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A Budget of Paradoxes, Volume I

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Title: A Budget of Paradoxes, Volume I

Author: Augustus De Morgan

Editor: David Eugene Smith


        
Release date: October 20, 2007 [eBook #23100]

Language: English

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*** START OF THE PROJECT GUTENBERG EBOOK A BUDGET OF PARADOXES, VOLUME I ***




Produced by David Starner, Keith Edkins and the Online
Distributed Proofreading Team at http://www.pgdp.net





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 _Athenaeum_
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 _Athenaeum_ 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 ueber die
Geschichte des Problemes von der Quadratur des Zirkels_, Leipsic, 1892;
Thomas Muir, "Circle," in the eleventh edition of the _Encyclopaedia
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 Scripturae
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 Philosophiae ope, antequam quod esset statuerent, secundum verae logices
praecepta 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 gratiae iniverit,
ita ex immotis Philosophiae 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 Brahe, 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 _Athenaeum_ 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
_Chrysaespis_, 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 facheux que cet ingenieux Naturaliste, qui nous a deja donne et qui
nous prepare encore des ouvrages plus utiles, emploie a cette odieuse tache
une plume qu'il trempe dans le fiel et dans l'absinthe. Il est vrai que
plusieurs de ses remarques sont fondees, et qu'a l'erreur qu'il indique, il
joint en meme tems la correction. Mais il n'est pas toujours equitable, et
ne manque jamais d'insulter. Que peut {24} apres tout prouver son livre, si
ce n'est que la quarante-cinquieme partie d'un tres-ample et tres-utile
Recueil n'est pas exempte d'erreurs? Devoit-il confondre avec des Ecrivains
superficiels, dont la Liberte du Corps ne permet pas de restreindre la
fertilite, cette foule de savans du Premier ordre, dont les Ecrits ont orne
et ornent encore les Transactions? A-t-il oublie qu'on y a vu frequemment
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 prefere a tous
les autres, je veux dire de Mr. Hill lui-meme?"[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 _elite_ 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 Scientiae_, but I
would not be taken for _Falsae 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
Amphisbaena 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 _Amphisbaena_." {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 praeclara (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
pestilentiae sedi praefuisset."[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 _Athenaeum_ 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 Pergaeus, 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 Nicaea 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 Gadaron]. 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 Cyclopaedia_,
art. "Quadrature of the Circle."

    Tetragonismus. Id est circuli quadratura per Campanum, Archimedem
    Syracusanum, atque Boetium mathematicae 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 etait impossible de le lui dire au juste, attendu
que personne n'avait encore pu trouver d'une maniere exacte le rapport de
la circonference 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 _seance_ 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 "Haec accurata recognitio trium voluminum operum clariss.
P. Nicolai Cusae ... 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 Librae_, 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 Thyraeus.

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 Finee; 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 Viete,
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 Sussannaeus 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 a 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 Turiae 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 praedicat.
  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 _Athenaeum_, 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
Grynaeus,[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 Cyclometriae Novae 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 crue,
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 venue 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 dure
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 ayme de Dieu, colomne de la foy, sorty de la race de Inda, etc.
Les limites de cet Empire touchent a la mer Rouge, et aux montagnes d'Azuma
vers {72} l'Orient, et du coste de l'Occident, il est borne du fleuue du
Nil, qui le separe de la Nubie, vers le Septentrion il a l'AEgypte, et au
Midy les Royaumes de Congo, et de Mozambique, sa longueur contenant
quarante degre, qui font mille vingt cinq lieues, et ce depuis Congo ou
Mozambique qui sont au Midy, iusqu'en AEgypte qui est au Septentrion, et sa
largeur contenant depuis le Nil qui est a l'Occident, iusqu'aux montagnes
d'Azuma, qui sont a l'Orient, sept cens vingt cinq lieues, qui font vingt
neuf degrez. Cet empire a sous soy trente grandes Prouinces, scavoir,
Medra, Gaga, Alchy, Cedalon, Mantro, Finazam, Barnaquez, Ambiam, Fungy,
Angote, 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 situees iustement sous la ligne equinoxiale, entres les Tropiques de
Capricorne, et de Cancer. Mais elles s'approchent de nostre Tropique, de
deux cens cinquante lieues 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 este 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
confere souuent par le moyen de nostre trucheman: il estoit d'vn port graue
et serieux, succiur (_sic_) en son parler, mais subtil a merueilles en tout
ce qu'il disoit. Il prenoit grand plaisir au recit que je luy faisais de
nos belles ceremonies, et de la grauite 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 salete du Tartare, ny a
l'affreux regard du miserable Arabe, mais ils sont fins et cauteleux, et ne
se fient en personne, soupconneux a 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 Thomae Fieni[106] et Liberti
    Fromondi[107] ... Equidem Thomae Fieni epistolica quaestio, 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 Brahe,[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: heureka] 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, divinae que Scripturae omnino
adversantem, de mobilitate Terrae et immobilitate Solis."[138]

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

{91}

"Omnino prohibendum atque damnandum," because "ostendere conatur praefatam
doctrinam ... consonam esse veritati et non adversari Sacrae
Scripturae."[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:

"Sacrae Scripturae, ejusque verae et Catholicae 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 Terrae
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 scripturae, 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 terrae
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. ecclesiasticae 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 haec quaestio 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 Terrae, 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 formae suae
a natura congruentem concedere, magisquam quod totus labatur mundus, cujus
finis ignoratur, scirique nequit, neque fateamur ipsius cotidianae
revolutionis in coelo apparentiam esse, et in terra veritatem? Et haec
perinde se habere, ac si diceret Virgilianus AEneas: Provehimur portu ...
_Emend._ Cur ergo non possum mobilitatem illi formae suae concedere, magisque
quod totus labatur mundus, cujus finis ignoratur scirique nequit, et quae
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 Terrae, quam ejus quies, praesertim in cotidiana revolutione,
tanquam terrae 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 Terrae, 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 terrae verificari. _Emend._ Non pudet nos assumere ... hoc
consequenter in mobilitate verificari."[150]

(Cap. 10. lib. i. p. 10.) "_Copernicus._ Tanta nimirum est divina haec. 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 Terrae, ejusque
demonstratione."[153]

(Cap. 10. lib. iv. p. 122.[154]) "_Copernicus._ De magnitudine horum trium
siderum, Solis, Lunae, et Terrae. _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 terrae 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 a 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 novercae creditum est;
  Cassandrae quia non creditum ruit Ilium:
  Ergo exploranda est veritas multum prius
  Quam stulta prove judicet sententia."[182]



    Nova Demonstratio immobilitatis terrae petita ex virtute magnetica. By
    Jacobus Grandamicus. Flexiae (La Fleche), 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 a 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.



    Controversiae 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 Mathematicae Hodiernae. 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 sphaerae,
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 aeque
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, haec 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
Finaeus, "Il se vanta sans raison avoir trouve la quadrature du cercle; la
gloire de cette admirable decouverte etait reservee a Joseph Scalinger,
comme l'a ecrit Scevole 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 Coryphaeus 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: Philomathematikos]. 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 [Liege], 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 Hyperbolae
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
Geometrique_, at Paris, in 1825. His method would make the circumference
less than three times the diameter.



BEAULIEU'S QUADRATURE.

    La Geometrie Francoise, ou la Pratique aisee.... La quadracture du
    cercle. Par le Sieur de Beaulieu, Ingenieur, Geographe 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 _Athenaeum_, 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, mathematicien, fort mal traite par
Descartes, et a 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
ecrits; et nous pourrions dire de luy, qu'il seroit le seul et unique en la
force de ses Problemes, si sa trop grande presomption ne l'avoit porte a
avancer en cette Science une proposition aussi absurde, qu'elle est contre
la Foy et raison, en faisant la circonference d'un Cercle fixe, immobile,
et le centre mobile, sur lequel principe Geometrique, il a avance en son
Traitte 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 Brahe[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 Sphaera_, 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 Scavans et specialement d'un General
d'Armee ou Capitaine, pour promptement ranger une Armee 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 a l'Armee
_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'Armee
_rang_. Q signifie _quare_ en l'un et l'autre usage. C signifie _cube_ en
la mesure, et _Cavallerie_ en la composition des bataillons et escadrons.
Quant a 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 trouve. Je
dis seulement cecy en passant pour ceux qui n'en scavent rien du
tout."[240]

This is the algebra of the Royal Household, seventy-three years after the
death of Vieta. Quaere, 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 Ch

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