, 1834. Col. Thompson, who then was a contributor
to--if not editor of--the _Westminster Review_, replied in an article the
authorship of which could not be mistaken.

Some more attempts upon the problem, by the same author, will be found in
the sequel. They are all of acute and legitimate speculation; but they do
not conquer the difficulty in the manner demanded by the conditions of the
problem. The paradox of parallels does not contribute much to my pages: its
cases are to be found for the most part in geometrical systems, or in notes
to them. Most of them consist in the proposal of additional postulates;
some are attempts to do without any new postulate. Gen. Perronet Thompson,
whose paradoxes are always constructed on much study of previous writers,
has collected in the work above named, a budget of attempts, the heads of
which are in the _Penny_ and _English Cyclopædias_, at "Parallels." He has
given thirty instances, selected from what he had found.[620]

{288}

Lagrange,[621] in one of the later years of his life, imagined that he had
overcome the difficulty. He went so far as to write a paper, which he took
with him to the Institute, and began to read it. But in the first paragraph
something struck him which he had not observed: he muttered _Il faut que
j'y songe encore_,[622] and put the paper in his pocket.



THE LUNAR CAUSTIC JOKE.

The following paragraph appeared in the _Morning Post_, May 4, 1831:

"We understand that although, owing to circumstances with which the public
are not concerned, Mr. Goulburn[623] declined becoming a candidate for
University honors, that his scientific attainments are far from
inconsiderable. He is well known to be the author of an essay in the
Philosophical Transactions on the accurate rectification of a circular arc,
and of an investigation of the equation of a lunar caustic--a problem
likely to become of great use in nautical astronomy."

{289}

This hoax--which would probably have succeeded with any journal--was palmed
upon the _Morning Post_, which supported Mr. Goulburn, by some Cambridge
wags who supported Mr. Lubbock, the other candidate for the University of
Cambridge. Putting on the usual concealment, I may say that I always
suspected Dr-nkw-t-r B-th-n-[624] of having a share in the matter. The
skill of the hoax lies in avoiding the words "quadrature of the circle,"
which all know, and speaking of "the accurate rectification of a circular
arc," which all do not know for its synonyme. The _Morning Post_ next day
gave a reproof to hoaxers in general, without referring to any particular
case. It must be added, that although there are _caustics_ in mathematics,
there is no _lunar_ caustic.

So far as Mr. Goulburn was concerned, the above was poetic justice. He was
the minister who, in old time, told a deputation from the Astronomical
Society that the Government "did not care twopence for all the science in
the country." There may be some still alive who remember this: I heard it
from more than one of those who were present, and are now gone. Matters are
much changed. I was thirty years in office at the Astronomical Society;
and, to my certain knowledge, every Government of that period, Whig and
Tory, showed itself ready to help with influence when wanted, and with
money whenever there was an answer for the House of Commons. The following
correction subsequently appeared. Referring to the hoax about Mr. Goulburn,
Messrs. C. H. and Thompson Cooper[625] have corrected an error, by stating
that the election which gave rise to the hoax was that in which Messrs.
Goulburn {290} and Yates Peel[626] defeated Lord Palmerston[627] and Mr.
Cavendish.[628] They add that Mr. Gunning, the well-known Esquire Bedell of
the University, attributed the hoax to the late Rev. R. Sheepshanks, to
whom, they state, are also attributed certain clever fictitious
biographies--of public men, as I understand it--which were palmed upon the
editor of the _Cambridge Chronicle_, who never suspected their genuineness
to the day of his death. Being in most confidential intercourse with Mr.
Sheepshanks,[629] both at the time and all the rest of his life
(twenty-five years), and never heard him allude to any such things--which
were not in his line, though he had satirical power of quite another {291}
kind--I feel satisfied he had nothing to do with them. I may add that
others, his nearest friends, and also members of his family, never heard
him allude to these hoaxes as their author, and disbelieve his authorship
as much as I do myself. I say this not as imputing any blame to the true
author, such hoaxes being fair election jokes in all time, but merely to
put the saddle off the wrong horse, and to give one more instance of the
insecurity of imputed authorship. Had Mr. Sheepshanks ever told me that he
had perpetrated the hoax, I should have had no hesitation in giving it to
him. I consider all clever election squibs, free from bitterness and
personal imputation, as giving the multitude good channels for the vent of
feelings which but for them would certainly find bad ones.

[But I now suspect that Mr. Babbage[630] had some hand in the hoax. He
gives it in his "Passages, &c." and is evidently writing from memory, for
he gives the wrong year. But he has given the paragraph, though not
accurately, yet with such a recollection of the points as brings suspicion
of the authorship upon him, perhaps in conjunction with D. B.[631] Both
were on Cavendish's committee. Mr. Babbage adds, that "late one evening a
cab drove up in hot haste to the office of the _Morning Post_, delivered
the copy as coming from Mr. Goulburn's committee, and at the same time
ordered fifty extra copies of the _Post_ to be sent next morning to their
committee-room." I think the man--the only one I ever heard of--who knew
all about the cab and the extra copies must have known more.]



ON M. DEMONVILLE.

_Demonville._--A Frenchman's Christian name is his own secret, unless there
be two of the surname. M. Demonville is a very good instance of the
difference between a {292} French and English discoverer. In England there
is a public to listen to discoveries in mathematical subjects made without
mathematics: a public which will hear, and wonder, and think it possible
that the pretensions of the discoverer have some foundation. The unnoticed
man may possibly be right: and the old country-town reputation which I once
heard of, attaching to a man who "had written a book about the signs of the
zodiac which all the philosophers in London could not answer," is fame as
far as it goes. Accordingly, we have plenty of discoverers who, even in
astronomy, pronounce the learned in error because of mathematics. In
France, beyond the sphere of influence of the Academy of Sciences, there is
no one to cast a thought upon the matter: all who take the least interest
repose entire faith in the Institute. Hence the French discoverer turns all
his thoughts to the Institute, and looks for his only hearing in that
quarter. He therefore throws no slur upon the means of knowledge, but would
say, with M. Demonville: "A l'égard de M. Poisson,[632] j'envie loyalement
la millième partie de ses connaissances mathématiques, pour prouver mon
systême d'astronomie aux plus incrédules."[633] This system is that the
only bodies of our system are the earth, the sun, and the moon; all the
others being illusions, caused by reflection of the sun and moon from the
ice of the polar regions. In mathematics, addition and subtraction are for
men; multiplication and division, which are in truth creation and
destruction, are prerogatives of deity. But _nothing_ multiplied by
_nothing_ is _one_. M. Demonville obtained an introduction to William the
Fourth, who desired the opinion of the Royal Society upon his system: the
{293} answer was very brief. The King was quite right; so was the Society:
the fault lay with those who advised His Majesty on a matter they knew
nothing about. The writings of M. Demonville in my possession are as
follows.[634] The dates--which were only on covers torn off in
binding--were about 1831-34:

_Petit cours d'astronomie_[635] followed by _Sur l'unité
mathématique._--_Principes de la physique de la création implicitement
admis dans la notice sur le tonnerre par M. Arago._--_Question de longitude
sur mer._[636]--_Vrai système du monde_[637] (pp. 92). Same title, four
pages, small type. Same title, four pages, addressed to the British
Association. Same title, four pages, addressed to M. Mathieu. Same title,
four pages, on M. Bouvard's report.--_Résumé de la physique de la création;
troisième partie du vrai système du monde._[638]



PARSEY'S PARADOX.

    The quadrature of the circle discovered, by Arthur Parsey,[639] author
    of the 'art of miniature painting.' Submitted to the consideration of
    the Royal Society, on whose protection the author humbly throws
    himself. London, 1832, 8vo.

Mr. Parsey was an artist, who also made himself conspicuous by a new view
of perspective. Seeing that the sides of a tower, for instance, would
appear to meet in a point if the tower were high enough, he thought that
these sides ought to slope to one another in the picture. On this {294}
theory he published a small work, of which I have not the title, with a
Grecian temple in the frontispiece, stated, if I remember rightly, to be
the first picture which had ever been drawn in true perspective. Of course
the building looked very Egyptian, with its sloping sides. The answer to
his notion is easy enough. What is called the picture is not the picture
from which the mind takes its perception; that picture is on the retina.
The _intermediate_ picture, as it may be called--the human artist's
work--is itself seen perspectively. If the tower were so high that the
sides, though parallel, appeared to meet in a point, the picture must also
be so high that the _picture-sides_, though parallel, would appear to meet
in a point. I never saw this answer given, though I have seen and heard the
remarks of artists on Mr. Parsey's work. I am inclined to think it is
commonly supposed that the artist's picture is the representation which
comes before the mind: this is not true; we might as well say the same of
the object itself. In July 1831, reading an article on squaring the circle,
and finding that there was a difficulty, he set to work, got a light denied
to all mathematicians in--some would say through--a crack, and advertised
in the _Times_ that he had done the trick. He then prepared this work, in
which, those who read it will see how, he showed that 3.14159... should be
3.0625. He might have found out his error by _stepping_ a draughtsman's
circle with the compasses.

Perspective has not had many paradoxes. The only other one I remember is
that of a writer on perspective, whose name I forget, and whose four pages
I do not possess. He circulated remarks on my notes on the subject,
published in the _Athenæum_, in which he denies that the stereographic
projection is a case of perspective, the reason being that the whole
hemisphere makes too large a picture for the eye conveniently to grasp at
once. That is to say, it is no perspective because there is too much
perspective. {295}



ON A COUPLE OF GEOMETRIES.

    Principles of Geometry familiarly illustrated. By the Rev. W.
    Ritchie,[640] LL.D. London, 1833, 12mo.

    A new Exposition of the system of Euclid's Elements, being an attempt
    to establish his work on a different basis. By Alfred Day,[641] LL.D.
    London, 1839, 12mo.

These works belong to a small class which have the peculiarity of insisting
that in the general propositions of geometry a proposition gives its
converse: that "Every B is A" follows from "Every A is B." Dr. Ritchie
says, "If it be proved that the equality of two of the angles of a triangle
depends _essentially_ upon the equality of the opposite sides, it follows
that the equality of opposite sides depends _essentially_ on the equality
of the angles." Dr. Day puts it as follows:

"That the converses of Euclid, so called, where no particular limitation is
specified or implied in the leading proposition, more than in the converse,
must be necessarily true; for as by the nature of the reasoning the leading
proposition must be universally true, should the converse be not so, it
cannot be so universally, but has at least all the exceptions conveyed in
the leading proposition, and the case is therefore unadapted to geometric
reasoning; or, what is the same thing, by the very nature of geometric
reasoning, the particular exceptions to the extended converse must be
identical with some one or other of the cases under the universal
affirmative proposition with which we set forth, which is absurd."

{296}

On this I cannot help transferring to my reader the words of the Pacha when
he orders the bastinado,--May it do you good! A rational study of logic is
much wanted to show many mathematicians, of all degrees of proficiency,
that there is nothing in the _reasoning_ of mathematics which differs from
other reasoning. Dr. Day repeated his argument in _A Treatise on
Proportion_, London, 1840, 8vo. Dr. Ritchie was a very clear-headed man. He
published, in 1818, a work on arithmetic, with rational explanations. This
was too early for such an improvement, and nearly the whole of his
excellent work was sold as waste paper. His elementary introduction to the
Differential Calculus was drawn up while he was learning the subject late
in life. Books of this sort are often very effective on points of
difficulty.



NEWTON AGAIN OBLITERATED.

    Letter to the Royal Astronomical Society in refutation of Mistaken
    Notions held in common, by the Society, and by all the Newtonian
    philosophers. By Capt. Forman,[642] R.N. Shepton-Mallet, 1833, 8vo.

Capt. Forman wrote against the whole system of gravitation, and got no
notice. He then wrote to Lord Brougham, Sir J. Herschel, and others I
suppose, desiring them to procure notice of his books in the reviews: this
not being acceded to, he wrote (in print) to Lord John Russell[643] to
complain of their "dishonest" conduct. He then sent a manuscript letter to
the Astronomical Society, inviting controversy: he was answered by a
recommendation to study {297} dynamics. The above pamphlet was the
consequence, in which, calling the Council of the Society "craven dunghill
cocks," he set them right about their doctrines. From all I can learn, the
life of a worthy man and a creditable officer was completely embittered by
his want of power to see that no person is bound in reason to enter into
controversy with every one who chooses to invite him to the field. This
mistake is not peculiar to philosophers, whether of orthodoxy or paradoxy;
a majority of educated persons imply, by their modes of proceeding, that no
one has a right to any opinion which he is not prepared to defend against
all comers.



    David and Goliath, or an attempt to prove that the Newtonian system of
    Astronomy is directly opposed to the Scriptures. By Wm. Lauder,[644]
    Sen., Mere, Wilts. Mere, 1833, 12mo.

Newton is Goliath; Mr. Lauder is David. David took five pebbles; Mr. Lauder
takes five arguments. He expects opposition; for Paul and Jesus both met
with it.

Mr. Lauder, in his comparison, seems to put himself in the divinely
inspired class. This would not be a fair inference in every case; but we
know not what to think when we remember that a tolerable number of
cyclometers have attributed their knowledge to direct revelation. The works
of this class are very scarce; I can only mention one or two from
Montucla.[645] Alphonso Cano de Molina,[646] in the last century, upset all
Euclid, and squared the circle upon the ruins; he found a follower, Janson,
who translated him from Spanish into Latin. He declared that he believed in
Euclid, until God, who humbles the proud, taught him better. One Paul Yvon,
called from his estate de la Leu, a merchant at Rochelle, supported by his
book-keeper, M. Pujos, and a {298} Scotchman, John Dunbar, solved the
problem by divine grace, in a manner which was to convert all Jews,
Infidels, etc. There seem to have been editions of his work in 1619 and
1628, and a controversial "Examen" in 1630, by Robert Sara. There was a
noted discussion, in which Mydorge,[647] Hardy,[648] and others took part
against de la Leu. I cannot find this name either in Lipenius[649] or
Murhard,[650] and I should not have known the dates if it had not been for
one of the keenest bibliographers of any time, my friend Prince Balthasar
Boncompagni,[651] who is trying to find copies of the works, and has
managed to find copies of the titles. In 1750, Henry Sullamar, an
Englishman, squared the circle by the number of the Beast: he published a
pamphlet every two or three years; but I cannot find any mention of him in
English works.[652] In France, in 1753, M. de Causans,[653] of the Guards,
cut a circular piece of turf, squared it, and {299} deduced original sin
and the Trinity. He found out that the circle was equal to the square in
which it is inscribed; and he offered a reward for detection of any error,
and actually deposited 10,000 francs as earnest of 300,000. But the courts
would not allow any one to recover.



SIR JOHN HERSCHEL.

1834. In this year Sir John Herschel[654] set up his telescope at
Feldhausen, Cape of Good Hope. He did much for astronomy, but not much for
the _Budget of Paradoxes_. He gives me, however, the following story. He
showed a resident a remarkable blood-red star, and some little time after
he heard of a sermon preached in those parts in which it was asserted that
the statements of the Bible must be true, for that Sir J. H. had seen in
his telescope "the very place where wicked people go."

But red is not always the color. Sir J. Herschel has in his possession a
letter written to his father, Sir W. H.,[655] dated April 3, 1787, and
signed "Eliza Cumyns," begging to know if any of the stars be _indigo_ in
color, "because, if there be, I think it may be deemed a strong conjectural
illustration of the expression, so often used by our Saviour in the Holy
Gospels, that 'the disobedient shall be cast into outer darkness'; for as
the Almighty Being can doubtless confine any of his creatures, whether
corporeal or spiritual, to what part of his creation He pleases, if
therefore any of the stars (which are beyond all doubt so many suns to
other systems) be of so dark a color as that above mentioned, they may be
calculated to give the most insufferable heat to those dolorous systems
dependent upon them (and to reprobate spirits placed there), without one
ray of cheerful light; and may therefore be the scenes of future
punishments." This letter is addressed to Dr. Heirschel at Slow. Some have
placed the infernal regions inside the earth, but {300} others have filled
this internal cavity--for cavity they will have--with refulgent light, and
made it the abode of the blessed. It is difficult to build without knowing
the number to be provided for. A friend of mine heard the following (part)
dialogue between two strong Scotch Calvinists: "Noo! hoo manny d'ye thank
there are of the alact on the arth at this moment?--Eh! mabbee a
doozen--Hoot! mon! nae so mony as thot!"



THE NAUTICAL ALMANAC.

1834. From 1769 to 1834 the _Nautical Almanac_ was published on a plan
which gradually fell behind what was wanted. In 1834 the new series began,
under a new superintendent (Lieut. W. S. Stratford).[656] There had been a
long scientific controversy, which would not be generally intelligible. To
set some of the points before the reader, I reprint a cutting which I have
by me. It is from the Nautical _Magazine_, but I did hear that some had an
idea that it was in the Nautical _Almanac_ itself. It certainly was not,
and I feel satisfied the Lords of the Admiralty would not have permitted
the insertion; they are never in advance of their age. The Almanac for 1834
was published in July 1833.

    THE NEW NAUTICAL ALMANAC--Extract from the 'Primum Mobile,' and 'Milky
    Way Gazette.' Communicated by AEROLITH.

A meeting of the different bodies composing the Solar System was this day
held at the Dragon's Tail, for the purpose of taking into consideration the
alterations and amendments introduced into the New Nautical Almanac. The
honorable luminaries had been individually summoned {301} by fast-sailing
comets, and there was a remarkably full attendance. Among the visitors we
_observed_ several nebulæ, and almost all the stars whose proper motions
would admit of their being present.

The SUN was unanimously called to the focus. The small planets took the
oaths, and their places, after a short discussion, in which it was decided
that the places should be those of the Almanac itself, with leave reserved
to move for corrections.

Petitions were presented from [alpha] and [delta] Ursæ Minoris, complaining
of being put on daily duty, and praying for an increase of salary.--Laid on
the plane of the ecliptic.

The trustees of the eccentricity[657] and inclination funds reported a
balance of .00001 in the former, and a deficit of 0".009 in the latter.
This announcement caused considerable surprise, and a committee was moved
for, to ascertain which of the bodies had more or less than his share.
After some discussion, in which the small planets offered to consent to a
reduction, if necessary, the motion was carried.

The FOCAL BODY then rose to address the meeting. He remarked that the
subject on which they were assembled was one of great importance to the
routes and revolutions of the heavenly bodies. For himself, though a
private arrangement between two of his honourable neighbours (here he
looked hard at the Earth and Venus) had prevented his hitherto paying that
close attention to the predictions of the Nautical Almanac which he
declared he always had wished to do; yet he felt consoled by knowing that
the conductors of that work had every disposition to take his peculiar
circumstances into consideration. He declared that he had never passed the
wires of a transit without deeply feeling his inability to adapt himself to
the present state of his theory; a feeling which he was afraid had
sometimes caused a slight tremor in his limb. Before {302} he sat down, he
expressed a hope that honourable luminaries would refrain as much as
possible from eclipsing each other, or causing mutual perturbations.
Indeed, he should be very sorry to see any interruption of the harmony of
the spheres. (Applause.)

The several articles of the New Nautical Almanac were then read over
without any comment; only we observed that Saturn shook his ring at every
novelty, and Jupiter gave his belt a hitch, and winked at the satellites at
page 21 of each month.

The MOON rose to propose a resolution. No one, he said, would be surprised
at his bringing this matter forward in the way he did, when it was
considered in how complete and satisfactory a manner his motions were now
represented. He must own he had trembled when the Lords of the Admiralty
dissolved the Board of Longitude, but his tranquillity was more than
reestablished by the adoption of the new system. He did not know but that
any little assistance he could give in Nautical Astronomy was becoming of
less and less value every day, owing to the improvement of chronometers.
But there was one thing, of which nothing could deprive him--he meant the
regulation of the tides. And, perhaps, when his attention was not occupied
by more than the latter, he should be able to introduce a little more
regularity into the phenomena. (Here the honourable luminary gave a sort of
modest libration, which convulsed the meeting with laughter.) They might
laugh at his natural infirmity if they pleased, but he could assure them it
arose only from the necessity he was under, when young, of watching the
motions of his worthy primary. He then moved a resolution highly laudatory
of the alterations which appeared in the New Nautical Almanac.

The EARTH rose, to second the motion. His honourable satellite had fully
expressed his opinions on the subject. He joined his honourable friend in
the focus in wishing to pay every attention to the Nautical Almanac, but,
{303} really, when so important an alteration had taken place in his
magnetic pole[658] (hear) and there might, for aught he knew, be a
successful attempt to reach his pole of rotation, he thought he could not
answer for the preservation of the precession in its present state. (Here
the hon. luminary, scratching his side, exclaimed, as he sat down, "More
steamboats--confound 'em!")

An honourable satellite (whose name we could not learn) proposed that the
resolution should be immediately despatched, corrected for refraction, when
he was called to order by the Focal Body, who reminded him that it was
contrary to the moving orders of the system to take cognizance of what
passed inside the atmosphere of any planet.

SATURN and PALLAS rose together. (Cries of "New member!" and the former
gave way.) The latter, in a long and eloquent speech, praised the
liberality with which he and his colleagues had at length been relieved
from astronomical disqualifications. He thought that it was contrary to the
spirit of the laws of gravitation to exclude any planet from office on
account of the eccentricity or inclination of his orbit. Honourable
luminaries need not talk of the want of convergency of his series. What had
they to do with any private arrangements between him and the general
equations of the system? (Murmurs from the opposition.) So long as he
obeyed the laws of motion, to which he had that day taken a solemn oath, he
would ask, were old planets, which were now so well known that nobody
trusted them, to....

The FOCAL BODY said he was sorry to break the continuity of the
proceedings, but he thought that remarks upon character, with a negative
sign, would introduce {304} differences of too high an order. The
honourable luminary must eliminate the expression which he had brought out,
in finite terms, and use smaller inequalities in future. (Hear, hear.)

PALLAS explained, that he was far from meaning to reflect upon the orbital
character of any planet present. He only meant to protest against being
judged by any laws but those of gravitation, and the differential calculus:
he thought it most unjust that astronomers should prevent the small planets
from being observed, and then reproach them with the imperfections of the
tables, which were the result of their own narrow-minded policy. (Cheers.)

SATURN thought that, as an old planet, he had not been treated with due
respect. (Hear, from his satellites.) He had long foretold the wreck of the
system from the friends of innovation. Why, he might ask, were his
satellites to be excluded, when small planets, trumpery comets, which could
not keep their mean distances (cries of oh! oh!), double stars, with
graphical approximations, and such obscure riff-raff of the heavens (great
uproar) found room enough. So help him Arithmetic, nothing could come of
it, but a stoppage of all revolution. His hon. friend in the focus might
smile, for he would be a gainer by such an event; but as for him (Saturn),
he had something to lose, and hon. luminaries well knew that, whatever they
might think _under_ an atmosphere, _above_ it continual revolution was the
only way of preventing perpetual anarchy. As to the hon. luminary who had
risen before him, he was not surprised at his remarks, for he had
invariably observed that he and his colleagues allowed themselves _too much
latitude_. The stability of the system required that they should be brought
down, and he, for one, would exert all his powers of attraction to
accomplish that end. If other bodies would cordially unite with him,
particularly his noble friend next him, than whom no luminary possessed
greater weight--

JUPITER rose to order. He conceived his noble friend {305} had no right to
allude to him in that manner, and was much surprised at his proposal,
considering the matters which remained in dispute between them. In the
present state of affairs, he would take care never to be in conjunction
with his hon. neighbour one moment longer than he could help. (Cries of
"Order, order, no long inequalities," during which he sat down.)

SATURN proceeded to say, that he did not know till then that a planet with
a ring could affront one who had only a belt, by proposing mutual
co-operation. He would now come to the subject under discussion. He should
think meanly of his hon. colleagues if they consented to bestow their
approbation upon a mere astronomical production. Had they forgotten that
they once were considered the arbiters of fate, and the prognosticators of
man's destiny? What had lost them that proud position? Was it not the
infernal march of intellect, which, after having turned the earth
topsy-turvy, was now disturbing the very universe? For himself (others
might do as they pleased), but he stuck to the venerable Partridge,[659]
and the Stationers' Company, and trusted that they would outlive infidels
and anarchists, whether of Astronomical or Diffusion of Knowledge
Societies. (Cries of oh! oh!)

MARS said he had been told, for he must confess he had not seen the work,
that the places of the planets were given for Sundays. This, he must be
allowed to say, was an indecorum he had not expected; and he was convinced
the Lords of the Admiralty had given no orders to that effect. He hoped
this point would be considered in the measure which had been introduced in
another place, and that some {306} one would move that the prohibition
against travelling on Sundays extend to the heavenly as well as earthly
bodies.

Several of the stars here declared, that they had been much annoyed by
being observed on Sunday evenings, during the hours of divine service.

The room was then cleared for a division, but we are unable to state what
took place. Several comets-at-arms were sent for, and we heard rumors of a
personal collision having taken place between two luminaries in opposition.
We were afterwards told that the resolution was carried by a majority, and
the luminaries elongated at 2 h. 15 m. 33,41 s. sidereal time.

* * * It is reported, but we hope without foundation, that Saturn, and
several other discontented planets, have accepted an invitation from Sirius
to join his system, on the most liberal appointments. We believe the report
to have originated in nothing more than the discovery of the annual
parallax of Sirius from the orbit of Saturn; but we may safely assure our
readers that no steps have as yet been taken to open any communication.

We are also happy to state, that there is no truth in the rumor of the laws
of gravitation being about to be repealed. We have traced this report, and
find it originated with a gentleman living near Bath (Captain Forman,
R.N),[660] whose name we forbear to mention.

A great excitement has been observed among the nebulæ, visible to the
earth's southern hemisphere, particularly among those which have not yet
been discovered from thence. We are at a loss to conjecture the cause, but
we shall not fail to report to our readers the news of any movement which
may take place. (Sir J. Herschel's visit. He could just see this before he
went out.)

{307}



WOODLEY'S DIVINE SYSTEM.

    A Treatise on the Divine System of the Universe, by Captain Woodley,
    R.N.,[661] and as demonstrated by his Universal Time-piece, and
    universal method of determining a ship's longitude by the apparent true
    place of the moon; with an introduction refuting the solar system of
    Copernicus, the Newtonian philosophy, and mathematics. 1834.[662] 8vo.

    Description of the Universal Time-piece. (4pp. 12mo.)

I think this divine system was published several years before, and was
republished with an introduction in 1834.[663] Capt. Woodley was very sure
that the earth does not move: he pointed out to me, in a conversation I had
with him, something--I forget what--in the motion of the Great Bear,
visible to any eye, which could not possibly be if the earth moved. He was
exceedingly ignorant, as the following quotation from his account of the
usual opinion will show:

"The north pole of the Earth's axis deserts, they say, the north star or
pole of the Heavens, at the rate of 1° in 71¾ years.... The fact is,
nothing can be more certain than that the Stars have not changed their
latitudes or declinations _one degree_ in the last 71¾ years."

This is a strong specimen of a class of men by whom all accessible persons
who have made any name in science are hunted. It is a pity that they cannot
be admitted into scientific societies, and allowed fairly to state their
cases, and stand quiet cross-examination, being kept in their answers very
close to the questions, and the answers written down. I am perfectly
satisfied that if one meeting in the year were devoted to the hearing of
those who chose to come forward on such conditions, much good would be
done. But I strongly suspect few would come forward {308} at first, and
none in a little while: and I have had some experience of the method I
recommend, privately tried. Capt. Woodley was proposed, a little after
1834, as a Fellow of the Astronomical Society; and, not caring whether he
moved the sun or the earth, or both--I could not have stood _neither_--I
signed the proposal. I always had a sneaking kindness for paradoxers, such
a one, perhaps, as Petit André had for his _lambs_, as he called them.
There was so little feeling against his opinions, that he only failed by a
fraction of a ball. Had I myself voted, he would have been elected; but
being engaged in conversation, and not having heard the slightest objection
to him, I did not think it worth while to cross the room for the purpose. I
regretted this at the time, but had I known how ignorant he was I should
not have supported him. Probably those who voted against him knew more of
his book than I did.

I remember no other instance of exclusion from a scientific society on the
ground of opinion, even if this be one; of which it may be that ignorance
had more to do with it than paradoxy. Mr. Frend,[664] a strong
anti-Newtonian, was a Fellow of the Astronomical Society, and for some
years in the Council. Lieut. Kerigan[665] was elected to the Royal Society
at a time when his proposers must have known that his immediate object was
to put F.R.S. on the title-page of a work against the tides. To give all I
know, I may add that the editor of some very ignorant bombast about the
"forehead of the solar sky," who did not know the difference between
_Bailly_[666] and _Baily_,[667] received hints which induced him to
withdraw his proposal for election into the Astronomical Society. But this
was an act of kindness; {309} for if he had seen Mr. Baily in the chair,
with his head on, he might have been political historian enough to faint
away.



    De la formation des Corps. Par Paul Laurent.[668] Nancy, 1834, 8vo.

Atoms, and ether, and ovules or eggs, which are planets, and their eggs,
which are satellites. These speculators can create worlds, in which they
cannot be refuted; but none of them dare attack the problem of a grain of
wheat, and its passage from a seed to a plant, bearing scores of seeds like
what it was itself.



ON JOHN FLAMSTEED.

    An account of the Rev. John Flamsteed,[669] the First
    Astronomer-Royal.... By Francis Baily,[670] Esq. London, 1835, 4to.
    Supplement, London, 1837, 4to.

My friend Francis Baily was a paradoxer: he brought forward things counter
to universal opinion. That Newton was impeccable in every point was the
national creed; and failings of temper and conduct would have been utterly
disbelieved, if the paradox had not come supported by very unusual
evidence. Anybody who impeached Newton on existing evidence might as well
have been squaring the circle, for any attention he would have got. About
this book I will tell a story. It was published by the Admiralty for
distribution; and the distribution was entrusted to Mr. Baily. On the eve
of its appearance, rumors of its extraordinary revelations got about, and
persons of influence applied to the Admiralty for copies. The Lords were in
a difficulty: but on looking at the list they saw names, as they {310}
thought, which were so obscure that they had a right to assume Mr. Baily
had included persons who had no claim to such a compliment as presentation
from the Admiralty. The Secretary requested Mr. Baily to call upon him.
"Mr. Baily, my Lords are inclined to think that some of the persons in this
list are perhaps not of that note which would justify their Lordships in
presenting this work."--"To whom does your observation apply, Mr.
Secretary?"--"Well, now, let us examine the list; let me see;
now,--now,--now,--come!--here's Gauss[671]--_who's Gauss_?"--"Gauss, Mr.
Secretary, is the oldest mathematician now living, and is generally thought
to be the greatest."--"O-o-oh! Well, Mr. Baily, we will see about it, and I
will write you a letter." The letter expressed their Lordships' perfect
satisfaction with the list.

There was a controversy about the revelations made in this work; but as the
eccentric anomalies took no part in it, there is nothing for my purpose.
The following valentine from Mrs. Flamsteed,[672] which I found among
Baily's papers, illustrates some of the points:

"3 Astronomers' Row, Paradise: February 14, 1836.

"Dear Sir,--I suppose you hardly expected to receive a letter from me,
dated from this place; but the truth is, a gentleman from our street was
appointed guardian angel to the American Treaty, in which there is some
astronomical question about boundaries. He has got leave to go back to
fetch some instruments which he left behind, and I take this opportunity of
making your acquaintance. That America has become a wonderful place since I
was down among you; you have no idea how grand the fire at New York {311}
looked up here. Poor dear Mr. Flamsteed does not know I am writing a letter
to a gentleman on Valentine's day; he is walked out with Sir Isaac Newton
(they are pretty good friends now, though they do squabble a little
sometimes) and Sir William Herschel, to see a new nebula. Sir Isaac says he
can't make out at all how it is managed; and I am sure I cannot help him. I
never bothered my head about those things down below, and I don't intend to
begin here.

"I have just received the news of your having written a book about my poor
dear man. It's a chance that I heard it at all; for the truth is, the
scientific gentlemen are somehow or other become so wicked, and go so
little to church, that very few of them are considered fit company for this
place. If it had not been for Dr. Brinkley,[673] who came here of course, I
should not have heard about it. He seems a nice man, but is not yet used to
our ways. As to Mr. Halley,[674] he is of course not here; which is lucky
for him, for Mr. Flamsteed swore the moment he caught him in a place where
there are no magistrates, he would make a sacrifice of him to heavenly
truth. It was very generous in Mr. F. not appearing against Sir Isaac when
he came up, for I am told that if he had, Sir Isaac would not have been
allowed to come in at all. I should have been sorry for that, for he is a
companionable man enough, only holds his head rather higher than he should
do. I met him the other day walking with Mr. Whiston,[675] and disputing
about the deluge. 'Well, Mrs. Flamsteed,' says he, 'does old Poke-the-Stars
understand gravitation yet?' Now you must know that is rather a sore point
with poor dear Mr. Flamsteed. He says that Sir Isaac is as crochetty about
the moon as ever; and as to {312} what some people say about what has been
done since his time, he says he should like to see somebody who knows
something about it of himself. For it is very singular that none of the
people who have carried on Sir Isaac's notions have been allowed to come
here.

"I hope you have not forgotten to tell how badly Sir Isaac used Mr.
Flamsteed about that book. I have never quite forgiven him; as for Mr.
Flamsteed, he says that as long as he does not come for observations, he
does not care about it, and that he will never trust him with any papers
again as long as he lives. I shall never forget what a rage he came home in
when Sir Isaac had called him a puppy. He struck the stairs all the way up
with his crutch, and said puppy at every step, and all the evening, as soon
as ever a star appeared in the telescope, he called it puppy. I could not
think what was the matter, and when I asked, he only called me puppy.

"I shall be very glad to see you if you come our way. Pray keep up some
appearances, and go to church a little. St. Peter is always uncommonly
civil to astronomers, and indeed to all scientific persons, and never
bothers them with many questions. If they can make anything out of the
case, he is sure to let them in. Indeed, he says, it is perfectly out of
the question expecting a mathematician to be as religious as an apostle,
but that it is as much as his place is worth to let in the greater number
of those who come. So try if you cannot manage it, for I am very curious to
know whether you found all the letters. I remain, dear sir, your faithful
servant,

"MARGARET FLAMSTEED.

  Francis Baily, Esq.

"P.S. Mr. Flamsteed has come in, and says he left Sir Isaac riding
cockhorse upon the nebula, and poring over it as if it were a book. He has
brought in his old acquaintance Ozanam,[676] who says that it was always
his maxim on {313} earth, that 'il appartient aux docteurs de Sorbonne de
disputer, au Pape de prononcer, et au mathématicien d'aller en Paradis en
ligne perpendiculaire.'"[677]



ON STEVIN.

The Secretary of the Admiralty was completely extinguished. I can recall
but two instances of demolition as complete, though no doubt there are many
others. The first is in

  Simon Stevin[678] and M. Dumortier. Nieuport, 1845, 12mo.

M. Dumortier was a member of the Academy of Brussels: there was a
discussion, I believe, about a national Pantheon for Belgium. The name of
Stevinus suggested itself as naturally as that of Newton to an Englishman;
probably no Belgian is better known to foreigners as illustrious in
science. Stevinus is great in the _Mécanique Analytique_ of Lagrange;[679]
Stevinus is great in the _Tristram Shandy_ of Sterne. M. Dumortier, who
believed that not one Belgian in a thousand knew Stevinus, and who
confesses with ironical shame that he was not the odd man, protested
against placing the statue of an obscure man in the Pantheon, to give
foreigners the notion that Belgium could show nothing greater. The work
above named is a slashing retort: any one who knows the history of science
ever so little may imagine what a dressing was given, by mere extract from
foreign writers. The tract is a letter signed J. du Fan, but this is a
pseudonym of Mr. Van de Weyer.[680] The Academician says Stevinus was a man
who was not {314} without merit for the time at which he lived: Sir! is the
answer, he was as much before his own time as you are behind yours. How
came a man who had never heard of Stevinus to be a member of the Brussels
Academy?

The second story was told me by Mr. Crabb Robinson,[681] who was long
connected with the _Times_, and intimately acquainted with Mr. W***.[682]
When W*** was an undergraduate at Cambridge, taking a walk, he came to a
stile, on which sat a bumpkin who did not make way for him: the gown in
that day looked down on the town. "Why do you not make way for a
gentleman?"--"Eh?"--"Yes, why do you not move? You deserve a good hiding,
and you shall get it if you don't take care!" The bumpkin raised his
muscular figure on its feet, patted his menacer on the head, and said, very
quietly,--"Young man! I'm Cribb."[683] W*** seized the great pugilist's
hand, and shook it warmly, got him to his own rooms in college, collected
some friends, and had a symposium which lasted until the large end of the
small hours.



FINLEYSON AS A PARADOXER.

    God's Creation of the Universe as it is, in support of the Scriptures.
    By Mr. Finleyson.[684] Sixth Edition, 1835, 8vo.

{315}

This writer, by his own account, succeeded in delivering the famous Lieut.
Richard Brothers[685] from the lunatic asylum, and tending him, not as a
keeper but as a disciple, till he died. Brothers was, by his own account,
the nephew of the Almighty, and Finleyson ought to have been the nephew of
Brothers. For Napoleon came to him in a vision, with a broken sword and an
arrow in his side, beseeching help: Finleyson pulled out the arrow, but
refused to give a new sword; whereby poor Napoleon, though he got off with
life, lost the battle of Waterloo. This story was written to the Duke of
Wellington, ending with "I pulled out the arrow, but left the broken sword.
Your Grace can supply the rest, and what followed is amply recorded in
history." The book contains a long account of applications to Government to
do three things: to pay 2,000l. for care taken of Brothers, to pay 10,000l.
for discovery of the longitude, and to prohibit the teaching of the
Newtonian system, which makes God a liar. The successive administrations
were threatened that they would have to turn out if they refused, which, it
is remarked, came to pass in every case. I have heard of a joke of Lord
Macaulay, that the House of Commons must be the Beast of the Revelations,
since 658 members, with the officers necessary for the action of the House,
make 666. Macaulay read most things, and the greater part of the rest: so
that he might be suspected of having appropriated as a joke one of
Finleyson's serious points--"I wrote Earl Grey[686] upon the 13th of July,
1831, informing him that his Reform {316} Bill could not be carried, as it
reduced the members below the present amount of 658, which, with the eight
principal clerks or officers of the House, make the number 666." But a
witness has informed me that Macaulay's joke was made in his hearing a
great many years before the Reform Bill was proposed; in fact, when both
were students at Cambridge. Earl Grey was, according to Finleyson, a
descendant of Uriah the Hittite. For a specimen of Lieut. Brothers, this
book would be worth picking up. Perhaps a specimen of the Lieutenant's
poetry may be acceptable: Brothers _loquitur_, remember:

 "Jerusalem ! Jerusalem! shall be built again!
    More rich, more grand then ever;
  And through it shall Jordan flow!(!)
    My people's favourite river.
  There I'll erect a splendid throne,
    And build on the wasted place;
  To fulfil my ancient covenant
    To King David and his race.
      *    *    *    *    *    *
 "Euphrates' stream shall flow with ships,
    And also my wedded Nile;
  And on my coast shall cities rise,
    Each one distant but a mile.
      *    *    *    *    *    *
 "My friends the Russians on the north
    With Persees and Arabs round,
  Do show the limits of my land,
    Here! Here! then I mark the ground."



ON THEOLOGICAL PARADOXERS.

Among the paradoxers are some of the theologians who in their own organs of
the press venture to criticise science. These may hold their ground when
they confine themselves to the geology of long past periods and to general
cosmogony: for it is the tug of Greek against Greek; and both sides deal
much in what is grand when called _hypothesis_, petty when called
_supposition_. And very often they are not conspicuous when they venture
upon things within knowledge; {317} wrong, but not quite wrong enough for a
Budget of Paradoxes. One case, however, is destined to live, as an instance
of a school which finds writers, editors, and readers. The double stars
have been seen from the seventeenth century, and diligently observed by
many from the time of Wm. Herschel, who first devoted continuous attention
to them. The year 1836 was that of a remarkable triumph of astronomical
prediction. The theory of gravitation had been applied to the motion of
binary stars about each other, in elliptic orbits, and in that year the two
stars of [gamma] Virginis, as had been predicted should happen within a few
years of that time--for years are small quantities in such long
revolutions--the two stars came to their nearest: in fact, they appeared to
be one as much with the telescope as without it. This remarkable
turning-point of the history of a long and widely-known branch of astronomy
was followed by an article in the _Church of England Quarterly Review_ for
April 1837, written against the Useful Knowledge Society. The notion that
there are any such things as double stars is (p. 460) implied to be
imposture or delusion, as in the following extract. I suspect that I myself
am the _Sidrophel_, and that my companion to the maps of the stars, written
for the Society and published in 1836, is the work to which the writer
refers:

"We have forgotten the name of that Sidrophel who lately discovered that
the fixed stars were not single stars, but appear in the heavens like soles
at Billingsgate, in pairs; while a second astronomer, under the influence
of that competition in trade which the political economists tell us is so
advantageous to the public, professes to show us, through his superior
telescope, that the apparently single stars are really three. Before such
wondrous mandarins of science, how continually must _homunculi_ like
ourselves keep in the background, lest we come between the wind and their
nobility."

If the _homunculus_ who wrote this be still above ground, {318} how
devoutly must he hope he may be able to keep in the background! But the
chief blame falls on the editor. The title of the article is:

"The new school of superficial pantology; a speech intended to be delivered
before a defunct Mechanics' Institute. By Swallow Swift, late M.P. for the
Borough of Cockney-Cloud, Witsbury: reprinted Balloon Island, Bubble year,
month _Ventose_. Long live Charlatan!"

As a rule, orthodox theologians should avoid humor, a weapon which all
history shows to be very difficult to employ in favor of establishment, and
which, nine times out of ten, leaves its wielder fighting on the side of
heterodoxy. Theological argument, when not enlivened by bigotry, is seldom
worse than narcotic: but theological fun, when not covert heresy, is almost
always sialagogue. The article in question is a craze, which no editor
should have admitted, except after severe inspection by qualified persons.
The author of this wit committed a mistake which occurs now and then in old
satire, the confusion between himself and the party aimed at. He ought to
be reviewing this fictitious book, but every now and then the article
becomes the book itself; not by quotation, but by the writer forgetting
that _he_ is not Mr. Swallow Swift, but his reviewer. In fact he and Mr. S.
Swift had each had a dose of the _Devil's Elixir_. A novel so called,
published about forty years ago, proceeds upon a legend of this kind. If
two parties both drink of the elixir, their identities get curiously
intermingled; each turns up in the character of the other throughout the
three volumes, without having his ideas clear as to whether he be himself
or the other. There is a similar confusion in the answer made to the famous
_Epistolæ Obscurorum Virorum_:[687] it is headed _Lamentationes Obscurorum
Virorum_.[688] {319} This is not a retort of the writer, throwing back the
imputation: the obscure men who had been satirized are themselves made, by
name, to wince under the disapprobation which the Pope had expressed at the
satire upon themselves.

Of course the book here reviewed is a transparent forgery. But I do not
know how often it may have happened that the book, in the journals which
always put a title at the head, may have been written after the review.
About the year 1830 a friend showed me the proof of an article of his on
the malt tax, for the next number of the _Edinburgh Review_. Nothing was
wanting except the title of the book reviewed; I asked what it was. He sat
down, and wrote as follows at the head, "The Maltster's Guide (pp. 124),"
and said that would do as well as anything.

But I myself, it will be remarked, have employed such humor as I can
command "in favor of establishment." What it is worth I am not to judge; as
usual in such cases, those who are of my cabal pronounce it good, but
cyclometers and other paradoxers either call it very poor, or commend it as
sheer buffoonery. Be it one or the other, I observe that all the effective
ridicule is, in this subject, on the side of establishment. This is partly
due to the difficulty of quizzing plain and sober demonstration; but so
much, if not more, to the ignorance of the paradoxers. For that which
cannot be _ridiculed_, can be _turned into ridicule_ by those who know how.
But by the time a person is deep enough in _negative_ quantities, and
_impossible_ quantities, to be able to satirize them, he is caught, and
being inclined to become a _user_, shrinks from being an _abuser_. Imagine
a person with a gift of ridicule, and knowledge enough, trying his hand on
the junction of the assertions which he will find in various books of
algebra. First, that a negative quantity has no logarithm; secondly, that a
{320} negative quantity has no square root; thirdly, that the first
non-existent is to the second as the circumference of a circle to its
diameter. One great reason of the allowance of such unsound modes of
expression is the confidence felt by the writers that [root]-1 and log(-1)
will make their way, however inaccurately described. I heartily wish that
the cyclometers had knowledge enough to attack the weak points of
algebraical diction: they would soon work a beneficial change.[689]



AN EARLY METEOROLOGIST.

    Recueil de ma vie, mes ouvrages et mes pensées. Par Thomas Ignace Marie
    Forster.[690] Brussels, 1836, 12mo.

Mr. Forster, an Englishman settled at Bruges, was an observer in many
subjects, but especially in meteorology. He communicated to the
Astronomical Society, in 1848, the information that, in the registers kept
by his grandfather, his father, and himself, beginning in 1767, new moon on
Saturday was followed, nineteen times out of twenty, by twenty days of rain
and wind. This statement being published in the _Athenæum_, a cluster of
correspondents averred that the belief is common among seamen, in all parts
of the world, and among landsmen too. Some one quoted a distich:

 "Saturday's moon and Sunday's full
  Never were fine and never _wull_."

{321} Another brought forward:

 "If a Saturday's moon
  Comes once in seven years it comes too soon."

Mr. Forster did not say he was aware of the proverbial character of the
phenomenon. He was a very eccentric man. He treated his dogs as friends,
and buried them with ceremony. He quarrelled with the _curé_ of his parish,
who remarked that he could not take his dogs to heaven with him. I will go
nowhere, said he, where I cannot take my dog. He was a sincere Catholic:
but there is a point beyond which even churches have no influence.

The following is some account of the announcement of 1849. The _Athenæum_
(Feb. 17), giving an account of the meeting of the Astronomical Society in
December, 1858, says:

"Dr. Forster of Bruges, who is well known as a meteorologist, made a
communication at which our readers will stare: he declares that by journals
of the weather kept by his grandfather, father, and himself, ever since
1767, to the present time, _whenever the new moon has fallen on a Saturday,
the following twenty days have been wet and windy_, in nineteen cases out
of twenty. In spite of our friend Zadkiel[691] and the others who declare
that we would smother every truth that does not happen to agree with us, we
are glad to see that the Society had the sense to publish this
communication, coming, as it does, from a veteran observer, and one whose
love of truth is undoubted. It must be that the fact is so set down in the
journals, because Dr. Forster says it: and whether it be only a fact of the
journals, or one of the heavens, can soon be tried. The new moon of March
next, falls on _Saturday_ the 24th, at 2 in the afternoon. We shall
certainly look out."

{322}

The following appeared in the number of March 31:

"The first _Saturday Moon_ since Dr. Forster's announcement came off a week
ago. We had previously received a number of letters from different
correspondents--all to the effect that the notion of new moon on Saturday
bringing wet weather is one of widely extended currency. One correspondent
(who gives his name) states that he has constantly heard it at sea, and
among the farmers and peasantry in Scotland, Ireland, and the North of
England. He proceeds thus: 'Since 1826, nineteen years of the time I have
spent in a seafaring life. I have constantly observed, though unable to
account for, the phenomenon. I have also heard the stormy qualities of a
Saturday's moon remarked by American, French, and Spanish seamen; and,
still more distant, a Chinese pilot, who was once doing duty on board my
vessel seemed to be perfectly cognizant of the fact.' So that it seems we
have, in giving currency to what we only knew as a very curious
communication from an earnest meteorologist, been repeating what is common
enough among sailors and farmers. Another correspondent affirms that the
thing is most devoutly believed in by seamen; who would as soon sail on a
Friday as be in the Channel after a Saturday moon.--After a tolerable
course of dry weather, there was some snow, accompanied by wind on Saturday
last, here in London; there were also heavy louring clouds. Sunday was
cloudy and cold, with a little rain; Monday was louring, Tuesday unsettled;
Wednesday quite overclouded, with rain in the morning. The present occasion
shows only a general change of weather with a tendency towards rain. If Dr.
Forster's theory be true, it is decidedly one of the minor instances, as
far as London weather is concerned.--It will take a good deal of evidence
to make us believe in the omen of a Saturday Moon. But, as we have said of
the Poughkeepsie Seer, the thing is very curious whether true or false.
Whence comes this universal proverb--and a hundred others--while the
meteorological observer {323} cannot, when he puts down a long series of
results, detect any weather cycles at all? One of our correspondents wrote
us something of a lecture for encouraging, he said, the notion that _names_
could influence the weather. He mistakes the question. If there be any
weather cycles depending on the moon, it is possible that one of them may
be so related to the week cycle of seven days, as to show recurrences which
are of the kind stated, or any other. For example, we know that if the new
moon of March fall on a Saturday in this year, it will most probably fall
on a Saturday nineteen years hence. This is not connected with the spelling
of Saturday--but with the connection between the motions of the sun and
moon. Nothing but the Moon can settle the question--and we are willing to
wait on her for further information. If the adage be true, then the
philosopher has missed what lies before his eyes; if false, then the world
can be led by the nose in spite of the eyes. Both these things happen
sometimes; and we are willing to take whichever of the two solutions is
borne out by future facts. In the mean time, we announce the next Saturday
Moon for the 18th of August."

How many coincidences are required to establish a law of connection? It
depends on the way in which the mind views the matter in question. Many of
the paradoxers are quite set up by a very few instances. I will now tell a
story about myself, and then ask them a question.

So far as instances can prove a law, the following is proved: no failure
has occurred. Let a clergyman be known to me, whether by personal
acquaintance or correspondence, or by being frequently brought before me by
those with whom I am connected in private life: that clergyman does not,
except in few cases, become a bishop; but _if_ he become a bishop, he is
sure, first or last, to become an arch-bishop. This has happened in every
case. As follows:

1. My last schoolmaster, a former Fellow of Oriel, was {324} a very
intimate college friend of Richard Whately[692], a younger man. Struck by
his friend's talents, he used to talk of him perpetually, and predict his
future eminence. Before I was sixteen, and before Whately had even given
his Bampton Lectures, I was very familiar with his name, and some of his
sayings. I need not say that he became Archbishop of Dublin.

2. When I was a child, a first cousin of John Bird Sumner[693] married a
sister of my mother. I cannot remember the time when I first heard his
name, but it was made very familiar to me. In time he became Bishop of
Chester, and then, Archbishop of Canterbury. My reader may say that Dr.
C. R. Sumner,[694] Bishop of Winchester, has just as good a claim: but it
is not so: those connected with me had more knowledge of Dr. J. B.
Sumner;[695] and said nothing, or next to nothing, of the other. Rumor says
that the Bishop of Winchester has _declined_ an Archbishopric: if so, my
rule is a rule of gradations.

3. Thomas Musgrave,[696] Fellow of Trinity College, Cambridge, was _Dean_
of the college when I was an undergraduate: this brought me into connection
with him, he giving impositions for not going to chapel, I writing them out
according. We had also friendly intercourse in after life; I forgiving, he
probably forgetting. Honest Tom {325} Musgrave, as he used to be called,
became Bishop of Hereford, and Archbishop of York.

4. About the time when I went to Cambridge, I heard a great deal about Mr.
C. T. Longley,[697] of Christchurch, from a cousin of my own of the same
college, long since deceased, who spoke of him much, and most
affectionately. Dr. Longley passed from Durham to York, and thence to
Canterbury. I cannot quite make out the two Archbishoprics; I do not
remember any other private channel through which the name came to me:
perhaps Dr. Longley, having two strings to his bow, would have been one
archbishop if I had never heard of him.

5. When Dr. Wm. Thomson[698] was appointed to the see of Gloucester in
1861, he and I had been correspondents on the subject of logic--on which we
had both written--for about fourteen years. On his elevation I wrote to
him, giving the preceding instances, and informing him that he would
certainly be an Archbishop. The case was a strong one, and the law acted
rapidly; for Dr. Thomson's elevation to the see of York took place in 1862.

Here are five cases; and there is no opposing instance. I have searched the
almanacs since 1828, and can find no instance of a Bishop not finally
Archbishop of whom I had known through private sources, direct or indirect.
Now what do my paradoxers say? Is this a pre-established harmony, or a
chain of coincidences? And how many instances will it require to establish
a law?[699]

{326}



THE HERSCHEL HOAX.

    Some account of the great astronomical discoveries lately made by Sir
    John Herschel at the Cape of Good Hope. Second Edition. London, 12mo.
    1836.

This is a curious hoax, evidently written by a person versed in astronomy
and clever at introducing probable circumstances and undesigned
coincidences.[700] It first appeared in a newspaper. It makes Sir J.
Herschel discover men, animals, etc. in the moon, of which much detail is
given. There seems to have been a French edition, the original, and English
editions in America, whence the work came into Britain: but whether the
French was published in America or at Paris I do not know. There is no
doubt that it was produced in the United States, by M. Nicollet,[701] an
astronomer, once of Paris, and a fugitive of some kind. About him I have
heard two stories. First that he fled to America with funds not his own,
and that this book was a mere device to raise the wind. Secondly, that he
was a protégé of Laplace, and of the Polignac party, and also an outspoken
man. That after the revolution he was so obnoxious to the republican party
that he judged it prudent to quit France; which he did in debt, leaving
money for his creditors, but not enough, with M. Bouvard. In America he
connected himself with an assurance office. {327} The moon-story was
written, and sent to France, chiefly with the intention of entrapping M.
Arago, Nicollet's especial foe, into the belief of it. And those who
narrate this version of the story wind up by saying that M. Arago _was_
entrapped, and circulated the wonders through Paris, until a letter from
Nicollet to M. Bouvard[702] explained the hoax. I have no personal
knowledge of either story: but as the poor man had to endure the first, it
is but right that the second should be told with it.



SOME MORE METEOROLOGY.

    The Weather Almanac for the Year 1838. By P. Murphy,[703] Esq., M.N.S.

By M. N. S. is meant _member of no society._. This almanac bears on the
title-page two recommendations. The _Morning Post_ calls it one of the most
important-if-true publications of our generation. The _Times_ says: "If the
basis of his theory prove sound, and its principles be sanctioned by a more
extended experience, it is not too much to say that the importance of the
discovery is equal to that of the longitude." Cautious journalist! Three
times that of the longitude would have been too little to say. That the
landsman might predict the weather of all the year, at its beginning, Jack
would cheerfully give up astronomical longitude--_the_ problem--altogether,
and fall back on chronometers with the older Ls, lead, latitude, and
look-out, applied to dead-reckoning. Mr. Murphy attempted to give the
weather day by day: thus the first seven days of March {328} bore
Changeable; Rain; Rain; Rain-_wind_; Changeable; Fair; Changeable. To aim
at such precision as to put a fair day between two changeable ones by
weather theory was going very near the wind and weather too. Murphy opened
the year with cold and frost; and the weather did the same. But Murphy,
opposite to Saturday, January 20, put down "Fair, Probable lowest degree of
winter temperature." When this Saturday came, it was not merely the
probably coldest of 1838, but certainly the coldest of many consecutive
years. Without knowing anything of Murphy, I felt it prudent to cover my
nose with my glove as I walked the street at eight in the morning. The
fortune of the Almanac was made. Nobody waited to see whether the future
would dement the prophecy: the shop was beset in a manner which brought the
police to keep order; and it was said that the Almanac for 1838 was a gain
of 5,000l. to the owners. It very soon appeared that this was only a lucky
hit: the weather-prophet had a modified reputation for a few years; and is
now no more heard of. A work of his will presently appear in the list.



THE GREAT PYRAMIDS.

    Letter from Alexandria on the evidence of the practical application of
    the quadrature of the circle in the great pyramids of Gizeh. By H. C.
    Agnew,[704] Esq. London, 1838, 4to.

{329}

Mr. Agnew detects proportions which he thinks were suggested by those of
the circumference and diameter of a circle.



THE MATHEMATICS OF A CREED.

    The creed of St. Athanasius proved by a mathematical parallel. Before
    you censure, condemn, or approve; read, examine, and understand. E. B.
    REVILO.[705] London, 1839, 8vo.

This author really believed himself, and was in earnest. He is not the only
person who has written nonsense by confounding the mathematical infinite
(of quantity) with what speculators now more correctly express by the
unlimited, the unconditioned, or the absolute. This tract is worth
preserving, as the extreme case of a particular kind. The following is a
specimen. Infinity being represented by [infinity], as usual, and f, s, g,
being finite integers, the three Persons are denoted by [infinity]^{f}, (m
[infinity])^{s}, [infinity]^{g}, the finite fraction m representing human
nature, as opposed to [infinity]. The clauses of the Creed are then given
with their mathematical parallels. I extract a couple:

 "But the Godhead of the
  Father, of the Son, and of
  the Holy Ghost, is all one:
  the glory equal, the Majesty
  co-eternal.

 "It has been shown that
  [infinity]^f, [infinity]^g, and (m [infinity])^s, together,
  are but [infinity], and that
  each is [infinity], and any magnitude
  in existence represented
  by [infinity] always was and always
  will be: for it cannot
  be made, or destroyed, and
  yet exists.

{330}

 "Equal to the Father, as
  touching his Godhead: and
  inferior  to the  Father,
  touching his Manhood."

 "(m [infinity])^s is equal to [infinity]^f as
  touching [infinity], but inferior to
  [infinity]^f as touching m: because
  m is not infinite."

I might have passed this over, as beneath even my present subject, but for
the way in which I became acquainted with it. A bookseller, _not the
publisher_, handed it to me over his counter: one who had published
mathematical works. He said, with an air of important communication, Have
you seen _this_, Sir! In reply, I recommended him to show it to my friend
Mr.----, for whom he had published mathematics. Educated men, used to books
and to the converse of learned men, look with mysterious wonder on such
productions as this: for which reason I have made a quotation which many
will judge had better have been omitted. But it would have been an
imposition on the public if I were, omitting this and some other uses of
the Bible and Common Prayer, to pretend that I had given a true picture of
my school.

[Since the publication of the above, it has been stated that the author is
Mr. Oliver Byrne, the author of the _Dual Arithmetic_ mentioned further on:
E. B. Revilo seems to be obviously a reversal.]



LOGIC HAS NO PARADOXERS.

    Old and new logic contrasted: being an attempt to elucidate, for
    ordinary comprehension, how Lord Bacon delivered the human mind from
    its 2,000 years' enslavement under Aristotle. By Justin Brenan.[706]
    London, 1839, 12mo.

Logic, though the other exact science, has not had the sort of assailants
who have clustered about mathematics. There is a sect which disputes the
utility of logic, but there are no special points, like the quadrature of
the circle, which {331} excite dispute among those who admit other things.
The old story about Aristotle having one logic to trammel us, and Bacon
another to set us free,--always laughed at by those who really knew either
Aristotle or Bacon,--now begins to be understood by a large section of the
educated world. The author of this tract connects the old logic with the
indecencies of the classical writers, and the new with moral purity: he
appeals to women, who, "when they see plainly the demoralizing tendency of
syllogistic logic, they will no doubt exert their powerful influence
against it, and support the Baconian method." This is the only work against
logic which I can introduce, but it is a rare one, I mean in contents. I
quote the author's idea of a syllogism:

"The basis of this system is the syllogism. This is a form of couching the
substance of your argument or investigation into one short line or
sentence--then corroborating or supporting it in another, and drawing your
conclusion or proof in a third."

On this definition he gives an example, as follows: "Every sin deserves
death," the substance of the "argument or investigation." Then comes,
"Every unlawful wish is a sin," which "corroborates or supports" the
preceding: and, lastly, "therefore every unlawful wish deserves death,"
which is the "conclusion or proof." We learn, also, that "sometimes the
first is called the premises (_sic_), and sometimes the first premiss"; as
also that "the first is sometimes called the proposition, or subject, or
affirmative, and the next the predicate, and sometimes the middle term." To
which is added, with a mark of exclamation at the end, "but in analyzing
the syllogism, there is a middle term, and a predicate too, in each of the
lines!" It is clear that Aristotle never enslaved this mind.

I have said that logic has no paradoxers, but I was speaking of old time.
This science has slept until our own day: Hamilton[707] says there has been
"no progress made in {332} the _general_ development of the syllogism since
the time of Aristotle; and in regard to the few _partial_ improvements, the
professed historians seem altogether ignorant." But in our time, the
paradoxer, the opponent of common opinion, has appeared in this field. I do
not refer to Prof. Boole,[708] who is not a _paradoxer_, but a
_discoverer_: his system could neither oppose nor support common opinion,
for its grounds were not in the conception of any one. I speak especially
of two others, who fought like cat and dog: one was dogmatical, the other
categorical. The first was Hamilton himself--Sir William Hamilton of
Edinburgh, the metaphysician, not Sir William _Rowan_ Hamilton[709] of
Dublin, the mathematician, a combination of peculiar genius with
unprecedented learning, erudite in all he could want except mathematics,
for which he had no turn, and in which he had not even a schoolboy's
knowledge, thanks to the Oxford of his younger day. The other was the
author of this work, so fully described in Hamilton's writings that there
is no occasion to describe him here. I shall try to say a few words in
common language about the paradoxers.

Hamilton's great paradox was the _quantification of the predicate_; a
fearful phrase, easily explained. We all know that when we say "Men are
animals," a form wholly unquantified in phrase, we speak of _all_ men, but
not of all animals: it is _some or all_, some may be all for aught the
proposition says. This some-may-be-all-for-aught-we-say, or _not-none,_ is
the logician's _some_. One would suppose {333} that "all men are some
animals," would have been the logical phrase in all time: but the predicate
never was quantified. The few who alluded to the possibility of such a
thing found reasons for not adopting it over and above the great reason,
that Aristotle did not adopt it. For Aristotle never ruled in physics or
metaphysics _in the old time_ with near so much of absolute sway as he has
ruled in logic _down to our own time_. The logicians knew that in the
proposition "all men are animals" the "animal" is not _universal_, but
_particular_ yet no one dared to say that _all_ men are _some_ animals, and
to invent the phrase, "_some_ animals are _all_ men" until Hamilton leaped
the ditch, and not only completed a system of enunciation, but applied it
to syllogism.

My own case is as peculiar as his: I have proposed to introduce
mathematical _thought_ into logic to an extent which makes the old stagers
cry:

 "St. Aristotle! what wild notions!
  Serve a _ne exeat regno_[710] on him!"

Hard upon twenty years ago, a friend and opponent who stands high in these
matters, and who is not nearly such a sectary of Aristotle and
establishment as most, wrote to me as follows: "It is said that next to the
man who forms the taste of the nation, the greatest genius is the man who
corrupts it. I mean therefore no disrespect, but very much the reverse,
when I say that I have hitherto always considered you as a great logical
heresiarch." Coleridge says he thinks that it was Sir Joshua Reynolds who
made the remark: which, to copy a bull I once heard, I cannot deny, because
I was not there when he said it. My friend did not call me to repentance
and reconciliation with the church: I think he had a guess that I was a
reprobate sinner. My offences at that time were but small: I went on
spinning syllogism systems, all alien from the common logic, until I had
six, the initial letters of which, put together, from the {334} names I
gave before I saw what they would make, bar all repentance by the words

  RUE NOT!

leaving to the followers of the old school the comfortable option of
placing the letters thus:

  TRUE? NO!

It should however be stated that the question is not about absolute truth
or falsehood. No one denies that anything I call an inference is an
inference: they say that my alterations are _extra-logical_; that they are
_material_, not _formal_; and that logic is a _formal_ science.

The distinction between material and formal is easily made, where the usual
perversions are not required. A _form_ is an empty machine, such as "Every
X is Y"; it may be supplied with _matter_, as in "Every _man_ is _animal_."
The logicians will not see that their _formal_ proposition, "Every X is Y,"
is material in three points, the degree of assertion, the quantity of the
proposition, and the copula. The purely formal proposition is "There is the
probability [alpha] that X stands in the relation L to Y." The time will
come when it will be regretted that logic went without paradoxers for two
thousand years: and when much that has been said on the distinction of form
and matter will breed jokes.

I give one instance of one mood of each of the systems, in the order of the
letters first written above.

_Relative._--In this system the formal relation is taken, that is, the
copula may be any whatever. As a material instance, in which the
_relations_ are those of consanguinity (of men understood), take the
following: X is the brother of Y; X is not the uncle of Z; therefore, Z is
not the child of Y. The discussion of relation, and of the objections to
the extension, is in the _Cambridge Transactions_, Vol. X, Part 2; a
crabbed conglomerate.

_Undecided._--In this system one premise, and want of power over another,
infer want of power over a conclusion. {335} As "Some men are not capable
of tracing consequences; we cannot be sure that there are beings
responsible for consequences who are incapable of tracing consequences;
therefore, we cannot be sure that all men are responsible for the
consequences of their actions."

_Exemplar._--This, long after it suggested itself to me as a means of
correcting a defect in Hamilton's system, I saw to be the very system of
Aristotle himself, though his followers have drifted into another. It makes
its subject and predicate examples, thus: Any one man is an animal; any one
animal is a mortal; therefore, any one man is a mortal.

_Numerical._--Suppose 100 Ys to exist: then if 70 Xs be Ys, and 40 Zs be
Ys, it follows that 10 Xs (at least) are Zs. Hamilton, whose mind could not
generalize on symbols, saw that the word _most_ would come under this
system, and admitted, as valid, such a syllogism as "most Ys are Xs; most
Ys are Zs; therefore, some Xs are Zs."

_Onymatic._--This is the ordinary system much enlarged in propositional
forms. It is fully discussed in my _Syllabus of Logic_.

_Transposed._--In this syllogism the quantity in one premise is transposed
into the other. As, some Xs are not Ys; for every X there is a Y which is
Z; therefore, some Zs are not Xs.

Sir William Hamilton of Edinburgh was one of the best friends and allies I
ever had. When I first began to publish speculation on this subject, he
introduced me to the logical world as having plagiarized from him. This
drew their attention: a mathematician might have written about logic under
forms which had something of mathematical look long enough before the
Aristotelians would have troubled themselves with him: as was done by John
Bernoulli,[711] {336} James Bernoulli,[712] Lambert,[713] and
Gergonne;[714] who, when our discussion began, were not known even to
omnilegent Hamilton. He retracted his accusation of _wilful_ theft in a
manly way when he found it untenable; but on this point he wavered a
little, and was convinced to the last that I had taken his principle
unconsciously. He thought I had done the same with Ploucquet[715] and
Lambert. It was his pet notion that I did not understand the commonest
principles of logic, that I did not always know the difference between the
middle term of a syllogism and its conclusion. It went against his grain to
imagine that a mathematician could be a logician. So long as he took me to
be riding my own hobby, he laughed consumedly: but when he thought he could
make out that I was mounted behind Ploucquet or Lambert, the current ran
thus: "It would indeed have been little short of a miracle had he, ignorant
even of the common principles of logic, been able of himself to rise to
generalization so lofty and so accurate as are supposed in the peculiar
doctrines of both the rival logicians, Lambert and Ploucquet--how useless
soever these may in practice prove to be." All this has been sufficiently
discussed elsewhere: "but, masters, remember that I am an ass."

I know that I never saw Lambert's work until after all Hamilton supposed me
to have taken was written: he himself, who read almost everything, knew
nothing about it until after I did. I cannot prove what I say about my
knowledge of Lambert: but the means of doing it may turn up. For, by the
casual turning up of an old letter, I _have_ {337} found the means of
clearing myself as to Ploucquet. Hamilton assumed that (unconsciously) I
took from Ploucquet the notion of a logical notation in which the symbol of
the conclusion is seen in the joint symbols of the premises. For example,
in my own fashion I write down ( . ) ( . ), two symbols of premises. By
these symbols I see that there is a valid conclusion, and that it may be
written in symbol by striking out the two middle parentheses, which gives (
. . ) and reading the two negative dots as an affirmative. And so I see in
( . ) ( . ) that ( ) is the conclusion. This, in full, is the perception
that "all are either Xs or Ys" and "all are either Ys or Zs" necessitates
"some Xs are Zs." Now in Ploucquet's book of 1763, is found, "Deleatur in
præmissis medius; id quod restat indicat conclusionem."[716] In the paper
in which I explain my symbols--which are altogether different from
Ploucquet's--there is found "Erase the symbols of the middle term; the
remaining symbols show the inference." There is very great likeness: and I
would have excused Hamilton for his notion if he had fairly given reference
to the part of the book in which his quotation was found. For I had shown
in my _Formal Logic_ what part of Ploucquet's book I had used: and a fair
disputant would either have strengthened his point by showing that I had
been at his part of the book, or allowed me the advantage of it being
apparent that I had not given evidence of having seen that part of the
book. My good friend, though an honest man, was sometimes unwilling to
allow due advantage to controversial opponents.

But to my point. The only work of Ploucquet I ever saw was lent me by my
friend Dr. Logan,[717] with whom I have often corresponded on logic, etc. I
chanced (in 1865) {338} to turn up the letter which he sent me (Sept. 12,
1847) _with the book_. Part of it runs thus: "I congratulate you on your
success in your logical researches [that is, in asking for the book, I had
described some results]. Since the reading of your first paper I have been
satisfied as to the possibility of inventing a logical notation in which
the rationale of the inference is contained in the symbol, though I never
attempted to verify it [what I communicated, then, satisfied the writer
that I had done and communicated what he, from my previous paper, suspected
to be practicable]. I send you Ploucquet's dissertation....'

It now being manifest that I cannot be souring grapes which have been taken
from me, I will say what I never said in print before. There is not the
slightest merit in making the symbols of the premises yield that of the
conclusion by erasure: _the thing must do itself in every system which
symbolises quantities_. For in every syllogism (except the inverted
_Bramantip_ of the Aristotelians) the conclusion is manifest in this way
without symbols. This _Bramantip_ destroys system in the Aristotelian lot:
and circumstances which I have pointed out destroy it in Hamilton's own
collection. But in that enlargement of the reputed Aristotelian system
which I have called _onymatic_, and in that correction of Hamilton's system
which I have called _exemplar_, the rule of erasure is universal, and may
be seen without symbols.

Our first controversy was in 1846. In 1847, in my _Formal Logic_, I gave
him back a little satire for satire, just to show, as I stated, that I
could employ ridicule if I pleased. He was so offended with the appendix in
which this was contained, that he would not accept the copy of the book I
sent him, but returned it. Copies of controversial works, sent from
opponent to opponent, are not _presents_, in the usual sense: it was a
marked success to make him angry enough to forget this. It had some effect
however: during the rest of his life I wished to avoid provocation; for I
{339} could not feel sure that excitement might not produce consequences. I
allowed his slashing account of me in the _Discussions_ to pass unanswered:
and before that, when he proposed to open a controversy in the _Athenæum_
upon my second Cambridge paper, I merely deferred the dispute until the
next edition of my _Formal Logic_. I cannot expect the account in the
_Discussions_ to amuse an unconcerned reader as much as it amused myself:
but for a cut-and-thrust, might-and-main, tooth-and-nail, hammer-and-tongs
assault, I can particularly recommend it. I never knew, until I read it,
how much I should enjoy a thundering onslought on myself, done with racy
insolence by a master hand, to whom my good genius had whispered _Ita feri
ut se sentiat emori_.[718] Since that time I have, as the Irishman said,
become "dry moulded for want of a bating." Some of my paradoxers have done
their best: but theirs is mere twopenny--"small swipes," as Peter Peebles
said. Brandy for heroes! I hope a reviewer or two will have mercy on me,
and will give me as good discipline as Strafford would have given Hampden
and his set: "much beholden," said he, "should they be to any one that
should thoroughly take pains with them in that kind"--meaning _objective_
flagellation. And I shall be the same to any one who will serve me so--but
in a literary and periodical sense: my corporeal cuticle is as thin as my
neighbors'.

Sir W. H. was suffering under local paralysis before our controversy
commenced: and though his mind was quite unaffected, a retort of as
downright a character as the attack might have produced serious effect upon
a person who had shown himself sensible of ridicule. Had a second attack of
his disorder followed an answer from me, I should have been held to have
caused it: though, looking at Hamilton's genial love of combat, I strongly
suspected that a retort in kind

{340}

 "Would cheer his heart, and warm his blood,
  And make him fight, and do him good."

But I could not venture to risk it. So all I did, in reply to the article
in the _Discussions_, was to write to him the following note: which, as
illustrating an etiquette of controversy, I insert.

"I beg to acknowledge and thank you for.... It is necessary that I should
say a word on my retention of this work, with reference to your return of
the copy of my _Formal Logic_, which I presented to you on its publication:
a return made on the ground of your disapproval of the account of our
controversy which that work contained. According to my view of the subject,
any one whose dealing with the author of a book is specially attacked in
it, has a right to expect from the author that part of the book in which
the attack is made, together with so much of the remaining part as is
fairly context. And I hold that the acceptance by the party assailed of
such work or part of a work does not imply any amount of approval of the
contents, or of want of disapproval. On this principle (though I am not
prepared to add the word _alone_) I forwarded to you the whole of my work
on _Formal Logic_ and my second Cambridge Memoir. And on this principle I
should have held you wanting in due regard to my literary rights if you had
not forwarded to me your asterisked pages, with all else that was necessary
to a full understanding of their scope and meaning, so far as the contents
of the book would furnish it. For the remaining portion, which it would be
a hundred pities to separate from the pages in which I am directly
concerned, I am your debtor on another principle; and shall be glad to
remain so if you will allow me to make a feint of balancing the account by
the offer of two small works on subjects as little connected with our
discussion as the _Epistolæ Obscurorum Virorum_, or the Lutheran dispute. I
trust that by accepting my _Opuscula_ you will enable me to avoid the {341}
use of the knife, and leave me to cut you up with the pen as occasion shall
serve, I remain, etc. (April 21, 1852)."

I received polite thanks, but not a word about the body of the letter: my
argument, I suppose, was admitted.



SOME DOGGEREL AND COUNTER DOGGEREL.

I find among my miscellaneous papers the following _jeu d'esprit_, or _jeu
de bêtise_,[719] whichever the reader pleases--I care not--intended, before
I saw ground for abstaining, to have, as the phrase is, come in somehow. I
think I could manage to bring anything into anything: certainly into a
Budget of Paradoxes. Sir W. H. rather piqued himself upon some caniculars,
or doggerel verses, which he had put together _in memoriam_ [_technicam_]
of the way in which A E I O are used in logic: he added U, Y, for the
addition of _meet_, etc., to the system. I took the liberty of concocting
some counter-doggerel, just to show that a mathematician may have
architectonic power as well as a metaphysician.



          DOGGEREL.
      BY SIR W.  HAMILTON.
  A it affirms of _this_, _these_, _all_,
    Whilst E denies of _any_;
  I it affirms (whilst O denies)
    Of some (or few, or many).

  Thus A affirms, as E denies,
    And definitely either;
  Thus I affirms, as O denies,
    And definitely neither.

  A half, left semidefinite,
    Is worthy of its score;
  U, then, affirms, as Y denies,
    This, neither less nor more.

  Indefinito-definites,
    I, UI, YO, last we come;
  {342}
  And this affirms, as that denies
    Of _more_, _most_ (_half_, _plus_, _some_).

    COUNTER DOGGEREL.
      BY PROF. DE MORGAN.
          (1847.)
  Great A affirms of all;
    Sir William does so too:
  When the subject is "my suspicion,"
    And the predicate "must be true."

  Great E denies of all;
    Sir William of all but one:
  When he speaks about this present time,
    And of those who in logic have done.

  Great I takes up but _some_;
    Sir William! my dear soul!
  Why then in all your writings,
    Does "Great I" fill[720] the whole!

  Great O says some are not;
    Sir William's readers catch,
  That some (modern) Athens is not without
    An Aristotle to match.

 "A half, left semi-definite,
    Is worthy of its score:"
  This looked very much like balderdash,
    And neither less nor more.

  It puzzled me like anything;
    In fact, it puzzled me worse:
  Isn't schoolman's logic hard enough,
    Without being in Sibyl's verse?

  {343}
  At last, thinks I, 'tis German;
    And I'll try it with some beer!
  The landlord asked what bothered me so,
    And at once he made it clear.

  It's _half-and-half_, the gentleman means;
    Don't you see he talks of _score_?
  That's the bit of memorandum
    That we chalk behind the door.

  _Semi-definite_'s outlandish;
    But I see, in half a squint,
  That he speaks of the lubbers who call for a quart,
    When they can't manage more than a pint.

  Now I'll read it into English,
    And then you'll answer me this:
  If it isn't good logic all the world round,
    I should like to know what is?

  When you call for a pot of half-and-half,
    If you're lost to sense of shame,
  You may leave it _semi-definite_,
    But you pay for it all just the same.
      *    *    *    *    *    *

I am unspeakably comforted when I look over the above in remembering that
the question is not whether it be Pindaric or Horatian, but whether the
copy be as good as the original. And I say it is: and will take no denial.

Long live--long will live--the glad memory of William Hamilton, Good,
Learned, Acute, and Disputatious! He fought upon principle: the motto of
his book is:

 "Truth, like a torch, the more it's shook it shines."

There is something in this; but metaphors, like puddings, quarrels, rivers,
and arguments, always have two sides to them. For instance,

 "Truth, like a torch, the more it's shook it shines;
    But those who want to use it, hold it steady.
  They shake the flame who like a glare to gaze at,
    They keep it still who want a light to see by."

{344}



ANOTHER THEORY OF PARALLELS.

    Theory of Parallels. The proof of Euclid's axiom looked for in the
    properties of the Equiangular Spiral. By Lieut-Col. G. Perronet
    Thompson.[721] The same, second edition, revised and corrected. The
    same, third edition, shortened, and freed from dependence on the theory
    of limits. The same, fourth edition, ditto, ditto. All London, 1840,
    8vo.

To explain these editions it should be noted that General Thompson rapidly
modified his notions, and republished his tracts accordingly.



SOME PRIMITIVE DARWINISM.

    Vestiges of the Natural History of Creation.[722] London, 1840, 12mo.

This is the first edition of this celebrated work. Its form is a case of
the theory: the book is an undeniable duodecimo, but the size of its paper
gives it the look of not the smallest of octavos. Does not this illustrate
the law of development, the gradation of families, the transference of
species, and so on? If so, I claim the discovery of this esoteric testimony
of the book to its own contents; I defy any one to point out the reviewer
who has mentioned it. The work itself is described by its author as "the
first attempt to connect the natural sciences into a history of creation."
The attempt was commenced, and has been carried on, both with marked
talent, and will be continued. Great advantage will result: at the worst we
are but in the alchemy of some new chemistry, or the astrology of some new
astronomy. Perhaps it would be as well not to be too sure on the matter,
until we have an antidote to possible consequences as exhibited under
another theory, on which {345} it is as reasonable to speculate as on that
of the _Vestiges_. I met long ago with a splendid player on the guitar, who
assured me, and was confirmed by his friends, that he _never practised_,
except in thought, and did not possess an instrument: he kept his fingers
acting in his mind, until they got their habits; and thus he learnt the
most difficult novelties of execution. Now what if this should be a minor
segment of a higher law? What if, by constantly thinking of ourselves as
descended from primeval monkeys, we should--if it be true--actually _get
our tails again_? What if the first man who was detected with such an
appendage should be obliged to confess himself the author of the
_Vestiges_--a person yet unknown--who would naturally get the start of his
species by having had the earliest habit of thinking on the matter? I
confess I never hear a man of note talk fluently about it without a curious
glance at his proportions, to see whether there may be ground to conjecture
that he may have more of "mortal coil" than others, in anaxyridical
concealment. I do not feel sure that even a paternal love for his theory
would induce him, in the case I am supposing, to exhibit himself at the
British Association,

  With a hole behind which his tail peeped through.

The first sentence of this book (1840) is a cast of the log, which shows
our rate of progress. "It is familiar knowledge that the earth which we
inhabit is a globe of somewhat less than 8,000 miles in diameter, being one
of a series of eleven which revolve at different distances around the sun."
The _eleven_! Not to mention the Iscariot which Le Verrier and Adams
calculated into existence, there is more than a septuagint of _new_
planetoids.



ON RELIGIOUS INSURANCE.

    The Constitution and Rules of the Ancient and Universal 'Benefit
    Society' established by Jesus Christ, exhibited, and its advantages and
    claims maintained, against all Modern and {346} merely Human
    Institutions of the kind: A Letter very respectfully addressed to the
    Rev. James Everett,[723] and occasioned by certain remarks made by him,
    in a speech to the Members of the 'Wesleyan Centenary Institute'
    Benefit Society. Dated York, Dec. 7, 1840. By Thomas Smith.[724] 12mo,
    (pp. 8.)

The Wesleyan minister addressed had advocated provision against old age,
etc.: the writer declares all _private_ provision un-Christian. After
decent maintenance and relief of family claims of indigence, he holds that
all the rest is to go to the "Benefit Society," of which he draws up the
rules, in technical form, with chapters of "Officers," "Contributors" etc.,
from the Acts of the Apostles, etc., and some of the early Fathers. He
holds that a Christian may not "make a _private_ provision against the
contingencies of the future": and that the great "Benefit Society" is the
divinely-ordained recipient of all the surplus of his income; capital,
beyond what is necessary for business, he is to have none. A real good
speculator shuts his eyes by instinct, when opening them would not serve
the purpose: he has the vizor of the Irish fairy tale, which fell of itself
over the eyes of the wearer the moment he turned them upon the enchanted
light which would have destroyed him if he had caught sight of it. "Whiles
it remained, was it not thine own? and after it was sold, was it (the
purchase-money) not in thine own power?" would have been awkward to quote,
and accordingly nothing is stated except the well-known result, which is
rule 3, cap. 5, "Prevention of Abuses." By putting his principles together,
the author can be made, logically, to mean that the successors of the
apostles should put to death all contributors who are detected in not
paying their full premiums.

{347}

I have known one or two cases in which policy-holders have surrendered
their policies through having arrived at a conviction that direct provision
is unlawful. So far as I could make it out, these parties did not think it
unlawful to lay by out of income, except when this was done in a manner
which involved calculation of death-chances. It is singular they did not
see that the entrance of chance of death was the entrance of the very
principle of the benefit society described in the Acts of the Apostles. The
family of the one who died young received more in proportion to _premiums_
paid than the family of one who died old. Every one who understands life
assurance sees that--_bonus_ apart--the difference between an assurance
office and a savings bank consists in the adoption, _pro tanto_, of the
principle of community of goods. In the original constitution of the oldest
assurance office, the _Amicable Society_, the plan with which they started
was nothing but this: persons of all ages under forty-five paid one common
premium, and the proceeds were divided among the representatives of those
who died within the year.



THE TWO OLD PARADOXES AGAIN.

[I omitted from its proper place a manuscript quadrature (3.1416 exactly)
addressed to an eminent mathematician, dated in 1842 from the debtor's ward
of a country gaol. The unfortunate speculator says, "I have labored many
years to find the precise ratio." I have heard of several cases in which
squaring the circle has produced an inability to square accounts. I remind
those who feel a kind of inspiration to employ native genius upon
difficulties, without gradual progression from elements, that the call is
one which becomes stronger and stronger, and may lead, as it has led, to
abandonment of the duties of life, and all the consequences.] {348}



    1842. Provisional Prospectus of the Double Acting Rotary Engine
    Company. Also Mechanic's Magazine, March 26, 1842.

Perpetual motion by a drum with one vertical half in mercury, the other in
a vacuum: the drum, I suppose, working round forever to find an easy
position. Steam to be superseded: steam and electricity convulsions of
nature never intended by Providence for the use of man. The price of the
present engines, as old iron, will buy new engines that will work without
fuel and at no expense. Guaranteed by the Count de Predaval,[725] the
discoverer. I was to have been a Director, but my name got no further than
ink, and not so far as official notification of the honor, partly owing to
my having communicated to the _Mechanic's Magazine_ information privately
given to me, which gave premature publicity, and knocked up the plan.



    An Exposition of the Nature, Force, Action, and other properties of
    Gravitation on the Planets. London, 1842, 12mo.

    An Investigation of the principles of the Rules for determining the
    Measures of the Areas and Circumferences of Circular Plane Surfaces ...
    London, 1844, 8vo.

These are anonymous; but the author (whom I believe to be Mr. Denison,[726]
presently noted) is described as author of a new system of mathematics, and
also of mechanics. He had need have both, for he shows that the line which
has a square equal to a given circle, has a cube equal to the sphere on the
same diameter: that is, in old mathematics, the diameter is to the
circumference as 9 to 16! Again, admitting that the velocities of planets
in circular orbits are inversely as the square roots of their distances,
that is, admitting Kepler's law, he manages to prove that gravitation is
inversely as the square _root_ of the distance: and suspects magnetism of
doing the difference between this and Newton's law. {349} Magnetism and
electricity are, in physics, the member of parliament and the cabman--at
every man's bidding, as Henry Warburton[727] said.

The above is an outrageous quadrature. In the preceding year, 1841, was
published what I suppose at first to be a Maori quadrature, by Maccook. But
I get it from a cutting out of some French periodical, and I incline to
think that it must be by a Mr. M^cCook. He makes [pi] to be 2 +
2[root](8[root]2 - 11).



THE DUPLICATION PROBLEM.

    Refutation of a Pamphlet written by the Rev. John Mackey, R.C.P.,[728]
    entitled "A method of making a cube double of a cube, founded on the
    principles of elementary geometry," wherein his principles are proved
    erroneous, and the required solution not yet obtained. By Robert
    Murphy.[729] Mallow, 1824, 12mo.

This refutation was the production of an Irish boy of eighteen years old,
self-educated in mathematics, the son of a shoemaker at Mallow. He died in
1843, leaving a name which is well known among mathematicians. His works on
the theory of equations and on electricity, and his papers in the
_Cambridge Transactions_, are all of high genius. The only account of him
which I know of is that which I wrote for the _Supplement_ of the _Penny
Cyclopædia_. He was thrown by his talents into a good income at Cambridge,
with no social training except penury, and very little intellectual
training except mathematics. He fell into dissipation, and his scientific
career was almost arrested: but he had great good in him, to my knowledge.
A sentence in {350} a letter from the late Dean Peacock[730] to me--giving
some advice about the means of serving Murphy--sets out the old case:
"Murphy is a man whose _special_ education is in advance of his _general_;
and such men are almost always difficult subjects to manage." This article
having been omitted in its proper place, I put it at 1843, the date of
Murphy's death.



A NEW VALUE OF [pi].

    The Invisible Universe disclosed; or, the real Plan and Government of
    the Universe. By Henry Coleman Johnson, Esq. London, 1843, 8vo.

The book opens abruptly with:

"First demonstration. Concerning the centre: showing that, because the
centre is an innermost point at an equal distance between two extreme
points of a right line, and from every two relative and opposite
intermediate points, it is composed of the two extreme internal points of
each half of the line; each extreme internal point attracting towards
itself all parts of that half to which it belongs...."

Of course the circle is squared: and the circumference is 3-1/21 diameters.



SOME MODERN ASTROLOGY.

    Combination of the Zodiacal and Cometical Systems. Printed for the
    London Society, Exeter Hall. Price Sixpence. (n. d. 1843.)

What this London Society was, or the "combination," did not appear. There
was a remarkable comet in 1843, the tail of which was at first confounded
with what is called the _zodiacal light_. This nicely-printed little tract,
evidently got up with less care for expense than is usual in such works,
brings together all the announcements of the astronomers, and adds a short
head and tail piece, which I shall quote entire. As the announcements are
very ordinary {351} astronomy, the reader will be able to detect, if
detection be possible, what is the meaning and force of the "Combination of
the Zodiacal and Cometical Systems":

"_Premonition._ It has pleased the AUTHOR _of_ CREATION to cause (to His
_human and reasoning_ Creatures of this generation, by a '_combined_'
appearance in His _Zodiacal_ and _Cometical_ system) a '_warning Crisis_'
of universal concernment to this our GLOBE. It is this '_Crisis_' that has
so generally 'ROUSED' at this moment the '_nations throughout the Earth_'
that no equal interest has ever before been excited by MAN; unless it be in
that caused by the 'PAGAN-TEMPLE IN ROME,' which is recorded by the elder
Pliny, '_Nat. Hist._' i. 23. iii. 3. HARDOUIN."

After the accounts given by the unperceiving astronomers, comes what
follows:

"Such has been (_hitherto_) the only object discerned by the '_Wise of this
World_,' in this _twofold union_ of the '_Zodiacal_' and '_Cometical_'
systems: yet it is nevertheless a most '_Thrilling Warning_,' to _all_ the
inhabitants of this precarious and transitory EARTH. We have no authorized
intimation or reasonable prospective contemplation, of '_current time_'
beyond a year 1860, of the present century; or rather, except '_the
interval which may now remain from the present year 1843, to a year 1860_'
([Greek: hêmeras HEXÊKONTA]--'_threescore or sixty days_'--'_I have
appointed each_ "DAY" _for a_ "YEAR,"' _Ezek._ iv. 6): and we know, from
our '_common experience_,' how speedily such a measure of time will pass
away.

"No words can be '_more explicit_' than these of OUR BLESSED LORD: viz.
'THIS GOSPEL _of the Kingdom shall be preached in_ ALL the EARTH, _for a
Witness to_ ALL NATIONS; AND THEN, _shall the_ END COME.' The '_next 18
years_' must therefore supply the interval of the '_special Episcopal
forerunners_.'

(Matt. xxiv. 14.)

"See the 'JEWISH INTELLIGENCER' of the present month (_April_), p. 153, for
the '_Debates in Parliament_,' respecting {352} the BISHOP OF JERUSALEM,
_viz._ Dr. Bowring,[731] Mr. Hume,[732] Sir R. Inglis,[733] Sir R.
Peel,[734] Viscount Palmerston.[735]"

I have quoted this at length, to show the awful threats which were
published at a time of some little excitement about the phenomenon, under
the name of the _London Society_. The assumption of a corporate appearance
is a very unfair trick: and there are junctures at which harm might be done
by it.



THE NUMBER OF THE BEAST.

    _Wealth_ the name and number of the Beast, 666, in the Book of
    Revelation. [by John Taylor.[736]] London, 1844, 8vo.

Whether Junius or the Beast be the more difficult to identify, must be
referred to Mr. Taylor, the only person who has attempted both. His cogent
argument on the political secret is not unworthily matched in his treatment
of the theological riddle. He sees the solution in [Greek: euporia], which
occurs in the Acts of the Apostles as the word for wealth in one of its
most disgusting forms, and makes 666 in the most straightforward way. This
explanation has as good a chance as any other. The work contains a general
{353} attempt at explanation of the Apocalypse, and some history of opinion
on the subject. It has not the prolixity which is so common a fault of
apocalyptic commentators.



    A practical Treatise on Eclipses ... with remarks on the anomalies of
    the present Theory of the Tides. By T. Kerigan,[737] F.R.S. 1844, 8vo.

Containing also a refutation of the theory of the tides, and afterwards
increased by a supplement, "Additional facts and arguments against the
theory of the tides," in answer to a short notice in the _Athenæum_
journal. Mr. Kerigan was a lieutenant in the Navy: he obtained admission to
the Royal Society just before the publication of his book.



    A new theory of Gravitation. By Joseph Denison,[738] Esq. London, 1844,
    12mo.

    Commentaries on the Principia. By the author of 'A new theory of
    Gravitation.' London, 1846, 8vo.

Honor to the speculator who can be put in his proper place by one sentence,
be that place where it may.

"But we have shown that the velocities are inversely as the square roots of
the mean distances from the sun; wherefore, by equality of ratios, the
forces of the sun's gravitation upon them are also inversely as the square
roots of their distances from the sun."



EASTER DAY PARADOXERS.

In the years 1818 and 1845 the full moon fell on Easter Day, having been
particularly directed to fall before it in the act for the change of style
and in the English missals and prayer-books of all time: perhaps it would
be more correct to say that Easter Day was directed to fall after the full
moon; "but the principle is the same." No explanation was given in 1818,
but Easter was kept by the tables, {354} in defiance of the rule, and of
several protests. A chronological panic was beginning in December 1844,
which was stopped by the _Times_ newspaper printing extracts from an
article of mine in the _Companion to the Almanac_ for 1845, which had then
just appeared. No one had guessed the true reason, which is that the thing
called the moon in the Gregorian Calendar is not the moon of the heavens,
but a fictitious imitation put wrong on purpose, as will presently appear,
partly to keep Easter out of the way of the Jews' Passover, partly for
convenience of calculation. The apparent error happens but rarely; and all
the work will perhaps have to be gone over next time. I now give two bits
of paradox.

Some theologians were angry at this explanation. A review called the
_Christian Observer_ (of which Christianity I do not know) got up a
crushing article against me. I did not look at it, feeling sure that an
article on such a subject which appeared on January 1, 1845, against a
publication made in December 1844, must be a second-hand job. But some
years afterwards (Sept. 10, 1850), the reviews, etc. having been just
placed at the disposal of readers in the _old_ reading-room of the Museum,
I made a tour of inspection, came upon my critic on his perch, and took a
look at him. I was very glad to remember this, for, though expecting only
second-hand, yet even of this there is good and bad; and I expected to find
some hints in the good second-hand of a respectable clerical publication. I
read on, therefore, attentively, but not long: I soon came to the
information that some additions to Delambre's[739] statement of the rule
for finding Easter, belonging to distant years, had been made by Sir Harris
Nicolas![740] Now as I myself furnished my friend Sir H. N. with Delambre's
digest of {355} Clavius's[741] rule, which I translated out of algebra into
common language for the purpose, I was pretty sure this was the ignorant
reading of a person to whom Sir H. N. was the highest _arithmetical_
authority on the subject. A person pretending to chronology, without being
able to distinguish the historical points--so clearly as they stand out--in
which Sir H. N. speaks with authority, from the arithmetical points of pure
reckoning on which he does not pretend to do more than directly repeat
others, must be as fit to talk about the construction of Easter Tables as
the Spanish are to talk French. I need hardly say that the additions for
distant years are as much from Clavius as the rest: my reviewer was not
deep enough in his subject to know that Clavius made and published, from
his rules, the full table up to A.D. 5000, for all the movable feasts of
every year! I gave only a glance at the rest: I found I was either knave or
fool, with a leaning to the second opinion; and I came away satisfied that
my critic was either ignoramus or novice, with a leaning to the first. I
afterwards found an ambiguity of expression in Sir H. N.'s account--whether
his or mine I could not tell--which might mislead a novice or content an
ignoramus, but would have been properly read or further inquired into by a
competent person.

The second case is this. Shortly after the publication of my article, a
gentleman called at my house, and, finding I was not at home, sent up his
card--with a stylish west-end club on it--to my wife, begging for a few
words on pressing business. With many well-expressed apologies, he stated
that he had been alarmed by hearing that Prof. De M. had an intention of
altering Easter next year. Mrs. De M. kept her countenance, and assured him
that I had no such intention, and further, that she greatly doubted my
having the power to do it. Was she quite sure? his authority was very good:
fresh assurances given. He was greatly relieved, for he had some horses
training for after Easter, which {356} would not be ready to run if it were
altered the wrong way. A doubt comes over him: would Mrs. De M., in the
event of her being mistaken, give him the very earliest information?
Promise given; profusion of thanks; more apologies; and departure.

Now, candid reader!--or uncandid either!--which most deserves to be laughed
at? A public instructor, who undertakes to settle for the world whether a
reader of Clavius, the constructor of the Gregorian Calendar, is fool or
knave, upon information derived from a compiler--in this matter--of his own
day; or a gentleman of horse and dog associations, who, misapprehending
something which he heard about a current topic, infers that the reader of
Clavius had the ear of the Government on a proposed alteration. I suppose
the querist had heard some one say, perhaps, that the day ought to be set
right, and some one else remark that I might be consulted, as the only
person who had discussed the matter from the original source of the
Calendar.

To give a better chance of the explanation being at once produced, next
time the real full moon and Easter Day shall fall together, I insert here a
summary which was printed in the Irish Prayer-book of the Ecclesiastical
Society. If the amusement given by paradoxers should prevent a useless
discussion some years hence, I and the paradoxers shall have done a little
good between us--at any rate, I have done my best to keep the heavy weight
afloat by tying bladders to it. I think the next occurrence will be in
1875.

EASTER DAY.

In the years 1818 and 1845, Easter Day, as given by the _rules in_ 24 Geo.
II cap. 23. (known as the act for the _change of style_) contradicted the
_precept_ given in the preliminary explanations. The precept is as follows:

"_Easter Day_, on which the rest" of the moveable feasts "depend, is always
the First Sunday after the Full Moon, which happens upon or next after the
Twenty-first Day of {357} _March_; and if the Full Moon happens upon a
Sunday, _Easter Day_ is the Sunday after."

But in 1818 and 1845, the full moon fell on a Sunday, and yet the rules
gave _that same Sunday_ for Easter Day. Much discussion was produced by
this circumstance in 1818: but a repetition of it in 1845 was nearly
altogether prevented by a timely[742] reference to the intention of those
who conducted the Gregorian reformation of the Calendar. Nevertheless,
seeing that the apparent error of the Calendar is due to the precept in the
Act of Parliament, which is both erroneous and insufficient, and that the
difficulty will recur so often as Easter Day falls on the day of full moon,
it may be advisable to select from the two articles cited in the note such
of their conclusions and rules, without proof or controversy, as will
enable the reader to understand the main points of the Easter question,
and, should he desire it, to calculate for himself the Easter of the old or
new style, for any given year.

1. In the very earliest age of Christianity, a controversy arose as to the
mode of keeping Easter, some desiring to perpetuate the _Passover_, others
to keep the _festival of the Resurrection_. The first afterwards obtained
the name of _Quartadecimans_, from their Easter being always kept on the
_fourteenth day_ of the moon (Exod. xii. 18, Levit. xxiii. 5.). But though
it is unquestionable that a Judaizing party existed, it is also likely that
many dissented on chronological grounds. It is clear that no _perfect_
anniversary can take place, except when the fourteenth of the moon, and
with it the passover, falls on a Friday. Suppose, for instance, it falls on
a Tuesday: one of three things must be {358} done. Either (which seems
never to have been proposed) the crucifixion and resurrection must be
celebrated on Tuesday and Sunday, with a wrong interval; or the former on
Tuesday, the latter on Thursday, abandoning the first day of the week; or
the former on Friday, and the latter on Sunday, abandoning the paschal
commemoration of the crucifixion.

The last mode has been, as every one knows, finally adopted. The disputes
of the first three centuries did not turn on any _calendar_ questions. The
Easter question was merely the symbol of the struggle between what we may
call the Jewish and Gentile sects of Christians: and it nearly divided the
Christian world, the Easterns, for the most part, being _Quartadecimans_.
It is very important to note that there is no recorded dispute about a
method of predicting the new moon, that is, no general dispute leading to
formation of sects: there may have been difficulties, and discussions about
them. The Metonic cycle, presently mentioned, must have been used by many,
perhaps most, churches.

2. The question came before the Nicene Council (A.D. 325) not as an
astronomical, but as a doctrinal, question: it was, in fact, this, Shall
the _passover_[743] be treated as a part of Christianity? The Council
resolved this question in the negative, and the only information on its
premises and conclusion, or either, which comes from itself, is contained
in the following sentence of the synodical epistle, which epistle is
preserved by Socrates[744] and Theodoret.[745] "We also send {359} you the
good news concerning the unanimous consent of all in reference to the
celebration of the most solemn feast of Easter, for this difference also
has been made up by the assistance of your prayers: so that all the
brethren in the East, who formerly celebrated this festival _at the same
time as the Jews_, will in future conform _to the Romans and to us_, and to
all who have of old observed _our manner_ of celebrating Easter." This is
all that can be found on the subject: none of the stories about the Council
ordaining the astronomical mode of finding Easter, and introducing the
Metonic cycle into ecclesiastical reckoning, have any contemporary
evidence: the canons which purport to be those of the Nicene Council do not
contain a word about Easter; and this is evidence, whether we suppose those
canons to be genuine or spurious.

3. The astronomical dispute about a lunar cycle for the prediction of
Easter either commenced, or became prominent, by the extinction of greater
ones, soon after the time of the Nicene Council. Pope Innocent I[746] met
with difficulty in 414. S. Leo,[747] in 454, ordained that Easter of 455
should be April 24; which is right. It is useless to record details of
these disputes in a summary: the result was, that in the year 463, Pope
Hilarius[748] employed Victorinus[749] of Aquitaine to correct the
Calendar, and Victorinus formed a rule which lasted until the sixteenth
century. He combined the Metonic cycle and the solar cycle presently
described. But {360} this cycle bears the name of Dionysius Exiguus,[750] a
Scythian settled at Rome, about A.D. 530, who adapted it to his new yearly
reckoning, when he abandoned the era of Diocletian as a commencement, and
constructed that which is now in common use.

4. With Dionysius, if not before, terminated all difference as to the mode
of keeping Easter which is of historical note: the increasing defects of
the Easter Cycle produced in time the remonstrance of persons versed in
astronomy, among whom may be mentioned Roger Bacon,[751] Sacrobosco,[752]
Cardinal Cusa,[753] Regiomontanus,[754] etc. From the middle of the sixth
to that of the sixteenth century, one rule was observed.

5. The mode of applying astronomy to chronology has always involved these
two principles. First, the actual position of the heavenly body is not the
object of consideration, but what astronomers call its _mean place_, which
may be described thus. Let a fictitious sun or moon move in the heavens, in
such manner as to revolve among the fixed stars at an average rate,
avoiding the alternate accelerations and retardations which take place in
every planetary motion. Thus the fictitious (say _mean_) sun and moon are
always very near to the real sun and moon. The ordinary clocks show time by
the mean, not the real, sun: and it was always laid down that Easter
depends on the opposition (or full moon) of the mean sun and moon, not of
the real ones. Thus we see that, were the Calendar ever so correct {361} as
to the _mean_ moon, it would be occasionally false as to the _true_ one:
if, for instance, the opposition of the mean sun and moon took place at one
second before midnight, and that of the real bodies only two seconds
afterwards, the calendar day of full moon would be one day before that of
the common almanacs. Here is a way in which the discussions of 1818 and
1845 might have arisen: the British legislature has defined _the moon_ as
the regulator of the paschal calendar. But this was only a part of the
mistake.

6. Secondly, in the absence of perfectly accurate knowledge of the solar
and lunar motion (and for convenience, even if such knowledge existed),
cycles are, and always have been taken, which serve to represent those
motions nearly. The famous Metonic cycle, which is introduced into
ecclesiastical chronology under the name of the cycle of the golden
numbers, is a period of 19 Julian[755] years. This period, in the old
Calendar, was taken to contain exactly 235 _lunations_, or intervals
between new moons, of the mean moon. Now the state of the case is:

19 average Julian years make 6939 days 18 hours.

235 average lunations make 6939 days 16 hours 31 minutes.

So that successive cycles of golden numbers, supposing the first to start
right, amount to making the new moons fall too late, gradually, so that the
mean moon _of this cycle_ gains 1 hour 29 minutes in 19 years upon the mean
moon of the heavens, or about a day in 300 years. When the Calendar was
reformed, the calendar new moons were four days in advance of the mean moon
of the heavens: so that, for instance, calendar full moon on the 18th
usually meant real full moon on the 14th.

7. If the difference above had not existed, the moon of the heavens (the
mean moon at least), would have returned {362} permanently to the same days
of the month in 19 years; with an occasional slip arising from the unequal
distribution of the leap years, of which a period contains sometimes five
and sometimes four. As a general rule, the days of new and full moon in any
one year would have been also the days of new and full moon of a year
having 19 more units in its date. Again, if there had been no leap years,
the days of the month would have returned to the same days of the week
every seven years. The introduction of occasional 29ths of February
disturbs this, and makes the permanent return of month days to week days
occur only after 28 years. If all had been true, the lapse of 28 times 19,
or 532 years, would have restored the year in every point: that is, A.D. 1,
for instance, and A.D. 533, would have had the same almanac in every matter
relating to week days, month days, sun, and moon (mean sun and moon at
least). And on the supposition of its truth, the old system of Dionysius
was framed. Its errors, are, first, that the moments of mean new moon
advance too much by 1 h. 29 m. in 19 average Julian years; secondly, that
the average Julian year of 365¼ days is too long by 11 m. 10 s.

8. The Council of Trent, moved by the representations made on the state of
the Calendar, referred the consideration of it to the Pope. In 1577,
Gregory XIII[756] submitted to the Roman Catholic Princes and Universities
a plan presented to him by the representatives of Aloysius Lilius,[757]
then deceased. This plan being approved of, the Pope nominated a commission
to consider its details, the working member of which was the Jesuit
Clavius. A short work was prepared by Clavius, descriptive of the new
Calendar: this {363} was published[758] in 1582, with the Pope's bull
(dated February 24, 1581) prefixed. A larger work was prepared by Clavius,
containing fuller explanation, and entitled _Romani Calendarii a Gregorio
XIII. Pontifice Maximo restituti Explicatio_. This was published at Rome in
1603, and again in the collection of the works of Clavius in 1612.

9. The following extracts from Clavius settle the question of the meaning
of the term _moon_, as used in the Calendar:

"Who, except a few who think they are very sharp-sighted in this matter, is
so blind as not to see that the 14th of the moon and the full moon are not
the same things in the Church of God?... Although the Church, in finding
the new moon, and from it the 14th day, _uses neither the true nor the mean
motion of the moon_, but measures only according to the order of a cycle,
it is nevertheless undeniable that the mean full moons found from
astronomical tables are of the greatest use in determining the cycle which
is to be preferred ... the new moons of which cycle, in order to the due
celebration of Easter, should be so arranged that the 14th days of those
moons, reckoning from the day of new moon _inclusive_, should not fall two
or more days before the mean full moon, but only one day, or else on the
very day itself, or not long after. And even thus far the Church need not
take very great pains ... for it is sufficient that all should reckon by
the 14th day of the moon in the cycle, even though sometimes it _should be
more than one day before or after_ the mean full moon.... We have taken
pains that in our cycle the new moons should _follow_ the real new moons,
so that the 14th of the moon should fall either the day before the mean
full moon, or on that day, or not long after; and this was done on purpose,
for if the new moon of the cycle fell on the same day as the mean new moon
of the {364} astronomers, it might chance that we should celebrate Easter
on the same day as the Jews or the Quartadeciman heretics, which would be
absurd, or else before them, which would be still more absurd."

From this it appears that Clavius continued the Calendar of his
predecessors in the choice of the _fourteenth_ day of the moon. Our
legislature lays down the day of the _full moon_: and this mistake appears
to be rather English than Protestant; for it occurs in missals published in
the reign of Queen Mary. The calendar lunation being 29½ days, the middle
day is the _fifteenth_ day, and this is and was reckoned as the day of the
full moon. There is every right to presume that the original passover was a
feast of the _real full moon_: but it is most probable that the moons were
then reckoned, not from the astronomical conjunction with the sun, which
nobody sees except at an eclipse, but from the day of _first visibility_ of
the new moon. In fine climates this would be the day or two days after
conjunction; and the fourteenth day from that of first visibility
inclusive, would very often be the day of full moon. The following is then
the proper correction of the precept in the Act of Parliament:

Easter Day, on which the rest depend, is always the First Sunday after the
_fourteenth day_ of the _calendar_ moon which happens upon or next after
the Twenty-first day of March, _according to the rules laid down for the
construction of the Calendar_; and if the _fourteenth day_ happens upon a
Sunday, Easter Day is the Sunday after.

10. Further, it appears that Clavius valued the celebration of the festival
after the Jews, etc., more than astronomical correctness. He gives
comparison tables which would startle a believer in the astronomical
intention of his Calendar: they are to show that a calendar in which the
moon is always made a day older than by him, _represents the heavens better
than he has done, or meant to do_. But it must be observed that this
diminution of the real moon's age has {365} a tendency to make the English
explanation often practically accordant with the Calendar. For the
fourteenth day of Clavius _is_ generally the fifteenth day of the mean moon
of the heavens, and therefore most often that of the real moon. But for
this, 1818 and 1845 would not have been the only instances of our day in
which the English precept would have contradicted the Calendar.

11. In the construction of the Calendar, Clavius adopted the ancient cycle
of 532 years, but, we may say, without ever allowing it to run out. At
certain periods, a shift is made from one part of the cycle into another.
This is done whenever what should be Julian leap year is made a common
year, as in 1700, 1800, 1900, 2100, etc. It is also done at certain times
to correct the error of 1 h. 19 m., before referred to, in each cycle of
golden numbers: Clavius, to meet his view of the amount of that error, put
forward the moon's age a day 8 times in 2,500 years. As we cannot enter at
full length into the explanation, we must content ourselves with giving a
set of rules, independent of tables, by which the reader may find Easter
for himself in any year, either by the old Calendar or the new. Any one who
has much occasion to find Easters and movable feasts should procure
Francoeur's[759] tables.

12. _Rule for determining Easter Day of the Gregorian Calendar in any year
of the new style._ To the several parts {366} of the rule are annexed, by
way of example, the results for the year 1849.

I. Add 1 to the given year. (1850).

II. Take the quotient of the given year divided by 4, neglecting the
remainder. (462).

III. Take 16 from the centurial figures of the given year, if it can be
done, and take the remainder. (2).

IV. Take the quotient of III. divided by 4, neglecting the remainder. (0).

V. From the sum of I, II, and IV., subtract III. (2310).

VI. Find the remainder of V. divided by 7. (0).

VII. Subtract VI. from 7; this is the number of the dominical letter

  1  2  3  4  5  6  7  (7; dominical letter G).
  A  B  C  D  E  F  G

VIII. Divide I. by 19, the remainder (or 19, if no remainder) is the
_golden number_. (7).

IX. From the centurial figures of the year subtract 17, divide by 25, and
keep the quotient. (0).

X. Subtract IX. and 15 from the centurial figures, divide by 3, and keep
the quotient. (1).

XI. To VIII. add ten times the next less number, divide by 30, and keep the
remainder. (7).

XII. To XI. add X. and IV., and take away III., throwing out thirties, if
any. If this give 24, change it into 25. If 25, change it into 26, whenever
the golden number is greater than 11. If 0, change it into 30. Thus we have
the epact, or age of the _Calendar_ moon at the beginning of the year. (6).

_When the Epact is 23, or less._

XIII. Subtract XII., the epact, from 45. (39).

XIV. Subtract the epact from 27, divide by 7, and keep the remainder, or 7,
if there be no remainder. (7)

_When the Epact is greater than 23._

XIII. Subtract XII., the epact, from 75.

XIV. Subtract the epact from 57, divide by 7, and keep the remainder, or 7,
if there be no remainder.

XV. To XIII. add VII., the dominical number, (and 7 besides, if XIV. be
greater than VII.,) and subtract XIV., the result is the day of March, or
if more than 31, subtract 31, and {367} the result is the day of April, on
which Easter Sunday falls. (39; Easter Day is April 8).

In the following examples, the several results leading to the final
conclusion are tabulated.

  ========================================================
  GIVEN YEAR | 1592 | 1637 | 1723 | 1853 | 2018 | 4686
  --------------------------------------------------------
        I.   | 1593 | 1638 | 1724 | 1854 | 2019 |   4687
       II.   |  398 |  409 |  430 |  463 |  504 |   1171
      III.   |  --- |    0 |    1 |    2 |    4 |     30
       IV.   |  --- |    0 |    0 |    0 |    1 |      7
        V.   | 1991 | 2047 | 2153 | 2315 | 2520 |   5835
       VI.   |    3 |    3 |    4 |    5 |    0 |      4
      VII.   |    4 |    4 |    3 |    2 |    7 |      3
     VIII.   |   16 |    4 |   14 |   11 |    5 |     13
       IX.   |  --- |  --- |    0 |    0 |    0 |      1
        X.   |    0 |    0 |    0 |    1 |    1 |     10
       XI.   |   16 |    4 |   24 |   21 |   15 |     13
      XII.   |   16 |    4 |   23 |   20 |   13 |0 say 30
     XIII.   |   29 |   41 |   22 |   25 |   32 |     45
      XIV.   |    4 |    2 |    4 |    7 |    7 |      6
       XV.   |   29 |   43 |   28 |   27 |   32 |     49
  Easter Day |Mar.29|Apr.12|Mar.28|Mar.27|Apr.1 | Apr.18
  --------------------------------------------------------

13. _Rule for determining Easter Day of the Antegregorian Calendar in any
year of the old style._ To the several parts of the rule are annexed, by
way of example, the results for the year 1287. The steps are numbered to
correspond with the steps of the Gregorian rule, so that it can be seen
what augmentations the latter requires.

I. Set down the given year. (1287).

II. Take the quotient of the given year divided by 4, neglecting the
remainder (321).

V. Take 4 more than the sum of I. and II. (1612).

VI. Find the remainder of V. divided by 7. (2).

VII. Subtract VI. from 7; this is the number of the dominical letter

  1  2  3  4  5  6  7  (5; dominical letter E).
  A  B  C  D  E  F  G

VIII. Divide one more than the given year by 19, the remainder (or 19 if no
remainder) is the golden number. (15).

XII. Divide 3 less than 11 times VIII. by 30; the remainder (or 30 if there
be no remainder) is the epact. (12).

{368}

_When the Epact is 23, or less._

XIII. Subtract XII., the epact, from 45. (33).

XIV. Subtract the epact from 27, divide by 7, and keep the remainder, or 7,
if there be no remainder, (1).

_When the Epact is greater than 23._

XIII. Subtract XII., the epact, from 75.

XIV. Subtract the epact from 57, divide by 7, and keep the remainder, or 7,
if there be no remainder.

XV. To XIII. add VII., the dominical number, (and 7 besides if XIV. be
greater than VII.,) and subtract XIV., the result is the day of March, or
if more than 31, subtract 31, and the result is the day of April, on which
Easter Sunday (old style) falls. (37; Easter Day is April 6).

These rules completely represent the old and new Calendars, so far as
Easter is concerned. For further explanation we must refer to the articles
cited at the commencement.

The annexed is the table of new and full moons of the Gregorian Calendar,
cleared of the errors made for the purpose of preventing Easter from
coinciding with the Jewish Passover.

The second table (page 370) contains _epacts_, or ages of the moon at the
beginning of the year: thus in 1913, the epact is 22, in 1868 it is 6. This
table goes from 1850 to 1999: should the New Zealander not have arrived by
that time, and should the churches of England and Rome then survive, the
epact table may be continued from their liturgy-books. The way of using the
table is as follows: Take the epact of the required year, and find it in
the first or last column of the first table, in line with it are seen the
calendar days of new and full moon. Thus, when the epact is 17, the new and
full moons of March fall on the 13th and 28th. The result is, for the most
part, correct: but in a minority of cases there is an error of a day. When
this happens, the error is almost always a fraction of a day much less than
twelve hours. Thus, when the table gives full moon on the 27th, and the
real truth is the 28th, we may be sure it is early on the 28th.

{369}

  -------------------------------------------------------------------------
        |Jan.|Feb.|Mar.|Apr.|May |June|July|Aug.|Sep.|Oct.|Nov.|Dec.|
  -------------------------------------------------------------------------
    1   | 29 | 27 | 29 | 27 | 27 | 25 | 25 | 23 | 22 | 21 | 20 | 19 |  1
        | 14 | 13 | 14 | 13 | 12 | 11 | 10 |  9 |  7 |  7 |  5 |  5 |
  -------------------------------------------------------------------------
    2   | 28 | 26 | 28 | 26 | 26 | 24 | 24 | 22 | 21 | 20 | 19 | 18 |  2
        | 13 | 12 | 13 | 12 | 11 | 10 |  9 |  8 |  6 |  6 |  4 |  4 |
  -------------------------------------------------------------------------
    3   | 27 | 25 | 27 | 25 | 25 | 23 | 23 | 21 | 20 | 19 | 18 | 17 |  3
        | 12 | 11 | 12 | 11 | 10 |  9 |  8 |  7 |  5 |  5 |  3 |  3 |
  -------------------------------------------------------------------------
    4   | 26 | 24 | 26 | 24 | 24 | 22 | 22 | 20 | 19 | 18 | 17 | 16 |  4
        | 11 | 10 | 11 | 10 |  9 |  8 |  7 |  6 |  4 |  4 |  2 |2,31|
  -------------------------------------------------------------------------
    5   | 25 | 23 | 25 | 23 | 23 | 21 | 21 | 19 | 18 | 17 | 16 | 15 |  5
        | 10 |  9 | 10 |  9 |  8 |  7 |  6 |  5 |  3 |  3 |  1 |1,30|
  -------------------------------------------------------------------------
    6   | 24 | 22 | 24 | 22 | 22 | 20 | 20 | 18 | 17 | 16 | 15 | 14 |  6
        |  9 |  8 |  9 |  8 |  7 |  6 |  5 |  4 |  2 |2,31| 30 | 29 |
  -------------------------------------------------------------------------
    7   | 23 | 21 | 23 | 21 | 21 | 19 | 19 | 17 | 16 | 15 | 14 | 13 |  7
        |  8 |  7 |  8 |  7 |  6 |  5 |  4 |  3 |  1 |1,30| 29 | 28 |
  -------------------------------------------------------------------------
    8   | 22 | 20 | 22 | 20 | 20 | 18 | 18 | 16 | 15 | 14 | 13 | 12 |  8
        |  7 |  6 |  7 |  6 |  5 |  4 |  3 |2,31| 30 | 29 | 28 | 27 |
  -------------------------------------------------------------------------
    9   | 21 | 19 | 21 | 19 | 19 | 17 | 17 | 15 | 14 | 13 | 12 | 11 |  9
        |  6 |  5 |  6 |  5 |  4 |  3 |  2 |1,30| 29 | 28 | 27 | 26 |
  -------------------------------------------------------------------------
    10  | 20 | 18 | 20 | 18 | 18 | 16 | 16 | 14 | 13 | 12 | 11 | 10 |  10
        |  5 |  4 |  5 |  4 |  3 |  2 |1,31| 29 | 28 | 27 | 26 | 25 |
  -------------------------------------------------------------------------
    11  | 19 | 17 | 19 | 17 | 17 | 15 | 15 | 13 | 12 | 11 | 10 |  9 |  11
        |  4 |  3 |  4 |  3 |  2 |1,30| 30 | 28 | 27 | 26 | 25 | 24 |
  -------------------------------------------------------------------------
    12  | 18 | 16 | 18 | 16 | 16 | 14 | 14 | 12 | 11 | 10 |  9 |  8 |  12
        |  3 |  2 |  3 |  2 |1,31| 29 | 29 | 27 | 26 | 25 | 24 | 23 |
  -------------------------------------------------------------------------
    13  | 17 | 15 | 17 | 15 | 15 | 13 | 13 | 11 | 10 |  9 |  8 |  7 |  13
        |  2 |  1 |  2 |1,30| 30 | 28 | 28 | 26 | 25 | 24 | 23 | 22 |
  -------------------------------------------------------------------------
    14  | 16 | 14 | 16 | 14 | 14 | 12 | 12 | 10 |  9 |  8 |  7 |  6 |  14
        |1,31| -- |1,31| 29 | 29 | 27 | 27 | 25 | 24 | 23 | 22 | 21 |
  -------------------------------------------------------------------------
    15  | 15 | 13 | 15 | 13 | 13 | 11 | 11 |  9 |  8 |  7 |  6 |  5 |  15
        | 30 | 28 | 30 | 28 | 28 | 26 | 26 | 24 | 23 | 22 | 21 | 20 |
  -------------------------------------------------------------------------
    16  | 14 | 12 | 14 | 12 | 12 | 10 | 10 |  8 |  7 |  6 |  5 |  4 |  16
        | 29 | 27 | 29 | 27 | 27 | 25 | 25 | 23 | 22 | 21 | 20 | 19 |
  -------------------------------------------------------------------------
    17  | 13 | 11 | 13 | 11 | 11 |  9 |  9 |  7 |  6 |  5 |  4 |  3 |  17
        | 28 | 26 | 28 | 26 | 26 | 24 | 24 | 22 | 21 | 20 | 19 | 18 |
  -------------------------------------------------------------------------
    18  | 12 | 10 | 12 | 10 | 10 |  8 |  8 |  6 |  5 |  4 |  3 |  2 |  18
        | 27 | 25 | 27 | 25 | 25 | 23 | 23 | 21 | 20 | 19 | 18 | 17 |
  -------------------------------------------------------------------------
    19  | 11 |  9 | 11 |  9 |  9 |  7 |  7 |  5 |  4 |  3 |  2 |1,31|  19
        | 26 | 24 | 26 | 24 | 24 | 22 | 22 | 20 | 19 | 18 | 17 | 16 |
  -------------------------------------------------------------------------
    20  | 10 |  8 | 10 |  8 |  8 |  6 |  6 |  4 |  3 |  2 |1,31| 30 |  20
        | 25 | 23 | 25 | 23 | 23 | 21 | 21 | 19 | 18 | 17 | 16 | 15 |
  -------------------------------------------------------------------------
    21  |  9 |  7 |  9 |  7 |  7 |  5 |  5 |  3 |  2 |1,31| 29 | 29 |  21
        | 24 | 22 | 24 | 22 | 22 | 20 | 20 | 18 | 17 | 16 | 15 | 14 |
  -------------------------------------------------------------------------
    22  |  8 |  6 |  8 |  6 |  6 |  4 |  4 |  2 |1,30| 30 | 28 | 28 |  22
        | 23 | 21 | 23 | 21 | 21 | 19 | 19 | 17 | 16 | 15 | 14 | 13 |
  -------------------------------------------------------------------------
    23  |  7 |  5 |  7 |  5 |  5 |  3 |  3 |1,31| 29 | 29 | 27 | 27 |  23
        | 22 | 20 | 22 | 20 | 20 | 18 | 18 | 16 | 15 | 14 | 13 | 12 |
  -------------------------------------------------------------------------
    24  |  6 |  5 |  6 |  5 |  4 |  3 |  2 |1,30| 29 | 28 | 27 | 26 |  24
        | 21 | 19 | 21 | 19 | 19 | 17 | 17 | 15 | 14 | 13 | 12 | 11 |
  -------------------------------------------------------------------------
    25  |  5 |  4 |  5 |  4 |  3 |  2 |1,31| 29 | 28 | 27 | 26 | 25 |  25
        | 20 | 19 | 20 | 19 | 18 | 17 | 16 | 15 | 13 | 13 | 11 | 11 |
  -------------------------------------------------------------------------
    26  |  4 |  3 |  4 |  3 |  2 |1,30| 30 | 28 | 27 | 26 | 25 | 24 |  26
        | 19 | 18 | 19 | 18 | 17 | 16 | 15 | 14 | 12 | 12 | 10 | 10 |
  -------------------------------------------------------------------------
    27  |  3 |  2 |  3 |  2 |1,31| 29 | 29 | 27 | 26 | 25 | 24 | 23 |  27
        | 18 | 17 | 18 | 17 | 16 | 15 | 14 | 13 | 11 | 11 |  9 |  9 |
  -------------------------------------------------------------------------
    28  |  2 |  1 |  2 |1,30| 30 | 28 | 28 | 26 | 25 | 24 | 23 | 22 |  28
        | 17 | 16 | 17 | 16 | 15 | 14 | 13 | 12 | 10 | 10 |  8 |  8 |
  -------------------------------------------------------------------------
    29  |1,31| -- |1,31| 29 | 29 | 27 | 27 | 25 | 24 | 23 | 22 | 21 |  29
        | 16 | 15 | 16 | 15 | 14 | 13 | 12 | 11 |  9 |  9 |  7 |  7 |
  -------------------------------------------------------------------------
    30  | 30 | 28 | 30 | 28 | 28 | 26 | 26 | 24 | 23 | 22 | 21 | 20 |  30
        | 15 | 14 | 15 | 14 | 13 | 12 | 11 | 10 |  8 |  8 |  6 |  6 |
  -------------------------------------------------------------------------
        |Jan.|Feb.|Mar.|Apr.|May |June|July|Aug.|Sep.|Oct.|Nov.|Dec.|
  -------------------------------------------------------------------------

{370}

  =======================================================
       |  0 |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9
  -------------------------------------------------------
   185 | 17 | 28 |  9 | 20 |  2 | 12 | 23 |  4 | 15 | 26
  -------------------------------------------------------
   186 |  7 | 18 | 30 | 11 | 22 |  3 | 14 | 25 |  6 | 17
  -------------------------------------------------------
   187 | 28 |  9 | 20 |  1 | 12 | 23 |  4 | 15 | 26 |  7
  -------------------------------------------------------
   188 | 18 | 30 | 11 | 22 |  3 | 14 | 25 |  6 | 17 | 28
  -------------------------------------------------------
   189 |  9 | 21 |  1 | 12 | 23 |  4 | 15 | 26 |  7 | 18
  -------------------------------------------------------
   190 | 29 | 10 | 21 |  2 | 13 | 24 |  5 | 16 | 27 |  8
  -------------------------------------------------------
   191 | 19 | 30 | 11 | 22 |  3 | 14 | 26 |  6 | 17 | 29
  -------------------------------------------------------
   192 | 10 | 21 |  2 | 13 | 24 |  5 | 16 | 27 |  8 | 19
  -------------------------------------------------------
   193 | 30 | 11 | 22 |  3 | 14 | 26 |  6 | 17 | 29 | 10
  -------------------------------------------------------
   194 | 21 |  2 | 13 | 24 |  5 | 16 | 27 |  8 | 19 | 30
  -------------------------------------------------------
   195 | 11 | 22 |  3 | 14 | 26 |  6 | 17 | 29 | 10 | 21
  -------------------------------------------------------
   196 |  2 | 13 | 24 |  5 | 16 | 27 |  8 | 19 | 30 | 11
  -------------------------------------------------------
   197 | 22 |  3 | 14 | 26 |  6 | 17 | 29 | 10 | 21 |  2
  -------------------------------------------------------
   198 | 13 | 24 |  5 | 16 | 27 |  8 | 19 | 30 | 11 | 22
  -------------------------------------------------------
   199 |  3 | 14 | 26 |  6 | 17 | 29 | 10 | 21 |  2 | 13
  =======================================================

For example, the year 1867. The epact is 25, and we find in the table:

         J.   F.   M.   AP.  M.   JU.  JL.  AU.  S.   O.   N.   D.
  New     5+   4    5+   4    3+   2  1,31  29   28-  27   26   25
  Full   20   19-  20   19-  18   17   16   15   13-  13   11+  11

When the truth is the day after + is written after the date; when the day
before, -. Thus, the new moon of March is on the 6th; the full moon of
April is on the 18th. {371}

I now introduce a small paradox of my own; and as I am not able to prove
it, I am compelled to declare that any one who shall dissent must be either
very foolish or very dishonest, and will make me quite uncomfortable about
the state of his soul. This being settled once for all, I proceed to say
that the necessity of arriving at the truth about the assertions that the
Nicene Council laid down astronomical tests led me to look at Fathers,
Church histories, etc. to an extent which I never dreamed of before. One
conclusion which I arrived at was, that the Nicene Fathers had a knack of
sticking to the question which many later councils could not acquire. In
our own day, it is not permitted to Convocation seriously to discuss any
one of the points which are bearing so hard upon their resources of
defence--the cursing clauses of the Athanasian Creed, for example. And it
may be collected that the prohibition arises partly from fear that there is
no saying where a beginning, if allowed, would end. There seems to be a
suspicion that debate, once let loose, would play up old Trent with the
liturgy, and bring the whole book to book. But if any one will examine the
real Nicene Creed, without the augmentation, he will admire the way in
which the framers stuck to the point, and settled what they had to decide,
according to their view of it. With such a presumption of good sense in
their favor, it becomes easier to believe in any claim which may be made on
their behalf to tact or sagacity in settling any other matter. And I
strongly suspect such a claim may be made for them on the Easter question.

I collect from many little indications, both before and after the Council,
that the division of the Christian world into Judaical and Gentile, though
not giving rise to a sectarian distinction expressed by names, was of far
greater force and meaning than historians prominently admit. I took _note_
of many indications of this, but not _notes_, as it was not to my purpose.
If it were so, we must admire the discretion of the Council. The Easter
question was the {372} fighting ground of the struggle: the Eastern or
Judaical Christians, with some varieties of usage and meaning, would have
the Passover itself to be the great feast, but taken in a Christian sense;
the Western or Gentile Christians, would have the commemoration of the
Resurrection, connected with the Passover only by chronology. To shift the
Passover in time, under its name, _Pascha_, without allusion to any of the
force of the change, was gently cutting away the ground from under the feet
of the Conservatives. And it was done in a very quiet way: no allusion to
the precise character of the change; no hint that the question was about
two different festivals: "all the brethren in the East, who formerly
celebrated this festival at the same time as the Jews, will in future
conform to the Romans and to us." The Judaizers meant to be keeping the
Passover _as_ a Christian feast: they are gently assumed to be keeping,
_not_ the Passover, _but_ a Christian feast; and a doctrinal decision is
quietly, but efficiently, announced under the form of a chronological
ordinance. Had the Council issued theses of doctrine, and excommunicated
all dissentients, the rupture of the East and West would have taken place
earlier by centuries than it did. The only place in which I ever saw any
part of my paradox advanced, was in an article in the _Examiner_ newspaper,
towards the end of 1866, after the above was written.

A story about Christopher Clavius, the workman of the new Calendar. I
chanced to pick up "Albertus Pighius Campensis de æquinoctiorum
solsticiorumque inventione... Ejusdem de ratione Paschalis celebrationis,
De que Restitutione ecclesiastici Kalendarii," Paris, 1520, folio.[760] On
the title-page were decayed words followed by ".._hristophor.. C..ii_, 1556
(or 8)," the last blank not entirely erased by time, but showing the lower
halves of an _l_ and of an _a_, and {373} rather too much room for a _v_.
It looked very like _E Libris Christophori Clavii_ 1556. By the courtesy of
some members of the Jesuit body in London, I procured a tracing of the
signature of Clavius from Rome, and the shapes of the letters, and the
modes of junction and disjunction, put the matter beyond question. Even the
extra space was explained; he wrote himself Cla_u_ius. Now in 1556, Clavius
was nineteen years old: it thus appears probable that the framer of the
Gregorian Calendar was selected, not merely as a learned astronomer, but as
one who had attended to the calendar, and to works on its reformation, from
early youth. When on the subject I found reason to think that Clavius had
really read this work, and taken from it a phrase or two and a notion or
two. Observe the advantage of writing the baptismal name at full length.



A COUPLE OF MINOR PARADOXES.

    The discovery of a general resolution of all superior finite equations,
    of every numerical both algebraick and transcendent form. By A. P.
    Vogel,[761] mathematician at Leipzick. Leipzick and London, 1845, 8vo.

This work is written in the English of a German who has not mastered the
idiom: but it is always intelligible. It professes to solve equations of
every degree "in a more extent sense, and till to every degree of
exactness." The general solution of equations of _all_ degrees is a vexed
question, which cannot have the mysterious interest of the circle problem,
and is of a comparatively modern date.[762] Mr. Vogel {374} announces a
forthcoming treatise in which are resolved the "last impossibilities of
pure mathematics."



    Elective Polarity the Universal Agent. By Frances Barbara Burton,
    authoress of 'Astronomy familiarized,' 'Physical Astronomy,' &c.
    London, 1845, 8vo.[763]

The title gives a notion of the theory. The first sentence states, that
12,500 years ago [alpha] Lyræ was the pole-star, and attributes the immense
magnitude of the now fossil animals to a star of such "polaric intensity as
Vega pouring its magnetic streams through our planet." Miss Burton was a
lady of property, and of very respectable acquirements, especially in
Hebrew; she was eccentric in all things.

1867.--Miss Burton is revived by the writer of a book on meteorology which
makes use of the planets: she is one of his leading minds.[764]



SPECULATIVE THOUGHT IN ENGLAND.

In the year 1845 the old _Mathematical Society_ was merged in the
Astronomical Society. The circle-squarers, etc., thrive more in England
than in any other country: there are most weeds where there is the largest
crop. Speculation, though not encouraged by our Government so much as by
those of the Continent, has had, not indeed such forcing, but much wider
diffusion: few tanks, but many rivulets. On this point I quote from the
preface to the reprint of the work of Ramchundra,[765] which I
superintended for the late Court of Directors of the East India Company.

{375}

"That sound judgment which gives men well to know what is best for them, as
well as that faculty of invention which leads to development of resources
and to the increase of wealth and comfort, are both materially advanced,
perhaps cannot rapidly be advanced without, a great taste for pure
speculation among the general mass of the people, down to the lowest of
those who can read and write. England is a marked example. Many persons
will be surprised at this assertion. They imagine that our country is the
great instance of the refusal of all _unpractical_ knowledge in favor of
what is _useful_. I affirm, on the contrary, that there is no country in
Europe in which there has been so wide a diffusion of speculation, theory,
or what other unpractical word the reader pleases. In our country, the
scientific _society_ is always formed and maintained by the people; in
every other, the scientific _academy_--most aptly named--has been the
creation of the government, of which it has never ceased to be the
nursling. In all the parts of England in which manufacturing pursuits have
given the artisan some command of time, the cultivation of mathematics and
other speculative studies has been, as is well known, a very frequent
occupation. In no other country has the weaver at his loom bent over the
_Principia_ of Newton; in no other country has the man of weekly wages
maintained his own scientific periodical. With us, since the beginning of
the last century, scores upon scores--perhaps hundreds, for I am far from
knowing all--of annuals have run, some their ten years, some their
half-century, some their century and a half, containing questions to be
answered, from which many of our examiners in the universities have culled
materials for the academical contests. And these questions have always been
answered, and in cases without number by the lower order of purchasers, the
mechanics, the weavers, and the printers' workmen. I cannot here digress to
point out the manner in which the concentration of manufactures, and the
general diffusion of education, have affected the {376} state of things; I
speak of the time during which the present system took its rise, and of the
circumstances under which many of its most effective promoters were
trained. In all this there is nothing which stands out, like the
state-nourished academy, with its few great names and brilliant single
achievements. This country has differed from all others in the wide
diffusion of the disposition to speculate, which disposition has found its
place among the ordinary habits of life, moderate in its action, healthy in
its amount."



THE OLD MATHEMATICAL SOCIETY.

Among the most remarkable proofs of the diffusion of speculation was the
Mathematical Society, which flourished from 1717 to 1845. Its habitat was
Spitalfields, and I think most of its existence was passed in Crispin
Street. It was originally a plain society, belonging to the studious
artisan. The members met for discussion once a week; and I believe I am
correct in saying that each man had his pipe, his pot, and his problem. One
of their old rules was that, "If any member shall so far forget himself and
the respect due to the Society as in the warmth of debate to threaten or
offer personal violence to any other member, he shall be liable to
immediate expulsion, or to pay such fine as the majority of the members
present shall decide." But their great rule, printed large on the back of
the title page of their last book of regulations, was "By the constitution
of the Society, it is the duty of every member, if he be asked any
mathematical or philosophical question by another member, to instruct him
in the plainest and easiest manner he is able." We shall presently see
that, in old time, the rule had a more homely form.

I have been told that De Moivre[766] was a member of this {377} Society.
This I cannot verify: circumstances render it unlikely; even though the
French refugees clustered in Spitalfields; many of them were of the
Society, which there is some reason to think was founded by them. But
Dolland,[767] Thomas Simpson,[768] Saunderson,[769] Crossley,[770] and
others of known name, were certainly members. The Society gradually
declined, and in 1845 was reduced to nineteen members. An arrangement was
made by which sixteen of these members, who where not already in the
Astronomical Society became Fellows without contribution, all the books and
other property of the old Society being transferred to the new one. I was
one of the committee which made the preliminary inquiries, and the reason
of the decline was soon manifest. The only question which could arise was
whether the members of the society of working men--for this repute still
continued--were of that class of educated men who could associate with the
Fellows of the Astronomical Society on terms agreeable to all parties. We
found that the artisan element had been extinct for many years; there was
not a man but might, as to education, manners, and position, have become a
Fellow in the usual way. The fact was that life in Spitalfields had become
harder: and the weaver could {378} only live from hand to mouth, and not up
to the brain. The material of the old Society no longer existed.

In 1798, experimental lectures were given, a small charge for admission
being taken at the door: by this hangs a tale--and a song. Many years ago,
I found among papers of a deceased friend, who certainly never had anything
to do with the Society, and who passed all his life far from London, a
song, headed "Song sung by the Mathematical Society in London, at a dinner
given Mr. Fletcher,[771] a solicitor, who had defended the Society gratis."
Mr. Williams,[772] the Assistant Secretary of the Astronomical Society,
formerly Secretary of the Mathematical Society, remembered that the Society
had had a solicitor named Fletcher among the members. Some years elapsed
before it struck me that my old friend Benjamin Gompertz,[773] who had long
been a member, might have some recollection of the matter. The following is
an extract of a letter from him (July 9, 1861):

"As to the Mathematical Society, of which I was a member when only 18 years
of age, [Mr. G. was born in 1779], having been, contrary to the rules,
elected under the age of 21. How I came to be a member of that Society--and
continued so until it joined the Astronomical Society, and was then the
President--was: I happened to pass a bookseller's small shop, of
second-hand books, kept by a poor taylor, but a good mathematician, John
Griffiths. I was very pleased to meet a mathematician, and I asked him if
he would give me some lessons; and his reply was that I was more capable to
teach him, but he belonged to a society of mathematicians, and he would
introduce me. I accepted the offer, and I was elected, and had many
scholars then to teach, as {379} one of the rules was, if a member asked
for information, and applied to any one who could give it, he was obliged
to give it, or fine one penny. Though I might say much with respect to the
Society which would be interesting, I will for the present reply only to
your question. I well knew Mr. Fletcher, who was a very clever and very
scientific person. He did, as solicitor, defend an action brought by an
informer against the Society--I think for 5,000l.--for giving lectures to
the public in philosophical subjects [i.e., for unlicensed public
exhibition with money taken at the doors]. I think the price for admission
was one shilling, and we used to have, if I rightly recollect, from two to
three hundred visitors. Mr. Fletcher was successful in his defence, and we
got out of our trouble. There was a collection made to reward his services,
but he did not accept of any reward: and I think we gave him a dinner, as
you state, and enjoyed ourselves; no doubt with astronomical songs and
other songs; but my recollection does not enable me to say if the
astronomical song was a drinking song. I think the anxiety caused by that
action was the cause of some of the members' death. [They had, no doubt,
broken the law in ignorance; and by the sum named, the informer must have
been present, and sued for a penalty on every shilling he could prove to
have been taken]."

I by no means guarantee that the whole song I proceed to give is what was
sung at the dinner: I suspect, by the completeness of the chain, that
augmentations have been made. My deceased friend was just the man to add
some verses, or the addition may have been made before it came into his
hands, or since his decease, for the scraps containing the verses passed
through several hands before they came into mine. We may, however, be
pretty sure that the original is substantially contained in what is given,
and that the character is therefore preserved. I have had myself to repair
damages every now and then, in the way of conjectural restoration of
defects caused by ill-usage. {380}



THE ASTRONOMER'S DRINKING SONG.

 "Whoe'er would search the starry sky,
    Its secrets to divine, sir,
  Should take his glass--I mean, should try
    A glass or two of wine, sir!
  True virtue lies in golden mean,
    And man must wet his clay, sir;
  Join these two maxims, and 'tis seen
    He should drink his bottle a day, sir!

 "Old Archimedes, reverend sage!
    By trump of fame renowned, sir,
  Deep problems solved in every page,
    And the sphere's curved surface found,[774] sir:
  Himself he would have far outshone,
    And borne a wider sway, sir,
  Had he our modern secret known,
    And drank a bottle a day, sir!

 "When Ptolemy,[775] now long ago,
    Believed the earth stood still, sir,
  He never would have blundered so,
    Had he but drunk his fill, sir:
  He'd then have felt[776] it circulate,
    And would have learnt to say, sir,
  The true way to investigate
    Is to drink your bottle a day, sir!

 "Copernicus,[777] that learned wight,
    The glory of his nation,
  With draughts of wine refreshed his sight,
    And saw the earth's rotation;
  {381}
  Each planet then its orb described,
    The moon got under way, sir;
  These truths from nature he imbibed
    For he drank his bottle a day, sir!

 "The noble[778] Tycho placed the stars,
    Each in its due location;
  He lost his nose[779] by spite of Mars,
    But that was no privation:
  Had he but lost his mouth, I grant
    He would have felt dismay, sir,
  Bless you! _he_ knew what he should want
    To drink his bottle a day, sir!

 "Cold water makes no lucky hits;
    On mysteries the head runs:
  Small drink let Kepler[780] time his wits
    On the regular polyhedrons:
  He took to wine, and it changed the chime,
    His genius swept away, sir,
  Through area varying[781] as the time
    At the rate of a bottle a day, sir!

 "Poor Galileo,[782] forced to rat
    Before the Inquisition,
  _E pur si muove_[783] was the pat
    He gave them in addition:
  {382}
  He meant, whate'er you think you prove,
    The earth must go its way, sirs;
  Spite of your teeth I'll make it move,
    For I'll drink my bottle a day, sirs!

 "Great Newton, who was never beat
    Whatever fools may think, sir;
  Though sometimes he forgot to eat,
    He never forgot to drink, sir:
  Descartes[784] took nought but lemonade,
    To conquer him was play, sir;
  The first advance that Newton made
    Was to drink his bottle a day, sir!

 "D'Alembert,[785] Euler,[786] and Clairaut,[787]
    Though they increased our store, sir,
  Much further had been seen to go
    Had they tippled a little more, sir!
  Lagrange[788] gets mellow with Laplace,[789]
    And both are wont to say, sir,
  The _philosophe_ who's not an ass
    Will drink his bottle a day, sir!

 "Astronomers! what can avail
    Those who calumniate us;
  Experiment can never fail
    With such an apparatus:
  Let him who'd have his merits known
    Remember what I say, sir;
  Fair science shines on him alone
    Who drinks his bottle a day, sir!

  {383}
 "How light we reck of those who mock
    By this we'll make to appear, sir,
  We'll dine by the sidereal[790] clock
    For one more bottle a year, sir:
  But choose which pendulum you will,
    You'll never make your way, sir,
  Unless you drink--and drink your fill,--
    At least a bottle a day, sir!"

Old times are changed, old manners gone!

There is a new Mathematical Society,[791] and I am, at this present writing
(1866), its first President. We are very high in the newest developments,
and bid fair to take a place among the scientific establishments. Benjamin
Gompertz, who was President of the old Society when it expired, was the
link between the old and new body: he was a member of _ours_ at his death.
But not a drop of liquor is seen at our meetings, except a decanter of
water: all our heavy is a fermentation of symbols; and we do not draw it
mild. There is no penny fine for reticence or occult science; and as to a
song! not the ghost of a chance.



1826. The time may have come when the original documents connected with the
discovery of Neptune may be worth revising. The following are extracts from
the _Athenæum_ of October 3 and October 17:



LE VERRIER'S[792] PLANET.

We have received, at the last moment before making up for press, the
following letter from Sir John Herschel,[793] {384} in reference to the
matter referred to in the communication from Mr. Hind[794] given below:

"Collingwood, Oct. 1.

"In my address to the British Association assembled at Southampton, on the
occasion of my resigning the chair to Sir R. Murchison,[795] I stated,
among the remarkable astronomical events of the last twelvemonth, that it
had added a new planet to our list,--adding, 'it has done more,--it has
given us the probable prospect of the discovery of another. We see it as
Columbus saw America from the shores of Spain. Its movements have been
felt, trembling along the far-reaching line of our analysis, with a
certainty hardly inferior to that of ocular demonstration.'--These
expressions are not reported in any of the papers which profess to give an
account of the proceedings, but I appeal to all present whether they were
not used.

"Give me leave to state my reasons for this confidence; and, in so doing,
to call attention to some facts which deserve to be put on record in the
history of this noble discovery. On July 12, 1842, the late illustrious
astronomer, Bessel,[796] honored me with a visit at my present residence.
On the evening of that day, conversing on the great work of the planetary
reductions undertaken by the Astronomer Royal[797]--then in progress, and
since published,[798]--M. Bessel remarked that the motions of Uranus, as he
had satisfied {385} himself by careful examination of the recorded
observations, could not be accounted for by the perturbations of the known
planets; and that the deviations far exceeded any possible limits of error
of observation. In reply to the question, Whether the deviations in
question might not be due to the action of an unknown planet?--he stated
that he considered it highly probable that such was the case,--being
systematic, and such as might be produced by an exterior planet. I then
inquired whether he had attempted, from the indications afforded by these
perturbations, to discover the position of the unknown body,--in order that
'a hue and cry' might be raised for it. From his reply, the words of which
I do not call to mind, I collected that he had not then gone into that
inquiry; but proposed to do so, having now completed certain works which
had occupied too much of his time. And, accordingly, in a letter which I
received from him after his return to Königsberg, dated November 14, 1842,
he says,--'In reference to our conversation at Collingwood, I _announce_ to
you (_melde_ ich Ihnen) that Uranus is not forgotten.' Doubtless,
therefore, among his papers will be found some researches on the subject.

"The remarkable calculations of M. Le Verrier--which have pointed out, as
now appears, nearly the true situation of the new planet, by resolving the
inverse problem of the perturbations--if uncorroborated by repetition of
the numerical calculations by another hand, or by independent investigation
from another quarter, would hardly justify so strong an assurance as that
conveyed by my expressions above alluded to. But it was known to me, at
that time, (I will take the liberty to cite the Astronomer Royal as my
authority) that a similar investigation had been independently entered
into, and a conclusion as to the situation of the new planet very nearly
coincident with M. Le Verrier's arrived at (in entire ignorance of his
conclusions), by a young Cambridge mathematician, Mr. Adams;[799]--who
will, I hope, {386} pardon this mention of his name (the matter being one
of great historical moment),--and who will, doubtless, in his own good time
and manner, place his calculations before the public.

"J. F. W. HERSCHEL."

_Discovery of Le Verrier's Planet._

Mr. Hind announces to the _Times_ that he has received a letter from Dr.
Brünnow, of the Royal Observatory at Berlin, giving the very important
information that Le Verrier's planet was found by M. Galle, on the night of
September 23. "In announcing this grand discovery," he says, "I think it
better to copy Dr. Brünnow's[800] letter."



"Berlin, Sept. 25.

"My dear Sir--M. Le Verrier's planet was discovered here the 23d of
September, by M. Galle.[801] It is a star of the 8th magnitude, but with a
diameter of two or three seconds. Here are its places:

             h. m. s.             R. A.           Declination.
  Sept. 23,  12  0 14.6 M.T.      328° 19' 16.0"  -13° 24'  8.2"
  Sept. 24,   8 54 40.9 M.T.      328° 18' 14.3"  -13° 24' 29.7"

The planet is now retrograde, its motion amounting daily to four seconds of
time.

"Yours most respectfully, BRÜNNOW."

"This discovery," Mr. Hind says, "may be justly considered one of the
greatest triumphs of theoretical astronomy;" and he adds, in a postscript,
that the planet was observed at Mr. Bishop's[802] Observatory, in the
Regent's Park, {387} on Wednesday night, notwithstanding the moonlight and
hazy sky. "It appears bright," he says, "and with a power of 320 I can see
the disc. The following position is the result of instrumental comparisons
with 33 Aquarii:

  Sept. 30, at 8h. 16m. 21s. Greenwich mean time--
      Right ascension of planet     21h. 52m. 47.15s.
      South declination             13°  27'  20"."



THE NEW PLANET.

"Cambridge Observatory, Oct. 15.

"The allusion made by Sir John Herschel, in his letter contained in the
_Athenæum_ of October 3, to the theoretical researches of Mr. Adams,
respecting the newly-discovered planet, has induced me to request that you
would make the following communication public. It is right that I should
first say that I have Mr. Adams's permission to make the statements that
follow, so far as they relate to his labors. I do not propose to enter into
a detail of the steps by which Mr. Adams was led, by his spontaneous and
independent researches, to a conclusion that a planet must exist more
distant than Uranus. The matter is of too great historical moment not to
receive a more formal record than it would be proper to give here. My
immediate object is to show, while the attention of the scientific public
is more particularly directed to the subject, that, with respect to this
remarkable discovery, English astronomers may lay claim to some merit.

"Mr. Adams formed the resolution of trying, by calculation, to account for
the anomalies in the motion of Uranus on the hypothesis of a more distant
planet, when he was an undergraduate in this university, and when his
exertions for the academical distinction, which he obtained in January
1843, left him no time for pursuing the research. In the course of that
year, he arrived at an approximation to the position of the supposed
planet; which, however, he did not consider to be worthy of confidence, on
account of his not {388} having employed a sufficient number of
observations of Uranus. Accordingly, he requested my intervention to obtain
for him the early Greenwich observations, then in course of
reduction;--which the Astronomer Royal immediately supplied, in the kindest
possible manner. This was in February, 1844. In September, 1845, Mr. Adams
communicated to me values which he had obtained for the heliocentric
longitude, excentricity of orbit, longitude of perihelion, and mass, of an
assumed exterior planet,--deduced entirely from unaccounted-for
perturbations of Uranus. The same results, somewhat corrected, he
communicated, in October, to the Astronomer Royal. M. Le Verrier, in an
investigation which was published in June of 1846, assigned very nearly the
same heliocentric longitude for the probable position of the planet as Mr.
Adams had arrived at, but gave no results respecting its mass and the form
of its orbit. The coincidence as to position from two entirely independent
investigations naturally inspired confidence; and the Astronomer Royal
shortly after suggested the employing of the Northumberland telescope of
this observatory in a systematic search after the hypothetical planet;
recommending, at the same time, a definite plan of operations. I undertook
to make the search,--and commenced observing on July 29. The observations
were directed, in the first instance, to the part of the heavens which
theory had pointed out as the most probable place of the planet; in
selecting which I was guided by a paper drawn up for me by Mr. Adams. Not
having hour xxi. of the Berlin star-maps--of the publication of which I was
not aware--I had to proceed on the principle of comparison of observations
made at intervals. On July 30, I went over a zone 9' broad, in such a
manner as to include all stars to the eleventh magnitude. On August 4, I
took a broader zone and recorded a place of the planet. My next
observations were on August 12; when I met with a star of the eighth
magnitude in the zone which I had gone over on July 30,--and which did not
then {389} contain this star. Of course, this was the planet;--the place of
which was, thus, recorded a second time in four days of observing. A
comparison of the observations of July 30 and August 12 would, according to
the principle of search which I employed, have shown me the planet. I did
not make the comparison till after the detection of it at Berlin--partly
because I had an impression that a much more extensive search was required
to give any probability of discovery--and partly from the press of other
occupation. The planet, however, was _secured_, and two positions of it
recorded six weeks earlier here than in any other observatory,--and in a
systematic search expressly undertaken for that purpose. I give now the
positions of the planet on August 4 and August 12.

  Greenwich mean time.

  Aug. 4, 13h. 36m. 25s.     {R.A.   21h. 58m. 14.70s.
                             {N.P.D. 102° 57'  32.2"

  Aug. 12, 13h. 3m. 26s.     {R.A.   21h. 57m. 26.13s.
                             {N.P.D. 103°  2'   0.2"

"From these places compared with recent observations Mr. Adams has obtained
the following results:

  Distance of the planet from the sun       30.05
  Inclination of the orbit                  1° 45'
  Longitude of the descending node        309° 43'
  Heliocentric longitude, Aug. 4          326° 39'

"The present distance from the sun is, therefore, thirty times the earth's
mean distance;--which is somewhat less than the theory had indicated. The
other elements of the orbit cannot be approximated to till the observations
shall have been continued for a longer period.

"The part taken by Mr. Adams in the theoretical search after this planet
will, perhaps, be considered to justify the suggesting of a name. With his
consent, I mention _Oceanus_ as one which may possibly receive the votes of
astronomers.--I {390} have authority to state that Mr. Adams's
investigations will in a short time, be published in detail.

"J. CHALLIS."[803]



ASTRONOMICAL POLICE REPORT.

"An ill-looking kind of a body, who declined to give any name, was brought
before the Academy of Sciences, charged with having assaulted a gentleman
of the name of Uranus in the public highway. The prosecutor was a youngish
looking person, wrapped up in two or three great coats; and looked chillier
than anything imaginable, except the prisoner,--whose teeth absolutely
shook, all the time.

Policeman Le Verrier[804] stated that he saw the prosecutor walking along
the pavement,--and sometimes turning sideways, and sometimes running up to
the railings and jerking about in a strange way. Calculated that somebody
must be pulling his coat, or otherwise assaulting him. It was so dark that
he could not see; but thought, if he watched the direction in which the
next odd move was made, he might find out something. When the time came, he
set Brünnow, a constable in another division of the same force, to watch
where he told him; and Brünnow caught the prisoner lurking about in the
very spot,--trying to look as if he was minding his own business. Had
suspected for a long time that somebody was lurking about in the
neighborhood. Brünnow was then called, and deposed to his catching the
prisoner as described.

_M. Arago._--Was the prosecutor sober?

_Le Verrier._--Lord, yes, your worship; no man who had a drop in him ever
looks so cold as he did.

_M. Arago._--Did you see the assault?

_Le Verrier._--I can't say I did; but I told Brünnow exactly how he'd be
crouched down;--just as he was.

{391}

_M. Arago (to Brünnow)._--Did _you_ see the assault?

_Brünnow._--No, your worship; but I caught the prisoner.

_M. Arago._--How did you know there was any assault at all?

_Le Verrier._--I reckoned it couldn't be otherwise, when I saw the
prosecutor making those odd turns on the pavement.

_M. Arago._--You reckon and you calculate! Why, you'll tell me, next, that
you policemen may sit at home and find out all that's going on in the
streets by arithmetic. Did you ever bring a case of this kind before me
till now?

_Le Verrier._--Why, you see, your worship, the police are growing cleverer
and cleverer every day. We can't help it:--it grows upon us.

_M. Arago._--You're getting too clever for me. What does the prosecutor
know about the matter?

The prosecutor said, all he knew was that he was pulled behind by somebody
several times. On being further examined, he said that he had seen the
prisoner often, but did not know his name, nor how he got his living; but
had understood he was called Neptune. He himself had paid rates and taxes a
good many years now. Had a family of six,--two of whom got their own
living.

The prisoner being called on for his defence, said that it was a quarrel.
He had pushed the prosecutor--and the prosecutor had pushed him. They had
known each other a long time, and were always quarreling;--he did not know
why. It was their nature, he supposed. He further said, that the prosecutor
had given a false account of himself;--that he went about under different
names. Sometimes he was called Uranus, sometimes Herschel, and sometimes
Georgium Sidus; and he had no character for regularity in the neighborhood.
Indeed, he was sometimes not to be seen for a long time at once.

The prosecutor, on being asked, admitted, after a little hesitation, that
he had pushed and pulled the prisoner too. {392} In the altercation which
followed, it was found very difficult to make out which began:--and the
worthy magistrate seemed to think they must have begun together.

_M. Arago._--Prisoner, have you any family?

The prisoner declined answering that question at present. He said he
thought the police might as well reckon it out whether he had or not.

_M. Arago_ said he didn't much differ from that opinion.--He then addressed
both prosecutor and prisoner; and told them that if they couldn't settle
their differences without quarreling in the streets, he should certainly
commit them both next time. In the meantime, he called upon both to enter
into their own recognizances; and directed the police to have an eye upon
both,--observing that the prisoner would be likely to want it a long time,
and the prosecutor would be not a hair the worse for it."



This quib was written by a person who was among the astronomers: and it
illustrates the fact that Le Verrier had sole possession of the field until
Mr. Challis's letter appeared. Sir John Herschel's previous communication
should have paved the way: but the wonder of the discovery drove it out of
many heads. There is an excellent account of the whole matter in Professor
Grant's[805] _History of Physical Astronomy_. The squib scandalized some
grave people, who wrote severe admonitions to the editor. There are
formalists who spend much time in writing propriety to journals, to which
they serve as foolometers. In a letter to the _Athenæum_, speaking of the
way in which people hawk fine terms for common things, I said that these
people ought to have a new translation of the Bible, which should contain
the verse "gentleman and lady, created He them." The editor was handsomely
fired and brimstoned!

{393}



A NEW THEORY OF TIDES.

    A new theory of the tides: in which the errors of the usual theory are
    demonstrated; and proof shewn that the full moon is not the cause of a
    concomitant spring tide, but actually the cause of the neaps.... By
    Comm^r. Debenham,[806] R.N. London, 1846, 8vo.

The author replied to a criticism in the _Athenæum_, and I remember how, in
a very few words, he showed that he had read nothing on the subject. The
reviewer spoke of the forces of the planets (i.e., the Sun and Moon) on the
ocean, on which the author remarks, "But N.B. the Sun is no planet, Mr.
Critic." Had he read any of the actual investigations on the usual theory,
he would have known that to this day the sun and moon continue to be called
_planets_--though the phrase is disappearing--in speaking of the tides; the
sense, of course, being the old one, wandering bodies.

A large class of the paradoxers, when they meet with something which taken
in their sense is absurd, do not take the trouble to find out the intended
meaning, but walk off with the words laden with their own first
construction. Such men are hardly fit to walk the streets without an
interpreter. I was startled for a moment, at the time when a recent
happy--and more recently happier--marriage occupied the public thoughts, by
seeing in a haberdasher's window, in staring large letters, an unpunctuated
sentence which read itself to me as "Princess Alexandra! collar and cuff!"
It immediately occurred to me that had I been any one of some scores of my
paradoxers, I should, no doubt, have proceeded to raise the mob against the
unscrupulous person who dared to hint to a young bride such maleficent--or
at least immellificent--conduct towards her new lord. But, as it was,
certain material contexts in the shop window suggested a less {394} savage
explanation. A paradoxer should not stop at reading the advertisements of
Newton or Laplace; he should learn to look at the stock of goods.

I think I must have an eye for double readings, when presented: though I
never guess riddles. On the day on which I first walked into the _Panizzi_
reading room[807]--as it ought to be called--at the Museum, I began my
circuit of the wall-shelves at the ladies' end: and perfectly coincided in
the propriety of the Bibles and theological works being placed there. But
the very first book I looked on the back of had, in flaming gold letters,
the following inscription--"Blast the Antinomians!"[808] If a line had been
drawn below the first word, Dr. Blast's history of the Antinomians would
not have been so fearfully misinterpreted. It seems that neither the binder
nor the arranger of the room had caught my reading. The book was removed
before the catalogue of books of reference was printed.



AN ASTRONOMICAL PARADOXER.

    Two systems of astronomy: first, the Newtonian system, showing the rise
    and progress thereof, with a short historical account; the general
    theory with a variety of remarks thereon: second, the system in
    accordance with the Holy Scriptures, showing the rise and progress from
    Enoch, the seventh from Adam, the prophets, Moses, and others, in the
    first Testament; our Lord Jesus Christ, and his apostles, in the new or
    second Testament; Reeve and Muggleton, in the third and last Testament;
    with a variety of remarks thereon. By Isaac Frost.[809] London, 1846,
    4to.

{395}

A very handsomely printed volume, with beautiful plates. Many readers who
have heard of Muggletonians have never had any distinct idea of Lodowick
Muggleton,[810] the inspired tailor, (1608-1698) who about 1650 received
his commission from heaven, wrote a Testament, founded a sect, and
descended to posterity. Of Reeve[811] less is usually said; according to
Mr. Frost, he and Muggleton are the two "witnesses." I shall content myself
with one specimen of Mr. Frost's science:

"I was once invited to hear read over 'Guthrie[812] on Astronomy,' and when
the reading was concluded I was asked my opinion thereon; when I said,
'Doctor, it appears to me that Sir I. Newton has only given two proofs in
support of his theory of the earth revolving round the sun: all the rest is
assertion without any proofs.'--'What are they?' inquired the
Doctor.--'Well,' I said, 'they are, first, the power of {396} attraction to
keep the earth to the sun; the second is the power of repulsion, by virtue
of the centrifugal motion of the earth: all the rest appears to me
assertion without proof.' The Doctor considered a short time and then said,
'It certainly did appear so.' I said, 'Sir Isaac has certainly obtained the
credit of completing the system, but really he has only half done his
work.'--'How is that,' inquired my friend the Doctor. My reply was this:
'You will observe his system shows the earth traverses round the sun on an
inclined plane; the consequence is, there are four powers required to make
his system complete:

  1st. The power of _attraction_.
  2ndly. The power of _repulsion_.
  3rdly. The power of _ascending_ the inclined plane.
  4thly. The power of _descending_ the inclined plane.

You will thus easily see the _four_ powers required, and Newton has only
accounted for _two_; the work is therefore only half done.' Upon due
reflection the Doctor said, 'It certainly was necessary to have these
_four_ points cleared up before the system could be said to be complete.'"



I have no doubt that Mr. Frost, and many others on my list, have really
encountered doctors who could be puzzled by such stuff as this, or nearly
as bad, among the votaries of existing systems, and have been encouraged
thereby to print their objections. But justice requires me to say that from
the words "power of repulsion by virtue of the centrifugal motion of the
earth," Mr. Frost may be suspected of having something more like a notion
of the much-mistaken term "centrifugal force" than many paradoxers of
greater fame. The Muggletonian sect is not altogether friendless: over and
above this handsome volume, the works of Reeve and Muggleton were printed,
in 1832, in three quarto volumes. See _Notes and Queries, 1st Series_, v,
80; 3d Series, iii, 303. {397}

[The system laid down by Mr. Frost, though intended to be substantially
that of Lodowick Muggleton, is not so vagarious. It is worthy of note how
very different have been the fates of two contemporary paradoxers,
Muggleton and George Fox.[813] They were friends and associates,[814] and
commenced their careers about the same time, 1647-1650. The followers of
Fox have made their sect an institution, and deserve to be called the
pioneers of philanthropy. But though there must still be Muggletonians,
since expensive books are published by men who take the name, no sect of
that name is known to the world. Nevertheless, Fox and Muggleton are men of
one type, developed by the same circumstances: it is for those who
investigate such men to point out why their teachings have had fates so
different. Macaulay says it was because Fox found followers of more sense
than himself. True enough: but why did Fox find such followers and not
Muggleton? The two were equally crazy, to all appearance: and the
difference required must be sought in the doctrines themselves.

Fox was not a _rational_ man: but the success of his sect and doctrines
entitles him to a letter of alteration of the phrase which I am surprised
has not become current. When Conduitt,[815] the husband of Newton's
half-niece, wrote a circular to Newton's friends, just after his death,
inviting them to bear their parts in a proper biography, he said, "As Sir
I. Newton was a _national_ man, I think every one ought to contribute to a
work intended to do him justice." Here is the very phrase which is often
wanted to signify that {398} celebrity which puts its mark, good or bad, on
the national history, in a manner which cannot be asserted of many
notorious or famous historical characters. Thus George Fox and Newton are
both _national_ men. Dr. Roget's[816] _Thesaurus_ gives more than fifty
synonyms--_colleagues_ would be the better word--of "_celebrated_," any one
of which might be applied, either in prose or poetry, to Newton or to his
works, no one of which comes near to the meaning which Conduitt's adjective
immediately suggests.

The truth is, that we are too _monarchical_ to be _national_. We have the
Queen's army, the Queen's navy, the Queen's highway, the Queen's English,
etc.; nothing is national except the _debt_. That this remark is not new is
an addition to its force; it has hardly been repeated since it was first
made. It is some excuse that _nation_ is not vernacular English: the
_country_ is our word, and _country man_ is appropriated.]



    Astronomical Aphorisms, or Theory of Nature; founded on the immutable
    basis of Meteoric Action. By P. Murphy,[817] Esq. London, 1847, 12mo.

This is by the framer of the Weather Almanac, who appeals to that work as
corroborative of his theory of planetary temperature, years after all the
world knew by experience that this meteorological theory was just as good
as the others.

{399}



    The conspiracy of the Bullionists as it affects the present system of
    the money laws. By Caleb Quotem. Birmingham, 1847, 8vo. (pp. 16).

This pamphlet is one of a class of which I know very little, in which the
effects of the laws relating to this or that political bone of contention
are imputed to deliberate conspiracy of one class to rob another of what
the one knew ought to belong to the other. The success of such writers in
believing what they have a bias to believe, would, if they knew themselves,
make them think it equally likely that the inculpated classes might really
believe what it is _their_ interest to believe. The idea of a _guilty_
understanding existing among fundholders, or landholders, or any holders,
all the country over, and never detected except by bouncing pamphleteers,
is a theory which should have been left for Cobbett[818] to propose, and
for Apella to believe.[819]

[_August_, 1866. A pamphlet shows how to pay the National Debt. Advance
paper to railways, etc., receivable in payment of taxes. The railways pay
interest and principal in money, with which you pay your national debt, and
redeem your notes. Twenty-five years of interest redeems the notes, and
then the principal pays the debt. Notes to be kept up to value by
penalties.]



THEISM INDEPENDENT OF REVELATION.

    The Reasoner. No. 45. Edited by G.J. Holyoake.[820] Price _2d._ Is
    there sufficient proof of the existence of God? 8vo. 1847.

This acorn of the holy oak was forwarded to me with a manuscript note,
signed by the editor, on the part of the {400} "London Society of
Theological Utilitarians," who say, "they trust you may be induced to give
this momentous subject your consideration." The supposition that a
middle-aged person, known as a student of thought on more subjects than
one, had that particular subject yet to begin, is a specimen of what I will
call the _assumption-trick_ of controversy, a habit which pervades all
sides of all subjects. The tract is a proof of the good policy of letting
opinions find their level, without any assistance from the Court of Queen's
Bench. Twenty years earlier the thesis would have been positive, "There is
sufficient proof of the non-existence of God," and bitter in its tone. As
it stands, we have a moderate and respectful treatment--wrong only in
making the opponent argue absurdly, as usually happens when one side
invents the other--of a question in which a great many Christians have
agreed with the atheist: that question being--Can the existence of God be
proved independently of revelation? Many very religious persons answer this
question in the negative, as well as Mr. Holyoake. And, this point being
settled, all who agree in the negative separate into those who can endure
scepticism, and those who cannot: the second class find their way to
Christianity. This very number of _The Reasoner_ announces the secession of
one of its correspondents, and his adoption of the Christian faith. This
would not have happened twenty years before: nor, had it happened, would it
have been respectfully announced.

There are people who are very unfortunate in the expression of their
meaning. Mr. Holyoake, in the name of the "London Society" etc., forwarded
a pamphlet on the existence of God, and said that the Society trusted I
"may be induced to give" the subject my "consideration." How could I know
the Society was one person, who supposed I had arrived at a conclusion and
wanted a "_guiding word_"? But so it seems it was: Mr. Holyoake, in the
_English {401} Leader_ of October 15, 1864, and in a private letter to me,
writes as follows:

"The gentleman who was the author of the argument, and who asked me to send
it to Mr. De Morgan, never assumed that that gentleman had 'that particular
subject to begin'--on the contrary, he supposed that one whom we all knew
to be eminent as a thinker _had_ come to a conclusion upon it, and would
perhaps vouchsafe a guiding word to one who was, as yet, seeking the
solution of the Great Problem of Theology. I told my friend that 'Mr. De
Morgan was doubtless preoccupied, and that he must be content to wait. On
some day of courtesy and leisure he might have the kindness to write.' Nor
was I wrong--the answer appears in your pages at the lapse of seventeen
years."

I suppose Mr. Holyoake's way of putting his request was the _stylus curiæ_
of the Society. A worthy Quaker who was sued for debt in the King's Bench
was horrified to find himself charged in the declaration with detaining his
creditor's money by force and arms, contrary to the peace of our Lord the
King, etc. It's only the _stylus curiæ_, said a friend: I don't know
_curiæ_, said the Quaker, but he shouldn't style us peace-breakers.

The notion that the _non_-existence of God can be _proved_, has died out
under the light of discussion: had the only lights shone from the pulpit
and the prison, so great a step would never have been made. The question
now is as above. The dictum that Christianity is "part and parcel of the
law of the land" is also abrogated: at the same time, and the coincidence
is not an accident, it is becoming somewhat nearer the truth that the law
of the land is part and parcel of Christianity. It must also be noticed
that _Christianity_ was part and parcel of the articles of _war_; and so
was _duelling_. Any officer speaking against religion was to be cashiered;
and any officer receiving an affront without, in the last resort,
attempting to kill his opponent, was also to be cashiered. Though somewhat
of a book-hunter, I {402} have never been able to ascertain the date of the
collected remonstrances of the prelates in the House of Lords against this
overt inculcation of murder, under the soft name of _satisfaction_: it is
neither in Watt,[821] nor in Lowndes,[822] nor in any edition of
Brunet;[823] and there is no copy in the British Museum. Was the collected
edition really published?

[The publication of the above in the _Athenæum_ has not produced reference
to a single copy. The collected edition seems to be doubted. I have even
met one or two persons who doubt the fact of the Bishops having
remonstrated at all: but their doubt was founded on an absurd supposition,
namely, that it was _no business of theirs_; that it was not the business
of the prelates of the church in union with the state to remonstrate
against the Crown commanding murder! Some say that the edition was
published, but under an irrelevant title, which prevented people from
knowing what it was about. Such things have happened: for example, arranged
extracts from Wellington's general orders, which would have attracted
attention, fell dead under the title of "Principles of War." It is surmised
that the book I am looking for also contains the protests of the Reverend
bench against other things besides the Thou-shalt-do-murder of the Articles
(of war), and is called "First Elements of Religion" or some similar title.
Time clears up all things.]

       *       *       *       *       *


Notes

[1] See Mrs. De Morgan's _Memoir of Augustus De Morgan_, London, 1882, p
61.

[2] In the first edition this reference was to page 11.

[3] In the first edition this read "at page 438," the work then appearing
in a single volume.

[4] "Just as it would surely have been better not to have considered it
(i.e., the trinity) as a mystery, and with Cl. Kleckermann to have
investigated by the aid of philosophy according to the teaching of true
logic what it might be, before they determined what it was; just so would
it have been better to withdraw zealously and industriously into the
deepest caverns and darkest recesses of metaphysical speculations and
suppositions in order to establish their opinion beyond danger from the
weapons of their adversaries.... Indeed that great man so explains and
demonstrates this dogma (although to theologians the word has not much
charm) from the immovable foundations of philosophy, that with but few
changes and additions a mind sincerely devoted to truth can desire nothing
more."

[5] Mrs. Wititterly, in _Nicholas Nickleby_.--A. De M.

[6] The brackets mean that the paragraph is substantially from some one of
the _Athenæum Supplements_.--S. E. De M.

[7] "It is annoying that this ingenious naturalist who has already given us
more useful works and has still others in preparation, uses for this odious
task, a pen dipped in gall and wormwood. It is true that many of his
remarks have some foundation, and that to each error that he points out he
at the same time adds its correction. But he is not always just and never
fails to insult. After all, what does his book prove except that a
forty-fifth part of a very useful review is not free from mistakes? Must we
confuse him with those superficial writers whose liberty of body does not
permit them to restrain their fruitfulness, that crowd of savants of the
highest rank whose writings have adorned and still adorn the
_Transactions_? Has he forgotten that the names of the Boyles, Newtons,
Halleys, De Moivres, Hans Sloanes, etc. have been seen frequently? and that
still are found those of the Wards, Bradleys, Grahams, Ellicots, Watsons,
and of an author whom Mr. Hill prefers to all others, I mean Mr. Hill
himself?"

[8] "Let no free man be seized or imprisoned or in any way harmed except by
trial of his peers."

[9] "The master can rob, wreck and punish his slave according to his
pleasure save only that he may not maim him."

[10] An Irish antiquary informs me that Virgil is mentioned in annals at
A.D. 784, as "Verghil, i.e., the geometer, Abbot of Achadhbo [and Bishop of
Saltzburg] died in Germany in the thirteenth year of his bishoprick." No
allusion is made to his opinions; but it seems he was, by tradition, a
mathematician. The Abbot of Aghabo (Queen's County) was canonized by
Gregory IX, in 1233. The story of the second, or scapegoat, Virgil would be
much damaged by the character given to the real bishop, if there were
anything in it to dilapidate.--A. De M.

[11] "He performed many acts befitting the Papal dignity, and likewise many
excellent (to be sure!) works."

[12] "After having been on the throne during ten years of pestilence."

[13] The work is the _Questiones Joannis Buridani super X libros
Aristotelis ad Nicomachum, curante Egidio Delfo_ ... Parisiis, 1489, folio.
It also appeared at Paris in editions of 1499, 1513, and 1518, and at
Oxford in 1637.

[14] Jean Buridan was born at Béthune about 1298, and died at Paris about
1358. He was professor of philosophy at the University of Paris and several
times held the office of Rector. As a philosopher he was classed among the
nominalists.

[15] So in the original.

[16] Baruch Spinoza, or Benedict de Spinoza as he later called himself, the
pantheistic philosopher, excommunicated from the Jewish faith for heresy,
was born at Amsterdam in 1632 and died there in 1677.

[17] Michael Scott, or Scot, was born about 1190, probably in Fifeshire,
Scotland, and died about 1291. He was one of the best known savants of the
court of Emperor Frederick II, and wrote upon astrology, alchemy, and the
occult sciences. He was looked upon as a great magician and is mentioned
among the wizards in Dante's _Inferno_.

             "That other, round the loins
  So slender of his shape, was Michael Scot,
  Practised in every slight of magic wile." _Inferno_, XX.

Boccaccio also speaks of him: "It is not long since there was in this city
(Florence) a great master in necromancy, who was called Michele Scotto,
because he was a Scot." _Decameron_, Dec. Giorno.

Scott's mention of him in Canto Second of his _Lay of the Last Minstrel_,
is well known:

 "In these fair climes, it was my lot
  To meet the wondrous Michael Scott;
    A wizard of such dreaded fame,
  That when, in Salamanca's cave,
  Him listed his magic wand to wave,
    The bells would ring in Notre Dame!"

Sir Walter's notes upon him are of interest.

[18] These were some of the forgeries which Michel Chasles (1793-1880) was
duped into buying. They purported to be a correspondence between Pascal and
Newton and to show that the former had anticipated some of the discoveries
of the great English physicist and mathematician. That they were forgeries
was shown by Sir David Brewster in 1855.

[19] "Let the serpent also break from its appointed path."

[20] Guglielmo Brutus Icilius Timoleon Libri-Carucci della Sommaja, born at
Florence in 1803; died at Fiesole in 1869. His _Histoire des Sciences
Mathématiques_ appeared at Paris in 1838, the entire first edition of
volume I, save some half dozen that he had carried home, being burned on
the day that the printing was completed. He was a great collector of early
printed works on mathematics, and was accused of having stolen large
numbers of them from other libraries. This accusation took him to London,
where he bitterly attacked his accusers. There were two auction sales of
his library, and a number of his books found their way into De Morgan's
collection.

[21] Philo of Gadara lived in the second century B.C. He was a pupil of
Sporus, who worked on the problem of the two mean proportionals.

[22] In his _Histoire des Mathématiques_, the first edition of which
appeared in 1758. Jean Etienne Montucla was born at Lyons in 1725 and died
at Versailles in 1799. He was therefore only thirty-three years old when
his great work appeared. The second edition, with additions by D'Alembert,
appeared in 1799-1802. He also wrote a work on the quadrature of the
circle, _Histoire des recherches sur la Quadrature du Cercle_, which
appeared in 1754.

[23] Eutocius of Ascalon was born in 480 A.D. He wrote commentaries on the
first four books of the conics of Apollonius of Perga (247-222 B.C.). He
also wrote on the Sphere and Cylinder and the Quadrature of the Circle, and
on the two books on Equilibrium of Archimedes (287-212 B.C.)

[24] Edward Cocker was born in 1631 and died between 1671 and 1677. His
famous arithmetic appeared in 1677 and went through many editions. It was
written in a style that appealed to teachers, and was so popular that the
expression "According to Cocker" became a household phrase. Early in the
nineteenth century there was a similar saying in America, "According to
Daboll," whose arithmetic had some points of analogy to that of Cocker.
Each had a well-known prototype in the ancient saying, "He reckons like
Nicomachus of Gerasa."

[25] So in the original, for Barrême. François Barrême was to France what
Cocker was to England. He was born at Lyons in 1640, and died at Paris in
1703. He published several arithmetics, dedicating them to his patron,
Colbert. One of the best known of his works is _L'arithmétique, ou le livre
facile pour apprendre l'arithmétique soi-mème_, 1677. The French word
_barême_ or _barrême_, a ready-reckoner, is derived from his name.

[26] Born at Rome, about 480 A.D.; died at Pavia, 524. Gibbon speaks of him
as "the last of the Romans whom Cato or Tully could have acknowledged for
their countryman." His works on arithmetic, music, and geometry were
classics in the medieval schools.

[27] Johannes Campanus, of Novarra, was chaplain to Pope Urban IV
(1261-1264). He was one of the early medieval translators of Euclid from
the Arabic into Latin, and the first printed edition of the _Elements_
(Venice, 1482) was from his translation. In this work he probably depended
not a little upon at least two or three earlier scholars. He also wrote _De
computo ecclesiastico Calendarium_, and _De quadratura circuli_.

[28] Archimedes gave 3-1/7, and 3-10/71 as the limits of the ratio of the
circumference to the diameter of a circle.

[29] Friedrich W. A. Murhard was born at Cassel in 1779 and died there in
1853. His _Bibliotheca Mathematica_, Leipsic, 1797-1805, is ill arranged
and inaccurate, but it is still a helpful bibliography. De Morgan speaks
somewhere of his indebtedness to it.

[30] Abraham Gotthelf Kästner was born at Leipsic in 1719, and died at
Göttingen in 1800. He was professor of mathematics and physics at
Göttingen. His _Geschichte der Mathematik_ (1796-1800) was a work of
considerable merit. In the text of the _Budget of Paradoxes_ the name
appears throughout as Kastner instead of Kästner.

[31] Lucas Gauricus, or Luca Gaurico, born at Giffoni, near Naples, in
1476; died at Rome in 1558. He was an astrologer and mathematician, and was
professor of mathematics at Ferrara in 1531. In 1545 he became bishop of
Cività Ducale.

[32] John Couch Adams was born at Lidcot, Cornwall, in 1819, and died in
1892. He and Leverrier predicted the discovery of Neptune from the
perturbations in Uranus.

[33] Urbain-Jean-Joseph Leverrier was born at Saint-Lô, Manche, in 1811,
and died at Paris in 1877. It was his data respecting the perturbations of
Uranus that were used by Adams and himself in locating Neptune.

[34] Joseph-Juste Scaliger, the celebrated philologist, was born at Agen in
1540, and died at Leyden in 1609. His _Cyclometrica elementa_, to which De
Morgan refers, appeared at Leyden in 1594.

[35] The title is: _In hoc libra contenta.... Introductio i
geometri[=a].... Liber de quadratura circuli. Liber de cubicatione sphere.
Perspectiva introductio_. Carolus Bovillus, or Charles Bouvelles (Boüelles,
Bouilles, Bouvel), was born at Saucourt, Picardy, about 1470, and died at
Noyon about 1533. He was canon and professor of theology at Noyon. His
_Introductio_ contains considerable work on star polygons, a favorite study
in the Middle Ages and early Renaissance. His work _Que hoc volumine
contin[=e]tur. Liber de intellectu. Liber de sensu_, etc., appeared at
Paris in 1509-10.

[36] Nicolaus Cusanus, Nicolaus Chrypffs or Krebs, was born at Kues on the
Mosel in 1401, and died at Todi, Umbria, August 11, 1464. He held positions
of honor in the church, including the bishopric of Brescia. He was made a
cardinal in 1448. He wrote several works on mathematics, his _Opuscula
varia_ appearing about 1490, probably at Strasburg, but published without
date or place. His _Opera_ appeared at Paris in 1511 and again in 1514, and
at Basel in 1565.

[37] Henry Stephens (born at Paris about 1528, died at Lyons in 1598) was
one of the most successful printers of his day. He was known as
_Typographus Parisiensis_, and to his press we owe some of the best works
of the period.

[38] Jacobus Faber Stapulensis (Jacques le Fèvre d'Estaples) was born at
Estaples, near Amiens, in 1455, and died at Nérac in 1536. He was a priest,
vicar of the bishop of Meaux, lecturer on philosophy at the Collège Lemoine
in Paris, and tutor to Charles, son of Francois I. He wrote on philosophy,
theology, and mathematics.

[39] Claude-François Milliet de Challes was born at Chambéry in 1621, and
died at Turin in 1678. He edited _Euclidis Elementorum libri octo_ in 1660,
and published a _Cursus seu mundus mathematicus_, which included a short
history of mathematics, in 1674. He also wrote on mathematical geography.

[40] This date should be 1503, if he refers to the first edition. It is
well known that this is the first encyclopedia worthy the name to appear in
print. It was written by Gregorius Reisch (born at Balingen, and died at
Freiburg in 1487), prior of the cloister at Freiburg and confessor to
Maximilian I. The first edition appeared at Freiburg in 1503, and it passed
through many editions in the sixteenth and seventeenth centuries. The title
of the 1504 edition reads: _Aepitoma omnis phylosophiae. alias Margarita
phylosophica tractans de omni genere scibili: Cum additionibus: Quae in
alijs non habentur_.

[41] This is the _Introductio in arithmeticam Divi S. Boetii.... Epitome
rerum geometricarum ex geometrica introductio C. Bovilli. De quadratura
circuli demonstratio ex Campano_, that appeared without date about 1507.

[42] Born at Liverpool in 1805, and died there about 1872. He was a
merchant, and in 1865 he published, at Liverpool, a work entitled _The
Quadrature of the Circle, or the True Ratio between the Diameter and
Circumference geometrically and mathematically demonstrated_. In this he
gives the ratio as exactly 3-1/8.

[43] "That it would be impossible to tell him exactly, since no one had yet
been able to find precisely the ratio of the circumference to the
diameter."

[44] This is the Paris edition: "Parisiis: ex officina Ascensiana anno
Christi ... MDXIIII," as appears by the colophon of the second volume to
which De Morgan refers.

[45] Regiomontanus, or Johann Müller of Königsberg (Regiomontanus), was
born at Königsberg in Franconia, June 5, 1436, and died at Rome July 6,
1476. He studied at Vienna under the great astronomer Peuerbach, and was
his most famous pupil. He wrote numerous works, chiefly on astronomy. He is
also known by the names Ioannes de Monte Regio, de Regiomonte, Ioannes
Germanus de Regiomonte, etc.

[46] Henry Cornelius Agrippa was born at Cologne in 1486 and died either at
Lyons in 1534 or at Grenoble in 1535. He was professor of theology at
Cologne and also at Turin. After the publication of his _De Occulta
Philosophia_ he was imprisoned for sorcery. Both works appeared at Antwerp
in 1530, and each passed through a large number of editions. A French
translation appeared in Paris in 1582, and an English one in London in
1651.

[47] Nicolaus Remegius was born in Lorraine in 1554, and died at Nancy in
1600. He was a jurist and historian, and held the office of procurator
general to the Duke of Lorraine.

[48] This was at the storming of the city by the British on May 4, 1799.
From his having been born in India, all this appealed strongly to the
interests of De Morgan.

[49] Orontius Finaeus, or Oronce Finé, was born at Briançon in 1494 and
died at Paris, October 6, 1555. He was imprisoned by François I for
refusing to recognize the concordat (1517). He was made professor of
mathematics in the Collège Royal (later called the Collège de France) in
1532. He wrote extensively on astronomy and geometry, but was by no means a
great scholar. He was a pretentious man, and his works went through several
editions. His _Protomathesis_ appeared at Paris in 1530-32. The work
referred to by De Morgan is the _Quadratura circuli tandem inventa &
clarissime demonstrata_ ... Lutetiae Parisiorum, 1544, fol. In the 1556
edition of his _De rebus mathematicis, hactenus desideratis, Libri IIII_,
published at Paris, the subtitle is: _Quibus inter cætera, Circuli
quadratura Centum modis, & suprà, per eundem Orontium recenter excogitatis,
demonstratus_, so that he kept up his efforts until his death.

[50] Johannes Buteo (Boteo, Butéon, Bateon) was born in Dauphiné c.
1485-1489, and died in a cloister in 1560 or 1564. Some writers give
Charpey as the place and 1492 as the date of his birth, and state that he
died at Canar in 1572. He belonged to the order of St. Anthony, and wrote
chiefly on geometry, exposing the pretenses of Finaeus. His _Opera
geometrica_ appeared at Lyons in 1554, and his _Logistica_ and _De
quadratura circuli libri duo_ at Lyons in 1559.

[51] This is the great French algebraist, François Viète (Vieta), who was
born at Fontenay-le-Comte in 1540, and died at Paris, December 13, 1603.
His well-known _Isagoge in artem analyticam_ appeared at Tours in 1591. His
_Opera mathematica_ was edited by Van Schooten in 1646.

[52] This is the _De Rebus mathematicis hactenus desideratis, Libri IIII_,
that appeared in Paris in 1556. For the title page see Smith, D. E., _Rara
Arithmetica_, Boston, 1908, p. 280.

[53] The title is correct except for a colon after _Astronomicum_. Nicolaus
Raimarus Ursus was born in Henstede or Hattstede, in Dithmarschen, and died
at Prague in 1599 or 1600. He was a pupil of Tycho Brahe. He also wrote _De
astronomis hypothesibus_ (1597) and _Arithmetica analytica vulgo Cosa oder
Algebra_ (1601).

[54] Born at Dôle, Franche-Comté, about 1550, died in Holland about 1600.
The work to which reference is made is the _Quadrature du cercle, ou
manière de trouver un quarré égal au cercle donné_, which appeared at Delft
in 1584. Duchesne had the courage of his convictions, not only on
circle-squaring but on religion as well, for he was obliged to leave France
because of his conversion to Calvinism. De Morgan's statement that his real
name is Van der Eycke is curious, since he was French born. The Dutch may
have translated his name when he became professor at Delft, but we might
equally well say, that his real name was Quercetanus or à Quercu.

[55] This was the father of Adriaan Metius (1571-1635). He was a
mathematician and military engineer, and suggested the ratio 355/113 for
[pi], a ratio afterwards published by his son. The ratio, then new to
Europe, had long been known and used in China, having been found by Tsu
Ch'ung-chih (428-499 A.D.).

[56] This was Jost Bürgi, or Justus Byrgius, the Swiss mathematician of
whom Kepler wrote in 1627: "Apices logistici Justo Byrgio multis annis ante
editionem Neperianam viam præiverunt ad hos ipsissimos logarithmos." He
constructed a table of antilogarithms (_Arithmetische und geometrische
Progress-Tabulen_), but it was not published until after Napier's work
appeared.

[57] Ludolphus Van Ceulen, born at Hildesheim, and died at Leyden in 1610.
It was he who first carried the computation of [pi] to 35 decimal places.

[58] Jens Jenssen Dodt, van Flensburg, a Dutch historian, who died in 1847.

[59] I do not know this edition. There was one "Antverpiae apud Petrum
Bellerum sub scuto Burgundiae," 4to, in 1591.

[60] Archytas of Tarentum (430-365 B.C.) who wrote on proportions,
irrationals, and the duplication of the cube.

[61]

      _The Circle Speaks._
 "At first a circle I was called,
  And was a curve around about
  Like lofty orbit of the sun
  Or rainbow arch among the clouds.
  A noble figure then was I--
  And lacking nothing but a start,
  And lacking nothing but an end.
  But now unlovely do I seem
  Polluted by some angles new.
  This thing Archytas hath not done
  Nor noble sire of Icarus
  Nor son of thine, Iapetus.
  What accident or god can then
  Have quadrated mine area?"

      _The Author Replies._
 "By deepest mouth of Turia
  And lake of limpid clearness, lies
  A happy state not far removed
  From old Saguntus; farther yet
  A little way from Sucro town.
  In this place doth a poet dwell,
  Who oft the stars will closely scan,
  And always for himself doth claim
  What is denied to wiser men;--
  An old man musing here and there
  And oft forgetful of himself,
  Not knowing how to rightly place
  The compasses, nor draw a line,
  As he doth of himself relate.
  This craftsman fine, in sooth it is
  Hath quadrated thine area."

[62] Pietro Bongo, or Petrus Bungus, was born at Bergamo, and died there in
1601. His work on the Mystery of Numbers is one of the most exhaustive and
erudite ones of the mystic writers. The first edition appeared at Bergamo
in 1583-84; the second, at Bergamo in 1584-85; the third, at Venice in
1585; the fourth, at Bergamo in 1590; and the fifth, which De Morgan calls
the second, in 1591. Other editions, before the Paris edition to which he
refers, appeared in 1599 and 1614; and the colophon of the Paris edition is
dated 1617. See the editor's _Rara Arithmetica_, pp. 380-383.

[63] William Warburton (1698-1779), Bishop of Gloucester, whose works got
him into numerous literary quarrels, being the subject of frequent satire.

[64] Thomas Galloway (1796-1851), who was professor of mathematics at
Sandhurst for a time, and was later the actuary of the Amicable Life
Assurance Company of London. In the latter capacity he naturally came to be
associated with De Morgan.

[65] Giordano Bruno was born near Naples about 1550. He left the Dominican
order to take up Calvinism, and among his publications was _L'expulsion de
la bête triomphante_. He taught philosophy at Paris and Wittenberg, and
some of his works were published in England in 1583-86. Whether or not he
was roasted alive "for the maintenance and defence of the holy Church," as
De Morgan states, depends upon one's religious point of view. At any rate,
he was roasted as a heretic.

[66] Referring to part of his _Discours de la méthode_, Leyden, 1637.

[67] Bartholomew Legate, who was born in Essex about 1575. He denied the
divinity of Christ and was the last heretic burned at Smithfield.

[68] Edward Wightman, born probably in Staffordshire. He was
anti-Trinitarian, and claimed to be the Messiah. He was the last man burned
for heresy in England.

[69] Gaspar Schopp, born at Neumarck in 1576, died at Padua in 1649;
grammarian, philologist, and satirist.

[70] Konrad Ritterhusius, born at Brunswick in 1560; died at Altdorf in
1613. He was a jurist of some power.

[71] Johann Jakob Brucker, born at Augsburg in 1696, died there in 1770. He
wrote on the history of philosophy (1731-36, and 1742-44).

[72] Daniel Georg Morhof, born at Wismar in 1639, died at Lübeck in 1691.
He was rector of the University of Kiel, and professor of eloquence,
poetry, and history.

[73] In the _Histoire des Sciences Mathématiques_, vol. IV, note X, pp.
416-435 of the 1841 edition.

[74] Colenso (1814-1883), missionary bishop of Natal, was one of the
leaders of his day in the field of higher biblical criticism. De Morgan
must have admired his mathematical works, which were not without merit.

[75] Samuel Roffey Maitland, born at London in 1792; died at Gloucester in
1866. He was an excellent linguist and a critical student of the Bible. He
became librarian at Lambeth in 1838.

[76] Archbishop Howley (1766-1848) was a thorough Tory. He was one of the
opponents of the Roman Catholic Relief bill, the Reform bill, and the
Jewish Civil Disabilities Relief bill.

[77] We have, in America at least, almost forgotten the great stir made by
Edward B. Pusey (1800-1882) in the great Oxford movement in the middle of
the nineteenth century. He was professor of Hebrew at Oxford, and canon of
Christ Church.

[78] That is, his _Magia universalis naturae et artis sive recondita
naturalium et artificialium rerum scientia_, Würzburg, 1657, 4to, with
editions at Bamberg in 1671, and at Frankfort in 1677. Gaspard Schott
(Königshofen 1608, Würzburg 1666) was a physicist and mathematician,
devoting most of his attention to the curiosities of his sciences. His type
of mind must have appealed to De Morgan.

[79] _Salicetti Quadratura circuli nova, perspicua, expedita, veraque tum
naturalis, tum geometrica_, etc., 1608.--_Consideratio nova in opusculum
Archimedis de circuli dimensione_, etc., 1609.

[80] Melchior Adam, who died at Heidelberg in 1622, wrote a collection of
biographies which was published at Heidelberg and Frankfort from 1615 to
1620.

[81] Born at Baden in 1524; died at Basel in 1583. The Erastians were
related to the Zwinglians, and opposed all power of excommunication and the
infliction of penalties by a church.

[82] See Acts xii. 20.

[83] Theodore de Bèse, a French theologian; born at Vezelay, in Burgundy,
in 1519; died at Geneva, in 1605.

[84] Dr. Robert Lee (1804-1868) had some celebrity in De Morgan's time
through his attempt to introduce music and written prayers into the service
of the Scotch Presbyterian church.

[85] Born at Veringen, Hohenzollern, in 1512; died at Röteln in 1564.

[86] Born at Kinnairdie, Bannfshire, in 1661; died at London in 1708. His
_Astronomiae Physicae et Geometriae Elementa_, Oxford, 1702, was an
influential work.

[87] The title was carelessly copied by De Morgan, not an unusual thing in
his case. The original reads: A Plaine Discovery, of the whole Revelation
of S. Iohn: set downe in two treatises ... set foorth by John Napier L. of
Marchiston ... whereunto are annexed, certaine Oracles of Sibylla ...
London ... 1611.

[88] I have not seen the first edition, but it seems to have appeared in
Edinburgh, in 1593, with a second edition there in 1594. The 1611 edition
was the third.

[89] It seems rather certain that Napier felt his theological work of
greater importance than that in logarithms. He was born at Merchiston, near
(now a part of) Edinburgh, in 1550, and died there in 1617, three years
after the appearance of his _Mirifici logarithmorum canonis descriptio_.

[90] Followed, in the third edition, from which he quotes, by a comma.

[91] There was an edition published at Stettin in 1633. An English
translation by P. F. Mottelay appeared at London in 1893. Gilbert
(1540-1603) was physician to Queen Elizabeth and President of the College
of Physicians at London. His _De Magnete_ was the first noteworthy treatise
on physics printed in England. He treated of the earth as a spherical
magnet and suggested the variation and declination of the needle as a means
of finding latitude at sea.

[92] The title says "ab authoris fratre collectum," although it was edited
by J. Gruterus.

[93] Porta was born at Naples in 1550 and died there in 1615. He studied
the subject of lenses and the theory of sight, did some work in hydraulics
and agriculture, and was well known as an astrologer. His _Magiae naturalis
libri XX_ was published at Naples in 1589. The above title should read
_curvilineorum_.

[94] Cataldi was born in 1548 and died at Bologna in 1626. He was professor
of mathematics at Perugia, Florence, and Bologna, and is known in
mathematics chiefly for his work in continued fractions. He was one of the
scholarly men of his day.

[95] Georg Joachim Rheticus was born at Feldkirch in 1514 and died at
Caschau, Hungary, in 1576. He was one of the most prominent pupils of
Copernicus, his _Narratio de libris revolutionum Copernici_ (Dantzig, 1540)
having done much to make the theory of his master known.

[96] Henry Briggs, who did so much to make logarithms known, and who used
the base 10, was born at Warley Wood, in Yorkshire, in 1560, and died at
Oxford in 1630. He was Savilian professor of mathematics at Oxford, and his
grave may still be seen there.

[97] He lived at "Reggio nella Emilia" in the 16th and 17th centuries. His
_Regola e modo facilissimo di quadrare il cerchio_ was published at Reggio
in 1609.

[98] Christoph Klau (Clavius) was born at Bamberg in 1537, and died at Rome
in 1612. He was a Jesuit priest and taught mathematics in the Jesuit
College at Rome. He wrote a number of works on mathematics, including
excellent text-books on arithmetic and algebra.

[99] Christopher Gruenberger, or Grienberger, was born at Halle in Tyrol in
1561, and died at Rome in 1636. He was, like Clavius, a Jesuit and a
mathematician, and he wrote a little upon the subject of projections. His
_Prospectiva nova coelestis_ appeared at Rome in 1612.

[100] The name should, of course, be Lansbergii in the genitive, and is so
in the original title. Philippus Lansbergius was born at Ghent in 1560, and
died at Middelburg in 1632. He was a Protestant theologian, and was also a
physician and astronomer. He was a well-known supporter of Galileo and
Copernicus. His _Commentationes in motum terrae diurnum et annuum_ appeared
at Middelburg in 1630 and did much to help the new theory.

[101] I have never seen the work. It is rare.

[102] The African explorer, born in Somersetshire in 1827, died at Bath in
1864. He was the first European to cross Central Africa from north to
south. He investigated the sources of the Nile.

[103] Prester (Presbyter, priest) John, the legendary Christian king whose
realm, in the Middle Ages, was placed both in Asia and in Africa, is first
mentioned in the chronicles of Otto of Freisingen in the 12th century. In
the 14th century his kingdom was supposed to be Abyssinia.

[104] "It is a profane and barbarous nation, dirty and slovenly, who eat
their meat half raw and drink mare's milk, and who use table-cloths and
napkins only to wipe their hands and mouths."

[105] "The great Prester John, who is the fourth in rank, is emperor of
Ethiopia and of the Abyssinians, and boasts of his descent from the race of
David, as having descended from the Queen of Sheba, Queen of Ethiopia. She,
having gone to Jerusalem to see the wisdom of Solomon, about the year of
the world 2952, returned pregnant with a son whom they called Moylech, from
whom they claim descent in a direct line. And so he glories in being the
most ancient monarch in the world, saying that his empire has endured for
more than three thousand years, which no other empire is able to assert. He
also puts into his titles the following: 'We, the sovereign in my realms,
uniquely beloved of God, pillar of the faith, sprung from the race of
Judah, etc.' The boundaries of this empire touch the Red Sea and the
mountains of Azuma on the east, and on the western side it is bordered by
the River Nile which separates it from Nubia. To the north lies Egypt, and
to the south the kingdoms of Congo and Mozambique. It extends forty degrees
in length, or one thousand twenty-five leagues, from Congo or Mozambique on
the south to Egypt on the north; and in width it reaches from the Nile on
the west to the mountains of Azuma on the east, seven hundred twenty-five
leagues, or twenty-nine degrees. This empire contains thirty large
provinces, namely Medra, Gaga, Alchy, Cedalon, Mantro, Finazam, Barnaquez,
Ambiam, Fungy, Angoté, Cigremaon, Gorga, Cafatez, Zastanla, Zeth, Barly,
Belangana, Tygra, Gorgany, Barganaza, d'Ancut, Dargaly, Ambiacatina,
Caracogly, Amara, Maon (_sic_), Guegiera, Bally, Dobora, and Macheda. All
of these provinces are situated directly under the equinoctial line between
the tropics of Capricorn and Cancer; but they are two hundred fifty leagues
nearer our tropic than the other. The name of Prester John signifies Great
Lord, and is not Priest [Presbyter] as many think. He has always been a
Christian, but often schismatic. At the present time he is a Catholic and
recognizes the Pope as sovereign pontiff. I met one of his bishops in
Jerusalem, and often conversed with him through the medium of our guide. He
was of grave and serious bearing, pleasant of speech, but wonderfully
subtle in everything he said. He took great delight in what I had to relate
concerning our beautiful ceremonies and the dignity of our prelates in
their pontifical vestments. As to other matters I will only say that the
Ethiopian is joyous and merry, not at all like the Tartar in the matter of
filth, nor like the wretched Arab. They are refined and subtle, trusting no
one, wonderfully suspicious, and very devout. They are not at all black as
is commonly supposed, by which I refer to those who do not live under the
equator or too near to it, for these are Moors as we shall see."

With respect to this translation it should be said that the original forms
of the proper names have been preserved, although they are not those found
in modern works. It should also be stated that the meaning of Prester is
not the one that was generally accepted by scholars at the time the work
was written, nor is it the one accepted to-day. There seems to be no doubt
that the word is derived from Presbyter as stated in note 103 on page 71,
since the above-mentioned chronicles of Otto, bishop of Freisingen about
the middle of the twelfth century, states this fact clearly. Otto received
his information from the bishop of Gabala (the Syrian Jibal) who told him
the story of John, _rex et sacerdos_, or Presbyter John as he liked to be
called. He goes on to say "Should it be asked why, with all this power and
splendor, he calls himself merely 'presbyter,' this is because of his
humility, and because it was not fitting for one whose server was a primate
and king, whose butler an archbishop and king, whose chamberlain a bishop
and king, whose master of the horse an archimandrite and king, whose chief
cook an abbot and king, to be called by such titles as these."

[106] Thomas Fienus (Fyens) was born at Antwerp in 1567 and died in 1631.
He was professor of medicine at Louvain. Besides the editions mentioned
below, his _De cometis anni 1618_ appeared at Leipsic in 1656. He also
wrote a _Disputatio an coelum moveatur et terra quiescat_, which appeared
at Antwerp in 1619, and again at Leipsic in 1656.

[107] Libertus Fromondus (1587-c 1653), a Belgian theologian, dean of the
College Church at Harcourt, and professor at Louvain. The name also appears
as Froidmont and Froimont.

[108] _L. Fromondi ... meteorologicorum libri sex.... Cui accessit T. Fieni
et L. Fromondi dissertationes de cometa anni 1618...._ This is from the
1670 edition. The 1619 edition was published at Antwerp. The
_Meteorologicorum libri VI_, appeared at Antwerp in 1627. He also wrote
_Anti-Aristarchus sive orbis terrae immobilis liber unicus_ (Antwerp,
1631); _Labyrrinthus sive de compositione continui liber unus, Philosophis,
Mathematicis, Theologis utilis et jucundus_ (Antwerp, 1631) and _Vesta sive
Anti-Aristarchi vindex adversus Jac. Lansbergium (Philippi filium) et
copernicanos_ (Antwerp, 1634).

[109] Snell was born at Leyden in 1591, and died there in 1626. He studied
under Tycho Brahe and Kepler, and is known for Snell's law of the
refraction of light. He was the first to determine the size of the earth by
measuring the arc of a meridian with any fair degree of accuracy. The title
should read: _Willebrordi Snellii R. F. Cyclometricus, de circuli
dimensione secundum Logistarum abacos, et ad Mechanicem accuratissima...._

[110] Bacon was born at York House, London, in 1561, and died near
Highgate, London, in 1626. His _Novum Organum Scientiarum or New Method of
employing the reasoning faculties in the pursuits of Truth_ appeared at
London in 1620. He had previously published a work entitled _Of the
Proficience and Advancement of Learning, divine and humane_ (London, 1605),
which again appeared in 1621. His _De augmentis scientiarum Libri IX_
appeared at Paris in 1624, and his _Historia naturalis et experimentalis de
ventis_ at Leyden in 1638. He was successively solicitor general, attorney
general, lord chancellor (1619), Baron Verulam and Viscount St. Albans. He
was deprived of office and was imprisoned in the Tower of London in 1621,
but was later pardoned.

[111] The Greek form, _Organon_, is sometimes used.

[112] James Spedding (1808-1881), fellow of Cambridge, who devoted his life
to his edition of Bacon.

[113] R. Leslie Ellis (1817-1859), editor of the _Cambridge Mathematical
Journal_. He also wrote on Roman aqueducts, on Boole's Laws of Thought, and
on the formation of a Chinese dictionary.

[114] Douglas Derion Heath (1811-1897), a classical and mathematical
scholar.

[115] There have been numerous editions of Bacon's complete works,
including the following: Frankfort, 1665; London, 1730, 1740, 1764, 1765,
1778, 1803, 1807, 1818, 1819, 1824, 1825-36, 1857-74, 1877. The edition to
which De Morgan refers is that of 1857-74, 14 vols., of which five were
apparently out at the time he wrote. There were also French editions in
1800 and 1835.

[116] So in the original for Tycho Brahe.

[117] In general these men acted before Baron wrote, or at any rate, before
he wrote the _Novum Organum_, but the statement must not be taken too
literally. The dates are as follows: Copernicus, 1473-1543; Tycho Brahe,
1546-1601; Gilbert, 1540-1603; Kepler, 1571-1630; Galileo, 1564-1642;
Harvey, 1578-1657. For example, Harvey's _Exercitatio Anatomica de Motu
Cordis et Sanguinis_ did not appear until 1628, and his _Exercitationes de
Generatione_ until 1651.

[118] Robert Hooke (1635-1703) studied under Robert Boyle at Oxford. He was
"Curator of Experiments" to the Royal Society and its secretary, and was
professor of geometry at Gresham College, London. It is true that he was
"very little of a mathematician" although he wrote on the motion of the
earth (1674), on helioscopes and other instruments (1675), on the rotation
of Jupiter (1666), and on barometers and sails.

[119] The son of the Sir William mentioned below. He was born in 1792 and
died in 1871. He wrote a treatise on light (1831) and one on astronomy
(1836), and established an observatory at the Cape of Good Hope where he
made observations during 1834-1838, publishing them in 1847. On his return
to England he was knighted, and in 1848 was made president of the Royal
Society. The title of the work to which reference is made is: _A
preliminary discourse on the Study of Natural Philosophy_. It appeared at
London in 1831.

[120] Sir William was horn at Hanover in 1738 and died at Slough, near
Windsor in 1822. He discovered the planet Uranus and six satellites,
besides two satellites of Saturn. He was knighted by George III.

[121] This was the work of 1836. He also published a work entitled
_Outlines of Astronomy_ in 1849.

[122] While Newton does not tell the story, he refers in the _Principia_
(1714 edition, p. 293) to the accident caused by his cat.

[123] Marino Ghetaldi (1566-1627), whose _Promotus Archimedes_ appeared at
Rome in 1603, _Nonnullae propositiones de parabola_ at Rome in 1603. and
_Apollonius redivivus_ at Venice in 1607. He was a nobleman and was
ambassador from Venice to Rome.

[124] Simon Stevin (born at Bruges, 1548; died at the Hague, 1620). He was
an engineer and a soldier, and his _La Disme_ (1585) was the first separate
treatise on the decimal fraction. The contribution referred to above is
probably that on the center of gravity of three bodies (1586).

[125] Habakuk Guldin (1577-1643), who took the name Paul on his conversion
to Catholicism. He became a Jesuit, and was professor of mathematics at
Vienna and later at Gratz. In his _Centrobaryca seu de centro gravitatis
trium specierum quantitatis continuae_ (1635), of the edition of 1641,
appears the Pappus rule for the volume of a solid formed by the revolution
of a plane figure about an axis, often spoken of as Guldin's Theorem.

[126] Edward Wright was born at Graveston, Norfolkshire, in 1560, and died
at London in 1615. He was a fellow of Caius College, Cambridge, and in his
work entitled _The correction of certain errors in Navigation_ (1599) he
gives the principle of Mercator's projection. He translated the _Portuum
investigandorum ratio_ of Stevin in 1599.

[127] De Morgan never wrote a more suggestive sentence. Its message is not
for his generation alone.

[128] The eminent French physicist, Jean Baptiste Biot (1779-1862),
professor in the Collège de France. His work _Sur les observatoires
météorologiques_ appeared in 1855.

[129] George Biddell Airy (1801-1892), professor of astronomy and physics
at Cambridge, and afterwards director of the Observatory at Greenwich.

[130] De Morgan would have rejoiced in the rôle played by Intuition in the
mathematics of to-day, notably among the followers of Professor Klein.

[131] Colburn was the best known of the calculating boys produced in
America. He was born at Cabot, Vermont, in 1804, and died at Norwich,
Vermont, in 1840. Having shown remarkable skill in numbers as early as
1810, he was taken to London in 1812, whence he toured through Great
Britain and to Paris. The Earl of Bristol placed him in Westminster School
(1816-1819). On his return to America he became a preacher, and later a
teacher of languages.

[132] The history of calculating boys is interesting. Mathieu le Coc (about
1664), a boy of Lorraine, could extract cube roots at sight at the age of
eight. Tom Fuller, a Virginian slave of the eighteenth century, although
illiterate, gave the number of seconds in 7 years 17 days 12 hours after
only a minute and a half of thought. Jedediah Buxton, an Englishman of the
eighteenth century, was studied by the Royal Society because of his
remarkable powers. Ampère, the physicist, made long calculations with
pebbles at the age of four. Gauss, one of the few infant prodigies to
become an adult prodigy, corrected his father's payroll at the age of
three. One of the most remarkable of the French calculating boys was Henri
Mondeux. He was investigated by Arago, Sturm, Cauchy, and Liouville, for
the Académie des Sciences, and a report was written by Cauchy. His
specialty was the solution of algebraic problems mentally. He seems to have
calculated squares and cubes by a binomial formula of his own invention. He
died in obscurity, but was the subject of a _Biographie_ by Jacoby (1846).
George P. Bidder, the Scotch engineer (1806-1878), was exhibited as an
arithmetical prodigy at the age of ten, and did not attend school until he
was twelve. Of the recent cases two deserve special mention, Inaudi and
Diamandi. Jacques Inaudi (born in 1867) was investigated for the Académie
in 1892 by a commission including Poincaré, Charcot, and Binet. (See the
_Revue des Deux Mondes_, June 15, 1892, and the laboratory bulletins of the
Sorbonne). He has frequently exhibited his remarkable powers in America.
Périclès Diamandi was investigated by the same commission in 1893. See
Alfred Binet, _Psychologie des Grands Calculateurs et Joueurs d'Echecs_,
Paris, 1894.

[133] John Flamsteed's (1646-1719) "old white house" was the first
Greenwich observatory. He was the Astronomer Royal and first head of this
observatory.

[134] It seems a pity that De Morgan should not have lived to lash those of
our time who are demanding only the immediately practical in mathematics.
His satire would have been worth the reading against those who seek to
stifle the science they pretend to foster.

[135] Ismael Bouillaud, or Boulliau, was born in 1605 and died at Paris in
1694. He was well known as an astronomer, mathematician, and jurist. He
lived with De Thou at Paris, and accompanied him to Holland. He traveled
extensively, and was versed in the astronomical work of the Persians and
Arabs. It was in his _Astronomia philolaica, opus novum_ (Paris, 1645) that
he attacked Kepler's laws. His tables were shown to be erroneous by the
fact that the solar eclipse did not take place as predicted by him in 1645.

[136] As it did, until 1892, when Airy had reached the ripe age of
ninety-one.

[137] _Didaci a Stunica ... In Job commentaria_ appeared at Toledo in 1584.

[138] "The false Pythagorean doctrine, absolutely opposed to the Holy
Scriptures, concerning the mobility of the earth and the immobility of the
sun."

[139] Paolo Antonio Foscarini (1580-1616), who taught theology and
philosophy at Naples and Messina, was one of the first to champion the
theories of Copernicus. This was in his _Lettera sopra l'opinione de'
Pittagorici e del Copernico, della mobilità della Terra e stabilità del
Sole, e il nuovo pittagorico sistema del mondo_, 4to, Naples, 1615. The
condemnation of the Congregation was published in the following spring, and
in the year of Foscarini's death at the early age of thirty-six.

[140] "To be wholly prohibited and condemned," because "it seeks to show
that the aforesaid doctrine is consonant with truth and is not opposed to
the Holy Scriptures."

[141] "As repugnant to the Holy Scriptures and to its true and Catholic
interpretation (which in a Christian man cannot be tolerated in the least),
he does not hesitate to treat (of his subject) '_by hypothesis_', but he
even adds '_as most true_'!"

[142] "To the places in which he discusses not by hypothesis but by making
assertions concerning the position and motion of the earth."

[143] "_Copernicus._ If by chance there shall be vain talkers who, although
ignorant of all mathematics, yet taking it upon themselves to sit in
judgment upon the subject on account of a certain passage of Scripture
badly distorted for their purposes, shall have dared to criticize and
censure this teaching of mine, I pay no attention to them, even to the
extent of despising their judgment as rash. For it is not unknown that
Lactantius, a writer of prominence in other lines although but little
versed in mathematics, spoke very childishly about the form of the earth
when he ridiculed those who declared that it was spherical. Hence it should
not seem strange to the learned if some shall look upon us in the same way.
Mathematics is written for mathematicians, to whom these labors of ours
will seem, if I mistake not, to add something even to the republic of the
Church.... _Emend._ Here strike out everything from 'if by chance' to the
words 'these labors of ours,' and adapt it thus: 'But these labors of
ours.'"

[144] "_Copernicus._ However if we consider the matter more carefully it
will be seen that the investigation is not yet completed, and therefore
ought by no means to be condemned. _Emend._ However, if we consider the
matter more carefully it is of no consequence whether we regard the earth
as existing in the center of the universe or outside of the center, so far
as the solution of the phenomena of celestial movements is concerned."

[145] "The whole of this chapter may be cut out, since it avowedly treats
of the earth's motion, while it refutes the reasons of the ancients proving
its immobility. Nevertheless, since it seems to speak problematically, in
order that it may satisfy the learned and keep intact the sequence and
unity of the book let it be emended as below."

[146] "_Copernicus._ Therefore why do we still hesitate to concede to it
motion which is by nature consistent with its form, the more so because the
whole universe is moving, whose end is not and cannot be known, and not
confess that there is in the sky an appearance of daily revolution, while
on the earth there is the truth of it? And in like manner these things are
as if Virgil's Æneas should say, 'We are borne from the harbor' ...
_Emend._ Hence I cannot concede motion to this form, the more so because
the universe would fall, whose end is not and cannot be known, and what
appears in the heavens is just as if ..."

[147] "_Copernicus_. I also add that it would seem very absurd that motion
should be ascribed to that which contains and locates, and not rather to
that which is contained and located, that is the earth. _Emend._ I also add
that it is not more difficult to ascribe motion to the contained and
located, which is the earth, than to that which contains it."

[148] "_Copernicus._ You see, therefore, that from all these things the
motion of the earth is more probable than its immobility, especially in the
daily revolution which is as it were a particular property of it. _Emend._
Omit from 'You see' to the end of the chapter."

[149] "_Copernicus._ Therefore, since there is nothing to hinder the motion
of the earth, it seems to me that we should consider whether it has several
motions, to the end that it may be looked upon as one of the moving stars.
_Emend._ Therefore, since I have assumed that the earth moves, it seems to
me that we should consider whether it has several motions."

[150] "_Copernicus._ We are not ashamed to acknowledge ... that this is
preferably verified in the motion of the earth. _Emend._ We are not ashamed
to assume ... that this is consequently verified in the motion."

[151] "_Copernicus._ So divine is surely this work of the Best and
Greatest. _Emend._ Strike out these last words."

[152] This should be Cap. 11, lib. i, p. 10.

[153] "_Copernicus._ Demonstration of the threefold motion of the earth.
_Emend._ On the hypothesis of the threefold motion of the earth and its
demonstration."

[154] This should be Cap. 20, lib. iv, p. 122.

[155] "_Copernicus._ Concerning the size of these three stars, the sun, the
moon and the earth. _Emend._ Strike out the words 'these three stars,'
because the earth is not a star as Copernicus would make it."

[156] He seems to speak problematically in order to satisfy the learned.

[157] One of the Church Fathers, born about 250 A.D., and died about 330,
probably at Trèves. He wrote _Divinarum Institutionum Libri VII._ and other
controversial and didactic works against the learning and philosophy of the
Greeks.

[158] Giovanni Battista Riccioli (1598-1671) taught philosophy and theology
at Parma and Bologna, and was later professor of astronomy. His _Almagestum
novum_ appeared in 1651, and his _Argomento fisico-matematico contro il
moto diurno della terra_ in 1668.

[159] He was a native of Arlington, Sussex, and a pensioner of Christ's
College, Cambridge. In 1603 he became a master of arts at Oxford.

[160] Straying, i.e., from the right way.

[161] "Private subjects may, in the presence of danger, defend themselves
or their families against a monarch as against any malefactor, if the
monarch assaults them like a bandit or a ravisher, and provided they are
unable to summon the usual protection and cannot in any way escape the
danger."

[162] Daniel Neal (1678-1743), an independent minister, wrote a _History of
the Puritans_ that appeared in 1732. The account may be found in the New
York edition of 1843-44, vol. I, p. 271.

[163] Anthony Wood (1632-1695), whose _Historia et Antiquitates
Universitatis Oxoniensis_ (1674) and _Athenae Oxoniensis_ (1691) are among
the classics on Oxford.

[164] Part of the title, not here quoted, shows the nature of the work more
clearly: "liber unicus, in quo decretum S. Congregationis S. R. E.
Cardinal. an. 1616, adversus Pythagorico-Copernicanos editum defenditur."

[165] This was John Elliot Drinkwater Bethune (1801-1851), the statesman
who did so much for legislative and educational reform in India. His
father, John Drinkwater Bethune, wrote a history of the siege of Gibraltar.

[166] The article referred to is about thirty years old; since it appeared
another has been given (_Dubl. Rev._, Sept. 1865) which is of much greater
depth. In it will also be found the Roman view of Bishop Virgil (_ante_, p.
32).--A. De M.

[167] Jean Baptiste Morin (1583-1656), in his younger days physician to the
Bishop of Boulogne and the Duke of Luxemburg, became in 1630 professor of
mathematics at the Collège Royale. His chief contribution to the problem of
the determination of longitude is his _Longitudinum terrestrium et
coelestium nova et hactenus optata scientia_ (1634). He also wrote against
Copernicus in his _Famosi problematis de telluris motu vel quiete hactenus
optata solutio_ (1631), and against Lansberg in his _Responsio pro telluris
quiete_ (1634).

[168] The work appeared at Leyden in 1626, at Amsterdam in 1634, at
Copenhagen in 1640 and again at Leyden in 1650. The title of the 1640
edition is _Arithmeticae Libri II et Geometriae Libri VI_. The work on
which it is based is the _Arithmeticae et Geometriae Practica_, which
appeared in 1611.

[169] The father's name was Adriaan, and Lalande says that it was Montucla
who first made the mistake of calling him Peter, thinking that the initials
P. M. stood for Petrus Metius, when in reality they stood for _piae
memoriae_! The ratio 355/113 was known in China hundreds of years before
his time. See note 55, page 52.

[170] Adrian Metius (1571-1635) was professor of medicine at the University
of Franeker. His work was, however, in the domain of astronomy, and in this
domain he published several treatises.

[171] The first edition was entitled: _The Discovery of a World in the
Moone. Or, a Discourse Tending to prove that 'tis probable there may be
another habitable World in that Planet_. 1638, 8vo. The fourth edition
appeared in 1684. John Wilkins (1614-1672) was Warden of Wadham College,
Oxford; master of Trinity, Cambridge; and, later, Bishop of Chester. He was
influential in founding the Royal Society.

[172] The first edition was entitled: _C. Hugenii_ [Greek: Kosmotheôros],
_sive de Terris coelestibus, earumque ornatu, conjecturae_, The Hague,
1698, 4to. There were several editions. It was also translated into French
(1718), and there was another English edition (1722). Huyghens (1629-1695)
was one of the best mathematical physicists of his time.

[173] It is hardly necessary to say that science has made enormous advance
in the chemistry of the universe since these words were written.

[174] William Whewell (1794-1866) is best known through his _History of the
Inductive Sciences_ (1837) and _Philosophy of the Inductive Sciences_
(1840).

[175] Thomas Chalmers (1780-1847), the celebrated Scotch preacher. These
discourses were delivered while he was minister in a large parish in the
poorest part of Glasgow, and in them he attempted to bring science into
harmony with the Bible. He was afterwards professor of moral philosophy at
St. Andrew's (1823-28), and professor of theology at Edinburgh (1828). He
became the leader of a schism from the Scotch Presbyterian Church,--the
Free Church.

[176] That is, in Robert Watt's (1774-1819) _Bibliotheca Britannica_
(posthumous, 1824). Nor is it given in the _Dictionary of National
Biography_.

[177] The late Greek satirist and poet, c. 120-c. 200 A.D.

[178] François Rabelais (c. 1490-1553) the humorist who created Pantagruel
(1533) and Gargantua (1532). His work as a physician and as editor of the
works of Galen and Hippocrates is less popularly known.

[179] Francis Godwin (1562-1633) bishop of Llandaff and Hereford. Besides
some valuable historical works he wrote _The Man in the Moone, or a
Discourse of a voyage thither by Domingo Gonsales, the Speed Messenger of
London_, 1638.

[180] Bernard Le Bovier de Fontenelle (1657-1757), historian, critic,
mathematician, Secretary of the Académie des Sciences, and member of the
Académie Française. His _Entretien sur la pluralité des mondes_ appeared at
Paris in 1686.

[181] Athanasius Kircher (1602-1680), Jesuit, professor of mathematics and
philosophy, and later of Hebrew and Syriac, at Wurzburg; still later
professor of mathematics and Hebrew at Rome. He wrote several works on
physics. His collection of mathematical instruments and other antiquities
became the basis of the Kircherian Museum at Rome.

[182] "Both belief and non-belief are dangerous. Hippolitus died because
his stepmother was believed. Troy fell because Cassandra was not believed.
Therefore the truth should be investigated long before foolish opinion can
properly judge." (Prove = probe?).

[183] Jacobus Grandamicus (Jacques Grandami) was born at Nantes in 1588 and
died at Paris in 1672. He was professor of theology and philosophy in the
Jesuit colleges at Rennes, Tours, Rouen, and other places. He wrote several
works on astronomy.

[184] "And I, if I be lifted up from the earth, will draw all men unto me."
John xii. 32.

[185] Andrea Argoli (1568-1657) wrote a number of works on astronomy, and
computed ephemerides from 1621 to 1700.

[186] So in the original edition of the _Budget_. It is Johannem Pellum in
the original title. John Pell (1610 or 1611-1685) studied at Cambridge and
Oxford, and was professor of mathematics at Amsterdam (1643-46) and Breda
(1646-52). He left many manuscripts but published little. His name attaches
by accident to an interesting equation recently studied with care by Dr.
E. E. Whitford (New York, 1912).

[187] Christianus Longomontanus (Christen Longberg or Lumborg) was born in
1569 at Longberg, Jutland, and died in 1647 at Copenhagen. He was an
assistant of Tycho Brahe and accepted the diurnal while denying the orbital
motion of the earth. His _Cyclometria e lunulis reciproce demonstrata_
appeared in 1612 under the name of Christen Severin, the latter being his
family name. He wrote several other works on the quadrature problem, and
some treatises on astronomy.

[188] The names are really pretty well known. Giles Persone de Roberval was
born at Roberval near Beauvais in 1602, and died at Paris in 1675. He was
professor of philosophy at the Collège Gervais at Paris, and later at the
Collège Royal. He claimed to have discovered the theory of indivisibles
before Cavalieri, and his work is set forth in his _Traité des
indivisibles_ which appeared posthumously in 1693.

Hobbes (1588-1679), the political and social philosopher, lived a good part
of his time (1610-41) in France where he was tutor to several young
noblemen, including the Cavendishes. His _Leviathan_ (1651) is said to have
influenced Spinoza, Leibnitz, and Rousseau. His _Quadratura circuli,
cubatio sphaerae, duplicatio cubi ..._ (London, 1669), _Rosetum geometricum
..._ (London, 1671), and _Lux Mathematica, censura doctrinae Wallisianae
contra Rosetum Hobbesii_ (London, 1674) are entirely forgotten to-day. (See
a further note, _infra_.)

Pierre de Carcavi, a native of Lyons, died at Paris in 1684. He was a
member of parliament, royal librarian, and member of the Académie des
Sciences. His attempt to prove the impossibility of the quadrature appeared
in 1645. He was a frequent correspondent of Descartes.

Cavendish (1591-1654) was Sir (not Lord) Charles. He was, like De Morgan
himself, a bibliophile in the domain of mathematics. His life was one of
struggle, his term as member of parliament under Charles I being followed
by gallant service in the royal army. After the war he sought refuge on the
continent where he met most of the mathematicians of his day. He left a
number of manuscripts on mathematics, which his widow promptly disposed of
for waste paper. If De Morgan's manuscripts had been so treated we should
not have had his revision of his _Budget of Paradoxes_.

Marin Mersenne (1588-1648), a minorite, living in the cloisters at Nevers
and Paris, was one of the greatest Franciscan scholars. He edited Euclid,
Apollonius, Archimedes, Theodosius, and Menelaus (Paris, 1626), translated
the Mechanics of Galileo into French (1634), wrote _Harmonicorum Libri XII_
(1636), and _Cogitata physico-mathematica_ (1644), and taught theology and
philosophy at Nevers.

Johann Adolph Tasse (Tassius) was born in 1585 and died at Hamburg in 1654.
He was professor of mathematics in the Gymnasium at Hamburg, and wrote
numerous works on astronomy, chronology, statics, and elementary
mathematics.

Johann Ludwig, Baron von Wolzogen, seems to have been one of the early
unitarians, called _Fratres Polonorum_ because they took refuge in Poland.
Some of his works appear in the _Bibliotheca Fratrum Polonorum_ (Amsterdam,
1656). I find no one by the name who was contributing to mathematics at
this time.

Descartes is too well known to need mention in this connection.

Bonaventura Cavalieri (1598-1647) was a Jesuit, a pupil of Galileo, and
professor of mathematics at Bologna. His greatest work, _Geometria
indivisibilibus continuorum nova quadam ratione promota_, in which he makes
a noteworthy step towards the calculus, appeared in 1635.

Jacob (Jacques) Golius was born at the Hague in 1596 and died at Leyden in
1667. His travels in Morocco and Asia Minor (1622-1629) gave him such
knowledge of Arabic that he became professor of that language at Leyden.
After Snell's death he became professor of mathematics there. He translated
Arabic works on mathematics and astronomy into Latin.

[189] It would be interesting to follow up these rumors, beginning perhaps
with the tomb of Archimedes. The Ludolph van Ceulen story is very likely a
myth. The one about Fagnano may be such. The Bernoulli tomb does have the
spiral, however (such as it is), as any one may see in the cloisters at
Basel to-day.

[190] Collins (1625-1683) was secretary of the Royal Society, and was "a
kind of register of all new improvements in mathematics." His office
brought him into correspondence with all of the English scientists, and he
was influential in the publication of various important works, including
Branker's translation of the algebra by Rhonius, with notes by Pell, which
was the first work to contain the present English-American symbol of
division. He also helped in the publication of editions of Archimedes and
Apollonius, of Kersey's Algebra, and of the works of Wallis. His profession
was that of accountant and civil engineer, and he wrote three unimportant
works on mathematics (one published posthumously, and the others in 1652
and 1658).

Heinrich Christian Schumacher (1780-1850) was professor of astronomy at
Copenhagen and director of the observatory at Altona. His translation of
Carnot's _Géométrie de position_ (1807) brought him into personal relations
with Gauss, and the friendship was helpful to Schumacher. He was a member
of many learned societies and had a large circle of acquaintances. He
published numerous monographs and works on astronomy.

Gassendi (1592-1655) might well have been included by De Morgan in the
group, since he knew and was a friend of most of the important
mathematicians of his day. Like Mersenne, he was a minorite, but he was a
friend of Galileo and Kepler, and wrote a work under the title _Institutio
astronomica, juxta hypotheses Copernici, Tychonis-Brahaei et Ptolemaei_
(1645). He taught philosophy at Aix, and was later professor of mathematics
at the College Royal at Paris.

Burnet is the Bishop Gilbert Burnet (1643-1715) who was so strongly
anti-Romanistic that he left England during the reign of James II and
joined the ranks of the Prince of Orange. William made him bishop of
Salisbury.

[191] There is some substantial basis for De Morgan's doubts as to the
connection of that _mirandula_ of his age, Sir Kenelm Digby (1603-1665),
with the famous _poudre de sympathie_. It is true that he was just the one
to prepare such a powder. A dilletante in everything,--learning, war,
diplomacy, religion, letters, and science--he was the one to exploit a
fraud of this nature. He was an astrologer, an alchemist, and a fabricator
of tales, and well did Henry Stubbes characterize him as "the very Pliny of
our age for lying." He first speaks of the powder in a lecture given at
Montpellier in 1658, and in the same year he published the address at Paris
under the title: _Discours fait en une célèbre assemblée par le chevalier
Digby .... touchant la guérison de playes par la poudre de sympathie_. The
London edition referred to by De Morgan also came out in 1658, and several
editions followed it in England, France and Germany. But Nathaniel Highmore
in his _History of Generation_ (1651) referred to the concoction as
"Talbot's Powder" some years before Digby took it up. The basis seems to
have been vitriol, and it was claimed that it would heal a wound by simply
being applied to a bandage taken from it.

[192] This work by Thomas Birch (1705-1766) came out in 1756-57. Birch was
a voluminous writer on English history. He was a friend of Dr. Johnson and
of Walpole, and he wrote a life of Robert Boyle.

[193] We know so much about John Evelyn (1620-1706) through the diary which
he began at the age of eleven, that we forget his works on navigation and
architecture.

[194] I suppose this was the seventh Earl of Shrewsbury (1553-1616).

[195] This is interesting in view of the modern aseptic practice of surgery
and the antiseptic treatment of wounds inaugurated by the late Lord Lister.

[196] Perhaps De Morgan had not heard the _bon mot_ of Dr. Holmes: "I
firmly believe that if the whole _materia medica_ could be sunk to the
bottom of the sea, it would be all the better for mankind and all the worse
for the fishes."

[197] The full title is worth giving, because it shows the mathematical
interests of Hobbes, and the nature of the six dialogues: _Examinatio et
emendatio mathematicae hodiernae qualis explicatur in libris Johannis
Wallisii geometriae professoris Saviliani in Academia Oxoniensi: distributa
in sex dialogos (1. De mathematicae origine ...; 2. De principiis traditis
ab Euclide; 3. De demonstratione operationum arithmeticarum ...; 4. De
rationibus; 5. De angula contactus, de sectionibus coni, et arithmetica
infinitorum; 6. Dimensio circuli tribus methodis demonstrata ... item
cycloidis verae descriptio et proprietates aliquot.)_ Londini, 1660 (not
1666). For a full discussion of the controversy over the circle, see George
Croom Robertson's biography of Hobbes in the eleventh edition of the
_Encyclopaedia Britannica_.

[198] This is his _Animadversions upon Mr. Hobbes' late book De principiis
et ratiocinatione geometrarum_, 1666, or his _Hobbianae quadraturae
circuli, cubationis sphaerae et duplicationis cubi confutatio_, also of
1669.

[199] This is the work of 1669 referred to above.

[200] Gregoire de St. Vincent (1584-1667) published his _Opus geometricum
quadraturae circuli et sectionum coni_ at Antwerp in 1647.

[201] This appears in _J. Scaligeri cyclometrica elementa duo_, Lugduni
Batav., 1594.

[202] Adriaen van Roomen (1561-1615) gave the value of [pi] to sixteen
decimal places in his _Ideae mathematicae pars prima_ (1593), and wrote his
_In Archimedis circuli dimensionem expositio & analysis_ in 1597.

[203] Kästner. See note 30 on page 43.

[204] Bentley (1662-1742) might have done it, for as the head of Trinity
College, Cambridge, and a follower of Newton, he knew some mathematics.
Erasmus (1466-1536) lived a little too early to attempt it, although his
brilliant satire might have been used to good advantage against those who
did try.

[205] "In grammar, to give the winds to the ships and to give the ships to
the winds mean the same thing. But in geometry it is one thing to assume
the circle BCD not greater than thirty-six segments BCDF, and another (to
assume) the thirty-six segments BCDF not greater than the circle. The one
assumption is true, the other false."

[206] The Greek scholar (1559-1614) who edited a Greek and Latin edition of
Aristotle in 1590.

[207] Jacques Auguste de Thou (1553-1617), the historian and statesman.

[208] "To value Scaliger higher even when wrong, than the multitude when
right."

[209] "I would rather err with Scaliger than be right with Clavius."

[210] "The perimeter of the dodecagon to be inscribed in a circle is
greater than the perimeter of the circle. And the more sides a polygon to
be inscribed in a circle successively has, so much the greater will the
perimeter of the polygon be than the perimeter of the circle."

[211] De Morgan took, perhaps, the more delight in speaking thus of Sir
William Hamilton (1788-1856) because of a spirited controversy that they
had in 1847 over the theory of logic. Possibly, too, Sir William's low
opinion of mathematics had its influence.

[212] Edwards (1699-1757) wrote _The canons of criticism_ (1747) in which
he gave a scathing burlesque on Warburton's Shakespeare. It went through
six editions.

[213] Antoine Teissier (born in 1632) published his _Eloges des hommes
savants, tirés de l'histoire de M. de Thou_ in 1683.

[214] "He boasted without reason of having found the quadrature of the
circle. The glory of this admirable discovery was reserved for Joseph
Scaliger, as Scévole de St. Marthe has written."

[215] _Natural and political observations mentioned in the following Index,
and made upon the Bills of Mortality.... With reference to the government,
religion, trade, growth, ayre, and diseases of the said city._ London,
1662, 4to. The book went through several editions.

[216] _Ne sutor ultra crepidam_, "Let the cobbler stick to his last," as we
now say.

[217] The author (1632-1695) of the _Historia et Antiquitates Universitatis
Oxoniensis_ (1674). See note 163, page 98.

[218] The mathematical guild owes Samuel Pepys (1633-1703) for something
besides his famous diary (1659-1669). Not only was he president of the
Royal Society (1684), but he was interested in establishing Sir William
Boreman's mathematical school at Greenwich.

[219] John Graunt (1620-1674) was a draper by trade, and was a member of
the Common Council of London until he lost office by turning Romanist.
Although a shopkeeper, he was elected to the Royal Society on the special
recommendation of Charles II. Petty edited the fifth edition of his work,
adding much to its size and value, and this may be the basis of Burnet's
account of the authorship.

[220] Petty (1623-1687) was a mathematician and economist, and a friend of
Pell and Sir Charles Cavendish. His survey of Ireland, made for Cromwell,
was one of the first to be made on a large scale in a scientific manner. He
was one of the founders of the Royal Society.

[221] The story probably arose from Graunt's recent conversion to the Roman
Catholic faith.

[222] He was born in 1627 and died in 1704. He published a series of
ephemerides, beginning in 1659. He was imprisoned in 1679, at the time of
the "Popish Plot," and again for treason in 1690. His important
astrological works are the _Animal Cornatum, or the Horn'd Beast_ (1654)
and _The Nativity of the late King Charls_ (1659).

[223] Isaac D'Israeli (1766-1848), in his _Curiosities of Literature_
(1791), speaking of Lilly, says: "I shall observe of this egregious
astronomer, that there is in this work, so much artless narrative, and at
the same time so much palpable imposture, that it is difficult to know when
he is speaking what he really believes to be the truth." He goes on to say
that Lilly relates that "those adepts whose characters he has drawn were
the lowest miscreants of the town. Most of them had taken the air in the
pillory, and others had conjured themselves up to the gallows. This seems a
true statement of facts."

[224] It is difficult to estimate William Lilly (1602-1681) fairly. His
_Merlini Anglici ephemeris_, issued annually from 1642 to 1681, brought him
a great deal of money. Sir George Wharton (1617-1681) also published an
almanac annually from 1641 to 1666. He tried to expose John Booker
(1603-1677) by a work entitled _Mercurio-Coelicio-Mastix; or, an
Anti-caveat to all such, as have (heretofore) had the misfortune to be
Cheated and Deluded by that Grand and Traiterous Impostor of this
Rebellious Age, John Booker_, 1644. Booker was "licenser of mathematical
[astrological] publications," and as such he had quarrels with Lilly,
Wharton, and others.

[225] See note 171 on page 100.

[226] This is the _Ars Signorum, vulgo character universalis et lingua
philosophica_, that appeared at London in 1661, 8vo. George Dalgarno
anticipated modern methods in the teaching of the deaf and dumb.

[227] See note 200 on page 110.

[228] If the hyperbola is referred to the asymptotes as axes, the area
between two ordinates (x = a, x = b) is the difference of the logarithms of
a and b to the base e. E.g., in the case of the hyperbola xy = 1, the area
between x = a and x = 1 is log a.

[229] "On ne peut lui refuser la justice de remarquer que personne avant
lui ne s'est porté dans cette recherche avec autant de génie, & même, si
nous en exceptons son objet principal, avec autant de succès." _Quadrature
du Cercle_, p. 66.

[230] The title proceeds: _Seu duae mediae proportionales inter extremas
datas per circulum et per infinitas hyperbolas, vel ellipses et per
quamlibet exhibitae_.... René Francois, Baron de Sluse (1622-1685) was
canon and chancellor of Liège, and a member of the Royal Society. He also
published a work on tangents (1672). The word _mesolabium_ is from the
Greek [Greek: mesolabion] or [Greek: mesolabon], an instrument invented by
Eratosthenes for finding two mean proportionals.

[231] The full title has some interest: _Vera circuli et hyperbolae
quadratura cui accedit geometriae pars universalis inserviens quantitatum
curvarum transmutationi et mensurae. Authore Jacobo Gregorio Abredonensi
Scoto ... Patavii_, 1667. That is, James Gregory (1638-1675) of Aberdeen
(he was really born near but not in the city), a good Scot, was publishing
his work down in Padua. The reason was that he had been studying in Italy,
and that this was a product of his youth. He had already (1663) published
his _Optica promota_, and it is not remarkable that his brilliancy brought
him a wide circle of friends on the continent and the offer of a pension
from Louis XIV. He became professor of mathematics at St Andrews and later
at Edinburgh, and invented the first successful reflecting telescope. The
distinctive feature of his _Vera quadratura_ is his use of an infinite
converging series, a plan that Archimedes used with the parabola.

[232] Jean de Beaulieu wrote several works on mathematics, including _La
lumière de l'arithmétique_ (n.d.), _La lumière des mathématiques_ (1673),
_Nouvelle invention d'arithmétique_ (1677), and some mathematical tables.

[233] A just estimate. There were several works published by Gérard
Desargues (1593-1661), of which the greatest was the _Brouillon Proiect_
(Paris, 1639). There is an excellent edition of the _Oeuvres de Desargues_
by M. Poudra, Paris, 1864.

[234] "A certain M. de Beaugrand, a mathematician, very badly treated by
Descartes, and, as it appears, rightly so."

[235] This is a very old approximation for [pi]. One of the latest
pretended geometric proofs resulting in this value appeared in New York in
1910, entitled _Quadrimetry_ (privately printed).

[236] "Copernicus, a German, made himself no less illustrious by his
learned writings; and we might say of him that he stood alone and unique in
the strength of his problems, if his excessive presumption had not led him
to set forth in this science a proposition so absurd that it is contrary to
faith and reason, namely that the circumference of a circle is fixed and
immovable while the center is movable: on which geometrical principle he
has declared in his astrological treatise that the sun is fixed and the
earth is in motion."

[237] So in the original.

[238] Franciscus Maurolycus (1494-1575) was really the best mathematician
produced by Sicily for a long period. He made Latin translations of
Theodosius, Menelaus, Euclid, Apollonius, and Archimedes, and wrote on
cosmography and other mathematical subjects.

[239] "Nicolaus Copernicus is also tolerated who asserted that the sun is
fixed and that the earth whirls about it; and he rather deserves a whip or
a lash than a reproof."

[240] "Algebra is the curious science of scholars, and particularly for a
general of an army, or a captain, in order quickly to draw up an army in
battle array and to number the musketeers and pikemen who compose it,
without the figures of arithmetic. This science has five special figures of
this kind: P means _plus_ in commerce and _pikemen_ in the army; M means
_minus_, and _musketeer_ in the art of war;... R signifies _root_ in the
measurement of a cube, and _rank_ in _the army_; Q means _square_ (French
_quarè_, as then spelled) in both cases; C means _cube_ in mensuration, and
_cavalry_ in arranging batallions and squadrons. As for the operations of
this science, they are as follows: to add a _plus_ and a _plus_, the sum
will be _plus_; to add _minus_ with _plus_, take the less from the greater
and the remainder will be the sum required or the number to be found. I say
this only in passing, for the benefit of those who are wholly ignorant of
it."

[241] He refers to the _Joannis de Beaugrand ... Geostatice, seu de vario
pondere gravium secundum varia a terrae (centro) intervalla dissertatio
mathematica_, Paris, 1636. Pascal relates that de Beaugrand sent all of
Roberval's theorems on the cycloid and Fermat's on maxima and minima to
Galileo in 1638, pretending that they were his own.

[242] More (1614-1687) was a theologian, a fellow of Christ College,
Cambridge, and a Christian Platonist.

[243] Matthew Hale (1609-1676) the famous jurist, wrote a number of tracts
on scientific, moral, and religious subjects. These were collected and
published in 1805.

[244] They might have been attributed to many a worse man than Dr. Hales
(1677-1761), who was a member of the Royal Society and of the Paris
Academy, and whose scheme for the ventilation of prisons reduced the
mortality at the Savoy prison from one hundred to only four a year. The
book to which reference is made is _Vegetable Staticks or an Account of
some statical experiments on the sap in Vegetables_, 1727.

[245] _Pleas of the Crown; or a Methodical Summary of the Principal Matters
relating to the subject_, 1678.

[246] _Thomae Streete Astronomia Carolina, a new theory of the celestial
motions_, 1661. It also appeared at Nuremberg in 1705, and at London in
1710 and 1716 (Halley's editions). He wrote other works on astronomy.

[247] This was the Sir Thomas Street (1626-1696) who passed sentence of
death on a Roman Catholic priest for saying mass. The priest was reprieved
by the king, but in the light of the present day one would think the
justice more in need of pardon. He took part in the trial of the Rye House
Conspirators in 1683.

[248] Edmund Halley (1656-1742), who succeeded Wallis (1703) as Savilian
professor of mathematics at Oxford, and Flamsteed (1720) as head of the
Greenwich observatory. It is of interest to note that he was instrumental
in getting Newton's _Principia_ printed.

[249] Shepherd (born in 1760) was one of the most famous lawyers of his
day. He was knighted in 1814 and became Attorney General in 1817.

[250] This was William Hone (1780-1842), a book publisher, who wrote
satires against the government, and who was tried three times because of
his parodies on the catechism, creed, and litany (illustrated by
Cruikshank). He was acquitted on all of the charges.

[251] Valentinus was a Benedictine monk and was still living at Erfurt in
1413. His _Currus triumphalis antimonii_ appeared in 1624. Synesius was
Bishop of Ptolemaide, who died about 430. His works were printed at Paris
in 1605. Theodor Kirckring (1640-1693) was a fellow-student of Spinoza's.
Besides the commentary on Valentine he left several works on anatomy. His
commentary appeared at Amsterdam in 1671. There were several editions of
the _Chariot_.

[252] The chief difficulty with this curious "monk-bane" etymology is its
absurdity. The real origin of the word has given etymologists a good deal
of trouble.

[253] Robert Boyle (1627-1691), son of "the Great Earl" (of Cork). Perhaps
his best-known discovery is the law concerning the volume of gases.

[254] The real name of Eirenaeus Philalethes (born in 1622) is unknown. It
may have been Childe. He claimed to have discovered the philosopher's stone
in 1645. His tract in this work is _The Secret of the Immortal Liquor
Alkahest or Ignis-Aqua_. See note 260, _infra_.

[255] Johann Baptist van Helmont, Herr von Merode, Royenborg etc.
(1577-1644). His chemical discoveries appeared in his _Ortus medicinae_
(1648), which went through many editions.

[256] De Morgan should have written up Francis Anthony (1550-1623), whose
_Panacea aurea sive tractatus duo de auro potabili_ (Hamburg, 1619)
described a panacea that he gave for every ill. He was repeatedly
imprisoned for practicing medicine without a license from the Royal College
of Physicians.

[257] Bernardus Trevisanus (1406-1490), who traveled even through Barbary,
Egypt, Palestine, and Persia in search of the philosopher's stone. He wrote
several works on alchemy,--_De Chemica_ (1567), _De Chemico Miraculo_
(1583), _Traité de la nature de l'oeuf des philosophes_ (1659), etc., all
published long after his death.

[258] George Ripley (1415-1490) was an Augustinian monk, later a
chamberlain of Innocent VIII, and still later a Carmelite monk. His _Liber
de mercuris philosophico_ and other tracts first appeared in _Opuscula
quaedam chymica_ (Frankfort, 1614).

[259] Besides the _Opus majus_, and other of the better known works of this
celebrated Franciscan (1214-1294), there are numerous tracts on alchemy
that appeared in the _Thesaurus chymicus_ (Frankfort, 1603).

[260] George Starkey (1606-1665 or 1666) has special interest for American
readers. He seems to have been born in the Bermudas and to have obtained
the bachelor's degree in England. He then went to America and in 1646
obtained the master's degree at Harvard, apparently under the name of
Stirk. He met Eirenaeus Philalethes (see note 254 above) in America and
learned alchemy from him. Returning to England, he sold quack medicines
there, and died in 1666 from the plague after dissecting a patient who had
died of the disease. Among his works was the _Liquor Alcahest, or a
Discourse of that Immortal Dissolvent of Paracelsus and Helmont_, which
appeared (1675) some nine years after his death.

[261] Platt (1552-1611) was the son of a London brewer. Although he left a
manuscript on alchemy, and wrote a book entitled _Delights for Ladies to
adorne their Persons_ (1607), he was knighted for some serious work on the
chemistry of agriculture, fertilizing, brewing, and the preserving of
foods, published in _The Jewell House of Art and Nature_ (1594).

[262] "Those who wish to call a man a liar and deceiver speak of him a
writer of almanacs; but those who (would call him) a scoundrel and an
imposter (speak of him as) a chemist."

[263] "Trust your barque to the winds but not your body to a chemist; any
breeze is safer than the faith of a chemist."

[264] Probably the Jesuit, Père Claude François Menestrier (1631-1705), a
well known historian.

[265] The author was Christopher Nesse (1621-1705), a belligerent
Calvinist, who wrote many controversial works and succeeded in getting
excommunicated four times. One of his most virulent works was _A Protestant
Antidote against the Poison of Popery_.

[266] John Case (c. 1660-1700) was a famous astrologer and physician. He
succeeded to Lilly's practice in London. In a darkened room, wherein he
kept an array of mystical apparatus, he pretended to show the credulous the
ghosts of their departed relatives. Besides his astrological works he wrote
one serious treatise, the _Compendium Anatomicum nova methodo institutum_
(1695), in which he defends Harvey's theories of embryology.

[267] Marcelis (1636-after 1714) was a soap maker of Amsterdam. It is to be
hoped that he made better soap than values of [pi].

[268] John Craig (died in 1731) was a Scotchman, but most of his life was
spent at Cambridge reading and writing on mathematics. He endeavored to
introduce the Leibnitz differential calculus into England. His mathematical
works include the _Methodus Figurarum ... Quadraturas determinandi_ (1685),
_Tractatus ... de Figurarum Curvilinearum Quadraturis et locis Geometricis_
(1693), and _De Calculo Fluentium libri duo_ (1718).

[269] As is well known, this subject owes much to the Bernoullis. Craig's
works on the calculus brought him into controversy with them. He also wrote
on other subjects in which they were interested, as in his memoir _On the
Curve of the quickest descent_ (1700), _On the Solid of least resistance_
(1700), and the _Solution of Bernoulli's problem on Curves_ (1704).

[270] This is Samuel Lee (1783-1852), the young prodigy in languages. He
was apprenticed to a carpenter at twelve and learned Greek while working at
the trade. Before he was twenty-five he knew Hebrew, Chaldee, Syriac,
Samaritan, Persian, and Hindustani. He later became Regius professor of
Hebrew at Cambridge.

[271] "Where the devil, Master Ludovico, did you pick up such a
collection?"

[272] Lord William Brounker (c. 1620-1684), the first president of the
Royal Society, is best known in mathematics for his contributions to
continued fractions.

[273] Horace Walpole (1717-1797) published his _Catalogue of the Royal and
Noble Authors of England_ in 1758. Since his time a number of worthy names
in the domain of science in general and of mathematics in particular might
be added from the peerage of England.

[274] It was written by Charles Hayes (1678-1760), a mathematician and
scholar of no mean attainments. He travelled extensively, and was deputy
governor of the Royal African Company. His _Treatise on Fluxions_ (London,
1704) was the first work in English to explain Newton's calculus. He wrote
a work entitled _The Moon_ (1723) to prove that our satellite shines by its
own as well as by reflected light. His _Chronographia Asiatica & Aegyptica_
(1758) gives the results of his travels.

[275] _Publick_ in the original.

[276] Whiston (1667-1752) succeeded Newton as Lucasian professor of
mathematics at Cambridge. In 1710 he turned Arian and was expelled from the
university. His work on _Primitive Christianity_ appeared the following
year. He wrote many works on astronomy and religion.

[277] Ditton (1675-1715) was, on Newton's recommendation, made Head of the
mathematical school at Christ's Hospital, London. He wrote a work on
fluxions (1706). His idea for finding longitude at sea was to place
stations in the Atlantic to fire off bombs at regular intervals, the time
between the sound and the flash giving the distance. He also corresponded
with Huyghens concerning the use of chronometers for the purpose.

[278] This was John Arbuthnot (c. 1658-1735), the mathematician, physician
and wit. He was intimate with Pope and Swift, and was Royal physician to
Queen Anne. Besides various satires he published a translation of
Huyghens's work on probabilities (1692) and a well-known treatise on
ancient coins, weights, and measures (1727).

[279] Greene (1678-1730) was a very eccentric individual and was generally
ridiculed by his contemporaries. In his will he directed that his body be
dissected and his skeleton hung in the library of King's College,
Cambridge. Unfortunately for his fame, this wish was never carried out.

[280] This was the historian, Robert Sanderson (1660-1741), who spent most
of his life at Cambridge.

[281] I presume this was William Jones (1675-1749) the friend of Newton and
Halley, vice-president of the Royal Society, in whose _Synopsis Palmariorum
Matheseos_ (1706) the symbol [pi] is first used for the circle ratio.

[282] This was the _Geometrica solidorum, sive materiae, seu de varia
compositione, progressione, rationeque velocitatum_, Cambridge, 1712. The
work was parodied in _A Taste of Philosophical Fanaticism ... by a
gentleman of the University of Gratz_.

[283] The antiquary and scientist (1690-1754), president of the Royal
Society, member of the Académie, friend of Newton, and authority on
numismatics.

[284] She was Catherine Barton, Newton's step-niece. She married John
Conduitt, master of the mint, who collected materials for a life of Newton.

_A propos_ of Mrs. Conduitt's life of her illustrious uncle, Sir George
Greenhill tells a very good story on Poincaré, the well-known French
mathematician. At an address given by the latter at the International
Congress of Mathematicians held in Rome in 1908 he spoke of the story of
Newton and the apple as a mere fable. After the address Sir George asked
him why he had done so, saying that the story was first published by
Voltaire, who had heard it from Newton's niece, Mrs. Conduitt. Poincaré
looked blank and said, "Newton, et la nièce de Newton, et Voltaire,--non!
je ne vous comprends pas!" He had thought Sir George meant Professor
Volterra of Rome, whose name in French is Voltaire, and who could not
possibly have known a niece of Newton without bridging a century or so.

[285] This was the Edmund Turnor (1755-1829) who wrote the _Collections for
the Town and Soke of Grantham, containing authentic Memoirs of Sir Isaac
Newton, from Lord Portsmouth's Manuscripts_, London, 1806.

[286] It may be recalled to mind that Sir David (1781-1868) wrote a life of
Newton (1855).

[287] "They are in the country. We rejoice."

[288] "I am here, chatterbox, suck!"

[289] "I have been graduated! I decline!"

[290] Giovanni Castiglioni (Castillon, Castiglione), was born at
Castiglione, in Tuscany, in 1708, and died at Berlin in 1791. He was
professor of mathematics at Utrecht and at Berlin. He wrote on De Moivre's
equations (1762), Cardan's rule (1783), and Euclid's treatment of parallels
(1788-89).

[291] This was the _Isaaci Newtoni, equitis aurati, opuscula mathematica,
philosophica et philologica_, Lausannae & Genevae, 1744.

[292] At London, 4to.

[293] "All the English attribute it to Newton."

[294] Stephen Peter Rigaud (1774-1839), Savilian professor of geometry at
Oxford (1810-27) and later professor of astronomy and head of the Radcliffe
Observatory. He wrote _An historical Essay on first publication of Sir
Isaac Newton's Principia_, Oxford, 1838, and a two-volume work entitled
_Correspondence of Scientific Men of the 17th Century_, 1841.

[295] It is no longer considered by scholars as the work of Newton.

[296] J. Edleston, the author of the _Correspondence of Sir Isaac Newton
and Professor Cotes_, London, 1850.

[297] Palmer (1601-1647) was Master of Queen's College, Cambridge, a
Puritan but not a separatist. His work, _The Characters of a believing
Christian, in Paradoxes and seeming contradictions_, appeared in 1645.

[298] Grosart (1827-1899) was a Presbyterian clergyman. He was a great
bibliophile, and issued numerous reprints of rare books.

[299] This was the year after Palmer's death. The title was, _The Remaines
of ... Francis Lord Verulam....; being Essays and severall Letters to
severall great personages, and other pieces of various and high concernment
not heretofore published_, London, 1648, 4to.

[300] Shaw (1694-1763) was physician extraordinary to George II. He wrote
on chemistry and medicine, and his edition of the _Philosophical Works of
Francis Bacon_ appeared at London in 1733.

[301] John Locke (1632-1704), the philosopher. This particular work
appeared in 1695. There was an edition in 1834 (vol. 25 of the _Sacred
Classics_) and one in 1836 (vol. 2 of the _Christian Library_).

[302] I use the word _Socinian_ because it was so much used in Locke's
time: it is used in our own day by the small fry, the unlearned clergy and
their immediate followers, as a term of reproach for _all_ Unitarians. I
suspect they have a kind of liking for the _word_; it sounds like _so
sinful_. The learned clergy and the higher laity know better: they know
that the bulk of the modern Unitarians go farther than Socinus, and are not
correctly named as his followers. The Unitarians themselves neither desire
nor deserve a name which puts them one point nearer to orthodoxy than they
put themselves. That point is the doctrine that direct prayer to Jesus
Christ is lawful and desirable: this Socinus held, and the modern
Unitarians do not hold. Socinus, in treating the subject in his own
_Institutio_, an imperfect catechism which he left, lays much more stress
on John xiv. 13 than on xv. 16 and xvi. 23. He is not disinclined to think
that _Patrem_ should be in the first citation, where some put it; but he
says that to ask the Father in the name of the Son is nothing but praying
to the Son in prayer to the Father. He labors the point with obvious wish
to secure a conclusive sanction. In the Racovian Catechism, of which
Faustus Socinus probably drew the first sketch, a clearer light is arrived
at. The translation says: "But wherein consists the divine honor due to
Christ? In adoration likewise and invocation. For we ought at all times to
adore Christ, and may in our necessities address our prayers to him as
often as we please; and there are many reasons to induce us to do this
freely." There are some who like accuracy, even in aspersion--A. De M.

Socinus, or Fausto Paolo Sozzini (1539-1604), was an antitrinitarian who
believed in prayer and homage to Christ. Leaving Italy after his views
became known, he repaired to Basel, but his opinions were too extreme even
for the Calvinists. He then tried Transylvania, attempting to convert to
his views the antitrinitarian Bishop Dávid. The only result of his efforts
was the imprisonment of Dávid and his own flight to Poland, in which
country he spent the rest of his life (1579-1604). His complete works
appeared first at Amsterdam in 1668, in the _Bibliotheca Fratres
Polonorum_. The _Racovian Catechism_ (1605) appeared after his death, but
it seems to have been planned by him.

[303] "As much of faith as is necessary to salvation is contained in this
article, Jesus is the Christ."

[304] Edwards (1637-1716) was a Cambridge fellow, strongly Calvinistic. He
published many theological works, attacking the Arminians and Socinians.
Locke and Whiston were special objects of attack.

[305] _Sir I. Newton's views on points of Trinitarian Doctrine; his
Articles of Faith, and the General Coincidence of his Opinions with those
of J. Locke; a Selection of Authorities, with Observations_, London, 1856.

[306] _A Confession of the Faith_, Bristol, 1752, 8vo.

[307] This was really very strange, because Laud (1573-1644), while he was
Archbishop of Canterbury, forced a good deal of High Church ritual on the
Puritan clergy, and even wished to compel the use of a prayer book in
Scotland. It was this intolerance that led to his impeachment and
execution.

[308] The name is Jonchère. He was a man of some merit, proposing (1718) an
important canal in Burgundy, and publishing a work on the _Découverte des
longitudes estimées généralement impossible à trouver_, 1734 (or 1735).

[309] Locke invented a kind of an instrument for finding longitude, and it
is described in the appendix, but I can find nothing about the man. There
was published some years later (London, 1751) another work of his, _A new
Problem to discover the longitude at sea_.

[310] Baxter, concerning whom I know merely that he was a schoolmaster,
starts with the assumption of this value, and deduces from it some fourteen
properties relating to the circle.

[311] John, who died in 1780, was a well-known character in his way. He was
a bookseller on Fleet Street, and his shop was a general rendezvous for the
literary men of his time. He wrote the _Memoirs of the Life and Writings of
Mr. William Whiston_ (1749, with another edition in 1753). He was one of
the first to issue regular catalogues of books with prices affixed.

[312] The name appears both as Hulls and as Hull. He was born in
Gloucestershire in 1699. In 1754 he published _The Art of Measuring made
Easy by the help of a new Sliding Scale_.

[313] Thomas Newcomen (1663-1729) invented the first practical steam engine
about 1710. It was of about five and a half horse power, and was used for
pumping water from coal mines. Savery had described such an engine in 1702,
but Newcomen improved upon it and made it practical.

[314] The well-known benefactor of art (1787-1863).

[315] The tract was again reprinted in 1860.

[316] Hulls made his experiment on the Avon, at Evesham, in 1737, having
patented his machine in 1736. He had a Newcomen engine connected with six
paddles. This was placed in the front of a small tow boat. The experiment
was a failure.

[317] William Symington (1763-1831). In 1786 he constructed a working model
of a steam road carriage. The machinery was applied to a small boat in
1788, and with such success as to be tried on a larger boat in 1789. The
machinery was clumsy, however, and in 1801 he took out a new patent for the
style of engine still used on paddle wheel steamers. This engine was
successfully used in 1802, on the Charlotte Dundas. Fulton (1765-1815) was
on board, and so impressed Robert Livingston with the idea that the latter
furnished the money to build the Clermont (1807), the beginning of
successful river navigation.

[318] Louis Bertrand Castel (1688-1757), most of whose life was spent in
trying to perfect his _Clavecin oculaire_, an instrument on the order of
the harpsichord, intended to produce melodies and harmonies of color. He
also wrote _L'Optique des couleurs_ (1740) and _Sur le fond de la Musique_
(1754).

[319] Dr. Robinson (1680-1754) was professor of physic at Trinity College,
Dublin, and three times president of King and Queen's College of
Physicians. In his _Treatise on the Animal Economy_ (1732-3, with a third
edition in 1738) he anticipated the discoveries of Lavoisier and Priestley
on the nature of oxygen.

[320] There was another edition, published at London in 1747, 8vo.

[321] The author seems to have shot his only bolt in this work. I can find
nothing about him.

[322] _Quod Deus sit, mundusque ab ipso creatus fuerit in tempore, ejusque
providentia gubernetur. Selecta aliquot theoremata adversos atheos_, etc.,
Paris, 1635, 4to.

[323] The British Museum Catalogue mentions a copy of 1740, but this is
possibly a misprint.

[324] This was Johann II (1710-1790), son of Johann I, who succeeded his
father as professor of mathematics at Basel.

[325] Samuel Koenig (1712-1757), who studied under Johann Bernoulli I. He
became professor of mathematics at Franeker (1747) and professor of
philosophy at the Hague (1749).

[326] "In accordance with the hypotheses laid down in this memoir it is so
evident that t must = 34, y = 1, and z = 1, that there is no need of proof
or authority for it to be recognized by every one."

[327] "I subscribe to the judgment of Mr. Bernoulli as a result of these
hypotheses."

[328] "It clearly appears from my present analysis and demonstration that
they have already recognized and perfectly agreed to the fact that the
quadrature of the circle is mathematically demonstrated."

[329] Dr. Knight (died in 1772) made some worthy contributions to the
literature of the mariner's compass. As De Morgan states, he was librarian
of the British Museum.

[330] Sir Anthony Panizzi (1797-1879) fled from Italy under sentence of
death (1822). He became assistant (1831) and chief (1856) librarian of the
British Museum, and was knighted in 1869. He began the catalogue of printed
books of the Museum.

[331] Wright (1711-1786) was a physicist. He was offered the professorship
of mathematics at the Imperial Academy of St. Petersburg but declined to
accept it. This work is devoted chiefly to the theory of the Milky Way, the
_via lactea_ as he calls it after the manner of the older writers.

[332] Troughton (1753-1835) was one of the world's greatest instrument
makers. He was apprenticed to his brother John, and the two succeeded
(1770) Wright and Cole in Fleet Street. Airy called his method of
graduating circles the greatest improvement ever made in instrument making.
He constructed (1800) the first modern transit circle, and his instruments
were used in many of the chief observatories of the world.

[333] William Simms (1793-1860) was taken into partnership by Troughton
(1826) after the death of the latter's brother. The firm manufactured some
well-known instruments.

[334] This was George Horne (1730-1792), fellow of Magdalen College,
Oxford, vice-Chancellor of the University (1776), Dean of Canterbury
(1781), and Bishop of Norwich (1790). He was a great satirist, but most of
his pamphlets against men like Adam Smith, Swedenborg, and Hume, were
anonymous, as in the case of this one against Newton. He was so liberal in
his attitude towards the Methodists that he would not have John Wesley
forbidden to preach in his diocese. He was twenty-one when this tract
appeared.

[335] Martin (1704-1782) was by no means "old Benjamin Martin" when Horne
wrote this pamphlet in 1749. In fact he was then only forty-five. He was a
physicist and a well-known writer on scientific instruments. He also wrote
_Philosophia Britannica or a new and comprehensive system of the Newtonian
Philosophy_ (1759).

[336] Jean Théophile Desaguliers, or Des Aguliers (1683-1744) was the son
of a Protestant who left France after the revocation of the Edict of
Nantes. He became professor of physics at Oxford, and afterwards gave
lectures in London. Later he became chaplain to the Prince of Wales. He
published several works on physics.

[337] Charles Hutton (1737-1823), professor of mathematics at Woolwich
(1772-1807). His _Mathematical Tables_ (1785) and _Mathematical and
Philosophical Dictionary_ (1795-1796) are well known.

[338] James Epps (1773-1839) contributed a number of memoirs on the use and
corrections of instruments. He was assistant secretary of the Astronomical
Society.

[339] John Hutchinson (1674-1737) was one of the first to try to reconcile
the new science of geology with Genesis. He denied the Newtonian hypothesis
as dangerous to religion, and because it necessitated a vacuum. He was a
mystic in his interpretation of the Scriptures, and created a sect that
went under the name of Hutchinsonians.

[340] John Rowning, a Lincolnshire rector, died in 1771. He wrote on
physics, and published a memoir on _A machine for finding the roots of
equations universally_ (1770).

[341] It is always difficult to sanction this spelling of the name of this
Jesuit father who is so often mentioned in the analytic treatment of
conics. He was born in Ragusa in 1711, and the original spelling was
Ru[=d]er Josip Bo[vs]kovi['c]. When he went to live in Italy, as professor
of mathematics at Rome (1740) and at Pavia, the name was spelled Ruggiero
Giuseppe Boscovich, although Boscovicci would seem to a foreigner more
natural. His astronomical work was notable, and in his _De maculis
solaribus_ (1736) there is the first determination of the equator of a
planet by observing the motion of spots on its surface. Boscovich came near
having some contact with America, for he was delegated to observe in
California the transit of Venus in 1755, being prevented by the dissolution
of his order just at that time. He died in 1787, at Milan.

[342] James Granger (1723-1776) who wrote the _Biographical History of
England_, London, 1769. His collection of prints was remarkable, numbering
some fourteen thousand.

[343] He was curator of experiments for the Royal Society. He wrote a large
number of books and monographs on physics. He died about 1713.

[344] Lee seems to have made no impression on biographers.

[345] This work appeared at London in 1852.

[346] Of course this is no longer true. The most scholarly work to-day is
that of Rudio, _Archimedes, Huygens, Lambert, Legendre, vier Abhandlungen
über die Kreismessung ... mit einer Uebersicht über die Geschichte des
Problems von der Quadratur des Zirkels, von den ältesten Zeiten bis auf
unsere Tage_, Leipsic, 1892.

[347] Joseph Jérome le François de Lalande (1732-1807), professor of
astronomy in the Collège de France (1753) and director of the Paris
Observatory (1761). His writings on astronomy and his _Bibliographie
astronomique, avec l'histoire de l'astronomie depuis 1781 jusqu'en 1802_
(Paris, 1803) are well known.

[348] De Morgan refers to his _Histoire de l'Astronomie au 18e siècle_,
which appeared in 1827, five years after Delambre's death. Jean Baptiste
Joseph Delambre (1749-1822) was a pupil of and a collaborator with Lalande,
following his master as professor of astronomy in the Collège de France.
His work on the measurements for the metric system is well known, and his
four histories of astronomy, _ancienne_ (1817), _au moyen âge_ (1819),
_moderne_ (1821), and _au 18e siècle_ (posthumous, 1827) are highly
esteemed.

[349] Jean-Joseph Rive (1730-1792), a priest who left his cure under grave
charges, and a quarrelsome character. His attack on Montucla was a case of
the pot calling the kettle black; for while he was a brilliant writer he
was a careless bibliographer.

[350] Isaac Barrow (1630-1677) was quite as well known as a theologian as
he was from his Lucasian professorship of mathematics at Cambridge.

[351] "Besides we can see by this that Barrow was a poor philosopher; for
he believed in the immortality of the soul and in a Divinity other than
universal nature."

[352] The _Récréations mathématiques et physiques_ (Paris, 1694) of Jacques
Ozanam (1640-1717) is a work that is still highly esteemed. Among various
other works he wrote a _Dictionnaire mathématique ou Idée générale des
mathématiques_ (1690) that was not without merit. The _Récréations_ went
through numerous editions (Paris, 1694, 1696, 1741, 1750, 1770, 1778, and
the Montucla edition of 1790; London, 1708, the Montucla-Hutton edition of
1803 and the Riddle edition of 1840; Dublin, 1790).

[353] Hendryk van Etten, the _nom de plume_ of Jean Leurechon (1591-1670),
rector of the Jesuit college at Bar, and professor of philosophy and
mathematics. He wrote on astronomy (1619) and horology (1616), and is known
for his _Selecta Propositiones in tota sparsim mathematica pulcherrime
propositae in solemni festo SS. Ignatii et Francesci Xaverii_, 1622. The
book to which De Morgan refers is his _Récréation mathématicque, composée
de plusieurs problèmes plaisants et facetieux_, Lyons, 1627, with an
edition at Pont-à-Mousson, 1629. There were English editions published at
London in 1633, 1653, and 1674, and Dutch editions in 1662 and 1672.

I do not understand how De Morgan happened to miss owning the work by
Claude Gaspar Bachet de Meziriac (1581-1638), _Problèmes plaisans et
délectables_, which appeared at Lyons in 1612, 8vo, with a second edition
in 1624. There was a fifth edition published at Paris in 1884.

[354] His title page closes with "Paris, Chez Ch. Ant. Jombert.... M DCC
LIV."

This was Charles-Antoine Jombert (1712-1784), a printer and bookseller with
some taste for painting and architecture. He wrote several works and edited
a number of early treatises.

[355] The late Professor Newcomb made the matter plain even to the
non-mathematical mind, when he said that "ten decimal places are sufficient
to give the circumference of the earth to the fraction of an inch, and
thirty decimal places would give the circumference of the whole visible
universe to a quantity imperceptible with the most powerful microscope."

[356] _Antinewtonianismi pars prima, in qua Newtoni de coloribus systema ex
propriis principiis geometrice evertitur, et nova de coloribus theoria
luculentissimis experimentis demonstrantur_.... Naples, 1754; _pars
secunda_, Naples, 1756.

[357] Celestino Cominale (1722-1785) was professor of medicine at the
University of Naples.

[358] The work appeared in the years from 1844 to 1849.

[359] There was a Vienna edition in 1758, 4to, and another in 1759, 4to.
This edition is described on the title page as _Editio Veneta prima ipso
auctore praesente, et corrigente_.

[360] The first edition was entitled _De solis ac lunae defectibus libri
V. P. Rogerii Josephi Boscovich ... cum ejusdem auctoris adnotationibus_,
London, 1760. It also appeared in Venice in 1761, and in French translation
by the Abbé de Baruel in 1779, and was a work of considerable influence.

[361] Paulian (1722-1802) was professor of physics at the Jesuit college at
Avignon. He wrote several works, the most popular of which, the
_Dictionnaire de physique_ (Avignon, 1761), went through nine editions by
1789.

[362] This is correct.

[363] Probably referring to the fact that Hill (1795-1879), who had done so
much for postal reform, was secretary to the postmaster general (1846), and
his name was a synonym for the post office directory.

[364] Richard Lovett (1692-1780) was a good deal of a charlatan. He claimed
to have studied electrical phenomena, and in 1758 advertised that he could
effect marvelous cures, especially of sore throat, by means of electricity.
Before publishing the works mentioned by De Morgan he had issued others of
similar character, including _The Subtile Medium proved_ (London, 1756) and
_The Reviewers Reviewed_ (London, 1760).

[365] Jean Sylvain Bailly (1736-1793), member of the _Académie française_
and of the _Académie des sciences_, first deputy elected to represent Paris
in the _Etats-généraux_ (1789), president of the first National Assembly,
and mayor of Paris (1789-1791). For his vigor as mayor in keeping the
peace, and for his manly defence of the Queen, he was guillotined. He was
an astronomer of ability, but is best known for his histories of the
science.

[366] These were the _Histoire de l'Astronomie ancienne_ (1775), _Histoire
de l'Astronomie moderne_ (1778-1783), _Histoire de l'Astronomie indienne et
orientale_ (1787), and _Lettres sur l'origine des peuples de l'Asie_
(1775).

[367] "The sick old man of Ferney, V., a boy of a hundred years." Voltaire
was born in 1694, and hence was eighty-three at this time.

[368] In Palmézeaux's _Vie de Bailly_, in Bailly's _Ouvrage Posthume_
(1810), M. de Sales is quoted as saying that the _Lettres sur l'Atlantide_
were sent to Voltaire and that the latter did not approve of the theory set
forth.

[369] The British Museum catalogue gives two editions, 1781 and 1782.

[370] A mystic and a spiritualist. His chief work was the one mentioned
here.

[371] Jacob Behmen, or Böhme (1575-1624), known as "the German
theosophist," was founder of the sect of Boehmists, a cult allied to the
Swedenborgians. He was given to the study of alchemy, and brought the
vocabulary of the science into his mystic writings. His sect was revived in
England in the eighteenth century through the efforts of William Law.
Saint-Martin translated into French two of his Latin works under the titles
_L'Aurore naissante, ou la Racine de la philosophie_ (1800), and _Les trois
principes de l'essence divine_ (1802). The originals had appeared nearly
two hundred years earlier,--_Aurora_ in 1612, and _De tribus principiis_ in
1619.

[372] "Unknown."

[373] "Skeptical."

[374] "Man, man, man."

[375] "Men, men, men."

[376] It is interesting to read De Morgan's argument against Saint-Martin's
authorship of this work. It is attributed to Saint-Martin both by the
_Biographie Universelle_ and by the _British Museum Catalogue_, and De
Morgan says by "various catalogues and biographies."

[377] "To explain things by man and not man by things. _On Errors and
Truth_, by a Ph.... Inc...."

[378] "If we would preserve ourselves from all illusions, and above all
from the allurements of pride, by which man is so often seduced, we should
never take man, but always God, for our term of comparison."

[379] "And here is found already an explanation of the numbers four and
nine which caused some perplexity in the work cited above. Man is lost in
passing from four to nine."

[380] Williams also took part in the preparation of some tables for the
government to assist in the determination of longitude. He had published a
work two years before the one here cited, on the same subject,--_An entire
new work and method to discover the variation of the Earth's Diameters_,
London, 1786.

[381] This is Gabriel Mouton (1618-1694), a vicar at Lyons, who suggested
as a basis for a natural system of measures the _mille_, a minute of a
degree of the meridian. This appeared in his _Observationes diametrorum
solis et lunae apparentium, meridianarumque aliquot altitudinum cum tabula
declinationum solis_.... Lyons, 1670.

[382] Jacques Cassini (1677-1756), one of the celebrated Cassini family of
astronomers. After the death of his father he became director of the
observatory at Paris. The basis for a metric unit was set forth by him in
his _Traité de la grandeur et de la figure de la terre_, Paris, 1720. He
was a prolific writer on astronomy.

[383] Alexis Jean Pierre Paucton (1732-1798). He was, for a time, professor
of mathematics at Strassburg, but later (1796) held office in Paris. His
leading contribution to metrology was his _Métrologie ou Traité des
mesures_, Paris, 1780.

[384] He was an obscure writer, born at Deptford.

[385] He was also a writer of no scientific merit, his chief contributions
being religious tracts. One of his productions, however, went through many
editions, even being translated into French; _Three dialogues between a
Minister and one of his Parishioners; on the true principles of Religion
and salvation for sinners by Jesus Christ_. The twentieth edition appeared
at Cambridge in 1786.

[386] This was the _Reflections on the Revolution in France, and on the
proceedings in certain societies in London relative to that event_ (London,
1790) by Edmund Burke (1729-1797). Eleven editions of the work appeared the
first year.

[387] Paine (1736-1809) was born in Norfolkshire, of Quaker parents. He
went to America at the beginning of the Revolution and published, in
January 1776, a violent pamphlet entitled _Common Sense_. He was a private
soldier under Washington, and on his return to England after the war he
published _The Rights of Man_. He was indicted for treason and was outlawed
to France. He was elected to represent Calais at the French convention, but
his plea for moderation led him perilously near the guillotine. His _Age of
Reason_ (1794) was dedicated to Washington. He returned to America in 1802
and remained there until his death.

[388] Part I appeared in 1791 and was so popular that eight editions
appeared in that year. It was followed in 1792 by Part II, of which nine
editions appeared in that year. Both parts were immediately republished in
Paris, and there have been several subsequent editions.

[389] Mary Wollstonecraft (1759-1797) was only thirty-three when this work
came out. She had already published _An historical and moral View of the
Origin and Progress of the French Revolution_ (1790), and _Original Stories
from Real Life_ (1791). She went to Paris in 1792 and remained during the
Reign of Terror.

[390] Samuel Parr (1747-1827) was for a time head assistant at Harrow
(1767-1771), afterwards headmaster in other schools. At the time this book
was written he was vicar of Hatton, where he took private pupils
(1785-1798) to the strictly limited number of seven. He was a violent Whig
and a caustic writer.

[391] On Mary Wollstonecraft's return from France she married (1797)
William Godwin (1756-1836). He had started as a strong Calvinistic
Nonconformist minister, but had become what would now be called an
anarchist, at least by conservatives. He had written an _Inquiry concerning
Political Justice_ (1793) and a novel entitled _Caleb Williams, or Things
as they are_ (1794), both of which were of a nature to attract his future
wife.

[392] This child was a daughter. She became Shelley's wife, and Godwin's
influence on Shelley was very marked.

[393] This was John Nichols (1745-1826), the publisher and antiquary. He
edited the _Gentleman's Magazine_ (1792-1826) and his works include the
_Literary Anecdotes of the Eighteenth Century_ (1812-1815), to which De
Morgan here refers.

[394] William Bellenden, a Scotch professor at the University of Paris, who
died about 1633. His textbooks are now forgotten, but Parr edited an
edition of his works in 1787. The Latin preface, _Praefatio ad Bellendum de
Statu_, was addressed to Burke, North, and Fox, and was a satire on their
political opponents.

[395] As we have seen, he had been head-master before he began taking "his
handful of private pupils."

[396] The story has evidently got mixed up in the telling, for Tom Sheridan
(1721-1788), the great actor, was old enough to have been Dr. Parr's
father. It was his son, Richard Brinsley Sheridan (1751-1816), the
dramatist and politician, who was the pupil of Parr. He wrote _The Rivals_
(1775) and _The School for Scandal_ (1777) soon after Parr left Harrow.

[397] Horner (1785-1864) was a geologist and social reformer. He was very
influential in improving the conditions of child labor.

[398] William Cobbett (1762-1835), the journalist, was a character not
without interest to Americans. Born in Surrey, he went to America at the
age of thirty and remained there eight years. Most of this time he was
occupied as a bookseller in Philadelphia, and while thus engaged he was
fined for libel against the celebrated Dr. Rush. On his return to England
he edited the _Weekly Political Register_ (1802-1835), a popular journal
among the working classes. He was fined and imprisoned for two years
because of his attack (1810) on military flogging, and was also (1831)
prosecuted for sedition. He further showed his paradox nature by his
_History of the Protestant Reformation_ (1824-1827), an attack on the
prevailing Protestant opinion. He also wrote a _Life of Andrew Jackson_
(1834). After repeated attempts he succeeded in entering parliament, a
result of the Reform Bill.

[399] Robinson (1735-1790) was a Baptist minister who wrote several
theological works and a number of hymns. His work at Cambridge so offended
the students that they at one time broke up the services.

[400] This work had passed through twelve editions by 1823.

[401] Dyer (1755-1841), the poet and reformer, edited Robinson's
_Ecclesiastical Researches_ (1790). He was a life-long friend of Charles
Lamb, and in their boyhood they were schoolmates at Christ's Hospital. His
_Complaints of the Poor People of England_ (1793) made him a worthy
companion of the paradoxers above mentioned.

[402] These were John Thelwall (1764-1834) whose _Politics for the People
or Hogswash_ (1794) took its title from the fact that Burke called the
people the "swinish multitude." The book resulted in sending the author to
the Tower for sedition. In 1798 he gave up politics and started a school of
elocution which became very famous. Thomas Hardy (1752-1832), who kept a
bootmaker's shop in Piccadilly, was a fellow prisoner with Thelwall, being
arrested for high treason. He was founder (1792) of The London
Corresponding Society, a kind of clearing house for radical associations
throughout the country. Horne Tooke was really John Horne (1736-1812), he
having taken the name of his friend William Tooke in 1782. He was a radical
of the radicals, and organized a number of reform societies. Among these
was the Constitutional Society that voted money (1775) to assist the
American revolutionists, appointing him to give the contribution to
Franklin. For this he was imprisoned for a year. With his fellow rebels in
the Tower in 1794, however, he was acquitted. As a philologist he is known
for his early advocacy of the study of Anglo-Saxon and Gothic, and his
_Diversions of Purley_ (1786) is still known to readers.

[403] This was the admiral, Adam Viscount Duncan (1731-1804), who defeated
the Dutch off Camperdown in 1797.

[404] He was created Duke of Clarence and St. Andrews in 1789 and was
Admiral of the Fleet escorting Louis XVIII on his return to France in 1814.
He became Lord High Admiral in 1827, and reigned as William IV from 1830 to
1837.

[405] This was Charles Abbott (1762-1832) first Lord Tenterden. He
succeeded Lord Ellenborough as Chief Justice (1818) and was raised to the
peerage in 1827. He was a strong Tory and opposed the Catholic Relief Bill,
the Reform Bill, and the abolition of the death penalty for forgery.

[406] Edward Law (1750-1818), first Baron Ellenborough. He was chief
counsel for Warren Hastings, and his famous speech in defense of his client
is well known. He became Chief Justice and was raised to the peerage in
1802. He opposed all efforts to modernize the criminal code, insisting upon
the reactionary principle of new death penalties.

[407] Edmund Law (1703-1787), Bishop of Carlisle (1768), was a good deal
more liberal than his son. His _Considerations on the Propriety of
requiring subscription to the Articles of Faith_ (1774) was published
anonymously. In it he asserts that not even the clergy should be required
to subscribe to the thirty-nine articles.

[408] Joe Miller (1684-1738), the famous Drury Lane comedian, was so
illiterate that he could not have written the _Joe Miller's Jests, or the
Wit's Vade-Mecum_ that appeared the year after his death. It was often
reprinted and probably contained more or less of Miller's own jokes.

[409] The sixth duke (1766-1839) was much interested in parliamentary
reform. He was a member of the Society of Friends of the People. He was for
fourteen years a member of parliament (1788-1802) and was later Lord
Lieutenant of Ireland (1806-1807). He afterwards gave up politics and
became interested in agricultural matters.

[410] George Jeffreys (c. 1648-1689), the favorite of James II, who was
active in prosecuting the Rye House conspirators. He was raised to the
peerage in 1684 and held the famous "bloody assize" in the following year,
being made Lord Chancellor as a result. He was imprisoned in the Tower by
William III and died there.

[411] _The Every Day Book, forming a Complete History of the Year, Months,
and Seasons, and a perpetual Key to the Almanack_, 1826-1827.

[412] The first and second editions appeared in 1820. Two others followed
in 1821.

[413] _The three trials of W. H., for publishing three parodies; viz the
late John Wilkes' Catechism, the Political Litany, and the Sinecurists
Creed; on three ex-officio informations, at Guildhall, London, ... Dec. 18,
19, & 20, 1817_,... London, 1818.

[414] The _Political Litany_ appeared in 1817.

[415] That is, Castlereagh's.

[416] The well-known caricaturist (1792-1878), then only twenty-nine years
old.

[417] Robert Stewart (1769-1822) was second Marquis of Londonderry and
Viscount Castlereagh. As Chief Secretary for Ireland he was largely
instrumental in bringing about the union of Ireland and Great Britain. He
was at the head of the war department during most of the Napoleonic wars,
and was to a great extent responsible for the European coalition against
the Emperor. He suicided in 1822.

[418] John Murray (1778-1843), the well-known London publisher. He refused
to finish the publication of Don Juan, after the first five cantos, because
of his Tory principles.

[419] Only the first two cantos appeared in 1819.

[420] Proclus (412-485), one of the greatest of the neo-Platonists, studied
at Alexandria and taught philosophy at Athens. He left commentaries on
Plato and on part of Euclid's _Elements_.

[421] Thomas Taylor (1758-1835), called "the Platonist," had a liking for
mathematics, and was probably led by his interest in number mysticism to a
study of neo-Platonism. He translated a number of works from the Latin and
Greek, and wrote two works on theoretical arithmetic (1816, 1823).

[422] There was an earlier edition, 1788-89.

[423] Georgius Gemistus, or Georgius Pletho (Plethon), lived in the
fourteenth and fifteenth centuries. He was a native of Constantinople, but
spent most of his time in Greece. He devoted much time to the propagation
of the Platonic philosophy, but also wrote on divinity, geography, and
history.

[424] Hannah More (1745-1833), was, in her younger days, a friend of Burke,
Reynolds, Dr. Johnson, and Garrick. At this time she wrote a number of
poems and aspired to become a dramatist. Her _Percy_ (1777), with a
prologue and epilogue by Garrick, had a long run at Covent Garden. Somewhat
later she came to believe that the playhouse was a grave public evil, and
refused to attend the revival of her own play with Mrs. Siddons in the
leading part. After 1789 she and her sisters devoted themselves to starting
schools for poor children, teaching them religion and housework, but
leaving them illiterate.

[425] These were issued at the rate of three each month,--a story, a
ballad, and a Sunday tract. They were collected and published in one volume
in 1795. It is said that two million copies were sold the first year. There
were also editions in 1798, 1819, 1827, and 1836-37.

[426] That is, Dr. Johnson (1709-1784). The _Rambler_ was published in
1750-1752, and was an imitation of Addison's _Spectator_.

[427] Dr. Moore, referred to below.

[428] Dr. John Moore (1729-1802), physician and novelist, is now best known
for his _Journal during a Residence in France from the beginning of August
to the middle of December, 1792_, a work quoted frequently by Carlyle in
his _French Revolution_.

[429] Sir John Moore (1761-1809), Lieutenant General in the Napoleonic
wars. He was killed in the battle of Corunna. The poem by Charles Wolfe
(1791-1823), _The Burial of Sir John Moore_ (1817), is well known.

[430] Referring to the novels of Thomas Love Peacock (1785-1866), who
succeeded James Mill as chief examiner of the East India Company, and was
in turn succeeded by John Stuart Mill.

[431] Frances Burney, Madame d'Arblay (1752-1840), married General
d'Arblay, a French officer and companion of Lafayette, in 1793. She was
only twenty-five when she acquired fame by her _Evelina, or a Young Lady's
Entrance into the World_. Her _Letters and Diaries_ appeared posthumously
(1842-45).

[432] Henry Peter, Baron Brougham and Vaux (1778-1868), well known in
politics, science, and letters. He was one of the founders of the
_Edinburgh Review_, became Lord Chancellor in 1830, and took part with men
like William Frend, De Morgan's father-in-law, in the establishing of
London University. He was also one of the founders of the Society for the
Diffusion of Useful Knowledge. He was always friendly to De Morgan, who
entered the faculty of London University, whose work on geometry was
published by the Society mentioned, and who was offered the degree of
doctor of laws by the University of Edinburgh while Lord Brougham was Lord
Rector. The Edinburgh honor was refused by De Morgan who said he "did not
feel like an LL.D."

[433] Maria Edgeworth (1767-1849).

[434] Sydney Owenson (c. 1783-1859) married Sir Thomas Morgan, a well-known
surgeon, in 1812. Her Irish stories were very popular with the patriots but
were attacked by the _Quarterly Review_. _The Wild Irish Girl_ (1806) went
through seven editions in two years.

[435] 1775-1817.

[436] 1771-1832.

[437] The famous preacher (1732-1808). He was the first chairman of the
Religious Tract Society. He is also known as one of the earliest advocates
of vaccination, in his _Cow-pock Inoculation vindicated and recommended
from matters of fact_, 1806.

[438] Sir Rowland Hill (1795-1879), the father of penny postage.

[439] Beilby Porteus (1731-1808), Bishop of Chester (1776) and Bishop of
London (1787). He encouraged the Sunday-school movement and the
dissemination of Hannah More's tracts. He was an active opponent of
slavery, but also of Catholic emancipation.

[440] Henrietta Maria Bowdler (1754-1830), generally known as Mrs. Harriet
Bowdler. She was the author of many religious tracts and poems. Her _Poems
and Essays_ (1786) were often reprinted. The story goes that on the
appearance of her _Sermons on the Doctrines and duties of Christianity_
(published anonymously), Bishop Porteus offered the author a living under
the impression that it was written by a man.

[441] William Frend (1757-1841), whose daughter Sophia Elizabeth became De
Morgan's wife (1837), was at one time a clergyman of the Established
Church, but was converted to Unitarianism (1787). He came under De Morgan's
definition of a true paradoxer, carrying on a zealous warfare for what he
thought right. As a result of his _Address to the Inhabitants of Cambridge_
(1787), and his efforts to have abrogated the requirement that candidates
for the M.A. must subscribe to the thirty-nine articles, he was deprived of
his tutorship in 1788. A little later he was banished (see De Morgan's
statement in the text) from Cambridge because of his denunciation of the
abuses of the Church and his condemnation of the liturgy. His eccentricity
is seen in his declining to use negative quantities in the operations of
algebra. He finally became an actuary at London and was prominent in
radical associations. He was a mathematician of ability, having been second
wrangler and having nearly attained the first place, and he was also an
excellent scholar in Latin, Greek, and Hebrew.

[442] George Peacock (1791-1858), Fellow of Trinity College, Cambridge,
Lowndean professor of astronomy, and Dean of Ely Cathedral (1839). His tomb
may be seen at Ely where he spent the latter part of his life. He was one
of the group that introduced the modern continental notation of the
calculus into England, replacing the cumbersome notation of Newton, passing
from "the _dot_age of fluxions to the _de_ism of the calculus."

[443] Robert Simson (1687-1768); professor of mathematics at Glasgow. His
restoration of Apollonius (1749) and his translation and restoration of
Euclid (1756, and 1776--posthumous) are well known.

[444] Francis Maseres (1731-1824), a prominent lawyer. His mathematical
works had some merit.

[445] These appeared annually from 1804 to 1822.

[446] Henry Gunning (1768-1854) was senior esquire bedell of Cambridge. The
_Reminiscences_ appeared in two volumes in 1854.

[447] John Singleton Copley, Baron Lyndhurst (1772-1863), the son of John
Singleton Copley the portrait painter, was born in Boston. He was educated
at Trinity College, Cambridge, and became a lawyer. He was made Lord
Chancellor in 1827.

[448] Sir William Rough (c. 1772-1838), a lawyer and poet, became Chief
Justice of Ceylon in 1836. He was knighted in 1837.

[449] Herbert Marsh, afterwards Bishop of Peterborough, a relation of my
father.--S. E. De M.

He was born in 1757 and died in 1839. On the trial of Frend he publicly
protested against testifying against a personal confidant, and was excused.
He was one of the first of the English clergy to study modern higher
criticism of the Bible, and amid much opposition he wrote numerous works on
the subject. He was professor of theology at Cambridge (1707), Bishop of
Llandaff (1816), and Bishop of Peterborough.

[450] George Butler (1774-1853), Headmaster of Harrow (1805-1829),
Chancellor of Peterborough (1836), and Dean of Peterborough (1842).

[451] James Tate (1771-1843), Headmaster of Richmond School (1796-1833) and
Canon of St. Paul's Cathedral (1833). He left several works on the
classics.

[452] Francis Place (1771-1854), at first a journeyman breeches maker, and
later a master tailor. He was a hundred years ahead of his time as a strike
leader, but was not so successful as an agitator as he was as a tailor,
since his shop in Charing Cross made him wealthy. He was a well-known
radical, and it was largely due to his efforts that the law against the
combinations of workmen was repealed in 1824. His chief work was _The
Principles of Population_ (1822).

[453] Speed (1552-1629) was a tailor until Grevil (Greville) made him
independent of his trade. He was not only an historian of some merit, but a
skilful cartographer. His maps of the counties were collected in the
_Theatre of the Empire of Great Britaine_, 1611. About this same time he
also published _Genealogies recorded in Sacred Scripture_, a work that had
passed through thirty-two editions by 1640.

[454] _The history of Great Britaine under the conquests of ye Romans,
Saxons, Danes, and Normans...._ London, 1611, folio. The second edition
appeared in 1623; the third, to which De Morgan here refers, posthumously
in 1632; and the fourth in 1650.

[455] William Nicolson (1655-1727) became Bishop of Carlisle in 1702, and
Bishop of Derry in 1718. His chief work was the _Historical Library_
(1696-1724), in the form of a collection of documents and chronicles. It
was reprinted in 1736 and in 1776.

[456] Sir Fulk Grevil, or Fulke Greville (1554-1628), was a favorite of
Queen Elizabeth, Chancellor of the Exchequer under James I, a patron of
literature, and a friend of Sir Philip Sidney.

[457] See note 443 on page 197.

[458] See note 444 on page 197.

[459] See note 439 on page 193.

[460] Edward Waring (1736-1796) was Lucasian professor of mathematics at
Cambridge. He published several works on analysis and curves. The work
referred to was the _Miscellanea Analytica de aequationibus algebraicis et
curvarum proprietatibus_, Cambridge, 1762.

[461] _A Dissertation on the use of the Negative Sign in Algebra...; to
which is added, Machin's Quadrature of the Circle_, London, 1758.

[462] The paper was probably one on complex numbers, or possibly one on
quaternions, in which direction as well as absolute value is involved.

[463] De Morgan quotes from one of the Latin editions. Descartes wrote in
French, the title of his first edition being: _Discours de la méthode pour
bien conduire sa raison et chercher la vérité dans les sciences, plus la
dioptrique, les météores et la géométrie qui sont des essais de cette
méthode_, Leyden, 1637, 4to.

[464] "I have observed that algebra indeed, as it is usually taught, is so
restricted by definite rules and formulas of calculation, that it seems
rather a confused kind of an art, by the practice of which the mind is in a
certain manner disturbed and obscured, than a science by which it is
cultivated and made acute."

[465] It appeared in 93 volumes, from 1758 to 1851.

[466] _The principles of the doctrine of life-annuities; explained in a
familiar manner ... with a variety of new tables_ ..., London, 1783.

[467] I suppose the one who wrote _Conjectures on the physical causes of
Earthquakes and Volcanoes_, Dublin, 1820.

[468] _Scriptores Logarithmici; or, a Collection of several curious_
_tracts on the nature and construction of Logarithms ... together with same
tracts on the Binomial Theorem_ ..., 6 vols., London, 1791-1807.

[469] Charles Babbage (1792-1871), whose work on the calculating machine is
well known. Maseres was, it is true, ninety-two at this time, but Babbage
was thirty-one instead of twenty-nine. He had already translated Lacroix's
_Treatise on the differential and integral calculus_ (1816), in
collaboration with Herschel and Peacock. He was Lucasian professor of
mathematics at Cambridge from 1828 to 1839.

[470] _The great and new Art of weighing Vanity, or a discovery of the
ignorance of the great and new artist in his pseudo-philosophical
writings._ The "great and new artist" was Sinclair.

[471] George Sinclair, probably a native of East Lothian, who died in 1696.
He was professor of philosophy and mathematics at Glasgow, and was one of
the first to use the barometer in measuring altitudes. The work to which De
Morgan refers is his _Hydrostaticks_ (1672). He was a firm believer in evil
spirits, his work on the subject going through four editions: _Satan's
Invisible World Discovered; or, a choice collection of modern relations,
proving evidently against the Saducees and Athiests of this present age,
that there are Devils, Spirits, Witches, and Apparitions_, Edinburgh, 1685.

[472] This was probably William Sanders, Regent of St. Leonard's College,
whose _Theses philosophicae_ appeared in 1674, and whose _Elementa
geometriae_ came out a dozen years later.

[473] _Ars nova et magna gravitatis et levitatis; sive dialogorum
philosophicorum libri sex de aeris vera ac reali gravitate_, Rotterdam,
1669, 4to.

[474] Volume I, Nos. 1 and 2, appeared in 1803.

[475] His daughter, Mrs. De Morgan, says in her _Memoir_ of her husband:
"My father had been second wrangler in a year in which the two highest were
close together, and was, as his son-in-law afterwards described him, an
exceedingly clear thinker. It is possible, as Mr. De Morgan said, that this
mental clearness and directness may have caused his mathematical heresy,
the rejection of the use of negative quantities in algebraical operations;
and it is probable that he thus deprived himself of an instrument of work,
the use of which might have led him to greater eminence in the higher
branches." _Memoir of Augustus De Morgan_, London, 1882, p. 19.

[476] "If it is not true it is a good invention." A well-known Italian
proverb.

[477] See page 86, note 132.

[478] He was born at Paris in 1713, and died there in 1765.

[479] _Recherches sur les courbes à double courbure_, Paris, 1731. Clairaut
was then only eighteen, and was in the same year made a member of the
Académie des sciences. His _Elémens de géométrie_ appeared in 1741.
Meantime he had taken part in the measurement of a degree in Lapland
(1736-1737). His _Traité de la figure de la terre_ was published in 1741.
The Academy of St. Petersburg awarded him a prize for his _Théorie de la
lune_ (1750). His various works on comets are well known, particularly his
_Théorie du mouvement des comètes_ (1760) in which he applied the "problem
of three bodies" to Halley's comet as retarded by Jupiter and Saturn.

[480] Joseph Privat, Abbé de Molières (1677-1742), was a priest of the
Congregation of the Oratorium. In 1723 he became a professor in the Collège
de France. He was well known as an astronomer and a mathematician, and
wrote in defense of Descartes's theory of vortices (1728, 1729). He also
contributed to the methods of finding prime numbers (1705).

[481] "Deserves not only to be printed, but to be admired as a marvel of
imagination, of understanding, and of ability."

[482] Blaise Pascal (1623-1662), the well-known French philosopher and
mathematician. He lived for some time with the Port Royalists, and defended
them against the Jesuits in his _Provincial Letters_. Among his works are
the following: _Essai pour les coniques_ (1640); _Recit de la grande
expérience de l'équilibre des liqueurs_ (1648), describing his experiment
in finding altitudes by barometric readings; _Histoire de la roulette_
(1658); _Traité du triangle arithmétique_ (1665); _Aleae geometria_ (1654).

[483] This proposition shows that if a hexagon is inscribed in a conic (in
particular a circle) and the opposite sides are produced to meet, the three
points determined by their intersections will be in the same straight line.

[484] Jacques Curabelle, _Examen des Oeuvres du Sr. Desargues_, Paris,
1644. He also published without date a work entitled: _Foiblesse pitoyable
du Sr. G. Desargues employée contre l'examen fait de ses oeuvres_.

[485] See page 119, note 233.

[486] Until "this great proposition called Pascal's should see the light."

[487] The story is that his father, Etienne Pascal, did not wish him to
study geometry until he was thoroughly grounded in Latin and Greek. Having
heard the nature of the subject, however, he began at the age of twelve to
construct figures by himself, drawing them on the floor with a piece of
charcoal. When his father discovered what he was doing he was attempting to
demonstrate that the sum of the angles of a triangle equals two right
angles. The story is given by his sister, Mme. Perier.

[488] Sir John Wilson (1741-1793) was knighted in 1786 and became
Commissioner of the Great Seal in 1792. He was a lawyer and jurist of
recognized merit. He stated his theorem without proof, the first
demonstration having been given by Lagrange in the Memoirs of the Berlin
Academy for 1771,--_Demonstration d'un théorème nouveau concernant les
nombres premiers_. Euler also gave a proof in his _Miscellanea Analytica_
(1773). Fermat's works should be consulted in connection with the early
history of this theorem.

[489] He wrote, in 1760, a tract in defense of Waring, a point of whose
algebra had been assailed by a Dr. Powell. Waring wrote another tract of
the same date.--A. De M.

William Samuel Powell (1717-1775) was at this time a fellow of St. John's
College, Cambridge. In 1765 he became Vice Chancellor of the University.
Waring was a Magdalene man, and while candidate for the Lucasian
professorship he circulated privately his _Miscellanea Analytica_. Powell
attacked this in his _Observations on the First Chapter of a Book called
Miscellanea_ (1760). This attack was probably in the interest of another
candidate, a man of his own college (St. John's), William Ludlam.

[490] William Paley (1743-1805) was afterwards a tutor at Christ's College,
Cambridge. He never contributed anything to mathematics, but his _Evidences
of Christianity_ (1794) was long considered somewhat of a classic. He also
wrote _Principles of Morality and Politics_ (1785), and _Natural Theology_
(1802).

[491] Edward, first Baron Thurlow (1731-1806) is known to Americans because
of his strong support of the Royal prerogative during the Revolution. He
was a favorite of George III, and became Lord Chancellor in 1778.

[492] George Wilson Meadley (1774-1818) published his _Memoirs of ...
Paley_ in 1809. He also published _Memoirs of Algernon Sidney_ in 1813. He
was a merchant and banker, and had traveled extensively in Europe and the
East. He was a convert to unitarianism, to which sect Paley had a strong
leaning.

[493] Watson (1737-1816) was a strange kind of man for a bishopric. He was
professor of chemistry at Cambridge (1764) at the age of twenty-seven. It
was his experiments that led to the invention of the black-bulb
thermometer. He is said to have saved the government £100,000 a year by his
advice on the manufacture of gunpowder. Even after he became professor of
divinity at Cambridge (1771) he published four volumes of _Chemical Essays_
(vol. I, 1781). He became Bishop of Llandaff in 1782.

[494] James Adair (died in 1798) was counsel for the defense in the trial
of the publishers of the _Letters of Junius_ (1771). As King's Serjeant he
assisted in prosecuting Hardy and Horne Tooke.

[495] Morgan (1750-1833) was actuary of the Equitable Assurance Society of
London (1774-1830), and it was to his great abilities that the success of
that company was due at a time when other corporations of similar kind were
meeting with disaster. The Royal Society awarded him a medal (1783) for a
paper on _Probability of Survivorship_. He wrote several important works on
insurance and finance.

[496] Dr. Price (1723-1791) was a non-conformist minister and a writer on
ethics, economics, politics, and insurance. He was a defender of the
American Revolution and a personal friend of Franklin. In 1778 Congress
invited him to America to assist in the financial administration of the new
republic, but he declined. His famous sermon on the French Revolution is
said to have inspired Burke's _Reflections on the Revolution in France_.

[497] Elizabeth Gurney (1780-1845), a Quaker, who married Joseph Fry
(1800), a London merchant. She was the prime mover in the Association for
the Improvement of the Female Prisoners in Newgate, founded in 1817. Her
influence in prison reform extended throughout Europe, and she visited the
prisons of many countries in her efforts to improve the conditions of penal
servitude. The friendship of Mrs. Fry with the De Morgans began in 1837.
Her scheme for a female benefit society proved worthless from the actuarial
standpoint, and would have been disastrous to all concerned if it had been
carried out, and it was therefore fortunate that De Morgan was consulted in
time. Mrs. De Morgan speaks of the consultation in these words: "My
husband, who was very sensitive on such points, was charmed with Mrs. Fry's
voice and manner as much as by the simple self-forgetfulness with which she
entered into this business; her own very uncomfortable share of it not
being felt as an element in the question, as long as she could be useful in
promoting good or preventing mischief. I can see her now as she came into
our room, took off her little round Quaker cap, and laying it down, went at
once into the matter. 'I have followed thy advice, and I think nothing
further can be done in this case; but all harm is prevented.' In the
following year I had an opportunity of seeing the effect of her most
musical tones. I visited her at Stratford, taking my little baby and nurse
with me, to consult her on some articles on prison discipline, which I had
written for a periodical. The baby--three months old--was restless, and the
nurse could not quiet her, neither could I entirely, until Mrs. Fry began
to read something connected with the subject of my visit, when the infant,
fixing her large eyes on the reader, lay listening till she fell asleep."
_Memoirs_, p. 91.

[498] Mrs. Fry certainly believed that the writer was the old actuary of
the Equitable, when she first consulted him upon the benevolent Assurance
project; but we were introduced to her by our old and dear friend Lady Noel
Byron, by whom she had been long known and venerated, and who referred her
to Mr. De Morgan for advice. An unusual degree of confidence in, and
appreciation of each other, arose on their first meeting between the two,
who had so much that was externally different, and so much that was
essentially alike, in their natures.--S. E. De M.

Anne Isabella Milbanke (1792-1860) married Lord Byron in 1815, when both
took the additional name of Noel, her mother's name. They were separated in
1816.

[499] An obscure writer not mentioned in the ordinary biographies.

[500] Not mentioned in the ordinary biographies, and for obvious reasons.

[501] "Before" and "after."

[502] On Bishop Wilkins see note 171 on page 100.

[503] Provision for a journey.

[504] See note 179 on page 103.

[505] Thomas Bradwardine (1290-1349), known as _Doctor Profundus_, proctor
and professor of theology at Oxford, and afterwards Chancellor of St.
Paul's and confessor to Edward III. The English ascribed their success at
Crécy to his prayers.

[506] He was consecrated Archbishop of Canterbury by the Pope at Avignon,
July 13, 1349, and died of the plague at London in the same year.

[507] "One paltry little year."

[508] The title is carelessly copied, as is so frequently the case in
catalogues, even of the Libri class. It should read: _Arithmetica thome
brauardini_ || _Olivier Senant_ || _Venum exponuntur ab Oliuiario senant in
vico diui Jacobi sub signo beate Barbare sedente_. The colophon reads:
_Explicit arithmetica speculatiua th[=o]e brauardini b[=n] reuisa et
correcta a Petro sanchez Ciruelo aragonensi mathematicas leg[=e]te
Parisius, [=i]pressa per Thom[=a] anguelart_. There were Paris editions of
1495, 1496, 1498, s. a. (c. 1500), 1502, 1504, 1505, s. a. (c. 1510), 1512,
1530, a Valencia edition of 1503, two Wittenberg editions of 1534 and 1536,
and doubtless several others. The work is not "very rare," although of
course no works of that period are common. See the editor's _Rara
Arithmetica_, page 61.

[509] This is his _Tractatus de proportionibus_, Paris, 1495; Venice, 1505;
Vienna, 1515, with other editions.

[510] The colophon of the 1495 edition reads: _Et sic explicit Geometria
Thome brauardini c[=u] tractatulo de quadratura circuli bene reuisa a Petro
sanchez ciruelo: operaqz Guidonis mercatoris dilig[=e]tissime impresse
parisi^o in c[=a]po gaillardi. Anno d[=n]i. 1495. die. 20, maij._

This Petro Ciruelo was born in Arragon, and died in 1560 at Salamanca. He
studied mathematics and philosophy at Paris, and took the doctor's degree
there. He taught at the University of Alcalà and became canon of the
Cathedral at Salamanca. Besides his editions of Bradwardine he wrote
several works, among them the _Liber arithmeticae practicae qui dicitur
algorithmus_ (Paris, 1495) and the _Cursus quatuor mathematicarum artium
liberalium_ (Alcalà, 1516).

[511] Star polygons, a subject of considerable study in the later Middle
Ages. See note 35 on page 44.

[512] "A new theory that adds lustre to the fourteenth century."

[513] There is nothing in the edition of 1495 that leads to this
conclusion.

[514] The full title is: _Nouvelle théorie des parallèles, avec un
appendice contenant la manière de perfectionner la théorie des parallèles
de A. M. Legendre_. The author had no standing as a scientist.

[515] Adrien Marie Legendre (1752-1833) was one of the great mathematicians
of the opening of the nineteenth century. His _Eléments de géométrie_
(1794) had great influence on the geometry of the United States. His _Essai
sur la théorie des nombres_ (1798) is one of the classics upon the subject.
The work to which Kircher refers is the _Nouvelle théorie des parallèles_
(1803), in which the attempt is made to avoid using Euclid's postulate of
parallels, the result being merely the substitution of another assumption
that was even more unsatisfactory. The best presentations of the general
theory are W. B. Frankland's _Theories of Parallelism_, Cambridge, 1910,
and Engel and Stäckel's _Die Theorie der Parallellinien von Euclid bis auf
Gauss_, Leipsic, 1895. Legendre published a second work on the theory the
year of his death, _Réflexions sur ... la théorie des parallèles_ (1833).
His other works include the _Nouvelles méthodes pour la détermination des
orbites des comètes_ (1805), in which he uses the method of least squares;
the _Traité des fonctions elliptiques et des intégrales_ (1827-1832), and
the _Exercises de calcul intégral_ (1811, 1816, 1817).

[516] Johann Joseph Ignatz von Hoffmann (1777-1866), professor of
mathematics at Aschaffenburg, published his _Theorie der Parallellinien_ in
1801. He supplemented this by his _Kritik der Parallelen-Theorie_ in 1807,
and his _Das eilfte Axiom der Elemente des Euclidis neu bewiesen_ in 1859.
He wrote other works on mathematics, but none of his contributions was of
any importance.

[517] Johann Karl Friedrich Hauff (1766-1846) was successively professor of
mathematics at Marburg, director of the polytechnic school at Augsburg,
professor at the Gymnasium at Cologne, and professor of mathematics and
physics at Ghent. The work to which Kircher refers is his memoirs on the
Euclidean _Theorie der Parallelen_ in Hindenburg's _Archiv_, vol. III
(1799), an article of no merit in the general theory.

[518] Wenceslaus Johann Gustav Karsten (1732-1787) was professor of logic
at Rostock (1758) and Butzow (1760), and later became professor of
mathematics and physics at Halle. His work on parallels is the _Versuch
einer völlig berichtigten Theorie der Parallellinien_ (1779). He also wrote
a work entitled _Anfangsgründe der mathematischen Wissenschaften_ (1780),
but neither of these works was more than mediocre.

[519] Johann Christoph Schwab (not Schwal) was born in 1743 and died in
1821. He was professor at the Karlsschule at Stuttgart. De Morgan's wish
was met, for the catalogues give "c. fig. 8," so that it evidently had
eight illustrations instead of eight volumes. He wrote several other works
on the principles of geometry, none of any importance.

[520] Gaetano Rossi of Catanzaro. This was the libretto writer (1772-1855),
and hence the imperfections of the work can better be condoned. De Morgan
should have given a little more of the title: _Solusione esatta e regolare
... del ... problema della quadratura del circolo_. There was a second
edition, London, 1805.

[521] This identifies Rossi, for Joséphine Grassini (1773-1850) was a
well-known contralto, _prima donna_ at Napoleon's court opera.

[522] William Spence (1783-1860) was an entomologist and economist of some
standing, a fellow of the Royal Society, and one of the founders of the
Entomological Society of London. The work here mentioned was a popular one,
the first edition appearing in 1807, and four editions being justified in a
single year. He also wrote _Agriculture the Source of Britain's Wealth_
(1808) and _Objections against the Corn Bill refuted_ (1815), besides a
work in four volumes on entomology (1815-1826) in collaboration with
William Kirby.

[523] "That used to be so, but we have changed all that."

[524] "Meet the coming disease."

[525] George Douglas (or Douglass) was a Scotch writer. He got out an
edition of the _Elements of Euclid_ in 1776, with an appendix on
trigonometry and a set of tables. His work on _Mathematical Tables_
appeared in 1809, and his _Art of Drawing in Perspective, from mathematical
principles_, in 1810.

[526] See note 443, on page 197.

[527] John Playfair (1748-1848) was professor of mathematics (1785) and
natural philosophy (1805) at the University of Edinburgh. His _Elements of
Geometry_ went through many editions.

[528] "Tell Apella" was an expression current in classical Rome to indicate
incredulity and to show the contempt in which the Jew was held. Horace
says: _Credat Judæus Apella_, "Let Apella the Jew believe it." Our "Tell it
to the marines," is a similar phrase.

[529] As De Morgan says two lines later, "No mistake is more common than
the natural one of imagining that the"--University of Virginia is at
Richmond. The fact is that it is not there, and that it did not exist in
1810. It was not chartered until 1819, and was not opened until 1825, and
then at Charlottesville. The act establishing the Central College, from
which the University of Virginia developed, was passed in 1816. The Jean
Wood to whom De Morgan refers was one John Wood who was born about 1775 in
Scotland and who emigrated to the United States in 1800. He published a
_History of the Administration of J. Adams_ (New York, 1802) that was
suppressed by Aaron Burr. This act called forth two works, a _Narrative of
the Suppression, by Col. Burr, of the 'History of the Administration of
John Adams'_ (1802), in which Wood was sustained; and the _Antidote to John
Wood's Poison_ (1802), in which he was attacked. The work referred to in
the "printed circular" may have been the _New theory of the diurnal
rotation of the earth_ (Richmond, Va., 1809). Wood spent the last years of
his life in Richmond, Va., making county maps. He died there in 1822. A
careful search through works relating to the University of Virginia fails
to show that Wood had any connection with it.

[530] There seems to be nothing to add to Dobson's biography beyond what De
Morgan has so deliciously set forth.

[531] "Give to each man his due."

[532] Hester Lynch Salusbury (1741-1821), the friend of Dr. Johnson,
married Henry Thrale (1763), a brewer, who died in 1781. She then married
Gabriel Piozzi (1784), an Italian musician. Her _Anecdotes of the late
Samuel Johnson_ (1786) and _Letters to and from Samuel Johnson_ (1788) are
well known. She also wrote numerous essays and poems.

[533] Samuel Pike (c. 1717-1773) was an independent minister, with a chapel
in London and a theological school in his house. He later became a disciple
of Robert Sandeman and left the Independents for the Sandemanian church
(1765). The _Philosophia Sacra_ was first published at London in 1753. De
Morgan here cites the second edition.

[534] Pike had been dead over forty years when Kittle published this second
edition. Kittle had already published a couple of works: _King Solomon's
portraiture of Old Age_ (Edinburgh, 1813), and _Critical and Practical
Lectures on the Apocalyptical Epistles to the Seven Churches of Asia Minor_
(London, 1814).

[535] See note 334, on page 152.

[536] William Stukely (1687-1765) was a fellow of the Royal Society and of
the College of Physicians and Surgeons. He afterwards (1729) entered the
Church. He was prominent as an antiquary, especially in the study of the
Roman and Druidic remains of Great Britain. He was the author of numerous
works, chiefly on paleography.

[537] William Jones (1726-1800), who should not be confused with his
namesake who is mentioned in note 281 on page 135. He was a lifelong friend
of Bishop Horne, and his vicarage at Nayland was a meeting place of an
influential group of High Churchmen. Besides the _Physiological
Disquisitions_ (1781) he wrote _The Catholic Doctrine of the Trinity_
(1756) and _The Grand Analogy_ (1793).

[538] Robert Spearman (1703-1761) was a pupil of John Hutchinson, and not
only edited his works but wrote his life. He wrote a work against the
Newtonian physics, entitled _An Enquiry after Philosophy and Theology_
(Edinburgh, 1755), besides the _Letters to a Friend concerning the
Septuagint Translation_ (Edinburgh, 1759) to which De Morgan refers.

[539] A writer of no importance, at least in the minds of British
biographers.

[540] Alexander Catcott (1725-1779), a theologian and geologist, wrote not
only a work on the creation (1756) but a _Treatise on the Deluge_ (1761,
with a second edition in 1768). Sir Charles Lyell considered the latter
work a valuable contribution to geology.

[541] James Robertson (1714-1795), professor of Hebrew at the University of
Edinburgh. Probably De Morgan refers to his _Grammatica Linguae Hebrææ_
(Edinburgh, 1758; with a second edition in 1783). He also wrote _Clavis
Pentateuchi_ (1770).

[542] Benjamin Holloway (c. 1691-1759), a geologist and theologian. He
translated Woodward's _Naturalis Historia Telluris_, and was introduced by
Woodward to Hutchinson. The work referred to by De Morgan appeared at
Oxford in two volumes in 1754.

[543] His work was _The Christian plan exhibited in the interpretation of
Elohim: with observations upon a few other matters relative to the same
subject_, Oxford, 1752, with a second edition in 1755.

[544] Duncan Forbes (1685-1747) studied Oriental languages and Civil law at
Leyden. He was Lord President of the Court of Sessions (1737). He wrote a
number of theological works.

[545] Should be 1756.

[546] Edward Henry Bickersteth (1825-1906), bishop of Exeter (1885-1900);
published _The Rock of Ages; or scripture testimony to the one Eternal
Godhead of the Father, and of the Son, and of the Holy Ghost_ at Hampstead
in 1859. A second edition appeared at London in 1860.

[547] Thomas Sadler (1822-1891) took his Ph.D. at Erlangen in 1844, and
became a Unitarian minister at Hampstead, where Bickersteth's work was
published. Besides writing the _Gloria Patri_ (1859), he edited Crabb
Robinson's Diaries.

[548] This was his _Virgil's Bucolics and the two first Satyrs of Juvenal_,
1634.

[549] Possibly in his _Twelve Questions or Arguments drawn out of
Scripture, wherein the commonly received Opinion touching the Deity of the
Holy Spirit is clearly and fully refuted_, 1647. This was his first
heretical work, and it was followed by a number of others that were written
during the intervals in which the Puritan parliament allowed him out of
prison. It was burned by the hangman as blasphemous. Biddle finally died in
prison, unrepentant to the last.

[550] The first edition of the anonymous [Greek: Haireseôn anastasis] (by
Vicars?) appeared in 1805.

[551] Possibly by Thomas Pearne (c. 1753-1827), a fellow of St. Peter's
College, Cambridge, and a Unitarian minister.

[552] Thomas Wentworth, Earl of Strafford, was borne in London in 1593, and
was executed there in 1641. He was privy councilor to Charles I, and was
Lord Deputy of Ireland. On account of his repressive measures to uphold the
absolute power of the king he was impeached by the Long Parliament and was
executed for treason. The essence of his defence is in the sentence quoted
by De Morgan, to which Pym replied that taken as a whole, the acts tended
to show an intention to change the government, and this was in itself
treason.

[553] The name assumed by a writer who professed to give a mathematical
explanation of the Trinity, see farther on.--S. E. De M.

[554] Sabellius (fl. 230 A.D.) was an early Christian of Libyan origin. He
taught that Father, Son, and Holy Spirit were different names for the same
person.

[555] Sir Richard Phillips was born in London in 1767 (not 1768 as stated
above), and died there in 1840. He was a bookseller and printer in
Leicester, where he also edited a radical newspaper. He went to London to
live in 1795 and started the _Monthly Magazine_ there in 1796. Besides the
works mentioned by De Morgan he wrote on law and economics.

[556] It was really eighteen months.

[557] While he was made sheriff in 1807 he was not knighted until the
following year.

[558] James Mitchell (c. 1786-1844) was a London actuary, or rather a
Scotch actuary living a good part of his life in London. Besides the work
mentioned he compiled a _Dictionary of Chemistry, Mineralogy, and Geology_
(1823), and wrote _On the Plurality of Worlds_ (1813) and _The Elements of
Astronomy_ (1820).

[559] Richarda Smith, wife of Sir George Biddell Airy (see note 129, page
85) the astronomer. In 1835 Sir Robert Peel offered a pension of £300 a
year to Airy, who requested that it be settled on his wife.

[560] Mary Fairfax (1780-1872) married as her second husband Dr. William
Somerville. In 1826 she presented to the Royal Society a paper on _The
Magnetic Properties of the Violet Rays of the Solar Spectrum_, which
attracted much attention. It was for her _Mechanism of the Heavens_ (1831),
a popular translation of Laplace's _Mécanique Céleste_, that she was
pensioned.

[561] Dominique François Jean Arago (1786-1853) the celebrated French
astronomer and physicist.

[562] For there is a well-known series

  1 + 1/2^2 + 1/3^2 + ... = [pi]^2/6.

If, therefore, the given series equals 1, we have

  2 = 1/6 [pi]^2

  or [pi]^2 = 12,

  whence [pi] = 2 [root]3.

But c = [pi]d, and twice the diagonal of a cube on the diameter is 2d
[root]3.

[563] There was a second edition in 1821.

[564] London, 1830.

[565] He was a resident of Chatham, and seems to have published no other
works.

[566] Richard Whately (1787-1863) was, as a child, a calculating prodigy
(see note 132, page 86), but lost the power as is usually the case with
well-balanced minds. He was a fellow of Oriel College, Oxford, and in 1825
became principal of St. Alban Hall. He was a friend of Newman, Keble, and
others who were interested in the religious questions of the day. He became
archbishop of Dublin in 1831. He was for a long time known to students
through his _Logic_ (1826) and _Rhetoric_ (1828).

[567] William King, D.C.L. (1663-1712), student at Christ Church, Oxford,
and celebrated as a wit and scholar. His _Dialogues of the Dead_ (1699) is
a satirical attack on Bentley.

[568] Thomas Ebrington (1760-1835) was a fellow of Trinity College, Dublin,
and taught divinity, mathematics, and natural philosophy there. He became
provost of the college in 1811, bishop of Limerick in 1820, and bishop of
Leighlin and Ferns in 1822. His edition of Euclid was reprinted a dozen
times. The _Reply to John Search's Considerations on the Law of Libel_
appeared at Dublin in 1834.

[569] Joseph Blanco White (1775-1841) was the son of an Irishman living in
Spain. He was born at Seville and studied for orders there, being ordained
priest in 1800. He lost his faith in the Roman Catholic Church, and gave up
the ministry, escaping to England at the time of the French invasion. At
London he edited _Español_, a patriotic journal extensively circulated in
Spain, and for this service he was pensioned after the expulsion of the
French. He then studied at Oriel College, Oxford, and became intimate with
men like Whately, Newman, and Keble. In 1835 he became a Unitarian. Among
his theological writings is his _Evidences against Catholicism_ (1825). The
"rejoinder" to which De Morgan refers consisted of two letters: _The law of
anti-religious Libel reconsidered_ (Dublin, 1834) and _An Answer to some
Friendly Remarks on "The Law of Anti-Religious Libel Reconsidered"_
(Dublin, 1834).

[570] The work was translated from the French.

[571] J. Hoëné Wronski (1778-1853) served, while yet a mere boy, as an
artillery officer in Kosciusko's army (1791-1794). He was imprisoned after
the battle of Maciejowice. He afterwards lived in Germany, and (after 1810)
in Paris. For the bibliography of his works see S. Dickstein's article in
the _Bibliotheca Mathematica_, vol. VI (2), page 48.

[572] Perhaps referring to his _Introduction à la philosophie des
mathématiques_ (1811).

[573] Read "equation of the."

[574] Thomas Young (1773-1829), physician and physicist, sometimes called
the founder of physiological optics. He seems to have initiated the theory
of color blindness that was later developed by Helmholtz. The attack
referred to was because of his connection with the Board of Longitude, he
having been made (1818) superintendent of the Nautical Almanac and
secretary of the Board. He opposed introducing into the Nautical Almanac
anything not immediately useful to navigation, and this antagonized many
scientists.

[575] Isaac Milner (1750-1820) was professor of natural philosophy at
Cambridge (1783) and later became, as De Morgan states, president of
Queens' College (1788). In 1791 he became dean of Carlisle, and in 1798
Lucasian professor of mathematics. His chief interest was in chemistry and
physics, but he contributed nothing of importance to these sciences or to
mathematics.

[576] Thomas Perronet Thompson (1783-1869), fellow of Queens' College,
Cambridge, saw service in Spain and India, but after 1822 lived in England.
He became major general in 1854, and general in 1868. Besides some works on
economics and politics he wrote a _Geometry without Axioms_ (1830) that De
Morgan includes later on in his _Budget_. In it Thompson endeavored to
prove the parallel postulate.

[577] De Morgan's father-in-law. See note 441, page 196.

[578] Johann Friedrich Herbart (1776-1841), successor of Kant as professor
of philosophy at Königsberg (1809-1833), where he established a school of
pedagogy. From 1833 until his death he was professor of philosophy at
Göttingen. The title of the pamphlet is: _De Attentionis mensura causisque
primariis. Psychologiae principia statica et mechanica exemplo
illustraturus.... Regiomonti,... 1822_. The formulas in question are given
on pages 15 and 17, and De Morgan has omitted the preliminary steps, which
are, for the first one:

  [beta] ([phi] - z) [delta]t = [delta]z

  unde [beta]t= Const / ([phi] - z).

  Pro t = 0 etiam z = 0; hinc [beta]t = log [phi]/([phi] - z).

  z = [phi] (1 - [epsilon]^{-[beta]t});

  et   [delta]z/[delta]t = [beta][phi][epsilon]^{-[beta]t}

These are, however, quite elementary as compared with other portions of the
theory.

[579] See note 371, page 168.

[580] William Law (1686-1761) was a clergyman, a fellow of Emanuel College,
Cambridge, and in later life a convert to Behmen's philosophy. He was so
free in his charities that the village in which he lived became so infested
by beggars that he was urged by the citizens to leave. He wrote _A serious
call to a devout and holy life_ (1728).

[581] He was a curate at Cheshunt, and wrote the _Spiritual voice to the
Christian Church and to the Jews_ (London, 1760), _A second warning to the
world by the Spirit of Prophecy_ (London, 1760), and _Signs of the Times;
or a Voice to Babylon_ (London, 1773).

[582] His real name was Thomas Vaughan (1622-1666). He was a fellow of
Jesus College, Oxford, taking orders, but was deprived of his living on
account of drunkenness. He became a mystic philosopher and gave attention
to alchemy. His works had a large circulation, particularly on the
continent. He wrote _Magia Adamica_ (London, 1650), _Euphrates; or the
Waters of the East_ (London, 1655), and _The Chymist's key to shut, and to
open; or the True Doctrine of Corruption and Generation_ (London, 1657).

[583] Emanuel Swedenborg, or Svedberg (1688-1772) the mystic. It is not
commonly known to mathematicians that he was one of their guild, but he
wrote on both mathematics and chemistry. Among his works are the
_Regelkonst eller algebra_ (Upsala, 1718) and the _Methodus nova inveniendi
longitudines locorum, terra marique, ope lunae_ (Amsterdam, 1721, 1727, and
1766). After 1747 he devoted his attention to mystic philosophy.

[584] Pierre Simon Laplace (1749-1827), whose _Exposition du système du
monde_ (1796) and _Traité de mécanique celeste_ (1799) are well known.

[585] See note 117, page 76.

[586] John Dalton (1766-1844), who taught mathematics and physics at New
College, Manchester (1793-1799) and was the first to state the law of the
expansion of gases known by his name and that of Gay-Lussac. His _New
system of Chemical Philosophy_ (Vol. I, pt. i, 1808; pt. ii, 1810; vol. II,
1827) sets forth his atomic theory.

[587] Howison was a poet and philosopher. He lived in Edinburgh and was a
friend of Sir Walter Scott. This work appeared in 1822.

[588] He was a shoemaker, born about 1765 at Haddiscoe, and his
"astro-historical" lectures at Norwich attracted a good deal of attention
at one time. He traced all geologic changes to differences in the
inclination of the earth's axis to the plane of its orbit. Of the works
mentioned by De Morgan the first appeared at Norwich in 1822-1823, and
there was a second edition in 1824. The second appeared in 1824-1825. The
fourth was _Urania's Key to the Revelation; or the analyzation of the
writings of the Jews..._, and was first published at Norwich in 1823, there
being a second edition at London in 1833. His books were evidently not a
financial success, for Mackey died in an almshouse at Norwich.

[589] Godfrey Higgins (1773-1833), the archeologist, was interested in the
history of religious beliefs and in practical sociology. He wrote _Horae
Sabbaticae_ (1826), _The Celtic Druids_ (1827 and 1829), and _Anacalypsis,
an attempt to draw aside the veil of the Saitic Isis; or an Inquiry into
the Origin of Languages, Nations, and Religions_ (posthumously published,
1836), and other works. See also page 274, _infra_.

[590] The work also appeared in French. Wirgman wrote, or at least began,
two other works: _Divarication of the New Testament into Doctrine and
History; part I, The Four Gospels_ (London, 1830), and _Mental Philosophy;
part I, Grammar of the five senses; being the first step to infant
education_ (London, 1838).

[591] He was born at Shandrum, County Limerick, and supported himself by
teaching writing and arithmetic. He died in an almshouse at Cork.

[592] George Boole (1815-1864), professor of mathematics at Queens'
College, Cork. His _Laws of Thought_ (1854) was the first work on the
algebra of logic.

[593] Oratio Grassi (1582-1654), the Jesuit who became famous for his
controversy with Galileo over the theory of comets. Galileo ridiculed him
in _Il Saggiatore_, although according to the modern view Grassi was the
more nearly right. It is said that the latter's resentment led to the
persecution of Galileo.

[594] De Morgan might have found much else for his satire in the letters of
Walsh. He sought, in his _Theory of Partial Functions_, to substitute
"partial equations" for the differential calculus. In his diary there is an
entry: "Discovered the general solution of numerical equations of the fifth
degree at 114 Evergreen Street, at the Cross of Evergreen, Cork, at nine
o'clock in the forenoon of July 7th, 1844; exactly twenty-two years after
the invention of the Geometry of Partial Equations, and the expulsion of
the differential calculus from Mathematical Science."

[595] "It has been ordered, sir, it has been ordered."

[596] Bartholomew Prescot was a Liverpool accountant. De Morgan gives this
correct spelling on page 278. He died after 1849. His _Inverted Scheme of
Copernicus_ appeared in Liverpool in 1822.

[597] Robert Taylor (1784-1844) had many more ups and downs than De Morgan
mentions. He was a priest of the Church of England, but resigned his parish
in 1818 after preaching against Christianity. He soon recanted and took
another parish, but was dismissed by the Bishop almost immediately on the
ground of heresy. As stated in the text, he was convicted of blasphemy in
1827 and was sentenced to a year's imprisonment, and again for two years on
the same charge in 1831. He then married a woman who was rich in money and
in years, and was thereupon sued for breach of promise by another woman. To
escape paying the judgment that was rendered against him he fled to Tours
where he took up surgery.

[598] Herbert Marsh, Bishop of Peterborough. See note 449 on page 199.

[599] "Argument from the prison."

[600] Richard Carlile (1790-1843), one of the leading radicals of his time.
He published Hone's parodies (see note 250, page 124) after they had been
suppressed, and an edition of Thomas Paine (1818). He was repeatedly
imprisoned, serving nine years in all. His continued conflict with the
authorities proved a good advertisement for his bookshop.

[601] Wilhelm Ludwig Christmann (1780-1835) was a protestant clergyman and
teacher of mathematics. For a while he taught under Pestalozzi.
Disappointed in his ambition to be professor of mathematics at Tubingen, he
became a confirmed misanthrope and is said never to have left his house
during the last ten years of his life. He wrote several works: _Ein Wort
über Pestalozzi und Pestalozzismus_ (1812); _Ars cossae promota_ (1814);
_Philosophia cossica_ (1815); _Aetas argentea cossae_ (1819); _Ueber
Tradition und Schrift, Logos und Kabbala_ (1829), besides the one mentioned
above. The word _coss_ in the above titles was a German name for algebra,
from the Italian _cosa_ (thing), the name for the unknown quantity. It
appears in English in the early name for algebra, "the cossic art."

[602] See note 174, page 101.

[603] See note 589, page 257.

[604] He seems to have written nothing else.

[605] See note 596 on page 270. The name is here spelled correctly.

[606] Joseph Jacotot (1770-1840), the father of this Fortuné Jacotot, was
an infant prodigy. At nineteen he was made professor of the humanities at
Dijon. He served in the army, and then became professor of mathematics at
Dijon. He continued in his chair until the restoration of the Bourbons, and
then fled to Louvain. It was here that he developed the method with which
his name is usually connected. He wrote a _Mathématiques_ in 1827, which
went through four editions. The _Epitomé_ is by his son, Fortuné.

[607] He wrote on educational topics and a _Sacred History_ that went
through several editions.

[608] "All is in all."

[609] "Know one thing and refer everything else to it," as it is often
translated.

[610] A writer of no reputation.

[611] Sir John Lubbock (1803-1865), banker, scientist, publicist,
astronomer, one of the versatile men of his time.

[612] See note 165, page 99.

[613] "Those about to die salute you."

[614] Georges Louis Leclerc Buffon (1707-1788), the well-known biologist.
He also experimented with burning mirrors, his results appearing in his
_Invention des miroirs ardens pour brûler à une grande distance_ (1747).
The reference here may be to his _Resolution des problèmes qui regardent le
jeu du franc carreau_ (1733). The prominence of his _Histoire naturelle_
(36 volumes, 1749-1788) has overshadowed the credit due to him for his
translation of Newton's work on Fluxions.

[615] See page 285. This article was a supplement to No. 14 in the
_Athenæum_ Budget.--A. De M.

[616] There are many similar series and products. Among the more
interesting are the following:

  [pi]   2·2·4·4·6·6·8...
  ---- = ----------------,
    2    1·3·3·5·5·7·7...

  [pi]-3  =   1       1       1
  ------  = ----- - ----- + ----- - ...,
    4       2·3·4   4·5·6   6·7·8

  [pi]        1         1      1       1       1
  ---- = sqrt - · (1 - --- + ----- - ----- + ----- - ...),
    6         3        3·3   3^2·5   3^3·7   3^4·9

  [pi]       1     1       1       1
  ---- = 4 ( - - ----- + ----- - ----- + ...)
   4         5   3·5^3   5·5^5   7·5^7

              1       1         1
         - ( --- - ------- + ------- - ...).
             239   3·239^3   5·239^5

[617] "To a privateer, a privateer and a half."

[618] Joshua Milne (1776-1851) was actuary of the Sun Life Assurance
Society. He wrote _A Treatise on the Valuation of Annuities and Assurances
on Lives and Survivorships; on the Construction of tables of mortality; and
on the Probabilities and Expectations of Life_, London, 1815. Upon the
basis of the Carlisle bills of mortality of Dr. Heysham he reconstructed
the mortality tables then in use and which were based upon the Northampton
table of Dr. Price. His work revolutionized the actuarial science of the
time. In later years he devoted his attention to natural history.

[619] See note 576, page 252. He also wrote the _Theory of Parallels. The
proof of Euclid's axiom looked for in the properties of the equiangular
spiral_ (London, 1840), which went through four editions, and the _Theory
of Parallels. The proof that the three angles of a triangle are equal to
two right angles looked for in the inflation of the sphere_ (London, 1853),
of which there were three editions.

[620] For the latest summary, see W. B. Frankland, _Theories of
Parallelism, an historical critique_, Cambridge, 1910.

[621] Joseph Louis Lagrange (1736-1813), author of the _Mécanique
analytique_ (1788), _Théorie des functions analytiques_ (1797), _Traité de
la résolution des équations numériques de tous degrés_ (1798), _Leçons sur
le calcul des fonctions_ (1806), and many memoirs. Although born in Turin
and spending twenty of his best years in Germany, he is commonly looked
upon as the great leader of French mathematicians. The last twenty-seven
years of his life were spent in Paris, and his remarkable productivity
continued to the time of his death. His genius in the theory of numbers was
probably never excelled except by Fermat. He received very high honors at
the hands of Napoleon and was on the first staff of the Ecole polytechnique
(1797).

[622] "I shall have to think it over again."

[623] Henry Goulburn (1784-1856) held various government posts. He was
under-secretary for war and the colonies (1813), commissioner to negotiate
peace with America (1814), chief secretary to the Lord Lieutenant of
Ireland (1821), and several times Chancellor of the Exchequer. On the
occasion mentioned by De Morgan he was standing for parliament, and was
successful.

[624] On Drinkwater Bethune see note 165, page 99.

[625] Charles Henry Cooper (1808-1866) was a biographer and antiquary. He
was town clerk of Cambridge (1849-1866) and wrote the _Annals of Cambridge_
(1842-1853). His _Memorials of Cambridge_ (1874) appeared after his death.
Thompson Cooper was his son, and the two collaborated in the _Athenae
Cantabrigiensis_ (1858).

[626] William Yates Peel (1789-1858) was a brother of Sir Robert Peel, he
whose name degenerated into the familiar title of the London "Bobby" or
"Peeler." Yates Peel was a member of parliament almost continuously from
1817 to 1852. He represented Cambridge at Westminster from 1831 to 1835.

[627] Henry John Temple, third Viscount of Palmerston (1784-1865), was
member for Cambridge in 1811, 1818, 1820, 1826 (defeating Goulburn), and
1830. He failed of reelection in 1831 because of his advocacy of reform.
This must have been the time when Goulburn defeated him. He was Foreign
Secretary (1827) and Secretary of State for Foreign Affairs (1830-1841, and
1846-1851). It is said of him that he "created Belgium, saved Portugal and
Spain from absolutism, rescued Turkey from Russia and the highway to India
from France." He was Prime Minister almost continuously from 1855 to 1865,
a period covering the Indian Mutiny and the American Civil War.

[628] William Cavendish, seventh Duke of Devonshire (1808-1891). He was
member for Cambridge from 1829 to 1831, but was defeated in 1831 because he
had favored parliamentary reform. He became Earl of Burlington in 1834, and
Duke of Devonshire in 1858. He was much interested in the promotion of
railroads and in the iron and steel industries.

[629] Richard Sheepshanks (1794-1855) was a brother of John Sheepshanks the
benefactor of art. (See note 314, p. 147.) He was a fellow of Trinity
College, Cambridge, a fellow of the Royal Society and secretary of the
Astronomical Society. Babbage (See note 469, p. 207) suspected him of
advising against the government support of his calculating machine and
attacked him severely in his _Exposition of 1851_, in the chapter on _The
Intrigues of Science_. Babbage also showed that Sheepshanks got an
astronomical instrument of French make through the custom house by having
Troughton's (See note 332, page 152) name engraved on it. Sheepshanks
admitted this second charge, but wrote a _Letter in Reply to the Calumnies
of Mr. Babbage_, which was published in 1854. He had a highly controversial
nature.

[630] See note 469, page 207. The work referred to is _Passages from the
Life of a Philosopher_, London, 1864.

[631] Drinkwater Bethune. See note 165, page 99.

[632] Siméon-Denis Poisson (1781-1840) was professor of calculus and
mechanics at the Ecole polytechnique. He was made a baron by Napoleon, and
was raised to the peerage in 1837. His chief works are the _Traité de
mécanìque_ (1811) and the _Traité mathématique de la chaleur_ (1835).

[633] "As to M. Poisson, I really wish I had a thousandth part of his
mathematical knowledge that I might prove my system to the incredulous."

[634] This list includes most of the works of Antoine-Louis-Guénard
Demonville. There was also the _Nouveau système du monde ... et hypothèses
conformes aux expériences sur les vents, sur la lumière et sur le fluide
électro-magnétique_, Paris, 1830.

[635] Paris, 1835.

[636] Paris, 1833.

[637] The second part appeared in 1837. There were also editions in 1850
and 1852, and one edition appeared without date.

[638] Paris, 1842.

[639] Parsey also wrote _The Art of Miniature Painting on Ivory_ (1831),
_Perspective Rectified_ (1836), and _The Science of Vision_ (1840), the
third being a revision of the second.

[640] William Ritchie (1790-1837) was a physicist who had studied at Paris
under Biot and Gay-Lussac. He contributed several papers on electricity,
heat, and elasticity, and was looked upon as a good experimenter. Besides
the geometry he wrote the _Principles of the Differential and Integral
Calculus_ (1836).

[641] Alfred Day (1810-1849) was a man who was about fifty years ahead of
his time in his attempt to get at the logical foundations of geometry. It
is true that he laid himself open to criticism, but his work was by no
means bad. He also wrote _A Treatise on Harmony_ (1849, second edition
1885), _The Rotation of the Pendulum_ (1851), and several works on Greek
and Latin Grammar.

[642] Walter Forman wrote a number of controversial tracts. His first seems
to have been _A plan for improving the Revenue without adding to the
burdens of the people_, a letter to Canning in 1813. He also wrote _A New
Theory of the Tides_ (1822). His _Letter to Lord John Russell, on Lord
Brougham's most extraordinary conduct; and another to Sir J. Herschel, on
the application of Kepler's third law_ appeared in 1832.

[643] Lord John Russell (1792-1878) first Earl Russell, was one of the
strongest supporters of the reform measures of the early Victorian period.
He became prime minister in 1847, and again in 1865.

[644] Lauder seems never to have written anything else.

[645] See note 22, page 40.

[646] The names of Alphonso Cano de Molina, Yvon, and Robert Sara have no
standing in the history of the subject beyond what would be inferred from
De Morgan's remark.

[647] Claude Mydorge (1585-1647), an intimate friend of Descartes, was a
dilletante in mathematics who read much but accomplished little. His
_Récréations mathématiques_ is his chief work. Boncompagni published the
"Problèmes de Mydorge" in his _Bulletino_.

[648] Claude Hardy was born towards the end of the 16th century and died at
Paris in 1678. In 1625 he edited the _Data Euclidis_, publishing the Greek
text with a Latin translation. He was a friend of Mydorge and Descartes,
but an opponent of Fermat.

[649] That is, in the _Bibliotheca Realis_ of Martin Lipen, or Lipenius
(1630-1692), which appeared in six folio volumes, at Frankfort, 1675-1685.

[650] See note 29, page 43.

[651] Baldassare Boncompagni (1821-1894) was the greatest general collector
of mathematical works that ever lived, possibly excepting Libri. His
magnificent library was dispersed at his death. His _Bulletino_ (1868-1887)
is one of the greatest source books on the history of mathematics that we
have. He also edited the works of Leonardo of Pisa.

[652] He seems to have attracted no attention since De Morgan's search, for
he is not mentioned in recent bibliographies.

[653] Joseph-Louis Vincens de Mouléon de Causans was born about the
beginning of the l8th century. He was a Knight of Malta, colonel in the
infantry, prince of Conti, and governor of the principality of Orange. His
works on geometry are the _Prospectus apologétique pour la quadrature du
cercle_ (1753), and _La vraie géométrie transcendante_ (1754).

[654] See note 119, page 80.

[655] See note 120, page 81.

[656] Lieut. William Samuel Stratford (1791-1853), was in active service
during the Napoleonic wars but retired from the army in 1815. He was first
secretary of the Astronomical Society (1820) and became superintendent of
the Nautical Almanac in 1831. With Francis Baily he compiled a star
catalogue, and wrote on Halley's (1835-1836) and Encke's (1838) comets.

[657] See Sir J. Herschel's _Astronomy_, p. 369.--A. De M.

[658] Captain Ross had just stuck a bit of brass there.--A. De M.

Sir James Clark Ross (1800-1862) was a rear admiral in the British navy and
an arctic and antarctic explorer of prominence. De Morgan's reference is to
Ross's discovery of the magnetic pole on June 1, 1831. In 1838 he was
employed by the Admiralty on a magnetic survey of the United Kingdom. He
was awarded the gold medal of the geographical societies of London and
Paris in 1842.

[659] John Partridge (1644-1715), the well-known astrologer and almanac
maker. Although bound to a shoemaker in his early boyhood, he had acquired
enough Latin at the age of eighteen to read the works of the astrologers.
He then mastered Greek and Hebrew and studied medicine. In 1680 he began
the publication of his almanac, the _Merlinus Liberatus_, a book that
acquired literary celebrity largely through the witty comments upon it by
such writers as Swift and Steele.

[660] See note 642 on page 296.

[661] William Woodley also published several almanacs (1838, 1839, 1840)
after his rejection by the Astronomical Society in 1834.

[662] It appeared at London.

[663] The first edition appeared in 1830, also at London.

[664] See note 441, page 196.

[665] Thomas Kerigan wrote _The Young Navigator's Guide to the siderial and
planetary parts of Nautical Astronomy_ (London, 1821, second edition 1828),
a work on eclipses (London, 1844), and the work on tides (London, 1847) to
which De Morgan refers.

[666] Jean Sylvain Bailly, who was guillotined. See note 365, page 166.

[667] See note 670, page 309.

[668] Laurent seems to have had faint glimpses of the modern theory of
matter. He is, however, unknown.

[669] See note 133, page 87.

[670] Francis Baily (1774-1844) was a London stockbroker. His interest in
science in general and in astronomy in particular led to his membership in
the Royal Society and to his presidency of the Astronomical Society. He
wrote on interest and annuities (1808), but his chief works were on
astronomy.

[671] If the story is correctly told Baily must have enjoyed his statement
that Gauss was "the oldest mathematician now living." As a matter of fact
he was then only 58, three years the junior of Baily himself. Gauss was
born in 1777 and died in 1855, and Baily was quite right in saying that he
was "generally thought to be the greatest" mathematician then living.

[672] Margaret Cooke, who married Flamsteed in 1692.

[673] John Brinkley (1763-1835), senior wrangler, first Smith's prize-man
(1788), Andrews professor of astronomy at Dublin, first Astronomer Royal
for Ireland (1792), F.R.S. (1803), Copley medallist, president of the Royal
Society and Bishop of Cloyne. His _Elements of Astronomy_ appeared in 1808.

[674] See note 248, page 124.

[675] See note 276, page 133.

[676] See note 352, page 161.

[677] "It becomes the doctors of the Sorbonne to dispute, the Pope to
decree, and the mathematician to go to Paradise on a perpendicular line."

[678] See note 124, page 83.

[679] See note 621, page 288.

[680] Sylvain van de Weyer, who was born at Louvain in 1802. He was a
jurist and statesman, holding the portfolio for foreign affairs
(1831-1833), and being at one time ambassador to England.

[681] Henry Crabb Robinson (1775-1867), correspondent of the _Times_ at
Altona and in the Peninsula, and later foreign editor. He was one of the
founders of the Athenæum Club and of University College, London. He seems
to have known pretty much every one of his day, and his posthumous _Diary_
attracted attention when it appeared.

[682] Was this Whewell, who was at Trinity from 1812 to 1816 and became a
fellow in 1817?

[683] Tom Cribb (1781-1848) the champion pugilist. He had worked as a coal
porter and hence received his nickname, the Black Diamond.

[684] John Finleyson, or Finlayson, was born in Scotland in 1770 and died
in London in 1854. He published a number of pamphlets that made a pretense
to being scientific. Among his striking phrases and sentences are the
statements that the stars were made "to amuse us in observing them"; that
the earth is "not shaped like a garden turnip as the Newtonians make it,"
and that the stars are "oval-shaped immense masses of frozen water." The
first edition of the work here mentioned appeared at London in 1830.

[685] Richard Brothers (1757-1824) was a native of Newfoundland. He went to
London when he was about 30, and a little later set forth his claim to
being a descendant of David, prince of the Hebrews, and ruler of the world.
He was confined as a criminal lunatic in 1795 but was released in 1806.

[686] Charles Grey (1764-1845), second Earl Grey, Viscount Howick, was then
Prime Minister. The Reform Bill was introduced and defeated in 1831. The
following year, with the Royal guarantees to allow him to create peers, he
finally carried the bill in spite of "the number of the beast."

[687] The letters of obscure men, the _Epistolæ obscurorum virorum ad
venerabilem virum Magistrum Ortuinum Gratium Dauentriensem_, by Joannes
Crotus, Ulrich von Hutten, and others appeared at Venice about 1516.

[688] The lamentations of obscure men, the _Lamentationes obscurorum
virorum, non prohibete per sedem Apostolicam. Epistola D. Erasmi
Roterodami: quid de obscuris sentiat_, by G. Ortwinus, appeared at Cologne
in 1518.

[689] The criticism was timely when De Morgan wrote it. At present it would
have but little force with respect to the better class of algebras.

[690] Thomas Ignatius Maria Forster (1789-1860) was more of a man than one
would infer from this satire upon his theory. He was a naturalist,
astronomer, and physiologist. In 1812 he published his _Researches about
Atmospheric Phenomena_, and seven years later (July 3, 1819) he discovered
a comet. With Sir Richard Phillips he founded a Meteorological Society, but
it was short lived. He declined a fellowship in the Royal Society because
he disapproved of certain of its rules, so that he had a recognized
standing in his day. The work mentioned by De Morgan is the second edition,
the first having appeared at Frankfort on the Main in 1835 under the title,
_Recueil des ouvrages et des pensées d'un physicien et metaphysicien_.

[691] Zadkiel, whose real name was Richard James Morrison (1795-1874), was
in his early years an officer in the navy. In 1831 he began the publication
of the _Herald of Astrology_, which was continued as _Zadkiel's Almanac_.
His name became familiar throughout Great Britain as a result.

[692] See note 566, page 246.

[693] Sumner (1780-1862) was an Eton boy. He went to King's College,
Cambridge, and was elected fellow in 1801. He took many honors, and in 1807
became M.A. He was successively Canon of Durham (1820), Bishop of Chester
(1828), and Archbishop of Canterbury (1848). Although he voted for the
Catholic Relief Bill (1829) and the Reform Bill (1832), he opposed the
removal of Jewish disabilities.

[694] Charles Richard Sumner (1790-1874) was not only Bishop of Winchester
(1827), but also Bishop of Llandaff and Dean of St. Paul's, London (1826).
He lost the king's favor by voting for the Catholic Relief Bill.

[695] John Bird Sumner, brother of Charles Richard.

[696] Thomas Musgrave (1788-1860) became Fellow of Trinity in 1812, and
senior proctor in 1831. He was also Dean of Bristol.

[697] Charles Thomas Longley (1794-1868) was educated at Westminster School
and at Christ Church, Oxford. He became M.A. in 1818 and D.D. in 1829.
Besides the bishoprics mentioned he was Bishop of Ripon (1836-1856), and
before that was headmaster of Harrow (1829-1836).

[698] Thomson (1819-1890) was scholar and fellow of Queen's College,
Oxford. He became chaplain to the Queen in 1859.

[699] This is worthy of the statistical psychologists of the present day.

[700] The famous Moon Hoax was written by Richard Adams Locke, who was born
in New York in 1800 and died in Staten Island in 1871. He was at one time
editor of the _Sun_, and the Hoax appeared in that journal in 1835. It was
reprinted in London (1836) and Germany, and was accepted seriously by most
readers. It was published in book form in New York in 1852 under the title
_The Moon Hoax_. Locke also wrote another hoax, the _Lost Manuscript of
Mungo Park_, but it attracted relatively little attention.

[701] It is true that Jean-Nicolas Nicollet (1756-1843) was at that time in
the United States, but there does not seem to be any very tangible evidence
to connect him with the story. He was secretary and librarian of the Paris
observatory (1817), member of the Bureau of Longitudes (1822), and teacher
of mathematics in the Lycée Louis-le-Grand. Having lost his money through
speculations he left France for the United States in 1831 and became
connected with the government survey of the Mississippi Valley.

[702] This was Alexis Bouvard (1767-1843), who made most of the
computations for Laplace's _Mécanique céleste_ (1793). He discovered eight
new comets and calculated their orbits. In his tables of Uranus (1821) he
attributed certain perturbations to the presence of an undiscovered planet,
but unlike Leverrier and Adams he did not follow up this clue and thus
discover Neptune.

[703] Patrick Murphy (1782-1847) awoke to find himself famous because of
his natural guess that there would be very cold weather on January 20,
although that is generally the season of lowest temperature. It turned out
that his forecasts were partly right on 168 days and very wrong on 197
days.

[704] He seems to have written nothing else. If one wishes to enter into
the subject of the mathematics of the Great Pyramid there is an extensive
literature awaiting him. Richard William Howard Vyse (1784-1853) published
in 1840 his _Operations carried on at the Pyramids of Gizeh in 1837_, and
in this he made a beginning of a scientific metrical study of the subject.
Charles Piazzi Smyth (1819-1900), astronomer Royal for Scotland (1845-1888)
was much carried away with the number mysticism of the Great Pyramid, so
much so that he published in 1864 a work entitled _Our Inheritance in the
Great Pyramid_, in which his vagaries were set forth. Although he was then
a Fellow of the Royal Society (1857), his work was so ill received that
when he offered a paper on the subject it was rejected (1874) and he
resigned in consequence of this action. The latest and perhaps the most
scholarly of all investigators of the subject is William Matthew Flinders
Petrie (born in 1853), Edwards professor of Egyptology at University
College, London, whose _Pyramids and Temples of Gizeh_ (1883) and
subsequent works are justly esteemed as authorities.

[705] As De Morgan subsequently found, this name reversed becomes Oliver
B...e, for Oliver Byrne, one of the odd characters among the minor
mathematical writers of the middle of the last century. One of his most
curious works is _The first six Books of the Elements of Euclid; in which
coloured diagrams and symbols are used instead of letters_ (1847). There is
some merit in speaking of the red triangle instead of the triangle ABC, but
not enough to give the method any standing. His _Dual Arithmetic_
(1863-1867) was also a curious work.

[706] Brenan also wrote on English composition (1829), a work that went
through fourteen editions by 1865; a work entitled _The Foreigner's English
Conjugator_ (1831), and a work on the national debt.

[707] See note 211, page 112.

[708] See note 592, page 261.

[709] Sir William Rowan Hamilton (1805-1865), the discoverer of quaternions
(1852), was an infant prodigy, competing with Zerah Colburn as a child. He
was a linguist of remarkable powers, being able, at thirteen years of age,
to boast that he knew as many languages as he had lived years. When only
sixteen he found an error in Laplace's _Mécanique céleste_. When only
twenty-two he was appointed Andrews professor of astronomy, and he soon
after became Astronomer Royal of Ireland. He was knighted in 1835. His
earlier work was on optics, his _Theory of Systems of Rays_ appearing in
1823. In 1827 he published a paper on the principle of _Varying Action_. He
also wrote on dynamics.

[710] "Let him not leave the kingdom,"--a legal phrase.

[711] Probably De Morgan is referring to Johann Bernoulli III (1744-1807),
who edited Lambert's _Logische und philosophische Abhandlungen_, Berlin,
1782. He was astronomer of the Academy of Sciences at Berlin.

[712] Jacob Bernoulli (1654-1705) was one of the two brothers who founded
the famous Bernoulli family of mathematicians, the other being Johann I.
His _Ars conjectandi_ (1713), published posthumously, was the first
distinct treatise on probabilities.

[713] Johann Heinrich Lambert (1728-1777) was one of the most learned men
of his time. Although interested chiefly in mathematics, he wrote also on
science, logic, and philosophy.

[714] Joseph Diez Gergonne (1771-1859), a soldier under Napoleon, and
founder of the _Annales de mathématiques_ (1810).

[715] Gottfried Ploucquet (1716-1790) was at first a clergyman, but
afterwards became professor of logic at Tübingen.

[716] "In the premises let the middle term be omitted; what remains
indicates the conclusion."

[717] Probably Sir William Edmond Logan (1789-1875), who became so
interested in geology as to be placed at the head of the geological survey
of Canada (1842). The University of Montreal conferred the title LL.D. upon
him, and Napoleon III gave him the cross of the Legion of Honor.

[718] "So strike that he may think himself to die."

[719] "Witticism or piece of stupidity."

[720] A very truculently unjust assertion: for Sir W. was as great a setter
up of some as he was a puller down of others. His writings are a congeries
of praises and blames, both _cruel smart_, as they say in the States. But
the combined instigation of prose, rhyme, and retort would send Aristides
himself to Tartarus, if it were not pretty certain that Minos would grant a
_stet processus_ under the circumstances. The first two verses are
exaggerations standing on a basis of truth. The fourth verse is quite true:
Sir W. H. was an Edinburgh Aristotle, with the difference of ancient and
modern Athens well marked, especially the _perfervidum ingenium
Scotorum_.--A. De M.

[721] See note 576, p. 252. There was also a _Theory of Parallels_ that
differed from these, London, 1853, second edition 1856, third edition 1856.

[722] The work was written by Robert Chambers (1802-1871), the Edinburgh
publisher, a friend of Scott and of many of his contemporaries in the
literary field. He published the _Vestiges of the Natural History of
Creation_ in 1844, not 1840.

[723] Everett (1784-1872) was at that time a good Wesleyan, but was
expelled from the ministry in 1849 for having written _Wesleyan Takings_
and as under suspicion for having started the _Fly Sheets_ in 1845. In 1857
he established the United Methodist Free Church.

[724] Smith was a Primitive Methodist preacher. He also wrote an _Earnest
Address to the Methodists_ (1841) and _The Wealth Question_ (1840?).

[725] He wrote the _Nouveau traité de Balistique_, Paris, 1837.

[726] Joseph Denison, known to fame only through De Morgan. See also page
353.

[727] The radical (1784?-1858), advocate of the founding of London
university (1826), of medical reform (1827-1834), and of the repeal of the
duties on newspapers and corn, and an ardent champion of penny postage.

[728] I. e., Roman Catholic Priest.

[729] Murphy (1806-1843) showed extraordinary powers in mathematics even
before the age of thirteen. He became a fellow of Caius College, Cambridge,
in 1829, dean in 1831, and examiner in mathematics in London University in
1838.

[730] See note 442, page 196.

[731] Sir John Bowring (1792-1872), the linguist, writer, and traveler,
member of many learned societies and a writer of high reputation in his
time. His works were not, however, of genuine merit.

[732] Joseph Hume (1777-1855) served as a surgeon with the British army in
India early in the nineteenth century. He returned to England in 1808 and
entered parliament as a radical in 1812. He was much interested in all
reform movements.

[733] Sir Robert Harry Inglis (1786-1855), a strong Tory, known for his
numerous addresses in the House of Commons rather than for any real
ability.

[734] Sir Robert Peel (1788-1850) began his parliamentary career in 1809
and was twice prime minister. He was prominent in most of the great reforms
of his time.

[735] See note 627, page 290.

[736] John Taylor (1781-1864) was a publisher, and published several
pamphlets opposed to Peel's currency measures. De Morgan refers to his work
on the Junius question. This was done early in his career, and resulted in
_A Discovery of the author of the Letters of Junius_ (1813), and _The
Identity of Junius with a distinguished living character established_
(1816), this being Sir Philip Francis.

[737] See note 665, page 308.

[738] See page 348.

[739] See note 348, page 160.

[740] Sir Nicholas Harris Nicolas (1799-1848) was a reformer in various
lines,--the Record Commission, the Society of Antiquaries, and the British
Museum,--and his work was not without good results.

[741] See note 98, page 69.

[742] In the _Companion to the Almanac_ for 1845 is a paper by Prof. De
Morgan, "On the Ecclesiastical Calendar," the statements of which, so far
as concerns the Gregorian Calendar, are taken direct from the work of
Clavius, the principal agent in the arrangement of the reformed reckoning.
This was followed, in the _Companion to the Almanac_ for 1846, by a second
paper, by the same author, headed "On the Earliest Printed Almanacs," much
of which is written in direct supplement to the former article.--S. E. De
Morgan.

[743] It may be necessary to remind some English readers that in Latin and
its derived European languages, what we call Easter is called the passover
(_pascha_). The Quartadecimans had the _name_ on their side: a possession
which often is, in this world, nine points of the law.--A. De M.

[744] Socrates Scholasticus was born at Constantinople c. 379, and died
after 439. His _Historia Ecclesiastica_ (in Greek) covers the period from
Constantine the Great to about 439, and includes the Council of Nicæa. The
work was printed in Paris 1544.

[745] Theodoretus or Theodoritus was born at Antioch and died about 457. He
was one of the greatest divines of the fifth century, a man of learning,
piety, and judicial mind, and a champion of freedom of opinion in all
religious matters.

[746] He died in 417. He was a man of great energy and of high attainments.

[747] He died in 461, having reigned as pope for twenty-one years. It was
he who induced Attila to spare Rome in 452.

[748] He succeeded Leo as pope in 461, and reigned for seven years.

[749] Victorinus or Victorius Marianus seems to have been born at Limoges.
He was a mathematician and astronomer, and the cycle mentioned by De Morgan
is one of 532 years, a combination of the Metonic cycle of 19 years with
the solar cycle of 28 years. His canon was published at Antwerp in 1633 or
1634, _De doctrina temporum sive commentarius in Victorii Aquitani et
aliorum canones paschales_.

[750] He went to Rome about 497, and died there in 540. He wrote his _Liber
de paschate_ in 525, and it was in this work that the Christian era was
first used for calendar purposes.

[751] See note 259, page 126.

[752] Johannes de Sacrobosco (Holy wood), or John of Holywood. The name was
often written, without regard to its etymology, Sacrobusto. He was educated
at Oxford and taught in Paris until his death (1256). He did much to make
the Hindu-Arabic numerals known to European scholars.

[753] See note 36, page 44.

[754] See note 45, page 48.

[755] The Julian year is a year of the Julian Calendar, in which there is
leap year every fourth year. Its average length is therefore 365 days and a
quarter.--A. De M.

[756] Ugo Buoncompagno (1502-1585) was elected pope in 1572.

[757] He was a Calabrian, and as early as 1552 was professor of medicine at
Perugia. In 1576 his manuscript on the reform of the calendar was presented
to the Roman Curia by his brother, Antonius. The manuscript was not printed
and it has not been preserved.

[758] The title of this work, which is the authority on all points of the
new Calendar, is _Kalendarium Gregorianum Perpetuum. Cum Privilegio Summi
Pontificis Et Aliorum Principum. Romæ, Ex Officina Dominici Basæ. MDLXXXII.
Cum Licentia Superiorum_ (quarto, pp. 60).--A. De M.

[759] _Manuels-Roret. Théorie du Calendrier et collection de tous les
Calendriers des Années passées et futures_.... Par L. B. Francoeur,...
Paris, à la librairie encyclopédique de Roret, rue Hautefeuille, 10 bis.
1842. (12mo.) In this valuable manual, the 35 possible almanacs are given
at length, with such preliminary tables as will enable any one to find, by
mere inspection, which almanac he is to choose for any year, whether of old
or new style. [1866. I may now refer to my own _Book of Almanacs_, for the
same purpose].--A. De M.

Louis Benjamin Francoeur (1773-1849), after holding positions in the Ecole
polytechnique (1804) and the Lycée Charlemagne (1805), became professor of
higher algebra in the University of Paris (1809). His _Cours complet des
mathématiques pures_ was well received, and he also wrote on mechanics,
astronomy, and geodesy.

[760] Albertus Pighius, or Albert Pigghe, was born at Kempen c. 1490 and
died at Utrecht in 1542. He was a mathematician and a firm defender of the
faith, asserting the supremacy of the Pope and attacking both Luther and
Calvin. He spent some time in Rome. His greatest work was his _Hierarchiæ
ecclesiasticæ assertio_ (1538).

[761] This was A. F. Vogel. The work was his translation from the German
edition which appeared at Leipsic the same year, _Entdeckung einer
numerischen General-Auflösung aller höheren endlichen Gleichungen von jeder
beliebigen algebraischen und transcendenten Form_.

[762] The latest edition of Burnside and Panton's _Theory of Equations_ has
this brief summary of the present status of the problem: "Demonstrations
have been given by Abel and Wantzel (see Serret's _Cours d'Algèbre
Supérieure_, Art. 516) of the impossibility of resolving algebraically
equations unrestricted in form, of a degree higher than the fourth. A
transcendental solution, however, of the quintic has been given by M.
Hermite, in a form involving elliptic integrals."

[763] There was a second edition of this work in 1846. The author's
_Astronomy Simplified_ was published in 1838, and the _Thoughts on Physical
Astronomy_ in 1840, with a second edition in 1842.

[764] This was _The Science of the Weather, by several authors... edited by
B._, Glasgow, 1867.

[765] This was Y. Ramachandra, son of Sundara L[=a]la. He was a teacher of
science in Delhi College, and the work to which De Morgan refers is _A
Treatise on problems of Maxima and Minima solved by Algebra_, which
appeared at Calcutta in 1850. De Morgan's edition was published at London
nine years later.

[766] Abraham de Moivre (1667-1754), French refugee in London, poor,
studying under difficulties, was a man with tastes in some respects like
those of De Morgan. For one thing, he was a lover of books, and he had a
good deal of interest in the theory of probabilities to which De Morgan
also gave much thought. His introduction of imaginary quantities into
trigonometry was an event of importance in the history of mathematics, and
the theorem that bears his name, (cos [phi] + i sin [phi])^{n} = cos n[phi]
+ i sin n[phi], is one of the most important ones in all analysis.

[767] John Dolland (1706-1761), the silk weaver who became the greatest
maker of optical instruments in his time.

[768] Thomas Simpson (1710-1761), also a weaver, taking his leisure from
his loom at Spitalfields to teach mathematics. His _New Treatise on
Fluxions_ (1737) was written only two years after he began working in
London, and six years later he was appointed professor of mathematics at
Woolwich. He wrote many works on mathematics and Simpson's Formulas for
computing trigonometric tables are still given in the text-books.

[769] Nicholas Saunderson (1682-1739), the blind mathematician. He lost his
eyesight through smallpox when only a year old. At the age of 25 he began
lecturing at Cambridge on the principles of the Newtonian philosophy. His
_Algebra_, in two large volumes, was long the standard treatise on the
subject.

[770] He was not in the class with the others mentioned.

[771] Not known in the literature of mathematics.

[772] Probably J. Butler Williams whose _Practical Geodesy_ appeared in
1842, with a third edition in 1855.

[773] Benjamin Gompertz (1779-1865) was debarred as a Jew from a university
education. He studied mathematics privately and became president of the
Mathematical Society. De Morgan knew him professionally through the fact
that he was prominent in actuarial work.

[774] Referring to the contributions of Archimedes (287-212 B.C.) to the
mensuration of the sphere.

[775] The famous Alexandrian astronomer (c. 87-c. 165 A.D.), author of the
_Almagest_, a treatise founded on the works of Hipparchus.

[776] Dr. Whewell, when I communicated this song to him, started the
opinion, which I had before him, that this was a very good idea, of which
too little was made.--A. De M.

[777] See note 117, page 76.

[778] The common epithet of rank: _nobilis Tycho_, as he was a nobleman.
The writer had been at history.--A. De M.

See note 117, page 76.

[779] He lost it in a duel, with Manderupius Pasbergius. A contemporary,
T. B. Laurus, insinuates that they fought to settle which was the best
mathematician! This seems odd, but it must be remembered they fought in the
dark, "_in tenebris densis_"; and it is a nice problem to shave off a nose
in the dark, without any other harm.--A. De M.

Was this T. B. Laurus Joannes Baptista Laurus or Giovanni Battista Lauro
(1581-1621), the poet and writer?

[780] See note 117, page 76.

[781] Referring to Kepler's celebrated law of planetary motion. He had
previously wasted his time on analogies between the planetary orbits and
the polyhedrons.--A. De M.

[782] See note 117, page 76.

[783] "It does move though."

[784] As great a lie as ever was told: but in 1800 a compliment to Newton
without a fling at Descartes would have been held a lopsided structure.--A.
De M.

[785] Jean-le-Rond D'Alembert (1717-1783), the foundling who was left on
the steps of Jean-le-Rond in Paris, and who became one of the greatest
mathematical physicists and astronomers of his century.

[786] Leonhard Euler (1707-1783), friend of the Bernoullis, the greatest of
Swiss mathematicians, prominent in the theory of numbers, and known for
discoveries in all lines of mathematics as then studied.

[787] See notes 478, 479, page 219.

[788] See note 621, page 288.

[789] See note 584, page 255.

[790] The _siderial_ day is about four minutes short of the solar; there
are 366 sidereal days in the year.--A. De M.

[791] The founding of the London Mathematical Society is discussed by Mrs.
De Morgan in her _Memoir_ (p. 281). The idea came from a conversation
between her brilliant son, George Campbell De Morgan, and his friend Arthur
Cowper Ranyard in 1864. The meeting of organization was held on Nov. 7,
1864, with Professor De Morgan in the chair, and the first regular meeting
on January 16, 1865.

[792] See note 33, page 43.

[793] See note 119, page 80.

[794] John Russell Hind (b. 1823), the astronomer. Between 1847 and 1854 he
discovered ten planetoids.

[795] Sir Roderick Impey Murchison (1792-1871), the great geologist. He was
knighted in 1846 and devoted the latter part of his life to the work of the
Royal Geographical Society and to the geology of Scotland.

[796] Friedrich Wilhelm Bessel (1784-1846), the astronomer and physicist.
He was professor of astronomy at Königsberg.

[797] This was the _Reduction of the Observations of Planets made ... from
1750 to 1830: computed ... under the superintendence of George Biddell
Airy_ (1848). See note 129, page 85.

[798] The expense of this magnificent work was defrayed by Government
grants, obtained, at the instance of the British Association, in 1833--A.
De M.

[799] See note 32, page 43.

[800] Franz Friedrich Ernst Brünnow (1821-1891) was at that time or shortly
before director of the observatory at Dusseldorf. He then went to Berlin
and thence (1854) to Ann Arbor, Michigan. He then went to Dublin and
finally became Royal Astronomer of Ireland.

[801] Johann Gottfried Galle (1812-1910), at that time connected with the
Berlin observatory, and later professor of astronomy at Breslau.

[802] George Bishop (1785-1861), in whose observatory in Regent's Park
important observations were made by Dawes, Hind, and Marth.

[803] James Challis (1803-1882), director of the Cambridge observatory, and
successor of Airy as Plumian professor of astronomy.

[804] On Leverrier and Arago see note 33, page 43, and note 561, page 243.

[805] Robert Grant's (1814-1892) _History of Physical Astronomy from the
Earliest Ages to the Middle of the Nineteenth Century_ appeared in 1852. He
was professor of astronomy and director of the observatory at Glasgow.

[806] John Debenham was more interested in religion than in astronomy. He
wrote _The Strait Gate; or, the true scripture doctrine of salvation
clearly explained_, London, 1843, and _Tractatus de magis et Bethlehemæ
stella et Christi in deserto tentatione_, privately printed at London in
1845.

[807] More properly the Sydney Smirke reading room, since it was built from
his designs.

[808] The Antinomians were followers of Johannes Agricola (1494-1566). They
believed that Christians as such were released from all obligations to the
Old Testament. Some went so far as to assert that, since all Christians
were sanctified, they could not lose this sanctity even though they
disobeyed God. The sect was prominent in England in the seventeenth
century, and was transferred to New England. Here it suffered a check in
the condemnation of Mrs. Ann Hutchinson (1636) by the Newton Synod.

[809] Aside from this work and his publications on Reeve and Muggleton he
wrote nothing. With Joseph Frost he published _A list_ _of Books and
general index to J. Reeve and L. Muggleton's works_ (1846), _Divine Songs
of the Muggletonians_ (1829), and the work mentioned on page 396. _The
works of J. Reeve and L. Muggleton_ (1832).

[810] About 1650 he and his cousin John Reeve (1608-1658) began to have
visions. As part of their creed they taught that astronomy was opposed by
the Bible. They asserted that the sun moves about the earth, and Reeve
figured out that heaven was exactly six miles away. Both Muggleton and
Reeve were imprisoned for their unitarian views. Muggleton wrote a
_Transcendant Spirituall Treatise_ (1652). I have before me _A true
Interpretation of All the Chief Texts ... of the whole Book of the
Revelation of St. John.... By Lodowick Muggleton, one of the two last
Commissioned Witnesses & Prophets of the onely high, immortal, glorious
God, Christ Jesus_ (1665), in which the interpretation of the "number of
the beast" occupies four pages without arriving anywhere.

[811] In 1652 he was, in a vision, named as the Lord's "last messenger,"
with Muggleton as his "mouth," and died six years later, probably of
nervous tension resulting from his divine "illumination." He was the more
spiritual of the two.

[812] William Guthrie (1708-1770) was a historian and political writer. His
_History of England_ (1744-1751) was the first attempt to base history on
parliamentary records. He also wrote a _General History of Scotland_ in 10
volumes (1767). The work to which Frost refers is the _Geographical,
Historical, and Commercial Grammar_ (1770) which contained an astronomical
part by J. Ferguson. By 1827 it had passed through 24 editions.

[813] George Fox (1624-1691), founder of the Society of Friends; a mystic
and a disciple of Boehme. He was eight times imprisoned for heresy.

[814] If they were friends they were literary antagonists, for Muggleton
wrote against Fox _The Neck of the Quakers Broken_ (1663), and Fox replied
in 1667. Muggleton also wrote _A Looking Glass for George Fox_.

[815] John Conduitt (1688-1737), who married (1717) Newton's half niece,
Mrs. Katherine Barton. See note 284, page 136.

[816] Probably Peter Mark Roget's (1779-1869) _Thesaurus of English Words_
(1852) is not much used at present, but it went through 28 editions in his
lifetime. Few who use the valuable work are aware that Roget was a
professor of physiology at the Royal Institution (London), that he achieved
his title of F. R. S. because of his work in perfecting the slide rule, and
that he followed Sir John Herschel as secretary of the Royal Society.

[817] See note 703, page 327. This work went into a second edition in the
year of its first publication.

[818] See note 398, page 177.

[819] See note 528, page 233.

[820] George Jacob Holyoake (1817-1906) entered into a controversial life
at an early age. In 1841 he was imprisoned for six months for blasphemy. He
founded and edited _The Reasoner_ (Vols. 1-26, 1846-1861). In his later
life he did much to promote cooperation among the working class.

[821] See note 176, page 102.

[822] William Thomas Lowndes (1798-1843), whose _Bibliographer's Manual of
English Literature_, 4 vols., London, 1834 (also 1857-1864, and 1869) is a
classic in its line.

[823] Jacques Charles Brunet (1780-1867), the author of the great French
bibliography, the _Manuel du Libraire_ (1810).

       *       *       *       *       *


Corrections made to printed original.

Page 5, "direct acquaintance with the whole of his mental ancestry":
'acquantance' in original.

Page 100, "The error is at the rate": 'it' (for 'is') in original.

Page 192, "the lineal successor of the Repository association":
'successsor' in original.

Page 211, "the doctors had finished their compliments": 'docters' in
original.

Page 302, "causing mutual perturbations": 'peturbations' in original.

Page 344, "The work itself is described": 'decribed' in original.

Page 370, The entry for 1852 is printed as 19, it appears that the correct
value should be 9.

Page 392, "Sir John Herschel's previous communication": 'pervious' in
original.

Note 317, "he constructed a working model of a steam road carriage":
'contructed' in original.

Note 380, "the variation of the Earth's Diameters": 'Diaameters' in
original.

Note 550, "The first edition of the anonymous [Greek]": 'anonynous' in
original.






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