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Title: A Budget of Paradoxes, Volume II

Author: Augustus De Morgan

Editor: David Eugene Smith

Release date: August 23, 2008 [eBook #26408]

Language: English

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PARADOXES, VOLUME II ***

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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 II

DOVER PUBLICATIONS, INC., NEW YORK

This new Dover Edition, published in 1954,
is an unabridged republication of the Second Edition
of 1915, with a new introduction by Professor Ernest Nagel.

Copyright 1954 by Dover Publications, Inc.
Manufactured in the United States of America

A BUDGET OF PARADOXES.
VOLUME II.

ON SOME PHILOSOPHICAL ATHEISTS.
With the general run of the philosophical atheists of the last century the
notion of a God was an hypothesis. There was left an admitted possibility
that the vague somewhat which went by more names than one, might be
personal, intelligent, and superintendent. In the works of Laplace,[1] who is
sometimes called an atheist from his writings, there is nothing from which
such an inference can be drawn: unless indeed a Reverend Fellow of the
Royal Society may be held to be the fool who said in his heart, etc., etc., if
his contributions to the Philosophical Transactions go no higher than
nature. The following anecdote is well known in Paris, but has never been
printed entire. Laplace once went in form to present some edition of his
"Système du Monde" to the First Consul, or Emperor. Napoleon, whom
some wags had told that this book contained no mention of the name of
God, and who was fond of putting embarrassing questions, received it with
—"M. Laplace, they tell me you have written this large book on the system
of the universe, and have never even mentioned its Creator." Laplace, who,
though the most supple of politicians, was as stiff as a martyr on every point
of his philosophy or religion (e. g., even under Charles X he never
concealed his dislike of the priests), drew himself up and answered bluntly,
"Je n'avais pas besoin de cette hypothèse-là."[2] Napoleon, greatly amused,
told this reply to Lagrange, who exclaimed, "Ah! c'est une belle hypothèse;
ça explique beaucoup de choses."[3]
It is commonly said that the last words of Laplace were, "Ce que nous
connaissons est peu de chose; ce que nous ignorons est immense."[4] This
looks like a parody on Newton's pebbles:[5] the following is the true
account; it comes to me through one remove from Poisson.[6] After the
publication (in 1825) of the fifth volume of the Mécanique Céleste, Laplace
became gradually weaker, and with it musing and abstracted. He thought

much on the great problems of existence, and often muttered to himself,
Qu'est ce que c'est que tout cela![7] After many alternations, he appeared at
last so permanently prostrated that his family applied to his favorite pupil,
M. Poisson, to try to get a word from him. Poisson paid a visit, and after a
few words of salutation, said, "J'ai une bonne nouvelle à vous annoncer: on
a reçu au Bureau des Longitudes une lettre d'Allemagne annonçant que M.
Bessel a vérifié par l'observation vos découvertes théoriques sur les
satellites de Jupiter."[8] Laplace opened his eyes and answered with deep
gravity, "L'homme ne poursuit que des chimères."[9] He never spoke again.
His death took place March 5, 1827.
The language used by the two great geometers illustrates what I have said: a
supreme and guiding intelligence—apart from a blind rule called nature of
things—was an hypothesis. The absolute denial of such a ruling power was
not in the plan of the higher philosophers: it was left for the smaller fry. A
round assertion of the non-existence of anything which stands in the way is
the refuge of a certain class of minds: but it succeeds only with things
subjective; the objective offers resistance. A philosopher of the
appropriative class tried it upon the constable who appropriated him: I deny
your existence, said he; Come along all the same, said the unpsychological
policeman.

Euler[10] was a believer in God, downright and straightforward. The
following story is told by Thiébault,[11] in his Souvenirs de vingt ans de
séjour à Berlin,[12] published in his old age, about 1804. This volume was
fully received as trustworthy; and Marshall Mollendorff[13] told the Duc de
Bassano[14] in 1807 that it was the most veracious of books written by the
most honest of men. Thiébault says that he has no personal knowledge of
the truth of the story, but that it was believed throughout the whole of the
north of Europe. Diderot[15] paid a visit to the Russian Court at the
invitation of the Empress. He conversed very freely, and gave the younger
members of the Court circle a good deal of lively atheism. The Empress
was much amused, but some of her councillors suggested that it might be
desirable to check these expositions of doctrine. The Empress did not like to
put a direct muzzle on her guest's tongue, so the following plot was
contrived. Diderot was informed that a learned mathematician was in
possession of an algebraical demonstration of the existence of God, and

would give it him before all the Court, if he desired to hear it. Diderot
gladly consented: though the name of the mathematician is not given, it was
Euler. He advanced towards Diderot, and said gravely, and in a tone of
perfect conviction: Monsieur, (a + bn) / n = x, donc Dieu existe; répondez!
[16]
Diderot, to whom algebra was Hebrew, was embarrassed and
disconcerted; while peals of laughter rose on all sides. He asked permission
to return to France at once, which was granted.

ROTATION OF THE MOON.

An examination of the Astronomical doctrine of the Moon's
rotation. By J. L.[17] Edinburgh, 1847, 8vo.

A systematic attack of the character afterwards made with less skill and
more notice by Mr. Jellinger Symons.
July 1866, J. L. appears as Mr. James Laurie, with a new pamphlet "The
Astronomical doctrines of the Moon's rotation ..." Edinburgh. Of all the
works I have seen on the question, this is the most confident, and the sorest.
A writer on astronomy said of Mr. Jellinger Symons,[18] "Of course he
convinced no one who knew anything of the subject." This "ungenerous
slur" on the speculator's memory appears to have been keenly felt; but its
truth is admitted. Those who knew anything of the subject are "the so-called
men of science," whose three P's were assailed; prestige, pride, and
prejudice: this the author tries to effect for himself with three Q's; quibble,
quirk, and quiddity. He explains that the Scribes and Pharisees would not
hear Jesus, and that the lordly bishop of Rome will not cast his tiara and
keys at the feet of the "humble presbyter" who now plays the part of pope in
Scotland. I do not know whom he means: but perhaps the friends of the
presbyter-pope may consider this an ungenerous slur. The best proof of the
astronomer is just such "as might have been expected from the merest of
blockheads"; but as the giver is of course not a blockhead, this circumstance
shows how deeply blinded by prejudice he must be.
Of course the paradoxers do not persuade any persons who know their
subjects: and so these Scribes and Pharisees reject the Messiah. We must

suppose that the makers of this comparison are Christians: for if they
thought the Messiah an enthusiast or an impostor, they would be absurd in
comparing those who reject what they take for truth with others who once
rejected what they take for falsehood. And if Christians, they are both
irreverent and blind to all analogy. The Messiah, with His Divine mission
proved by miracles which all might see who chose to look, is degraded into
a prototype of James Laurie, ingeniously astronomizing upon ignorant
geometry and false logic, and comparing to blockheads those who expose
his nonsense. Their comparison is as foolish as—supposing them Christians
—it is profane: but, like errors in general, its other end points to truth. There
were Pseudochrists and Antichrists; and a Concordance would find the real
forerunners of all the paradoxers. But they are not so clever as the old false
prophets: there are none of whom we should be inclined to say that, if it
were possible, they would deceive the very educated. Not an Egyptian
among them all can make uproar enough to collect four thousand men that
are murderers—of common sense—to lead out into the wilderness.
Nothing, says the motto of this work, is so difficult to destroy as the errors
and false facts propagated by illustrious men whose words have authority. I
deny it altogether. There are things much more difficult to destroy: it is
much more difficult to destroy the truths and real facts supported by such
men. And again, it is much more difficult to prevent men of no authority
from setting up false pretensions; and it is much more difficult to destroy
assertions of fancy speculation. Many an error of thought and learning has
fallen before a gradual growth of thoughtful and learned opposition. But
such things as the quadrature of the circle, etc., are never put down. And
why? Because thought can influence thought, but thought cannot influence
self-conceit: learning can annihilate learning: but learning cannot annihilate
ignorance. A sword may cut through an iron bar; and the severed ends will
not reunite: let it go through the air, and the yielding substance is whole
again in a moment.

Miracles versus Nature: being an application of certain
propositions in the theory of chances to the Christian miracles. By
Protimalethes.[19] Cambridge, 1847, 8vo.

The theory, as may be supposed, is carried further than most students of the
subject would hold defensible.

An astronomical Lecture. By the Rev. R. Wilson.[20] Greenock,
1847, 12mo.

Against the moon's rotation on her axis.

[Handed about in the streets in 1847: I quote the whole:]
Important discovery in astronomy, communicated to the
Astronomer Royal, December 21st, 1846. That the Sun revolve
round the Planets in 25748-2/5 years, in consequence of the
combined attraction of the planets and their satellites, and that the
Earth revolve round the Moon in 18 years and 228 days. D. T.
Glazier [altered with a pen into Glazion.] Price one penny.

1847. In the United Service Magazine for September, 1847, Mrs. Borron,[21]
of Shrewsbury, published some remarks tending to impeach the fact that
Neptune, the planet found by Galle,[22] really was the planet which Le
Verrier and Adams[23] had a right to claim. This was followed (September
14) by two pages, separately circulated, of "Further Observations upon the
Planets Neptune and Uranus, with a Theory of Perturbations"; and (October
19, 1848) by three pages of "A Review of M. Leverrier's Exposition."
Several persons, when the remarkable discovery was made, contended that
the planet actually discovered was an intruder; and the future histories of
the discovery must contain some account of this little afterpiece. Tim
Linkinwater's theory that there is no place like London for coincidences,
would have been utterly overthrown in favor of what they used to call the
celestial spaces, if there had been a planet which by chance was put near the
place assigned to Neptune at the time when the discovery was made.

EARLY IDEAS OF AVIATION.

Aerial Navigation; containing a description of a proposed flying
machine, on a new principle. By Dædalus Britannicus. London,
1847, 8vo.

In 1842-43 a Mr. Henson[24] had proposed what he called an aeronaut
steam-engine, and a Bill was brought in to incorporate an "Aerial Transit
Company." The present plan is altogether different, the moving power being
the explosion of mixed hydrogen and air. Nothing came of it—not even a
Bill. What the final destiny of the balloon may be no one knows: it may
reasonably be suspected that difficulties will at last be overcome. Darwin,
[25]
in his "Botanic Garden" (1781), has the following prophecy:

"Soon shall thy arm, unconquered Steam! afar
Drag the slow barge, or drive the rapid car;
Or, on wide-waving wings expanded, bear
The flying chariot through the fields of air."

Darwin's contemporaries, no doubt, smiled pity on the poor man. It is worth
note that the two true prophecies have been fulfilled in a sense different
from that of the predictions. Darwin was thinking of the suggestion of
Jonathan Hulls,[26] when he spoke of dragging the slow barge: it is only
very recently that the steam-tug has been employed on the canals. The car
was to be driven, not drawn, and on the common roads. Perhaps, the flying
chariot will be something of a character which we cannot imagine, even
with the two prophecies and their fulfilments to help us.[27]

THE SECRET OF THE UNIVERSE DIVULGED.

A book for the public. New Discovery. The causes of the
circulation of the blood; and the true nature of the planetary
system. London, 1848, 8vo.

Light is the sustainer of motion both in the earth and in the blood. The
natural standard, the pulse of a person in health, four beats to one
respiration, gives the natural second, which is the measure of the earth's
progress in its daily revolution. The Greek fable of the Titans is an elaborate

exposition of the atomic theory: but any attempt to convince learned
classics would only meet their derision; so much does long-fostered
prejudice stand in the way of truth. The author complains bitterly that men
of science will not attend to him and others like him: he observes, that "in
the time occupied in declining, a man of science might test the merits." This
is, alas! too true; so well do applicants of this kind know how to stick on.
But every rule has its exception: I have heard of one. The late Lord
Spencer[28]—the Lord Althorp of the House of Commons—told me that a
speculator once got access to him at the Home Office, and was proceeding
to unfold his way of serving the public. "I do not understand these things,"
said Lord Althorp, "but I happen to have —— (naming an eminent
engineer) upstairs; suppose you talk to him on the subject." The discoverer
went up, and in half-an-hour returned, and said, "I am very much obliged to
your Lordship for introducing me to Mr. ——; he has convinced me that I
am quite wrong." I supposed, when I heard the story—but it would not have
been seemly to say it—that Lord A. exhaled candor and sense, which
infected those who came within reach: he would have done so, if anybody.

THE TRISECTION AND QUADRATURE AGAIN.

A method to trisect a series of angles having relation to each
other; also another to trisect any given angle. By James Sabben.
1848 (two quarto pages).

"The consequence of years of intense thought": very likely, and very sad.
1848. The following was sent to me in manuscript. I give the whole of it:
"Quadrature of the Circle.—A quadrant is a curvilinear angle traversing
round and at an equal distance from a given point, called a center, no two
points in the curve being at the same angle, but irreptitiously graduating
from 90 to 60. It is therefore a mean angle of 90 and 60, which is 75,
because it is more than 60, and less than 90, approximately from 60 to 90,
and from 90 to 60, with equal generation in each irreptitious approximation,
therefore meeting in 75, and which is the mean angle of the quadrant.

"Or suppose a line drawn from a given point at 90, and from the same point
at 60. Let each of these lines revolve on this point toward each other at an
equal ratio. They will become one line at 75, and bisect the curve, which is
one-sixth of the entire circle. The result, taking 16 as a diameter, gives an
area of 201.072400, and a circumference of 50.2681.
"The original conception, its natural harmony, and the result, to my own
mind is a demonstrative truth, which I presume it right to make known,
though perhaps at the hazard of unpleasant if not uncourteous remarks."
I have added punctuation: the handwriting and spelling are those of an
educated person; the word irreptitious is indubitable. The whole is a natural
curiosity.

The quadrature and exact area of the circle demonstrated. By
Wm. Peters. 8vo. n. d. (circa 1848).[29]
Suggestions as to the necessity for a revolution in philosophy; and
prospectus for the establishment of a new quarterly, to be called
the Physical Philosopher and Heterodox Review. By Q. E. D.
8vo. 1848.

These works are by one author, who also published, as appears by
advertisement,
"Newton rescued from the precipitancy of his followers through a century
and a half,"[30] and "Dangers along a coast by correcting (as it is called) a
ship's reckoning by bearings of the land at night fall, or in a fog, nearly out
of print. Subscriptions are requested for a new edition."
The area of a circle is made four-fifths of the circumscribed square: proved
on an assumption which it is purposed to explain in a longer essay.[31] The
author, as Q. E. D., was in controversy with the Athenæum journal, and
criticised a correspondent, D., who wrote against a certain class of
discoverers. He believed the common theories of hydrostatics to be wrong,
and one of his questions was:

"Have you ever taken into account anent gravity and gravitation the fact
that a five grain cube of cork will of itself half sink in the water, whilst it
will take 20 grains of brass, which will sink of itself, to pull under the other
half? Fit this if you can, friend D., to your notions of gravity and specific
gravity, as applied to the construction of a universal law of gravitation."
This the Athenæum published—but without some Italics, for which the
editor was sharply reproved, as a sufficient specimen of the quod erat D.
monstrandum: on which the author remarks—"D,—Wherefore the e caret?
is it D apostrophe? D', D'M, D'Mo, D'Monstrandum; we cannot find the wit
of it." This I conjecture to contain an illusion to the name of the supposed
author; but whether De Mocritus, De Mosthenes, or De Moivre was
intended, I am not willing to decide.

The Scriptural Calendar and Chronological Reformer, for the
statute year 1849. Including a review of recent publications on the
Sabbath question. London, 1849, 12mo.[32]

This is the almanac of a sect of Christians who keep the Jewish Sabbath,
having a chapel at Mill Yard, Goodman's Fields. They wrote controversial
works, and perhaps do so still; but I never chanced to see one.

Geometry versus Algebra; or the trisection of an angle
geometrically solved. By W. Upton, B.A.[33] Bath (circa 1849).
8vo.

The author published two tracts under this title, containing different alleged
proofs: but neither gives any notice of the change. Both contain the same
preface, complaining of the British Association for refusing to examine the
production. I suppose that the author, finding his first proof wrong, invented
the second, of which the Association never had the offer; and, feeling sure
that they would have equally refused to examine the second, thought it
justifiable to present that second as the one which they had refused. Mr.
Upton has discovered that the common way of finding the circumference is

wrong, would set it right if he had leisure, and, in the mean time, has solved
the problem of the duplication of the cube.
The trisector of an angle, if he demand attention from any mathematician, is
bound to produce, from his construction, an expression for the sine or
cosine of the third part of any angle, in terms of the sine or cosine of the
angle itself, obtained by help of no higher than the square root. The
mathematician knows that such a thing cannot be; but the trisector virtually
says it can be, and is bound to produce it, to save time. This is the
misfortune of most of the solvers of the celebrated problems, that they have
not knowledge enough to present those consequences of their results by
which they can be easily judged. Sometimes they have the knowledge and
quibble out of the use of it. In many cases a person makes an honest
beginning and presents what he is sure is a solution. By conference with
others he at last feels uneasy, fears the light, and puts self-love in the way of
it. Dishonesty sometimes follows. The speculators are, as a class, very apt
to imagine that the mathematicians are in fraudulent confederacy against
them: I ought rather to say that each one of them consents to the mode in
which the rest are treated, and fancies conspiracy against himself. The
mania of conspiracy is a very curious subject. I do not mean these remarks
to apply to the author before me.
One of Mr. Upton's trisections, if true, would prove the truth of the
following equation:

3 cos (θ / 3) = 1 + √(4 - sin2θ)

which is certainly false.[34]
In 1852 I examined a terrific construction, at the request of the late Dr.
Wallich,[35] who was anxious to persuade a poor countryman of his, that
trisection of the angle was waste of time. One of the principles was, that
"magnitude and direction determine each other." The construction was
equivalent to the assertion that, θ being any angle, the cosine of its third
part is

sin 3θ . cos(5θ/2) + sin2 θ sin (5θ/2)

divided by the square root of

sin2 3θ . cos2 (5θ/2) + sin4 θ + sin 3θ . sin 5θ . sin2 θ.

This is from my rough notes, and I believe it is correct.[36] It is so nearly
true, unless the angle be very obtuse, that common drawing, applied to the
construction, will not detect the error. There are many formulae of this kind:
and I have several times found a speculator who has discovered the
corresponding construction, has seen the approximate success of his
drawing—often as great as absolute truth could give in graphical practice,
—and has then set about his demonstration, in which he always succeeds to
his own content.
There is a trisection of which I have lost both cutting and reference: I think
it is in the United Service Journal. I could not detect any error in it, though
certain there must be one. At least I discovered that two parts of the diagram
were incompatible unless a certain point lay in line with two others, by
which the angle to be trisected—and which was trisected—was bound to be
either 0° or 180°.
Aug. 22, 1866. Mr. Upton sticks to his subject. He has just published "The
Uptonian Trisection. Respectfully dedicated to the schoolmasters of the
United Kingdom." It seems to be a new attempt. He takes no notice of the
sentence I have put in italics: nor does he mention my notice of him, unless
he means to include me among those by whom he has been "ridiculed and
sneered at" or "branded as a brainless heretic." I did neither one nor the
other: I thought Mr. Upton a paradoxer to whom it was likely to be worth
while to propound the definite assertion now in italics; and Mr. Upton does
not find it convenient to take issue on the point. He prefers general
assertions about algebra. So long as he cannot meet algebra on the above
question, he may issue as many "respectful challenges" to the
mathematicians as he can find paper to write: he will meet with no
attention.

There is one trisection which is of more importance than that of the angle. It
is easy to get half the paper on which you write for margin; or a quarter; but

very troublesome to get a third. Show us how, easily and certainly, to fold
the paper into three, and you will be a real benefactor to society.
Early in the century there was a Turkish trisector of the angle, Hussein
Effendi, who published two methods. He was the father of Ameen Bey, who
was well known in England thirty years ago as a most amiable and
cultivated gentleman and an excellent mathematician. He was then a student
at Cambridge; and he died, years ago, in command of the army in Syria.
Hussein Effendi was instructed in mathematics by Ingliz Selim Effendi,
who translated a work of Bonnycastle[37] into Turkish.[38] This Englishman
was Richard Baily, brother of Francis Baily[39] the astronomer, who
emigrated to Turkey in his youth, and adopted the manners of the Turks, but
whether their religion also I never heard, though I should suppose he did.
I now give the letters from the agricultural laborer and his friend, described
on page 12, Vol. I. They are curiosities; and the history of the quadrature
can never be well written without some specimens of this kind:
"Doctor Morgan, Sir. Permit me to address you
"Brute Creation may perhaps enjoy the faculty of beholding visible things
with a more penitrating eye than ourselves. But Spiritual objects are as far
out of their reach as though they had no being
"Nearest therefore to the brute Creation are those men who Suppose
themselves to be so far governed by external objects as to believe nothing
but what they See and feel And Can accomedate to their Shallow
understanding and Imaginations
"My Dear Sir Let us all Consult ourselves by the wise proverb.

"I believe that evry mans merit & ability aught to be appreciated and valued
In proportion to its worth & utility
"In whatever State or Circumstances they may fortunately or unfortunately
be placed
"And happy it is for evry man to know his worth and place

"When a Gentleman of your Standing in Society Clad with those honors
Can not understand or Solve a problem That is explicitly explained by
words and Letters and mathematically operated by figuers He had best
consult the wise proverd
"Do that which thou Canst understand and Comprehend for thy good.
"I would recommend that Such Gentleman Change his business
"And appropriate his time and attention to a Sunday School to Learn what
he Could and keep the Litle Children form durting their Close
"With Sincere feelings of Gratitude for your weakness and Inability I am

"Sir your Superior in Mathematics ——"

"1849 June th29."

"Dor Morgin Sir
"I wrote and Sent my work to Professor —— of —— State of —— United
States
"I am now in the possession of the facts that he highly approves of my
work. And Says he will Insure me Reward in the States
"I write this that you may understand that I have knowledge of the unfair
way that I am treated In my own nati County
"I am told and have reasons to believe that it is the Clergy that treat me so
unjust.
"I am not Desirous of heaping Disonors upon my own nation. But if I have
to Leave this kingdom without my Just dues. The world Shall know how I
am and have been treated.

"I am Sir Desirous of my
"Just dues ——"

"1849 July 3."

"July 7th, 1849.
"Sir, I have been given to understand that a friend of mine one whom I shall
never be ashamed to acknowledge as such tho' lowly his origine; nay not
only not ashamed but proud of doing so for I am one of those who esteem
and respect a man according to his ability and probity, deeming with Dr.
Watts 'that the mind is the standard of the man,'[40] has laid before you and
asked your opinion of his extraordinary performance, viz. the quadrature of
the circle, he did this with the firmest belief that you would not only treat
the matter in a straightforward manner but with the conviction that from
your known or supposed knowledge of mathematicks would have given an
upright and honorable decision upon the subject; but the question is have
you done so? Could I say yes I would with the greatest of pleasure and have
congratulated you upon your decision whatever it might have been but I am
sorry to say that I cannot your letter is a paltry evasion, you say 'that it is a
great pity that you (Mr. ——) should have attempted this (the quadrature of
the circle) for your mathematical knowledge is not sufficient to make you
know in what the problem consists,' you don't say in what it does consist
according to your ideas, oh! no nothing of the sort, you enter into no
disquisition upon the subject in order to show where you think Mr. —— is
wrong and why you have not is simply—because you cannot—you know
that he has done it and what is if I am not wrongly informed you have been
heard to say so. He has done what you nor any other mathematician as
those who call themselves such have done. And what is the reason that you
will not candidly acknowledge to him as you have to others that he has
squared the circle shall I tell you? it is because he has performed the feat to
obtain the glory of which mathematicians have battled from time
immemorial that they might encircle their brows with a wreath of laurels far
more glorious than ever conqueror won it is simply this that it is a poor man
a humble artisan who has gained that victory that you don't like to
acknowledge it you don't like to be beaten and worse to acknowledge that
you have miscalculated, you have in short too small a soul to acknowledge
that he is right.

"I was asked my opinion and I gave it unhesitatingly in the affirmative and I
am backed in my opinion not only by Mr. —— a mathematician and
watchmaker residing in the boro of Southwark but by no less an authority
than the Professor of mathematics of —— College —— —— United States
Mr. —— and I presume that he at least is your equal as an authority and Mr.
—— says that the government of the U.S. will recompense M. D. for the
discovery he has made if so what a reflection upon Old england the boasted
land of freedom the nursery of arts and sciences that her sons are obliged to
go to a foreign country to obtain that recompense to which they are justly
entitled
"In conclusion I had to contradict an assertion you made to the effect that
'there is not nor ever was any reward offered by the government of this
country for the discovery of the quadrature of the circle.' I beg to inform
you that there was but that it having been deemed an impossibility the
government has withdrawn it. I do this upon no less an authority than the
Marquis of Northampton.[41]

"I am, sir, yours ——"

"Dr. Morgan."

THE MOON'S ROTATION.

Notes on the Kinematic Effects of Revolution and Rotation, with
reference to the Motions of the Moon and of the earth. By Henry
Perigal, Jun. Esq. London, 1846-1849, 8vo.
On the misuse of technical terms. Ambiguity of the terms
Rotation and Revolution, owing to the double meaning
improperly attributed to each of the words. (No date nor place,
but by Mr. Perigal,[42] I have no doubt, and containing letters of
1849 and 1850.)
The moon controversy. Facts v. Definitions. By H. P., Jun.
London, 1856, 8vo. (pp. 4.)

Mr. Henry Perigal helped me twenty years ago with the diagrams, direct
from the lathe to the wood, for the article "Trochoidal Curves," in the Penny
Cyclopædia: these cuts add very greatly to the value of the article, which,
indeed, could not have been made intelligible without them. He has had
many years' experience, as an amateur turner, in combination of double and
triple circular motions, and has published valuable diagrams in profusion. A
person to whom the double circular motion is familiar in the lathe naturally
looks upon one circle moving upon another as in simple motion, if the
second circle be fixed to the revolving radius, so that one and the same
point of the moving circle travels upon the fixed circle. Mr. Perigal
commenced his attack upon the moon for moving about her axis, in the first
of the tracts above, ten years before Mr. Jellinger Symons;[43] but he did not
think it necessary to make it a subject for the Times newspaper. His
familiarity with combined motions enabled him to handle his arguments
much better than Mr. J. Symons could do: in fact, he is the clearest assailant
of the lot which turned out with Mr. J. Symons. But he is as wrong as the
rest. The assault is now, I suppose, abandoned, until it becomes epidemic
again. This it will do: it is one of those fallacies which are very tempting.
There was a dispute on the subject in 1748, between James Ferguson[44] and
an anonymous opponent; and I think there have been others.
A poet appears in the field (July 19, 1863) who calls himself Cyclops, and
writes four octavo pages. He makes a distinction between rotation and
revolution; and his doctrines and phrases are so like those of Mr. Perigal
that he is a follower at least. One of his arguments has so often been used
that it is worth while to cite it:

"Would Mathematicals—forsooth—
If true, have failed to prove its truth?
Would not they—if they could—submit
Some overwhelming proofs of it?
But still it totters proofless! Hence
There's strong presumptive evidence
None do—or can—such proof profound
Because the dogma is unsound.
For, were there means of doing so,
They would have proved it long ago."

This is only one of the alternatives. Proof requires a person who can give
and a person who can receive. I feel inspired to add the following:

"A blind man said, As to the Sun,
I'll take my Bible oath there's none;
For if there had been one to show
They would have shown it long ago.
How came he such a goose to be?
Did he not know he couldn't see?
Not he!"

The absurdity of the verses is in the argument. The writer was not so
ignorant or so dishonest as to affirm that nothing had been offered by the
other side as proof; accordingly, his syllogism amounts to this: If your
proposition were true, you could have given proof satisfactory to me; but
this you have not done, therefore, your proposition is not true.
The echoes of the moon-controversy reached Benares in 1857, in which
year was there published a pamphlet "Does the Moon Rotate?" in Sanskrit
and English. The arguments are much the same as those of the discussion at
home.

ON THE NAMES OF RELIGIOUS BODIES.
We see that there are paradoxers in argument as well as in assertion of fact:
my plan does not bring me much into contact with these; but another
instance may be useful. Sects, whether religious or political, give
themselves names which, in meaning, are claimed also by their opponents;
loyal, liberal, conservative (of good), etc. have been severally appropriated
by parties. Whig and Tory are unobjectionable names: the first—which
occurs in English ballad as well as in Scotland—is sour milk;[45] the second
is a robber. In theology, the Greek Church is Orthodox, the Roman is
Catholic, the modern Puritan is Evangelical, etc.

The word Christian (Vol. I, p. 248[46]) is an instance. When words begin,
they carry their meanings. The Jews, who had their Messiah to come, and
the followers of Jesus of Nazareth, who took Him for their Messiah, were

both Christians (which means Messianites): the Jews would never have
invented the term to signify Jesuans, nor would the disciples have invented
such an ambiguous term for themselves; had they done so, the Jews would
have disputed it, as they would have done in later times if they had had fair
play. The Jews of our day, I see by their newspapers, speak of Jesus Christ
as the Rabbi Joshua. But the heathens, who knew little or nothing about the
Jewish hope, would naturally apply the term Christians to the only
followers of a Messiah of whom they had heard. For the Jesuans invaded
them in a missionary way; while the Jews did not attempt, at least openly, to
make proselytes.
All such words as Catholic, etc., are well enough as mere nomenclature;
and the world falls for the most part, into any names which parties choose
to give themselves. Silly people found inferences on this concession; and,
as usually happens, they can cite some of their betters. St. Augustine,[47] a
freakish arguer, or, to put it in the way of an old writer, lectorem ne
multiloquii tædio fastidiat, Punicis quibusdam argutiis recreare solet,[48]
asks, with triumph, to what chapel a stranger would be directed, if he
inquired the way to the Catholic assembly. But the best exhibition of this
kind in our own century is that made by the excellent Dr. John Milner,[49] in
a work (first published in 1801 or 1802) which I suppose still circulates,
"The End of Religious Controversy": a startling title which, so far as its
truth is concerned, might as well have been "The floor of the bottomless
pit." This writer, whom every one of his readers will swear to have been a
worthy soul, though many, even of his own sect, will not admire some of
his logic, speaks as follows:
"Letter xxv. On the true Church being Catholic. In treating of this third
mark of the true Church, as expressed in our common creed, I feel my
spirits sink within me, and I am almost tempted to throw away my pen in
despair. For what chance is there of opening the eyes of candid Protestants
to the other marks of the Church, if they are capable of keeping them shut
to this? Every time they address the God of Truth, either in solemn worship
or in private devotion [stretch of rhetoric], they are forced, each of them, to
repeat: I believe in the Catholic Church, and yet if I ask any of them the
question: Are you a Catholic? he is sure to answer me, No, I am a

Protestant! Was there ever a more glaring instance of inconsistency and
self-condemnation among rational beings!"

"John Milner, honest and true,
Did what honest people still may do,
If they write for the many and not for the few,
But what by and bye they must eschew."

He shortened his clause; and for a reason. If he had used the whole epithet
which he knew so well, any one might have given his argument a half-turn.
Had he written, as he ought, "the Holy Catholic Church" and then argued as
above, some sly Protestant would have parodied him with "and yet if I ask
any of them the question: Are you HOLY? he is sure to answer me No, I am a
SINNER." To take the adjective from the Church, and apply it to the
individual partisan, is recognized slipslop, but not ground of argument. If
Dr. M. had asked his Protestant whether he belonged to the Catholic
Church, the answer would have been Yes, but not to the Roman branch.
When he put his question as he did, he was rightly answered and in his own
division. This leaving out words is a common practice, especially when the
omitter is in authority, and cannot be exposed. A year or two ago a bishop
wrote a snubbing letter to a poor parson, who had complained that he was
obliged, in burial, to send the worst of sinners to everlasting happiness. The
bishop sternly said, "hope[50] is not assurance." Could the clergyman have
dared to answer, he would have said, "No, my Lord! but 'sure and certain
hope' is as like assurance as a minikin man is like a dwarf." Sad to say, a
theologian must be illogical: I feel sure that if you took the clearest headed
writer on logic that ever lived, and made a bishop of him, he would be
shamed by his own books in a twelvemonth.
Milner's sophism is glaring: but why should Dr. Milner be wiser than St.
Augustine, one of his teachers? I am tempted to let out the true derivation of
the word Catholic, as exclusively applied to the Church of Rome. All can
find it who have access to the Rituale of Bonaventura Piscator[51] (lib. i. c.
12, de nomine Sacræ Ecclesiæ, p. 87 of the Venice folio of 1537). I am told
that there is a Rituale in the Index Expurgatorius, but I have not thought it
worth while to examine whether this be the one: I am rather inclined to
think, as I have heard elsewhere, that the book was held too dangerous for

the faithful to know of it, even by a prohibition: it would not surprise me at
all if Roman Christians should deny its existence.[52]
It amuses me to give, at a great distance of time, a small Rowland for a
small Oliver,[53] which I received, de par l'Eglise,[54] so far as lay in the
Oliver-carrier more than twenty years ago. The following contribution of
mine to Notes and Queries (3d Ser. vi. p. 175, Aug. 27, 1864) will explain
what I say. There had been a complaint that a contributor had used the term
Papist, which a very excellent dignitary of the Papal system pronounced an
offensive term:

PAPIST.
The term papist should be stripped of all except its etymological meaning,
and applied to those who give the higher and final authority to the
declaration ex cathedrâ[55] of the Pope. See Dr. Wiseman's[56] article,
Catholic Church, in the Penny Cyclopædia.
What is one to do about these names? First, it is clear that offence should,
when possible, be avoided: secondly, no one must be required to give a
name which favors any assumption made by those to whom it is given, and
not granted by those who give it. Thus the subdivision which calls itself
distinctly Evangelical has no right to expect others to concede the title.
Now the word Catholic, of course, falls under this rule; and even Roman
Catholic may be refused to those who would restrict the word Catholic to
themselves. Roman Christian is unobjectionable, since the Roman Church
does not deny the name of Christian to those whom she calls heretics. No
one is bound in this matter by Acts of Parliament. In many cases, no doubt,
names which have offensive association are used merely by habit,
sometimes by hereditary transmission. Boswell records of Johnson that he
always used the words "dissenting teacher," refusing minister and
clergyman to all but the recipients of episcopal ordination.
This distinctive phrase has been widely adopted: it occurs in the Index of 3d
S. iv. [Notes and Queries]. Here we find "Platts (Rev. John), Unitarian
teacher, 412;" the article indexed has "Unitarian minister."

This, of course is habit: an intentional refusal of the word minister would
never occur in an index. I remember that, when I first read about Sam
Johnson's little bit of exclusiveness, I said to myself: "Teacher? Teacher?
surely I remember One who is often called teacher, but never minister or
clergyman: have not the dissenters got the best of it?"
When I said that the Roman Church concedes the epithet Christians to
Protestants, I did not mean that all its adherents do the same. There is, or
was, a Roman newspaper, the Tablet, which, seven or eight years ago, was
one of the most virulent of the party journals. In it I read, referring to some
complaint of grievance about mixed marriages, that if Christians would
marry Protestants they must take the consequences. My memory notes this
well; because I recollected, when I saw it, that there was in the stable a
horse fit to run in the curricle with this one. About seventeen years ago an
Oxford M. A., who hated mathematics like a genuine Oxonian of the last
century, was writing on education, and was compelled to give some
countenance to the nasty subject. He got out cleverly; for he gave as his
reason for the permission, that man is an arithmetical, geometrical, and
mechanical animal, as well as a rational soul.

The Tablet was founded by an old pupil of mine, Mr. Frederic Lucas,[57]
who availed himself of his knowledge of me to write some severe articles—
even abusive, I was told, but I never saw them—against me, for
contributing to the Dublin Review, and poking my heretic nose into
orthodox places. Dr. Wiseman, the editor, came in for his share, and ought
to have got all. Who ever blamed the pig for intruding himself into the
cabin when the door was left open? When Mr. Lucas was my pupil, he was
of the Society of Friends—in any article but this I should say Quaker—and
was quiet and gentlemanly, as members of that Church—in any article but
this I should, from mere habit, say sect—usually are. This is due to his
memory; for, by all I heard, when he changed his religion he ceased to be
Lucas couchant, and became Lucas rampant, fanged and langued gules. (I
looked into Guillim[58] to see if my terms were right: I could not find them;
but to prove I have been there, I notice that he calls a violin a violent. How
comes the word to take this form?) I met with several Roman Christians,
born and bred, who were very much annoyed at Mr. Lucas and his doings;
and said some severe things about new converts needing kicking-straps.

The mention of Dr. Wiseman reminds me of another word, appropriated by
Christians to themselves: fides;[59] the Roman faith is fides, and nothing
else; and the adherents are fideles.[60] Hereby hangs a retort. When Dr.
Wiseman was first in England, he gave a course of lectures in defence of his
creed, which were thought very convincing by those who were already
convinced. They determined to give him a medal, and there was a very
serious discussion about the legend. Dr. Wiseman told me himself that he
had answered to his subscribers that he would not have the medal at all
unless—(naming some Italian authority, whom I forget) approved of the
legend. At last pro fide vindicata[61] was chosen: this may be read either in a
Popish or heretical sense. The feminine substantive fides means confidence,
trust, (it is made to mean belief), but fidis, with the same ablative, fide, and
also feminine, is a fiddle-string.[62] If a Latin writer had had to make a
legend signifying "For the defence of the fiddle-string," he could not have
done it otherwise, in the terseness of a legend, than by writing pro fide
vindicata. Accordingly, when a Roman Christian talks to you of the faith, as
a thing which is his and not yours, you may say fiddle. I have searched
Bonaventura Piscator in vain for notice of this ambiguity. But the Greeks
said fiddle; according to Suidas,[63] σκινδαψος[64]—a word meaning a four
stringed instrument played with a quill—was an exclamation of
contemptuous dissent. How the wits of different races jump!
I am reminded of a case of fides vindicata, which, being in a public letter,
responding to a public invitation, was not meant to be confidential. Some of
the pupils of University College, in which all subdivisions of religion are
(1866; were, 1867) on a level, have of course changed their views in after
life, and become adherents of various high churches. On the occasion of a
dinner of old students of the College, convened by circular, one of these
students, whether then Roman or Tractarian Christian I do not remember,
not content with simply giving negative answer, or none at all, concocted a
jorum of theological rebuke, and sent it to the Dinner Committee. Heyday!
said one of them, this man got out of bed backwards! How is that? said the
rest. Why, read his name backwards, and you will see. As thus read it was—
No grub![65]

THE WORD CHURCH.
To return to Notes and Queries. The substitution in the (editorial) index of
"Unitarian teacher," for the contributor's "Unitarian minister," struck me
very much. I have seldom found such things unmeaning. But as the journal
had always been free from editorial sectarianisms,—and very apt to check
the contributorial,—I could not be sure in this case. True it was, that the
editor and publisher had been changed more than a year before; but this was
not of much force. Though one swallow does not make a summer, I have
generally found it show that summer is coming. However, thought I to
myself, if this be Little Shibboleth, we shall have Big Shibboleth by-and-
bye. At last it came. About a twelvemonth afterwards, (3d S. vii. p. 36) the
following was the editorial answer to the question when the establishment
was first called the "Church of England and Ireland":
"That unmeaning clause, 'The United Church of England and Ireland,'
which occurs on the title-page of The Book of Common Prayer, was first
used at the commencement of the present century. The authority for this
phrase is the fifth article of the Union of 1800: 'That the Churches of
England and Ireland be united into one Protestant (!) episcopal Church, to
be called "The United Church of England and Ireland."' Of course,
churchmen are not responsible for the theology of Acts of Parliament,
especially those passed during the dark ages of the Georgian era."
That is to say, the journal gives its adhesion to the party which—under the
assumed title of the Church of England—claims for the endowed
corporation for the support of religion rights which Parliament cannot
control, and makes it, in fact, a power above the State. The State has given
an inch: it calls this corporation by the name of the "United Church of
England and Ireland," as if neither England nor Ireland had any other
Church. The corporation, accordingly aspires to an ell. But this the nation
will only give with the aspiration prefixed. To illustrate my allusion in a
delicate way to polite ears, I will relate what happened in a Johnian lecture-
room at Cambridge, some fifty years ago, my informant being present. A
youth of undue aspirations was giving a proposition, and at last said, "Let E
F be produced to 'L':" "Not quite so far, Mr. ——," said the lecturer, quietly,
to the great amusement of the class, and the utter astonishment of the

aspirant, who knew no more than a Tractarian the tendency of his
construction.
This word Church is made to have a very mystical meaning. The following
dialogue between Ecclesiastes and Hæreticus, which I cannot vouch for, has
often taken place in spirit, if not in letter: E. The word Church (ἐκκλησια)
[66] is never used in the New Testament except generally or locally for that

holy and mystical body to which the sacraments and the ordinances of
Christianity are entrusted. H. Indeed! E. It is beyond a doubt (here he
quoted half a dozen texts in support). H. Do you mean that any doctrine or
ordinance which was solemnly practised by the ἐκκλησια is binding upon
you and me? E. Certainly, unless we should be cut off from the
congregation of the faithful. H. Have you a couple of hours to spare? E.
What for? H. If you have, I propose we spend them in crying, Great is
Diana of the Ephesians! E. What do you mean? H. You ought to know the
solemn service of the ἐκκλησια (Acts xix. 32, 41), at Ephesus; which any
one might take to be true Church, by the more part not knowing wherefore
they were come together, and which was dismissed, after one of the most
sensible sermons ever preached, by the Recorder. E. I see your meaning: it
is true, there is that one exception! H. Why, the Recorder's sermon itself
contains another, the ἐννομος ἐκκλησια,[67] legislative assembly. E. Ah!
the New Testament can only be interpreted by the Church! H. I see! the
Church interprets itself into existence out of the New Testament, and then
interprets the New Testament out of existence into itself!
I look upon all the Churches as fair game which declare of me that absque
dubio in æternum peribo;[68] not for their presumption towards God, but for
their personal insolence towards myself. I find that their sectaries stare
when I say this. Why! they do not speak of you in particular! These poor
reasoners seem to think that there could be no meaning, as against me,
unless it should be propounded that "without doubt he shall perish
everlastingly, especially A. De Morgan." But I hold, with the schoolmen,
that "Omnis homo est animal" in conjunction with "Sortes est homo"
amounts to "Sortes est animal."[69] But they do not mean it personally!
Every universal proposition is personal to every instance of the subject. If
this be not conceded, then I retort, in their own sense and manner,
"Whosoever would serve God, before all things he must not pronounce

God's decision upon his neighbor. Which decision, except every one leave
to God himself, without doubt he is a bigoted noodle."
The reasoning habit of the educated community, in four cases out of five,
permits universal propositions to be stated at one time, and denied, pro re
nata,[70] at another. "Before we proceed to consider any question involving
physical principles, we should set out with clear ideas of the naturally
possible and impossible." The eminent man who said this, when wanting it
for his views of mental education (!) never meant it for more than what was
in hand, never assumed it in the researches which will give him to posterity!
I have heard half-a-dozen defences of his having said this, not one of which
affirmed the truth of what was said. A worthy clergyman wrote that if A. B.
had said a certain thing the point in question would have been established.
It was shown to him that A. B. had said it, to which the reply was a refusal
to admit the point because A. B. said it in a second pamphlet and in answer
to objections. And I might give fifty such instances with very little search.
Always assume more than you want; because you cannot tell how much
you may want: put what is over into the didn't-mean-that basket, or the
extreme case what-not.

PROTESTANT AND PAPAL CHRISTENDOM.
Something near forty years of examination of the theologies on and off—
more years very much on than quite off—have given me a good title—to
myself, I ask no one else for leave—to make the following remarks: A
conclusion has premises, facts or doctrines from proof or authority, and
mode of inference. There may be invention or falsehood of premise, with
good logic; and there may be tenable premise, followed by bad logic; and
there may be both false premise and bad logic. The Roman system has such
a powerful manufactory of premises, that bad logic is little wanted; there is
comparatively little of it. The doctrine-forge of the Roman Church is one
glorious compound of everything that could make Heraclitus[71] sob and
Democritus[72] snigger. But not the only one. The Protestants, in tearing
away from the Church of Rome, took with them a fair quantity of the results
of the Roman forge, which they could not bring themselves to give up.
They had more in them of Martin than of Jack. But they would have no

premises, except from the New Testament; though some eked out with a
few general Councils. The consequence is that they have been obliged to
find such a logic as would bring the conclusions they require out of the
canonical books. And a queer logic it is; nothing but the Roman forge can
be compared with the Protestant loom. The picking, the patching, the
piecing, which goes to the Protestant termini ad quem,[73] would be as
remarkable to the general eye, as the Roman manufacture of termini a quo,
[74]
if it were not that the world at large seizes the character of an asserted
fact better than that of a mode of inference. A grand step towards the
deification of a lady, made by alleged revelation 1800 years after her death,
is of glaring evidence: two or three additional shiffle-shuffles towards
defence of saying the Athanasian curse in church and unsaying it out of
church, are hardly noticed. Swift has bungled his satire where he makes
Peter a party to finding out what he wants, totidem syllabis and totidem
literis, when he cannot find it totidem verbis[75] This is Protestant method:
the Roman plan is viam faciam; the Protestant plan is viam inveniam.[76]
The public at large begins to be conversant with the ways of wriggling out,
as shown in the interpretations of the damnatory parts of the Athanasian
Creed, the phrases of the Burial Service, etc. The time will come when the
same public will begin to see the ways of wriggling in. But one thing at a
time: neither Papal Rome nor Protestant Rome was built—nor will be
pulled down—in a day.
The distinction above drawn between the two great antitheses of
Christendom may be illustrated as follows. Two sets of little general dealers
lived opposite to one another: all sold milk. Each vaunted its own produce:
one set said that the stuff on the other side the way was only chalk and
water; the other said that the opposites sold all sorts of filth, of which
calves' brain was the least nasty. Now the fact was that both sets sold milk,
and from the same dairy: but adulterated with different sorts of dirty water:
and both honestly believed that the mixture was what they were meant to
sell and ought to sell. The great difference between them, about which the
apprentices fought each other like Trojans, was that the calves' brain men
poured milk into the water, and the chalk men poured water into the milk.
The Greek and Roman sects on one side, the Protestant sects on the other,
must all have churches: the Greek and Roman sects pour the New
Testament into their churches; the Protestant sects pour their churches into

the New Testament. The Greek and Roman insist upon the New Testament
being no more than part and parcel of their churches: the Protestant insist
upon their churches being as much part and parcel of the New Testament.
All dwell vehemently upon the doctrine that there must be milk somewhere;
and each says—I have it. The doctrine is true: and can be verified by any
one who can and will go to the dairy for himself. Him will the several
traders declare to have no milk at all. They will bring their own wares, and
challenge a trial: they want nothing but to name the judges. To vary the
metaphor, those who have looked at Christianity in open day, know that all
who see it through painted windows shut out much of the light of heaven
and color the rest; it matters nothing that the stains are shaped into what are
meant for saints and angels.
But there is another side to the question. To decompose any substance, it
must be placed between the poles of the battery. Now theology is but one
pole; philosophy is the other. No one can make out the combinations of our
day unless he read the writings both of the priest and the philosopher: and if
any one should hold the first word offensive, I tell him that I mean both
words to be significant. In reading these writings, he will need to bring both
wires together to find out what it is all about. Time was when most priests
were very explicit about the fate of philosophers, and most philosophers
were very candid about their opinion of priests. But though some extremes
of the old sorts still remain, there is now, in the middle, such a fusion of the
two pursuits that a plain man is wofully puzzled. The theologian writes a
philosophy which seems to tell us that the New Testament is a system of
psychology; and the philosopher writes a Christianity which is utterly
unintelligible as to the question whether the Resurrection be a fact or a
transcendental allegory. What between the theologian who assents to the
Athanasian denunciation in what seems the sense of no denunciation, and
the philosopher who parades a Christianity which looks like no revelation,
there is a maze which threatens to have the only possible clue in the theory
that everything is something else, and nothing is anything at all. But this is
a paradox far beyond my handling: it is a Budget of itself.

RELIGION AND PHILOSOPHY.

Religion and Philosophy, the two best gifts of Heaven, set up in opposition
to each other at the revival of letters; and never did competing tradesmen
more grossly misbehave. Bad wishes and bad names flew about like
swarms of wasps. The Athanasian curses were intended against
philosophers; who, had they been a corporation, with state powers to protect
them, would have formulized a per contra. But the tradesmen are beginning
to combine: they are civil to each other; too civil by half. I speak especially
of Great Britain. Old theology has run off to ritualism, much lamenting,
with no comfort except the discovery that the cloak Paul left at Troas was a
chasuble. Philosophy, which always had a little sense sewed up in its
garments—to pay for its funeral?—has expended a trifle in accommodating
itself to the new system. But the two are poles of a battery; and a question
arises.

If Peter Piper picked a peck of pepper,
Where is the peck of pepper Peter Piper picked?

If Religion and Philosophy be the two poles of a battery, whose is the
battery Religion and Philosophy have been made the poles of? Is the change
in the relation of the wires any presumption of a removal of the managers?
We know pretty well who handled the instrument: has he resigned or
been[77] turned out? Has he been put under restriction? A fool may ask more
questions than twenty sages can answer: but there is hope; for twenty sages
cannot ask more questions than one reviewer can answer. I should like to
see the opposite sides employed upon the question, What are the commoda,
and what the pericula,[78] of the current approximation of Religion and
Philosophy?
All this is very profane and irreverent! It has always been so held by those
whose position demands such holding. To describe the Church as it is
passes for assailing the Church as it ought to be with all who cannot do
without it. In Bedlam[79] a poor creature who fancied he was St. Paul, was
told by another patient that he was an impostor; the first maniac lodged a
complaint against the second for calling St. Paul an impostor, which, he
argued, with much appearance of sanity, ought not to be permitted in a well
regulated madhouse. Nothing could persuade him that he had missed the
question, which was whether he was St. Paul. The same thing takes place in

the world at large. And especially must be noted the refusal to permit to the
profane the millionth part of the licence assumed by the sacred. I give a
sound churchman the epitaph of St. John Long; the usual pronunciation of
whose name must be noted—

"Behold! ye quacks, the vengeance strong
On deeds like yours impinging:
For here below lies St. John Long[80]
Who now must be long singeing."

How shameful to pronounce this of the poor man! What, Mr. Orthodox!
may I not do in joke to one pretender what you do in earnest—unless you
quibble—to all the millions of the Greek Church, and a great many others.
Enough of you and your reasoning! Go and square the circle!
The few years which end with 1867 have shown, not merely the
intermediate fusion of Theology and Philosophy of which I have spoken,
but much concentration of the two extremes, which looks like a gathering of
forces for some very hard fought Armageddon. Extreme theology has been
aiming at a high Church in England, which is to show a new front to all
heresy: and extreme philosophy is contriving a physical organization which
is to think, and to show that mind is a consequence of matter, or thought a
recreation of brain. The physical speculators begin with a possible
hypothesis, in which they aim at explanation: and so the bold aspirations of
the author of the Vestiges find standing-ground in the variation of species by
"natural selection." Some relics—so supposed—of extremely ancient men
are brought to help the general cause. Only distant hints are given that by
possibility it may end in the formation of all living organisms from a very
few, if not from one. The better heads above mentioned know that their
theory, if true, does not bear upon morals. The formation of solar systems
from a nebular hypothesis, followed by organizations gradually emerging
from some curious play of particles, nay, the very evolution of mind and
thought from such an apparatus, are all as consistent with a Personal
creative power to whom homage and obedience are due, and who has
declared himself, as with a blind Nature of Things. A pure materialist, as to
all things visible, may be even a bigotted Christian: this is not frequent, but
it is possible. There is a proverb which says, A pig may fly, but it isn't a
likely bird. But when the psychological speculator comes in, he often

undertakes to draw inferences from the physical conclusions, by joining on
his tremendous apparatus of a priori knowledge. He deduces that he can do
without a God: he can deduce all things without any such necessity. With
Occam[81] and Newton he will have no more causes than are necessary to
explain phenomena to him: and if by pure head-work combined with results
of physical observation he can construct his universe, he must be a very
unphilosophical man who would encumber himself with a useless Creator!
There is something tangible about my method, says he; yours is vague. He
requires it to be granted that his system is positive and that yours is
impositive. So reasoned the stage coachman when the railroads began to
depose him—"If you're upset in a stage-coach, why, there you are! but if
you're upset on the railroad, where are you?" The answer lies in another
question, Which is most positive knowledge, God deduced from man and
his history, or the postulates of the few who think they can reason a priori
on the tacit assumption of unlimited command of data?
We are not yet come to the existence of a school of philosophers who
explicitly deny a Creator: but we are on the way, though common sense
may interpose. There are always straws which show the direction of the
wind. I have before me the printed letter of a medical man—to whose
professional ability I have good testimony—who finds the vital principle in
highly rarefied oxygen. With the usual logic of such thinkers, he dismisses
the "eternal personal identity" because "If soul, spirit, mind, which are
merely modes of sensation, be the attribute or function of nerve-tissue, it
cannot possibly have any existence apart from its material organism!" How
does he know this impossibility? If all the mind we know be from nerve-
tissue, how does it appear that mind in other planets may not be another
thing? Nay, when we come to possibilities, does not his own system give a
queer one? If highly rarefied oxygen be vital power, more highly rarefied
oxygen may be more vital and more powerful. Where is this to stop? Is it
impossible that a finite quantity, rarefied ad infinitum, may be an
Omnipotent? Perhaps the true Genesis, when written, will open with "In the
beginning was an imperial quart of oxygen at 60° of Fahrenheit, and the
pressure of the atmosphere; and this oxygen was infinitely rarefied; and this
oxygen became God." For myself, my aspirations as to this system are
Manichæan. The quart of oxygen is the Ormuzd, or good principle: another
quart, of hydrogen, is the Ahriman, or evil principle! My author says that

his system explains Freewill and Immortality so obviously that it is difficult
to read previous speculations with becoming gravity. My deduction
explains the conflict of good and evil with such clearness that no one can
henceforward read the New Testament with becoming reverence. The
surgeon whom I have described is an early bud which will probably be
nipped by the frost and wither on the ground: but there is a good crop
coming. Material pneuma is destined to high functions; and man is to read
by gas-light.

THE SUN AN ELECTRIC SPACE.

The solar system truly solved; demonstrating by the perfect
harmony of the planets, founded on the four universal laws, the
Sun to be an electric space; and a source of every natural
production displayed throughout the solar system. By James
Hopkins.[82] London, 1849, 8vo.

The author says:
"I am satisfied that I have given the true laws constituting the Sun to be
space; and I call upon those disposed to maintain the contrary, to give true
laws showing him to be a body: until such can be satisfactorily established,
I have an undoubted claim to the credit of my theory,—That the Sun is an
Electric Space, fed and governed by the planets, which have the property of
attracting heat from it; and the means of supplying the necessary pabulum
by their degenerated air driven off towards the central space—the
wonderful alembic in which it becomes transmuted to the revivifying
necessities of continuous action; and the central space or Sun being
perfectly electric, has the counter property of repulsing the bodies that
attract it. How wonderful a conception! How beautiful, how magnificent an
arrangement!
"O Centre! O Space! O Electric Space!"

JOSEPH ADY.

1849. Joseph Ady[83] is entitled to a place in this list of discoverers: his
great fault, like that of some others, lay in pushing his method too far. He
began by detecting unclaimed dividends, and disclosing them to their right
owners, exacting his fee before he made his communication. He then
generalized into trying to get fees from all of the name belonging to a
dividend; and he gave mysterious hints of danger impending. For instance,
he would write to a clergyman that a legal penalty was hanging over him;
and when the alarmed divine forwarded the sum required for disclosure, he
was favored with an extract from some old statute or canon, never repealed,
forbidding a clergyman to be a member of a corporation, and was reminded
that he had insured his life in the —— Office, which had a royal charter. He
was facetious, was Joseph: he described himself in his circulars as
"personally known to Sir Peter Laurie[84] and all other aldermen"; which
was nearly true, as he had been before most of them on charges of false
pretence; but I believe he was nearly always within the law. Sir James
Duke, when Lord Mayor, having particularly displeased him by a decision,
his circulars of 1849 contain the following:
"Should you have cause to complain of any party, Sir J. Duke has contrived
a new law of evidence, viz., write to him, he will consider your letter
sufficient proof, and make the parties complained of pay without judge or
jury, and will frank you from every expense."
I strongly suspect that Joseph Ady believed in himself.
He sometimes issued a second warning, of a Sibylline character:
"Should you find cause to complain of anybody, my voluntary referee, the
Rt. Hon. Sir Peter Laurie, Kt., perpetual Deputy Lord Mayor, will see
justice done you without any charge whatever: he and his toady, — ——
——. The accursed of Moses can hang any man: thus, by catching him
alone and swearing Naboth spake evil against God and the King. Therefore
(!) I admit no strangers to a personal conference without a prepayment of
20s. each. Had you attended to my former notice you would have received
twice as much: neglect this and you will lose all."

ON MODERN ASTROLOGY.

Zadkiel's Almanac for 1849. Nineteenth number.
Raphael's Prophetic Almanac for 1849. Twenty-ninth number.
Reasons for belief in judicial astrology, and remarks on the
dangerous character of popish priestcraft. London, 1849, 12mo.
Astronomy in a nutshell: or the leading problems of the solar
system solved by simple proportion only, on the theory of
magnetic attraction. By Lieut. Morrison,[85] N. N. London (s. a.)
12mo.

Lieut. Morrison is Zadkiel Tao Sze, and declares himself in real earnest an
astrologer. There are a great many books on astrology, but I have not felt
interest enough to preserve many of them which have come in my way. If
anything ever had a fair trial, it was astrology. The idea itself is natural
enough. A human being, set down on this earth, without any tradition,
would probably suspect that the heavenly bodies had something to do with
the guidance of affairs. I think that any one who tries will ascertain that the
planets do not prophesy: but if he should find to the contrary, he will of
course go on asking. A great many persons class together belief in astrology
and belief in apparitions: the two things differ in precisely the way in which
a science of observation differs from a science of experiment. Many make
the mistake which M. le Marquis made when he came too late, and hoped
M. Cassini[86] would do the eclipse over again for his ladies. The apparition
chooses its own time, and comes as seldom or as often as it pleases, be it
departed spirit, nervous derangement, or imposition. Consequently it can
only be observed, and not experimented upon. But the heavens, if astrology
be true, are prophesying away day and night all the year round, and about
every body. Experiments can be made, then, except only on rare
phenomena, such as eclipses: anybody may choose his time and his
question. This is the great difference: and experiments were made, century
after century. If astrology had been true, it must have lasted in an ever-
improving state. If it be true, it is a truth, and a useful truth, which had
experience and prejudice both in its favor, and yet lost ground as soon as
astronomy, its working tool, began to improve.

1850. A letter in the handwriting of an educated man, dated from a street in
which it must be taken that educated persons live, is addressed to the
Secretary of the Astronomical Society about a matter on which the writer
says "his professional pursuit will enable him to give a satisfactory reply."
In a question before a court of law it is sworn on one side that the moon was
shining at a certain hour of a certain night on a certain spot in London; on
the other side it is affirmed that she was clouded. The Secretary is requested
to decide. This is curious, as the question is not astrological. Persons still
send to Greenwich, now and then, to have their fortunes told. In one case,
not very many years ago, a young gentleman begged to know who his wife
was to be, and what fee he was to remit.
Sometimes the astronomer turns conjurer for fun, and his prophesies are
fulfilled. It is related of Flamsteed[87] that an old woman came to know the
whereabouts of a bundle of linen which had strayed. Flamsteed drew a
circle, put a square into it, and gravely pointed out a ditch, near her cottage,
in which he said it would be found. He meant to have given the woman a
little good advice when she came back: but she came back in great delight,
with the bundle in her hand, found in the very place. The late Baron
Zach[88] received a letter from Pons,[89] a successful finder of comets,
complaining that for a certain period he had found no comets, though he
had searched diligently. Zach, a man of much sly humor, told him that no
spots had been seen on the sun for about the same time—which was true,—
and assured him that when the spots came back, the comets would come
with them. Some time after he got a letter from Pons, who informed him
with great satisfaction that he was quite right, that very large spots had
appeared on the sun, and that he had found a fine comet shortly after. I do
not vouch for the first story, but I have the second in Zach's handwriting. It
would mend the joke exceedingly if some day a real relation should be
established between comets and solar spots: of late years good reason has
been shown for advancing a connection between these spots and the earth's
magnetism.[90] If the two things had been put to Zach, he would probably
have chosen the comets. Here is a hint for a paradox: the solar spots are the
dead comets, which have parted with their light and heat to feed the sun, as
was once suggested. I should not wonder if I were too late, and the thing
had been actually maintained. My list does not contain the twentieth part of
the possible whole.

The mention of coincidences suggests an everlasting source of
explanations, applicable to all that is extraordinary. The great paradox of
coincidence is that of Leibnitz, known as the pre-established harmony, or
law of coincidences, by which, separately and independently, the body
receives impressions, and the mind proceeds as if it had perceived them
from without. Every sensation, and the consequent state of the soul, are
independent things coincident in time by the pre-established law. The
philosopher could not otherwise account for the connection of mind and
matter; and he never goes by so vulgar a rule as Whatever is, is; to him that
which is not clear as to how, is not at all. Philosophers in general, who
tolerate each other's theories much better than Christians do each other's
failings, seldom revive Leibnitz's fantasy: they seem to act upon the maxim
quoted by Father Eustace[91] from the Decretals, Facinora ostendi dum
puniuntur, flagitia autem abscondi debent.[92]
The great ghost-paradox, and its theory of coincidences, will rise to the
surface in the mind of every one. But the use of the word coincidence is
here at variance with its common meaning. When A is constantly
happening, and also B, the occurrence of A and B at the same moment is the
mere coincidence which may be casualty. But the case before us is that A is
constantly happening, while B, when it does happen, almost always
happens with A, and very rarely without it. That is to say, such is the
phenomenon asserted: and all who rationally refer it to casualty, affirm that
B is happening very often as well as A, but that it is not thought worthy of
being recorded except when A is simultaneous. Of course A is here a death,
and B the spectral appearance of the person who dies. In talking of this
subject it is necessary to put out of the question all who play fast and loose
with their secret convictions: these had better give us a reason, when they
feel internal pressure for explanation, that there is no weathercock at Kilve;
this would do for all cases. But persons of real inquiry will see that first,
experience does not bear out the asserted frequency of the spectre, without
the alleged coincidence of death: and secondly, that if the crowd of purely
casual spectres were so great that it is no wonder that, now and then the
person should have died at or near the moment, we ought to expect a much
larger proportion of cases in which the spectre should come at the moment
of the death of one or another of all the cluster who are closely connected
with the original of the spectre. But this, we know, is almost without

example. It remains then, for all, who speculate at all, to look upon the
asserted phenomenon, think what they may of it, the thing which is to be
explained, as a connection in time of the death, and the simultaneous
appearance of the dead. Any person the least used to the theory of
probabilities will see that purely casual coincidence, the wrong spectre
being comparatively so rare that it may be said never to occur, is not within
the rational field of possibility.
The purely casual coincidence, from which there is no escape except the
actual doctrine of special providences, carried down to a very low point of
special intention, requires a junction of the things the like of each of which
is always happening. I will give three instances which have occurred to
myself within the last few years: I solemnly vouch for the literal truth of
every part of all three:

In August 1861, M. Senarmont,[93] of the French Institute, wrote to me to
the effect that Fresnel[94] had sent to England, in or shortly after 1824, a
paper for translation and insertion in the European Review, which shortly
afterwards expired. The question was what had become of that paper. I
examined the Review at the Museum, found no trace of the paper, and wrote
back to that effect at the Museum, adding that everything now depended on
ascertaining the name of the editor, and tracing his papers: of this I thought
there was no chance. I posted this letter on my way home, at a Post Office
in the Hampstead Road at the junction with Edward Street, on the opposite
side of which is a bookstall. Lounging for a moment over the exposed
books, sicut meus est mos,[95] I saw, within a few minutes of the posting of
the letter, a little catch-penny book of anecdotes of Macaulay, which I
bought, and ran over for a minute. My eye was soon caught by this
sentence: "One of the young fellows immediately wrote to the editor (Mr.
Walker) of the European Review." I thus got the clue by which I ascertained
that there was no chance of recovering Fresnel's paper. Of the mention of
current reviews, not one in a thousand names the editor.
In the summer of 1865 I made my first acquaintance with the tales of
Nathaniel Hawthorne, and the first I read was about the siege of Boston in
the War of Independence. I could not make it out: everybody seemed to
have got into somebody else's place. I was beginning the second tale, when
a parcel arrived: it was a lot of old pamphlets and other rubbish, as he called

it, sent by a friend who had lately sold his books, had not thought it worth
while to send these things for sale, but thought I might like to look at them
and possibly keep some. The first thing I looked at was a sheet which, being
opened, displayed "A plan of Boston and its environs, shewing the true
situation of his Majesty's army and also that of the rebels, drawn by an
engineer, at Boston Oct. 1775." Such detailed plans of current sieges being
then uncommon, it is explained that "The principal part of this plan was
surveyed by Richard Williams, Lieutenant at Boston; and sent over by the
son of a nobleman to his father in town, by whose permission it was
published." I immediately saw that my confusion arose from my supposing
that the king's troops were besieging the rebels, when it was just the other
way.
April 1, 1853, while engaged in making some notes on a logical point, an
idea occurred which was perfectly new to me, on the mode of conciliating
the notions omnipresence and indivisibility into parts. What it was is no
matter here: suffice it that, since it was published elsewhere (in a paper on
Infinity, Camb. Phil. Trans. vol. xi. p. 1) I have not had it produced to me. I
had just finished a paragraph on the subject, when a parcel came in from a
bookseller containing Heywood's[96] Analysis of Kant's Critick, 1844.
On turning over the leaves I found (p. 109) the identical thought which up
to this day, I only know as in my own paper, or in Kant. I feel sure I had not
seen it before, for it is in Kant's first edition, which was never translated to
my knowledge; and it does not appear in the later editions. Mr. Heywood
gives some account of the first edition.
In the broadsheet which gave account of the dying scene of Charles II, it is
said that the Roman Catholic priest was introduced by P. M. A. C. F. The
chain was this: the Duchess of Portsmouth[97] applied to the Duke of York,
who may have consulted his Cordelier confessor, Mansuete, about
procuring a priest, and the priest was smuggled into the king's room by the
Duchess and Chiffinch.[98] Now the letters are a verbal acrostic of Père
Mansuete a Cordelier Friar, and a syllabic acrostic of PortsMouth and
ChifFinch. This is a singular coincidence. Macaulay adopted the first
interpretation, preferring it to the second, which I brought before him as the
conjecture of a near relative of my own. But Mansuete is not mentioned in
his narrative: it may well be doubted whether the writer of a broadside for

English readers would use Père instead of Father. And the person who
really "reminded" the Duke of "the duty he owed to his brother," was the
Duchess and not Mansuete. But my affair is only with the coincidence.
But there are coincidences which are really connected without the
connection being known to those who find in them matter of astonishment.
Presentiments furnish marked cases: sometimes there is no mystery to those
who have the clue. In the Gentleman's Magazine (vol. 80, part 2, p. 33) we
read, the subject being presentiment of death, as follows: "In 1778, to come
nearer the recollection of survivors, at the taking of Pondicherry, Captain
John Fletcher, Captain De Morgan, and Lieutenant Bosanquet, each
distinctly foretold his own death on the morning of his fate." I have no
doubt of all three; and I knew it of my grandfather long before I read the
above passage. He saw that the battery he commanded was unduly exposed:
I think by the sap running through the fort when produced. He represented
this to the engineer officers, and to the commander-in-chief; the engineers
denied the truth of the statement, the commander believed them, my
grandfather quietly observed that he must make his will, and the French
fulfilled his prediction. His will bore date the day of his death; and I always
thought it more remarkable than the fulfilment of the prophecy that a
soldier should not consider any danger short of one like the above,
sufficient reason to make his will. I suppose the other officers were
similarly posted. I am told that military men very often defer making their
wills until just before an action: but to face the ordinary risks intestate, and
to wait until speedy death must be the all but certain consequence of a
stupid mistake, is carrying the principle very far. In the matter of
coincidences there are, as in other cases, two wonderful extremes with
every intermediate degree. At one end we have the confident people who
can attribute anything to casual coincidence; who allow Zadok Imposture
and Nathan Coincidence to anoint Solomon Selfconceit king. At the other
end we have those who see something very curious in any coincidence you
please, and whose minds yearn for a deep reason. A speculator of this class
happened to find that Matthew viii. 28-33 and Luke viii. 26-33 contain the
same account, that of the demons entering into the swine. Very odd!
chapters tallying, and verses so nearly: is the versification rightly managed?
Examination is sure to show that there are monstrous inconsistencies in the
mode of division, which being corrected, the verses tally as well as the

chapters. And then how comes it? I cannot go on, for I have no gift at
torturing a coincidence, but I would lay twopence, if I could make a bet—
which I never did in all my life—that some one or more of my readers will
try it. Some people say that the study of chances tends to awaken a spirit of
gambling: I suspect the contrary. At any rate, I myself, the writer of a
mathematical book and a comparatively popular book, have never laid a bet
nor played for a stake, however small: not one single time.
It is useful to record such instances as I have given, with precision and on
the solemn word of the recorder. When such a story as that of Flamsteed is
told, a priori assures us that it could not have been: the story may have been
a ben trovato,[99] but not the bundle. It is also useful to establish some of the
good jokes which all take for inventions. My friend Mr. J. Bellingham
Inglis,[100] before 1800, saw the tobacconist's carriage with a sample of
tobacco in a shield, and the motto Quid rides[101] (N. & Q., 3d S. i. 245).
His father was able to tell him all about it. The tobacconist was Jacob
Brandon, well known to the elder Mr. Inglis, and the person who started the
motto, the instant he was asked for such a thing, was Harry Calender of
Lloyd's, a scholar and a wit. My friend Mr. H. Crabb Robinson[102]
remembers the King's Counsel (Samuel Marryat) who took the motto
Causes produce effects, when his success enabled him to start a carriage.
The coincidences of errata are sometimes very remarkable: it may be that
the misprint has a sting. The death of Sir W. Hamilton[103] of Edinburgh
was known in London on a Thursday, and the editor of the Athenæum wrote
to me in the afternoon for a short obituary notice to appear on Saturday. I
dashed off the few lines which appeared without a moment to think: and
those of my readers who might perhaps think me capable of contriving
errata with meaning will, I am sure, allow the hurry, the occasion, and my
own peculiar relation to the departed, as sufficient reasons for believing in
my entire innocence. Of course I could not see a proof: and two errata
occurred. The words "addition to Stewart"[104] require "for addition to read
edition of." This represents what had been insisted on by the Edinburgh
publisher, who, frightened by the edition of Reid,[105] had stipulated for a
simple reprint without notes. Again "principles of logic and mathematics"
required "for mathematics read metaphysics." No four words could be put
together which would have so good a title to be Hamilton's motto.

April 1850, found in the letter-box, three loose leaves, well printed and over
punctuated, being

Chapter VI. Brethren, lo I come, holding forth the word of life,
for so I am commanded.... Chapter VII. Hear my prayer, O
generations! and walk by the way, to drink the waters of the
river.... Chapter VIII. Hearken o earth, earth, earth, and the kings
of the earth, and their armies....

A very large collection might be made of such apostolic writings. They go
on well enough in a misty—meant for mystical—imitation of St. Paul or the
prophets, until at last some prodigious want of keeping shows the education
of the writer. For example, after half a page which might pass for
Irving's[106] preaching—though a person to whom it was presented as such
would say that most likely the head and tail would make something more
like head and tail of it—we are astounded by a declaration from the Holy
Spirit, speaking of himself, that he is "not ashamed of the Gospel of Christ."
It would be long before we should find in educated rhapsody—of which
there are specimens enough—such a thing as a person of the Trinity taking
merit for moral courage enough to stand where St. Peter fell. The following
declaration comes next—"I will judge between cattle and cattle, that use
their tongues."

THE FIGURE OF THE EARTH.

The figure of the earth. By J. L. Murphy,[107] of Birmingham.
(London and Birmingham, 4 pages, 12mo.) (1850?)

Mr. Murphy invites attention and objection to some assertions, as that the
earth is prolate, not oblate. "If the philosopher's conclusion be right, then
the pole is the center of a valley (!) thirteen miles deep." Hence it would be
very warm. It is answer enough to ask—Who knows that it is not?

*** A paragraph in the MS. appears to have been inserted in this
place by mistake. It will be found in the Appendix at the end of
this volume.—S. E. De M.

PERPETUAL MOTION.
1851. The following letter was written by one of a class of persons whom,
after much experience of them, I do not pronounce insane. But in this case
the second sentence gives a suspicion of actual delusion of the senses; the
third looks like that eye for the main chance which passes for sanity on the
Stock Exchange and elsewhere:
15th Sept. 1851.
"Gentlemen,—I pray you take steps to make known that yesterday I
completed my invention which will give motion to every country on the
Earth;—to move Machinery!—the long sought in vain 'Perpetual Motion'!!
—I was supported at the time by the Queen and H.R.H. Prince Albert. If,
Gentlemen, you can advise me how to proceed to claim the reward, if any is
offered by the Government, or how to secure the Patent for the machine, or
in any way assist me by advice in this great work, I shall most graciously
acknowledge your consideration.
These are my convictions that my SEVERAL discoveries will be realized: and
this great one can be at once acted upon: although at this moment it only
exists in my mind, from my knowledge of certain fixed principles in nature:
—the Machine I have not made, as I only completed the discovery
YESTERDAY, Sunday!

I have, etc. —— ——"

To the Directors of the
London University, Gower Street.

ON SPIRITUALISM.

The Divine Drama of History and Civilisation. By the Rev. James
Smith, M.A.[108] London, 1854, 8vo.

I have several books on that great paradox of our day, Spiritualism, but I
shall exclude all but three. The bibliography of this subject is now very
large. The question is one both of evidence and speculation;—Are the facts
true? Are they caused by spirits? These I shall not enter upon: I shall merely
recommend this work as that of a spiritualist who does not enter on the
subject, which he takes for granted, but applies his derived views to the
history of mankind with learning and thought. Mr. Smith was a man of a
very peculiar turn of thinking. He was, when alive, the editor, or an editor,
of the Family Herald: I say when alive, to speak according to knowledge;
for, if his own views be true, he may have a hand in it still. The answers to
correspondents, in his time, were piquant and original above any I ever saw.
I think a very readable book might be made out of them, resembling
"Guesses at Truth:" the turn given to an inquiry about morals, religion, or
socials, is often of the highest degree of unexpectedness; the poor querist
would find himself right in a most unpalatable way.
Answers to correspondents, in newspapers, are very often the fag ends of
literature. I shall never forget the following. A person was invited to name a
rule without exception, if he could: he answered "A man must be present
when he is shaved." A lady—what right have ladies to decide questions
about shaving?—said this was not properly a rule; and the oracle was
consulted. The editor agreed with the lady; he said that "a man must be
present when he is shaved" is not a rule, but a fact.

[Among my anonymous communicants is one who states that I have done
injustice to the Rev. James Smith in "referring to him as a spiritualist," and
placing his "Divine Drama" among paradoxes: "it is no paradox, nor do
spiritualistic views mar or weaken the execution of the design." Quite true:
for the design is to produce and enforce "spiritualistic views"; and leather
does not mar nor weaken a shoemaker's plan. I knew Mr. Smith well, and
have often talked to him on the subject: but more testimony from me is
unnecessary; his book will speak for itself. His peculiar style will justify a
little more quotation than is just necessary to prove the point. Looking at

the "battle of opinion" now in progress, we see that Mr. Smith was a
prescient:
(P. 588.) "From the general review of parties in England, it is evident that
no country in the world is better prepared for the great Battle of Opinion.
Where else can the battle be fought but where the armies are arrayed? And
here they all are, Greek, Roman, Anglican, Scotch, Lutheran, Calvinist,
Established and Territorial, with Baronial Bishops, and Nonestablished of
every grade—churches with living prophets and apostles, and churches with
dead prophets and apostles, and apostolical churches without apostles, and
philosophies without either prophets or apostles, and only wanting one
more, 'the Christian Church,' like Aaron's rod, to swallow up and digest
them all, and then bud and flourish. As if to prepare our minds for this
desirable and inevitable consummation, different parties have been favored
with a revival of that very spirit of revelation by which the Church itself
was originally founded. There is a complete series of spiritual revelations in
England and the United States, besides mesmeric phenomena that bear a
resemblance to revelation, and thus gradually open the mind of the
philosophical and infidel classes, as well as the professed believers of that
old revelation which they never witnessed in living action, to a better
understanding of that Law of Nature (for it is a Law of Nature) in which all
revelation originates and by which its spiritual communications are
regulated."
Mr. Smith proceeds to say that there are only thirty-five incorporated
churches in England, all formed from the New Testament except five, to
each of which five he concedes a revelation of its own. The five are the
Quakers, the Swedenborgians, the Southcottians, the Irvingites, and the
Mormonites. Of Joanna Southcott he speaks as follows:

(P. 592.) "Joanna Southcott[109] is not very gallantly treated by the
gentlemen of the Press, who, we believe, without knowing anything about
her, merely pick up their idea of her character from the rabble. We once
entertained the same rabble idea of her; but having read her works—for we
really have read them—we now regard her with great respect. However,
there is a great abundance of chaff and straw to her grain; but the grain is
good, and as we do not eat either the chaff or straw if we can avoid it, nor
even the raw grain, but thrash it and winnow it, and grind it and bake it, we

find it, after undergoing this process, not only very palatable, but a special
dainty of its kind. But the husk is an insurmountable obstacle to those
learned and educated gentlemen who judge of books entirely by the style
and the grammar, or those who eat grain as it grows, like the cattle. Such
men would reject all prological revelation; for there never was and probably
never will be a revelation by voice and vision communicated in classical
manner. It would be an invasion of the rights and prerogatives of Humanity,
and as contrary to the Divine and Established order of mundane
government, as a field of quartern loaves or hot French rolls."

Mr. Smith's book is spiritualism from beginning to end; and my anonymous
gainsayer, honest of course, is either ignorant of the work he thinks he has
read, or has a most remarkable development of the organ of imperception.]

A CONDENSED HISTORY OF MATHEMATICS.
I cut the following from a Sunday paper in 1849:
"X. Y.—The Chaldeans began the mathematics, in which the Egyptians
excelled. Then crossing the sea, by means of Thales,[110] the Milesian, they
came into Greece, where they were improved very much by Pythagoras,[111]
Anaxagoras,[112] and Anopides[113] of Chios. These were followed by Briso,
[114] Antipho, [two circle-squarers; where is Euclid?] and Hippocrates,[115]

but the excellence of the algebraic art was begun by Geber,[116] an Arabian
astronomer, and was carried on by Cardanus,[117] Tartaglia,[118] Clavius,
[119], Stevinus,[120] Ghetaldus,[121] Herigenius,[122] Fran. Van Schooten

[meaning Francis Van Schooten[123]], Florida de Beaume,[124] etc."
Bryso was a mistaken man. Antipho had the disadvantage of being in
advance of his age. He had the notion of which the modern geometry has
made so much, that of a circle being the polygon of an infinitely great
number of sides. He could make no use of it, but the notion itself made him
a sophist in the eyes of Aristotle, Eutocius,[125] etc. Geber, an Arab
astronomer, and a reputed conjurer in Europe, seems to have given his name

to unintelligible language in the word gibberish. At one time algebra was
traced to him; but very absurdly, though I have heard it suggested that
algebra and gibberish must have had one inventor.
Any person who meddles with the circle may find himself the crane who
was netted among the geese: as Antipho for one, and Olivier de Serres[126]
for another. This last gentleman ascertained, by weighing, that the area of
the circle is very nearly that of the square on the side of the inscribed
equilateral triangle: which it is, as near as 3.162 ... to 3.141.... He did not
pretend to more than approximation; but Montucla and others
misunderstood him, and, still worse, misunderstood their own
misunderstanding, and made him say the circle was exactly double of the
equilateral triangle. He was let out of limbo by Lacroix, in a note to his
edition of Montucla's History of Quadrature.

ST. VITUS, PATRON OF CYCLOMETERS.

Quadratura del cerchio, trisezione dell' angulo, et duplicazione del
cubo, problemi geometricamente risolute e dimostrate dal
Reverendo Arciprete di San Vito D. Domenico Angherà,[127]
Malta, 1854, 8vo.
Equazioni geometriche, estratte dalla lettera del Rev. Arciprete ...
al Professore Pullicino[128] sulla quadratura del cerchio. Milan,
1855 or 1856, 8vo.
Il Mediterraneo gazetta di Malta, 26 Decembre 1855, No. 909:
also 911, 912, 913, 914, 936, 939.
The Malta Times, Tuesday, 9th June 1857.
Misura esatta del cerchio, dal Rev. D. Angherà. Malta, 1857,
12mo.
Quadrature of the circle ... by the Rev. D. Angherà, Archpriest of
St. Vito. Malta, 1858, 12mo.

I have looked for St. Vitus in catalogues of saints, but never found his
legend, though he figures as a day-mark in the oldest almanacs. He must be
properly accredited, since he was an archpriest. And I pronounce and
ordain, by right accruing from the trouble I have taken in this subject, that
he, St. Vitus, who leads his votaries a never-ending and unmeaning dance,
shall henceforth be held and taken to be the patron saint of the circle-
squarer. His day is the 15th of June, which is also that of St. Modestus,[129]
with whom the said circle-squarer often has nothing to do. And he must not
put himself under the first saint with a slantendicular reference to the other,
as is much to be feared was done by the Cardinal who came to govern
England with a title containing St. Pudentiana,[130] who shares a day with
St. Dunstan. The Archpriest of St. Vitus will have it that the square
inscribed in a semicircle is half of the semicircle, or the circumference 3-1/5
diameters. He is active and able, with nothing wrong about him except his
paradoxes. In the second tract named he has given the testimonials of
crowned heads and ministers, etc. as follows. Louis-Napoleon gives thanks.
The minister at Turin refers it to the Academy of Sciences, and hopes so
much labor will be judged degna di pregio.[131] The Vice-Chancellor of
Oxford—a blunt Englishman—begs to say that the University has never
proposed the problem, as some affirm. The Prince Regent of Baden has
received the work with lively interest. The Academy of Vienna is not in a
position to enter into the question. The Academy of Turin offers the most
distinct thanks. The Academy della Crusca attends only to literature, but
gives thanks. The Queen of Spain has received the work with the highest
appreciation. The University of Salamanca gives infinite thanks, and feels
true satisfaction in having the book. Lord Palmerston gives thanks, by the
hand of "William San." The Viceroy of Egypt, not being yet up in Italian,
will spend his first moments of leisure in studying the book, when it shall
have been translated into French: in the mean time he congratulates the
author upon his victory over a problem so long held insoluble. All this is
seriously published as a rate in aid of demonstration. If these royal
compliments cannot make the circumference of a circle about 2 per cent.
larger than geometry will have it —which is all that is wanted—no wonder
that thrones are shaky.

I am informed that the legend of St. Vitus is given by Ribadeneira[132] in his
lives of Saints, and that Baronius,[133] in his Martyrologium Romanum,

refers to several authors who have written concerning him. There is an
account in Mrs. Jameson's[134] History of Sacred and Legendary Art (ed. of
1863, p. 544). But it seems that St. Vitus is the patron saint of all dances; so
that I was not so far wrong in making him the protector of the cyclometers.
Why he is represented with a cock is a disputed point, which is now made
clear: next after gallus gallinaceus[135] himself, there is no crower like the
circle-squarer.

CELEBRATED APPROXIMATIONS OF π.
The following is an extract from the English Cyclopædia, Art. Tables:

"1853. William Shanks,[136] Contributions to Mathematics, comprising
chiefly the Rectification of the Circle to 607 Places of Tables, London,
1853. (Quadrature of the Circle.) Here is a table, because it tabulates the
results of the subordinate steps of this enormous calculation as far as 527
decimals: the remainder being added as results only during the printing. For
instance, one step is the calculation of the reciprocal of 601.5601; and the
result is given. The number of pages required to describe these results is 87.
Mr. Shanks has also thrown off, as chips or splinters, the values of the base
of Napier's logarithms, and of its logarithms of 2, 3, 5, 10, to 137 decimals;
and the value of the modulus .4342 ... to 136 decimals: with the 13th, 25th,
37th ... up to the 721st powers of 2. These tremendous stretches of
calculation—at least we so call them in our day—are useful in several
respects; they prove more than the capacity of this or that computer for
labor and accuracy; they show that there is in the community an increase of
skill and courage. We say in the community: we fully believe that the
unequalled turnip which every now and then appears in the newspapers is a
sufficient presumption that the average turnip is growing bigger, and the
whole crop heavier. All who know the history of the quadrature are aware
that the several increases of numbers of decimals to which π has been
carried have been indications of a general increase in the power to calculate,
and in courage to face the labor. Here is a comparison of two different
times. In the day of Cocker,[137] the pupil was directed to perform a
common subtraction with a voice-accompaniment of this kind: '7 from 4 I
cannot, but add 10, 7 from 14 remains 7, set down 7 and carry 1; 8 and 1

which I carry is 9, 9 from 2 I cannot, etc.' We have before us the
announcement of the following table, undated, as open to inspection at the
Crystal Palace, Sydenham, in two diagrams of 7 ft. 2 in, by 6 ft. 6 in.: 'The
figure 9 involved into the 912th power, and antecedent powers or
involutions, containing upwards of 73,000 figures. Also, the proofs of the
above, containing upwards of 146,000 figures. By Samuel Fancourt, of
Mincing Lane, London, and completed by him in the year 1837, at the age
of sixteen. N.B. The whole operation performed by simple arithmetic.' The
young operator calculated by successive squaring the 2d, 4th, 8th, etc.,
powers up to the 512th, with proof by division. But 511 multiplications by
9, in the short (or 10-1) way, would have been much easier. The 2d, 32d,
64th, 128th, 256th, and 512th powers are given at the back of the
announcement. The powers of 2 have been calculated for many purposes. In
Vol. II of his Magia Universalis Naturæ et Artis, Herbipoli, 1658, 4to, the
Jesuit Gaspar Schott[138] having discovered, on some grounds of theological
magic, that the degrees of grace of the Virgin Mary were in number the
256th power of 2, calculated that number. Whether or no his number
correctly represented the result he announced, he certainly calculated it
rightly, as we find by comparison with Mr. Shanks."

There is a point about Mr. Shanks's 608 figures of the value of π which
attracts attention, perhaps without deserving it. It might be expected that, in
so many figures, the nine digits and the cipher would occur each about the
same number of times; that is, each about 61 times. But the fact stands thus:
3 occurs 68 times; 9 and 2 occur 67 times each; 4 occurs 64 times; 1 and 6
occur 62 times each; 0 occurs 60 times; 8 occurs 58 times; 5 occurs 56
times; and 7 occurs only 44 times. Now, if all the digits were equally likely,
and 608 drawings were made, it is 45 to 1 against the number of sevens
being as distant from the probable average (say 61) as 44 on one side or 78
on the other. There must be some reason why the number 7 is thus deprived
of its fair share in the structure. Here is a field of speculation in which two
branches of inquirers might unite. There is but one number which is treated
with an unfairness which is incredible as an accident; and that number is the
mystic number seven! If the cyclometers and the apocalyptics would lay
their heads together until they come to a unanimous verdict on this
phenomenon, and would publish nothing until they are of one mind, they

would earn the gratitude of their race.—I was wrong: it is the Pyramid-
speculator who should have been appealed to. A correspondent of my friend
Prof. Piazzi Smyth[139] notices that 3 is the number of most frequency, and
that 3-1/7 is the nearest approximation to it in simple digits. Professor
Smyth himself, whose word on Egypt is paradox of a very high order,
backed by a great quantity of useful labor, the results which will be made
available by those who do not receive the paradoxes, is inclined to see
confirmation for some of his theory in these phenomena.

CURIOUS CALCULATIONS.
These paradoxes of calculation sometimes appear as illustrations of the
value of a new method. In 1863, Mr. G. Suffield,[140] M.A., and Mr. J. R.
Lunn,[141] M.A., of Clare College and of St. John's College, Cambridge,
published the whole quotient of 10000 ... divided by 7699, throughout the
whole of one of the recurring periods, having 7698 digits. This was done in
illustration of Mr. Suffield's method of Synthetic division.
Another instance of computation carried to paradoxical length, in order to
illustrate a method, is the solution of x3 - 2x = 5, the example given of
Newton's method, on which all improvements have been tested. In 1831,
Fourier's[142] posthumous work on equations showed 33 figures of solution,
got with enormous labor. Thinking this a good opportunity to illustrate the
superiority of the method of W. G. Horner,[143] not yet known in France,
and not much known in England, I proposed to one of my classes, in 1841,
to beat Fourier on this point, as a Christmas exercise. I received several
answers, agreeing with each other, to 50 places of decimals. In 1848, I
repeated the proposal, requesting that 50 places might be exceeded: I
obtained answers of 75, 65, 63, 58, 57, and 52 places. But one answer, by
Mr. W. Harris Johnston,[144] of Dundalk, and of the Excise Office, went to
101 decimal places. To test the accuracy of this, I requested Mr. Johnston to
undertake another equation, connected with the former one in a way which I
did not explain. His solution verified the former one, but he was unable to
see the connection, even when his result was obtained. My reader may be as
much at a loss: the two solutions are:

2.0945514815423265...
9.0544851845767340...

The results are published in the Mathematician, Vol. III, p. 290. In 1851,
another pupil of mine, Mr. J. Power Hicks,[145] carried the result to 152
decimal places, without knowing what Mr. Johnston had done. The result is
in the English Cyclopædia, article Involution and Evolution.
I remark that when I write the initial of a Christian name, the most usual
name of that initial is understood. I never saw the name of W. G. Horner
written at length, until I applied to a relative of his, who told me that he
was, as I supposed, Wm. George, but that he was named after a relative of
that surname.
The square root of 2, to 110 decimal places, was given me in 1852 by my
pupil, Mr. William Henry Colvill, now (1867) Civil Surgeon at Baghdad. It
was

1.4142135623730950488016887242096980785696
7187537694807317667973799073247846210703
885038753432764157273501384623

Mr. James Steel[146] of Birkenhead verified this by actual multiplication,
and produced

2580413
2-
10117

as the square.

Calcolo decidozzinale del Barone Silvio Ferrari. Turin, 1854, 4to.

This is a serious proposal to alter our numeral system and to count by
twelves. Thus 10 would be twelve, 11 thirteen, etc., two new symbols being
invented for ten and eleven. The names of numbers must of course be

changed. There are persons who think such changes practicable. I thought
this proposal absurd when I first saw it, and I think so still:[147] but the one I
shall presently describe beats it so completely in that point, that I have not a
smile left for this one.

ON COMETS.

The successful and therefore probably true theory of Comets.
London, 1854. (4pp. duodecimo.)

The author is the late Mr. Peter Legh,[148] of Norbury Booths Hall,
Knutsford, who published for eight or ten years the Ombrological Almanac,
a work of asserted discovery in meteorology. The theory of comets is that
the joint attraction of the new moon and several planets in the direction of
the sun, draws off the gases from the earth, and forms these cometic
meteors. But how these meteors come to describe orbits round the sun, and
to become capable of having their returns predicted, is not explained.

A NEW PHASE OF MORMONISM.

The Mormon, New York, Saturday, Oct. 27, 1855.

A newspaper headed by a grand picture of starred and striped banners,
beehive, and eagle surmounting it. A scroll on each side: on the left,
"Mormon creed. Mind your own business. Brigham Young;"[149] on the
right, "Given by inspiration of God. Joseph Smith."[150] A leading article on
the discoveries of Prof. Orson Pratt[151] says, "Mormonism has long taken
the lead in religion: it will soon be in the van both in science and politics."
At the beginning of the paper is Professor Pratt's "Law of Planetary
Rotation." The cube roots of the densities of the planets are as the square
roots of their periods of rotation. The squares of the cube roots of the
masses divided by the squares of the diameters are as the periods of
rotation. Arithmetical verification attempted, and the whole very modestly
stated and commented on. Dated G. S. L. City, Utah Ter., Aug. 1, 1855. If

the creed, as above, be correctly given, no wonder the Mormonites are in
such bad odor.

MATHEMATICAL ILLUSTRATIONS OF DOCTRINE.

The two estates; or both worlds mathematically considered.
London, 1855, small (pp. 16).

The author has published mathematical works with his name. The present
tract is intended to illustrate mathematically a point which may be guessed
from the title. But the symbols do very little in the way of illustration: thus,
x being the present value of the future estate (eternal happiness), and a of
all that this world can give, the author impresses it on the mathematician
that, x being infinitely greater than a, x + a = x, so that a need not be
considered. This will not act much more powerfully on a mathematician by
virtue of the symbols than if those same symbols had been dispensed with:
even though, as the author adds, "It was this method of neglecting infinitely
small quantities that Sir Isaac Newton was indebted to for his greatest
discoveries."
There has been a moderate quantity of well-meant attempt to enforce,
sometimes motive, sometimes doctrine, by arguments drawn from
mathematics, the proponents being persons unskilled in that science for the
most part. The ground is very dangerous: for the illustration often turns the
other way with greater power, in a manner which requires only a little more
knowledge to see. I have, in my life, heard from the pulpit or read, at least a
dozen times, that all sin is infinitely great, proved as follows. The greater
the being, the greater the sin of any offence against him: therefore the
offence committed against an infinite being is infinitely great. Now the
mathematician, of which the proposers of this argument are not aware, is
perfectly familiar with quantities which increase together, and never cease
increasing, but so that one of them remains finite when the other becomes
infinite. In fact, the argument is a perfect non sequitur.[152] Those who
propose it have in their minds, though in a cloudy and indefinite form, the
idea of the increase of guilt being proportionate to the increase of greatness
in the being offended. But this it would never do to state: for by such

statement not only would the argument lose all that it has of the picturesque,
but the asserted premise would have no strong air of exact truth. How could
any one undertake to appeal to conscience to declare that an offence against
a being 4-7/10 times as great as another is exactly, no more and no less, 4-
7/10 times as great an offence against the other?
The infinite character of the offence against an infinite being is laid down in
Dryden's Religio Laici,[153] and is, no doubt, an old argument:

"For, granting we have sinned, and that th' offence
Of man is made against Omnipotence,
Some price that bears proportion must be paid,
And infinite with infinite be weighed.
See then the Deist lost; remorse for vice
Not paid; or, paid, inadequate in price."

Dryden, in the words "bears proportion" is in verse more accurate than most
of the recent repeaters in prose. And this is not the only case of the kind in
his argumentative poetry.

My old friend, the late Dr. Olinthus Gregory,[154] who was a sound and
learned mathematician, adopted this dangerous kind of illustration in his
Letters on the Christian Religion. He argued, by parallel, from what he
supposed to be the necessarily mysterious nature of the impossible quantity
of algebra to the necessarily mysterious nature of certain doctrines of his
system of Christianity. But all the difficulty and mystery of the impossible
quantity is now cleared away by the advance of algebraical thought: and yet
Dr. Gregory's book continues to be sold, and no doubt the illustration is still
accepted as appropriate.
The mode of argument used by the author of the tract above named has a
striking defect. He talks of reducing this world and the next to "present
value," as an actuary does with successive lives or next presentations. Does
value make interest? and if not, why? And if it do, then the present value of
an eternity is not infinitely great. Who is ignorant that a perpetual annuity at
five per cent is worth only twenty years' purchase? This point ought to be
discussed by a person who treats heaven as a deferred perpetual annuity. I

do not ask him to do so, and would rather he did not; but if he will do it, he
must either deal with the question of discount, or be asked the reason why.
When a very young man, I was frequently exhorted to one or another view
of religion by pastors and others who thought that a mathematical argument
would be irresistible. And I heard the following more than once, and have
since seen it in print, I forget where. Since eternal happiness belonged to the
particular views in question, a benefit infinitely great, then, even if the
probability of their arguments were small, or even infinitely small, yet the
product of the chance and benefit, according to the usual rule, might give a
result which no one ought in prudence to pass over. They did not see that
this applied to all systems as well as their own. I take this argument to be
the most perverse of all the perversions I have heard or read on the subject:
there is some high authority for it, whom I forget.
The moral of all this is, that such things as the preceding should be kept out
of the way of those who are not mathematicians, because they do not
understand the argument; and of those who are, because they do.
[The high authority referred to above is Pascal, an early cultivator of
mathematical probability, and obviously too much enamoured of his new
pursuit. But he conceives himself bound to wager on one side or the other.
To the argument (Pensées, ch. 7)[155] that "le juste est de ne point parier," he
answers, "Oui: mais il faut parier: vous êtes embarqué; et ne parier point
que Dieu est, c'est parier qu'il n'est pas."[156] Leaving Pascal's argument to
make its way with a person who, being a sceptic, is yet positive that the
issue is salvation or perdition, if a God there be,—for the case as put by
Pascal requires this,—I shall merely observe that a person who elects to
believe in God, as the best chance of gain, is not one who, according to
Pascal's creed, or any other worth naming, will really secure that gain. I
wonder whether Pascal's curious imagination ever presented to him in sleep
his convert, in the future state, shaken out of a red-hot dice-box upon a red-
hot hazard-table, as perhaps he might have been, if Dante had been the later
of the two. The original idea is due to the elder Arnobius,[157] who, as cited
by Bayle,[158] speaks thus:
"Sed et ipse [Christus] quæ pollicetur, non probat. Ita est. Nulla enim, ut
dixi, futurorum potest existere comprobatio. Cum ergo hæc sit conditio

futurorum, ut teneri et comprehendi nullius possint anticipationis attactu;
nonne purior ratio est, ex duobus incertis, et in ambigua expectatione
pendentibus, id potius credere, quod aliquas spes ferat, quam omnino quod
nullas? In illo enim periculi nihil est, si quod dicitur imminere, cassum fiat
et vacuum: in hoc damnum est maximum, id est salutis amissio, si cum
tempus advenerit aperiatur non fuisse mendacium."[159]
Really Arnobius seems to have got as much out of the notion, in the third
century, as if he had been fourteen centuries later, with the arithmetic of
chances to help him.]

NOVUM ORGANUM MORALIUM.

The Sentinel, vol. ix. no. 27. London, Saturday, May 26, 1855.

This is the first London number of an Irish paper, Protestant in politics. It
opens with "Suggestions on the subject of a Novum Organum Moralium,"
which is the application of algebra and the differential calculus to morals,
socials, and politics. There is also a leading article on the subject, and some
applications in notes to other articles. A separate publication was afterwards
made, with the addition of a long Preface; the author being a clergyman
who I presume must have been the editor of the Sentinel.

Suggestions as to the employment of a Novum Organum
Moralium. Or, thoughts on the nature of the Differential Calculus,
and on the application of its principles to metaphysics, with a
view to the attainment of demonstration and certainty in moral,
political and ecclesiastical affairs. By Tresham Dames Gregg,[160]
Chaplain of St. Mary's, within the church of St. Nicholas intra
muros, Dublin. London, 1859, 8vo. (pp. xl + 32).

I have a personal interest in this system, as will appear from the following
extract from the newspaper:

"We were subsequently referred to De Morgan's Formal Logic
and Boole's Laws of Thought[161] both very elaborate works, and

greatly in the direction taken by ourselves. That the writers
amazingly surpass us in learning we most willingly admit, but we
venture to pronounce of both their learned treatises, that they deal
with the subject in a mode that is scholastic to an excess.... That
their works have been for a considerable space of time before the
world and effected nothing, would argue that they have
overlooked the vital nature of the theme.... On the whole, the
writings of De Morgan and Boole go to the full justification of
our principle without in any wise so trenching upon our ground as
to render us open to reproach in claiming our Calculus as a great
discovery.... But we renounce any paltry jealousy as to a matter so
vast. If De Morgan and Boole have had a priority in the case, to
them we cheerfully shall resign the glory and honor. If such be the
truth, they have neither done justice to the discovery, nor to
themselves [quite true]. They have, under the circumstances,
acted like 'the foolish man, who roasteth not that which he taketh
in hunting.... It will be sufficient for us, however, to be the
Columbus of these great Americi, and popularize what they
found, if they found it. We, as from the mountain top, will then
become their trumpeters, and cry glory to De Morgan and glory to
Boole, under Him who is the source of all glory, the only good
and wise, to Whom be glory for ever! If they be our predecessors
in this matter, they have, under Him, taken moral questions out of
the category of probabilities, and rendered them perfectly certain.
In that case, let their books be read by those who may doubt the
principles this day laid before the world as a great discovery, by
our newspaper. Our cry shall be ευρηκασι![162] Let us hope that
they will join us, and henceforth keep their light [sic] from under
their bushel."

For myself, and for my old friend Mr. Boole, who I am sure would join me,
I disclaim both priority, simultaneity, and posteriority, and request that
nothing may be trumpeted from the mountain top except our abjuration of
all community of thought or operation with this Novum Organum.
To such community we can make no more claim than Americus could make
to being the forerunner of Columbus who popularized his discoveries. We

do not wish for any ευρηκασι and not even for εὑρηκασι. For self and
Boole, I point out what would have convinced either of us that this house is
divided against itself.
Α being an apostolic element, δ the doctrinal element, and Χ the body of the
faithful, the church is Α δ Χ, we are told. Also, that if Α become negative,
or the Apostolicity become Diabolicity [my words]; or if δ become
negative, and doctrine become heresy; or if Χ become negative, that is, if
the faithful become unfaithful; the church becomes negative, "the very
opposite to what it ought to be." For self and Boole, I admit this. But—
which is not noticed—if Α and δ should both become negative, diabolical
origin and heretical doctrine, then the church, Α δ Χ, is still positive, what it
ought to be, unless Χ be also negative, or the people unfaithful to it, in
which case it is a bad church. Now, self and Boole—though I admit I have
not asked my partner—are of opinion that a diabolical church with false
doctrine does harm when the people are faithful, and can do good only
when the people are unfaithful. We may be wrong, but this is what we do
think. Accordingly, we have caught nothing, and can therefore roast nothing
of our own: I content myself with roasting a joint of Mr. Gregg's larder.
These mathematical vagaries have uses which will justify a large amount of
quotation: and in a score of years this may perhaps be the only attainable
record. I therefore proceed.
After observing that by this calculus juries (heaven help them! say I) can
calculate damages "almost to a nicety," and further that it is made
abundantly evident that c e x is "the general expression for an individual," it
is noted that the number of the Beast is not given in the Revelation in words
at length, but as χξϜ'.[163] On this the following remark is made:
"Can it be possible that we have in this case a specimen given to us of the
arithmetic of heaven, and an expression revealed, which indicates by its
function of addibility, the name of the church in question, and of each
member of it; and by its function of multiplicability the doctrine, the
mission, and the members of the great Synagogue of Apostacy? We merely
propound these questions;—we do not pretend to solve them."
After a translation in blank verse—a very pretty one—of the 18th Psalm,
the author proceeds as follows, to render it into differential calculus:

"And the whole tells us just this, that David did what he could. He
augmented those elements of his constitution which were (exceptis
excipiendis)[164] subject to himself, and the Almighty then augmented his
personal qualities, and his vocational status. Otherwise, to throw the matter
into the expression of our notation, the variable e was augmented, and c x
rose proportionally. The law of the variation, according to our theory, would
be thus expressed. The resultant was David the king c e x [c = r?] (who had
been David the shepherd boy), and from the conditions of the theorem we
have

du dx dc
= ce + ex x + cx
de de de

which, in the terms of ordinary language, just means, the increase of
David's educational excellence or qualities—his piety, his prayerfulness, his
humility, obedience, etc.—was so great, that when multiplied by his
original talent and position, it produced a product so great as to be equal in
its amount to royalty, honor, wealth, and power, etc.: in short, to all the
attributes of majesty."[165]
The "solution of the family problem" is of high interest. It is to determine
the effect on the family in general from a change [of conduct] in one of
them. The person chosen is one of the maid-servants.
"Let c e x be the father; c1e1x1 the mother, etc. The family then consists of
the maid's master, her mistress, her young master, her young mistress, and
fellow servant. Now the master's calling (or c) is to exercise his share of
control over this servant, and mind the rest of his business: call this
remainder a, and let his calling generally, or all his affairs, be to his maid-
servant as m : y, i.e., y = (mz/c); ... and this expression will represent his
relation to the servant. Consequently,

mz mz
cex= a+ e x; otherwise a + ex
c c

is the expression for the father when viewed as the girl's master."

I have no objection to repeat so far; but I will not give the formula for the
maid's relation to her young master; for I am not quite sure that all young
masters are to be trusted with it. Suffice it that the son will be affected
directly as his influence over her, and inversely as his vocational power: if
then he should have some influence and no vocational power, the effect on
him would be infinite. This is dismal to think of. Further, the formula brings
out that if one servant improve, the other must deteriorate, and vice versa.
This is not the experience of most families: and the author remarks as
follows:
"That is, we should venture to say, a very beautiful result, and we may say it
yielded us no little astonishment. What our calculation might lead to we
never dreamt of; that it should educe a conclusion so recondite that our
unassisted power never could have attained to, and which, if we could have
conjectured it, would have been at best the most distant probability, that
conclusion being itself, as it would appear, the quintessence of truth,
afforded us a measure of satisfaction that was not slight."
That the writings of Mr. Boole and myself "go to the full justification of"
this "principle," is only true in the sense in which the Scotch use, or did use,
the word justification.

A TRIBUTE TO BOOLE.
[The last number of this Budget had stood in type for months, waiting until
there should be a little cessation of correspondence more connected with the
things of the day. I had quite forgotten what it was to contain; and little
thought, when I read the proof, that my allusions to my friend Mr. Boole,
then in life and health, would not be printed till many weeks after his death.
Had I remembered what my last number contained, I should have added my
expression of regret and admiration to the numerous obituary testimonials,
which this great loss to science has called forth.
The system of logic alluded to in the last number of this series is but one of
many proofs of genius and patience combined. I might legitimately have
entered it among my paradoxes, or things counter to general opinion: but it
is a paradox which, like that of Copernicus, excited admiration from its first

appearance. That the symbolic processes of algebra, invented as tools of
numerical calculation, should be competent to express every act of thought,
and to furnish the grammar and dictionary of an all-containing system of
logic, would not have been believed until it was proved. When Hobbes,[166]
in the time of the Commonwealth, published his Computation or Logique,
he had a remote glimpse of some of the points which are placed in the light
of day by Mr. Boole. The unity of the forms of thought in all the
applications of reason, however remotely separated, will one day be matter
of notoriety and common wonder: and Boole's name will be remembered in
connection with one of the most important steps towards the attainment of
this knowledge.]

DECIMALS RUN RIOT.

The Decimal System as a whole. By Dover Statter.[167] London
and Liverpool, 1856, 8vo.

The proposition is to make everything decimal. The day, now 24 hours, is to
be made 10 hours. The year is to have ten months, Unusber, Duober, etc.
Fortunately there are ten commandments, so there will be neither addition
to, nor deduction from, the moral law. But the twelve apostles! Even
rejecting Judas, there is a whole apostle of difficulty. These points the
author does not touch.

ON PHONETIC SPELLING.

The first book of Phonetic Reading. London, Fred. Pitman,[168]
Phonetic Depot, 20, Paternoster Row, 1856, 12mo.
The Phonetic Journal. Devoted to the propagation of phonetic
reading, phonetic longhand, phonetic shorthand, and phonetic
printing. No. 46. Saturday, 15 November 1856. Vol. 15.

I write the titles of a couple out of several tracts which I have by me. But
the number of publications issued by the promoters of this spirited attempt

is very large indeed.[169] The attempt itself has had no success with the mass
of the public. This I do not regret. Had the world found that the change was
useful, I should have gone contentedly with the stream; but not without
regretting our old language. I admit the difficulties which our
unpronounceable spelling puts in the way of learning to read: and I have no
doubt that, as affirmed, it is easier to teach children phonetically, and
afterwards to introduce them to our common system, than to proceed in the
usual way. But by the usual way I mean proceeding by letters from the very
beginning. If, which I am sure is a better plan, children be taught at the
commencement very much by complete words, as if they were learning
Chinese, and be gradually accustomed to resolve the known words into
letters, a fraction, perhaps a considerable one, of the advantage of the
phonetic system is destroyed. It must be remembered that a phonetic system
can only be an approximation. The differences of pronunciation existing
among educated persons are so great, that, on the phonetic system, different
persons ought to spell differently.
But the phonetic party have produced something which will immortalize
their plan: I mean their shorthand, which has had a fraction of the success it
deserves. All who know anything of shorthand must see that nothing but a
phonetic system can be worthy of the name: and the system promulgated is
skilfully done. Were I a young man I should apply myself to it
systematically. I believe this is the only system in which books were ever
published. I wish some one would contribute to a public journal a brief
account of the dates and circumstances of the phonetic movement, not
forgetting a list of the books published in shorthand.
A child beginning to read by himself may owe terrible dreams and waking
images of horror to our spelling, as I did when six years old. In one of the
common poetry-books there is an admonition against confining little birds
in cages, and the child is asked what if a great giant, amazingly strong, were
to take you away, shut you up,

And feed you with vic-tu-als you ne-ver could bear.

The book was hyphened for the beginner's use; and I had not the least idea
that vic-tu-als were vittles: by the sound of the word I judged they must be
of iron; and it entered into my soul.

The worst of the phonetic shorthand book is that they nowhere, so far as I
have seen, give all the symbols, in every stage of advancement, together, in
one or following pages. It is symbols and talk, more symbols and more talk,
etc. A universal view of the signs ought to begin the works.

A HANDFUL OF LITTLE PARADOXERS.

Ombrological Almanac. Seventeenth year. An essay on
Anemology and Ombrology. By Peter Legh,[170] Esq. London,
1856, 12mo.

Mr. Legh, already mentioned, was an intelligent country gentleman, and a
legitimate speculator. But the clue was not reserved for him.

The proof that the three angles of a triangle are equal to two right
angles looked for in the inflation of the circle. By Gen. Perronet
Thompson. London, 1856, 8vo. (pp. 4.)

Another attempt, the third, at this old difficulty, which cannot be put into
few words of explanation.[171]

Comets considered as volcanoes, and the cause of their velocity
and other phenomena thereby explained. London (circa 1856),
8vo.

The title explains the book better than the book explains the title.

1856. A stranger applied to me to know what the ideas of a friend of his
were worth upon the magnitude of the earth. The matter being one
involving points of antiquity, I mentioned various persons whose
speculations he seemed to have ignored; among others, Thales. The reply
was, "I am instructed by the author to inform you that he is perfectly
acquainted with the works of Thales, Euclid, Archimedes, ..." I had some
thought of asking whether he had used the Elzevir edition of Thales,[172]
which is known to be very incomplete, or that of Professor Niemand with

the lections, Nirgend, 1824, 2 vols. folio; just to see whether the last would
not have been the very edition he had read. But I refrained, in mercy.

The moon is the image of the Earth, and is not a solid body. By
The Longitude.[173] (Private Circulation.) In five parts. London,
1856, 1857, 1857; Calcutta, 1858, 1858, 8vo.

The earth is "brought to a focus"; it describes a "looped orbit round the
sun." The eclipse of the sun is thus explained: "At the time of eclipses, the
image is more or less so directly before or behind the earth that, in the case
of new moon, bright rays of the sun fall and bear upon the spot where the
figure of the earth is brought to a focus, that is, bear upon the image of the
earth, when a darkness beyond is produced reaching to the earth, and the
sun becomes more or less eclipsed." How the earth is "brought to a focus"
we do not find stated. Writers of this kind always have the argument that
some things which have been ridiculed at first have been finally established.
Those who put into the lottery had the same kind of argument; but were
always answered by being reminded how many blanks there were to one
prize. I am loath to pronounce against anything: but it does force itself upon
me that the author of these tracts has drawn a blank.

LUNAR MOTION AGAIN.

Times, April 6 or 7, 1856. The moon has no rotary motion.

A letter from Mr. Jellinger Symons,[174] inspector of schools, which
commenced a controversy of many letters and pamphlets. This dispute
comes on at intervals, and will continue to do so. It sometimes arises from
inability to understand the character of simple rotation, geometrically;
sometimes from not understanding the mechanical doctrine of rotation.

Lunar Motion. The whole argument stated, and illustrated by
diagrams; with letters from the Astronomer Royal. By Jellinger C.

Symons. London, 1856, 8vo.

The Astronomer Royal endeavored to disentangle Mr. J. C. Symons, but
failed. Mr. Airy[175] can correct the error of a ship's compasses, because he
can put her head which way he pleases: but this he cannot do with a
speculator.
Mr. Symons, in this tract, insinuated that the rotation of the moon is one of
the silver shrines of the craftsmen. To see a thing so clearly as to be
satisfied that all who say they do not see it are telling wilful falsehood, is
the nature of man. Many of all sects find much comfort in it, when they
think of the others; many unbelievers solace themselves with it against
believers; priests of old time founded the right of persecution upon it, and
of our time, in some cases, the right of slander: many of the paradoxers
make it an argument against students of science. But I must say for men of
science, for the whole body, that they are fully persuaded of the honesty of
the paradoxers. The simple truth is, that all those I have mentioned,
believers, unbelievers, priests, paradoxers, are not so sure they are right in
their points of difference that they can safely allow themselves to be
persuaded of the honesty of opponents. Those who know demonstration are
differently situated. I suspect a train might be laid for the formation of a
better habit in this way. We know that Suvaroff[176] taught his Russians at
Ismail not to fear the Turks by accustoming them to charge bundles of
faggots dressed in turbans, etc.

At which your wise men sneered in phrases witty,
He made no answer—but he took the city!

Would it not be a good thing to exercise boys, in pairs, in the following
dialogue:—Sir, you are quite wrong!—Sir, I am sure you honestly think so!
This was suggested by what used to take place at Cambridge in my day. By
statute, every B.A. was obliged to perform a certain number of disputations,
and the father of the college had to affirm that it had been done. Some were
performed in earnest: the rest were huddled over as follows. Two candidates
occupied the places of the respondent and the opponent: Recte statuit
Newtonus, said the respondent: Recte non statuit Newtonus,[177] said the
opponent. This was repeated the requisite number of times, and counted for

as many acts and opponencies. The parties then changed places, and each
unsaid what he had said on the other side of the house: I remember thinking
that it was capital drill for the House of Commons, if any of us should ever
get there. The process was repeated with every pair of candidates.
The real disputations were very severe exercises. I was badgered for two
hours with arguments given and answered in Latin,—or what we called
Latin—against Newton's first section, Lagrange's[178] derived functions, and
Locke[179] on innate principles. And though I took off everything, and was
pronounced by the moderator to have disputed magno honore,[180] I never
had such a strain of thought in my life. For the inferior opponents were
made as sharp as their betters by their tutors, who kept lists of queer
objections, drawn from all quarters. The opponents used to meet the day
before to compare their arguments, that the same might not come twice
over. But, after I left Cambridge, it became the fashion to invite the
respondent to be present, who therefore learnt all that was to be brought
against him. This made the whole thing a farce: and the disputations were
abolished.

The Doctrine of the Moon's Rotation, considered in a letter to the
Astronomical Censor of the Athenæum. By Jones L.
MacElshender.[181] Edinburgh, 1856, 8vo.

This is an appeal to those cultivated persons who will read it "to overrule
the dicta of judges who would sacrifice truth and justice to professional
rule, or personal pique, pride, or prejudice"; meaning, the great mass of
those who have studied the subject. But how? Suppose the "cultivated
persons" were to side with the author, would those who have conclusions to
draw and applications to make consent to be wrong because the "general
body of intelligent men," who make no special study of the subject, are
against them? They would do no such thing: they would request the general
body of intelligent men to find their own astronomy, and welcome. But the
truth is, that this intelligent body knows better: and no persons know better
that they know better than the speculators themselves.

But suppose the general body were to combine, in opposition to those who
have studied. Of course all my list must be admitted to their trial; and then
arises the question whether both sides are to be heard. If so, the general
body of the intelligent must hear all the established side have to say: that is,
they must become just as much of students as the inculpated orthodox
themselves. And will they not then get into professional rule, pique, pride,
and prejudice, as the others did? But if, which I suspect, they are intended
to judge as they are, they will be in a rare difficulty. All the paradoxers are
of like pretensions: they cannot, as a class, be right, for each one contradicts
a great many of the rest. There will be the puzzle which silenced the crew of
the cutter in Marryat's novel of the Dog Fiend.[182] "A tog is a tog," said
Jansen.—"Yes," replied another, "we all know a dog is a dog; but the
question is—Is this dog a dog?" And this question would arise upon every
dog of them all.

ZETETIC ASTRONOMY.

Zetetic Astronomy: Earth not a globe. 1857 (Broadsheet).

Though only a traveling lecturer's advertisement, there are so many
arguments and quotations that it is a little pamphlet. The lecturer gained
great praise from provincial newspapers for his ingenuity in proving that the
earth is a flat, surrounded by ice. Some of the journals rather incline to the
view: but the Leicester Advertiser thinks that the statements "would seem
very seriously to invalidate some of the most important conclusions of
modern astronomy," while the Norfolk Herald is clear that "there must be a
great error on one side or the other." This broadsheet is printed at Aylesbury
in 1857, and the lecturer calls himself Parallax: but at Trowbridge, in 1849,
he was S. Goulden.[183] In this last advertisement is the following
announcement: "A paper on the above subjects was read before the Council
and Members of the Royal Astronomical Society, Somerset House, Strand,
London (Sir John F. W. Herschel,[184] President), Friday, Dec. 8, 1848." No
account of such a paper appears in the Notice for that month: I suspect that
the above is Mr. S. Goulden's way of representing the following occurrence:
Dec. 8, 1848, the Secretary of the Astronomical Society (De Morgan by

name) said, at the close of the proceedings,—"Now, gentlemen, if you will
promise not to tell the Council, I will read something for your amusement":
and he then read a few of the arguments which had been transmitted by the
lecturer. The fact is worth noting that from 1849 to 1857, arguments on the
roundness or flatness of the earth did itinerate. I have no doubt they did
much good: for very few persons have any distinct idea of the evidence for
the rotundity of the earth. The Blackburn Standard and Preston Guardian
(Dec. 12 and 16, 1849) unite in stating that the lecturer ran away from his
second lecture at Burnley, having been rather too hard pressed at the end of
his first lecture to explain why the large hull of a ship disappeared before
the sails. The persons present and waiting for the second lecture assuaged
their disappointment by concluding that the lecturer had slipped off the icy
edge of his flat disk, and that he would not be seen again till he peeped up
on the opposite side.
But, strange as it may appear, the opposer of the earth's roundness has more
of a case—or less of a want of case—than the arithmetical squarer of the
circle. The evidence that the earth is round is but cumulative and
circumstantial: scores of phenomena ask, separately and independently,
what other explanation can be imagined except the sphericity of the earth.
The evidence for the earth's figure is tremendously powerful of its kind; but
the proof that the circumference is 3.14159265... times the diameter is of a
higher kind, being absolute mathematical demonstration.
The Zetetic system still lives in lectures and books; as it ought to do, for
there is no way of teaching a truth comparable to opposition. The last I
heard of it was in lectures at Plymouth, in October, 1864. Since this time a
prospectus has been issued of a work entitled "The Earth not a Globe"; but
whether it has been published I do not know. The contents are as follows:

"The Earth a Plane—How circumnavigated.—How time is lost or gained.—
Why a ship's hull disappears (when outward bound) before the mast head.
—Why the Polar Star sets when we proceed Southward, etc.—Why a
pendulum vibrates with less velocity at the Equator than at the Pole.—The
allowance for rotundity supposed to be made by surveyors, not made in
practice.—Measurement of Arcs of the Meridian unsatisfactory.—Degrees

of Longitude North and South of the Equator considered.—Eclipses and
Earth's form considered.—The Earth no motion on axis or in orbit.—How
the Sun moves above the Earth's surface concentric with the North Pole.—
Cause of Day and Night, Winter and Summer; the long alternation of light
and darkness at the Pole.—Cause of the Sun rising and setting.—Distance
of the Sun from London, 4,028 miles—How measured.—Challenge to
Mathematicians.—Cause of Tides.—Moon self-luminous, NOT a reflector.
—Cause of Solar and Lunar eclipses.—Stars not worlds; their distance.—
Earth, the only material world; its true position in the universe; its condition
and ultimate destruction by fire (2 Peter iii.), etc."
I wish there were geoplatylogical lectures in every town; in England
(platylogical, in composition, need not mean babbling). The late Mr. Henry
Archer[185] would, if alive, be very much obliged to me for recording his
vehement denial of the roundness of the earth: he was excited if he heard
any one call it a globe. I cannot produce his proof from the Pyramids, and
from some caves in Arabia. He had other curious notions, of course: I
should no more believe that a flat earth was a man's only paradox, than I
should that Dutens,[186] the editor of Leibnitz, was eccentric only in
supplying a tooth which he had lost by one which he found in an Italian
tomb, and fully believed that it had once belonged to Scipio Africanus,
whose family vault was discovered, it is supposed, in 1780. Mr. Archer is of
note as the suggester of the perforated border of the postage-stamps, and, I
think, of the way of doing it; for this he got 4000l. reward. He was a civil
engineer.
(August 28, 1865.) The Zetetic Astronomy has come into my hands. When,
in 1851, I went to see the Great Exhibition, I heard an organ played by a
performer who seemed very desirous to exhibit one particular stop. "What
do you think of that stop?" I was asked.—"That depends on the name of it,"
said I.—"Oh! what can the name have to do with the sound? 'that which we
call a rose,' etc."—"The name has everything to do with it: if it be a flute-
stop, I think it very harsh; but if it be a railway-whistle-stop, I think it very
sweet." So as to this book: if it be childish, it is clever; if it be mannish, it is
unusually foolish. The flat earth, floating tremulously on the sea; the sun
moving always over the flat, giving day when near enough, and night when
too far off; the self-luminous moon, with a semi-transparent invisible moon,
created to give her an eclipse now and then; the new law of perspective, by

which the vanishing of the hull before the masts, usually thought to prove
the earth globular, really proves it flat;—all these and other things are well
fitted to form exercises for a person who is learning the elements of
astronomy. The manner in which the sun dips into the sea, especially in
tropical climates, upsets the whole. Mungo Park,[187] I think, gives an
African hypothesis which explains phenomena better than this. The sun dips
into the western ocean, and the people there cut him in pieces, fry him in a
pan, and then join him together again, take him round the underway, and set
him up in the east. I hope this book will be read, and that many will be
puzzled by it: for there are many whose notions of astronomy deserve no
better fate. There is no subject on which there is so little accurate
conception as that of the motions of the heavenly bodies. The author,
though confident in the extreme, neither impeaches the honesty of those
whose opinions he assails, nor allots them any future inconvenience: in
these points he is worthy to live on a globe, and to revolve in twenty-four
hours.

(October, 1866.) A follower appears, in a work dedicated to the preceding
author: it is Theoretical Astronomy examined and exposed by Common
Sense. The author has 128 well-stuffed octavo pages. I hope he will not be
the last. He prints the newspaper accounts of his work: the Church Times
says—not seeing how the satire might be retorted—"We never began to
despair of Scripture until we discovered that 'Common Sense' had taken up
the cudgels in its defence." This paper considers our author as the type of a
Protestant. The author himself, who gives a summary of his arguments in
verse, has one couplet which is worth quoting:

"How is't that sailors, bound to sea, with a 'globe' would never start,
But in its place will always take Mercator's[188] Level chart!"

To which I answer:

Why, really Mr. Common Sense, you've never got so far
As to think Mercator's planisphere shows countries as they are;
It won't do to measure distances; it points out how to steer,
But this distortion's not for you; another is, I fear.

The earth must be a cylinder, if seaman's charts be true,
Or else the boundaries, right and left, are one as well as two;
They contradict the notion that we dwell upon a plain,
For straight away, without a turn, will bring you home again.
There are various plane projections; and each one has its use:
I wish a milder word would rhyme—but really you're a goose!

The great wish of persons who expose themselves as above, is to be argued
with, and to be treated as reputable and refutable opponents. "Common
Sense" reminds us that no amount of "blatant ridicule" will turn right into
wrong. He is perfectly correct: but then no amount of bad argument will
turn wrong into right. These two things balance; and we are just where we
were: but you should answer our arguments, for whom, I ask? Would reason
convince this kind of reasoner? The issue is a short and a clear one. If these
parties be what I contend they are, then ridicule is made for them: if not, for
what or for whom? If they be right, they are only passing through the
appointed trial of all good things. Appeal is made to the future: and my
Budget is intended to show samples of the long line of heroes who have
fallen without victory, each of whom had his day of confidence and his
prophecy of success. Let the future decide: they say roundly that the earth is
flat; I say flatly that it is round.
The paradoxers all want reason, and not ridicule: they are all accessible, and
would yield to conviction. Well then, let them reason with one another!
They divide into squads, each with a subject, and as many different
opinions as persons in each squad. If they be really what they say they are,
the true man of each set can put down all the rest, and can come crowned
with glory and girdled with scalps, to the attack on the orthodox
misbelievers. But they know, to a man, that the rest are not fit to be
reasoned with: they pay the regulars the compliment of believing that the
only chance lies with them. They think in their hearts, each one for himself,
that ridicule is of fit appliance to the rest.

Miranda. A book divided into three parts, entitled Souls,
Numbers, Stars, on the Neo-Christian Religion ... Vol. i. London,
1858, 1859, 1860. 8vo.

The name of the author is Filopanti.[189] He announces himself as the 49th
and last Emanuel: his immediate predecessors were Emanuel Washington,
Emanuel Newton, and Emanuel Galileo. He is to collect nations into one
family. He knows the transmigrations of the whole human race. Thus
Descartes became William III of England: Roger Bacon became Boccaccio.
But Charles IX,[190] in retribution for the massacre of St. Bartholomew, was
hanged in London under the name of Barthélemy for the murder of Collard:
and many of the Protestants whom he killed as King of France were
shouting at his death before the Old Bailey.

THE SABBATH—THE GREAT PYRAMID

A Letter to the members of the Anglo-Biblical Institute, dated
Sept. 7, 1858, and signed 'Herman Heinfetter.'[191] (Broadsheet.)

This gentleman is well known to the readers of the Athenæum, in which, for
nearly twenty years, he has inserted, as advertisements, long arguments in
favor of Christians keeping the Jewish Sabbath, beginning on Friday
Evening. The present letter maintains that, by the force of the definite
article, the days of creation may not be consecutive, but may have any time
—millions of years—between them. This ingenious way of reconciling the
author of Genesis and the indications of geology is worthy to be added to
the list, already pretty numerous. Mr. Heinfetter has taken such pains to
make himself a public agitator, that I do not feel it to be any invasion of
private life if I state that I have heard he is a large corn-dealer. No doubt he
is a member of the congregation whose almanac has already been
described.

The great Pyramid. Why was it built? And who built it? By John
Taylor, 1859,[192] 12mo.

This work is very learned, and may be referred to for the history of previous
speculations. It professes to connect the dimensions of the Pyramid with a
system of metrology which is supposed to have left strong traces in the

systems of modern times; showing the Egyptians to have had good
approximate knowledge of the dimensions of the earth, and of the
quadrature of the circle. These are points on which coincidence is hard to
distinguish from intention. Sir John Herschel[193] noticed this work, and
gave several coincidences, in the Athenæum, Nos. 1696 and 1697, April 28
and May 5, 1860: and there are some remarks by Mr. Taylor in No. 1701,
June 2, 1860.
Mr. Taylor's most recent publication is—

The battle of the Standards: the ancient, of four thousand years,
against the modern, of the last fifty years—the less perfect of the
two. London, 1864, 12mo.

This is intended as an appendix to the work on the Pyramid. Mr. Taylor
distinctly attributes the original system to revelation, of which he says the
Great Pyramid is the record. We are advancing, he remarks, towards the end
of the Christian dispensation, and he adds that it is satisfactory to see that
we retain the standards which were given by unwritten revelation 700 years
before Moses. This is lighting the candle at both ends; for myself, I shall not
undertake to deny or affirm either what is said about the dark past or what is
hinted about the dark future.
My old friend Mr. Taylor is well known as the author of the argument which
has convinced many, even most, that Sir Philip Francis[194] was Junius:
pamphlet, 1813; supplement, 1817; second edition "The Identity of Junius
with a distinguished living character established," London, 1818, 8vo. He
told me that Sir Philip Francis, in a short conversation with him, made only
this remark, "You may depend upon it you are quite mistaken:" the phrase
appears to me remarkable; it has an air of criticism on the book, free from
all personal denial. He also mentioned that a hearer told him that Sir Philip
said, speaking of writers on the question,—"Those fellows, for half-a-
crown, would prove that Jesus Christ was Junius."
Mr. Taylor implies, I think, that he is the first who started the suggestion
that Sir Philip Francis was Junius, which I have no means either of
confirming or refuting. If it be so [and I now know that Mr. Taylor himself
never heard of any predecessor], the circumstance is very remarkable: it is

seldom indeed that the first proposer of any solution of a great and vexed
question is the person who so nearly establishes his point in general opinion
as Mr. Taylor has done.
As to the Junius question in general, there is a little bit of the philosophy of
horse-racing which may be usefully applied. A man who is so confident of
his horse that he places him far above any other, may nevertheless, and
does, refuse to give odds against all in the field: for many small adverse
chances united make a big chance for one or other of the opponents. I
suspect Mr. Taylor has made it at least 20 to 1 for Francis against any one
competitor who has been named: but what the odds may be against the
whole field is more difficult to settle. What if the real Junius should be
some person not yet named?
Mr. Jopling, Leisure Hour, May 23, 1863, relies on the porphyry coffer of
the Great Pyramid, in which he finds "the most ancient and accurate
standard of measure in existence."
I am shocked at being obliged to place a thoughtful and learned writer, and
an old friend, before such a successor as he here meets with. But
chronological arrangement defies all other arrangement.
(I had hoped that the preceding account would have met Mr. Taylor's eye in
print: but he died during the last summer. For a man of a very thoughtful
and quiet temperament, he had a curious turn for vexed questions. But he
reflected very long and very patiently before he published: and all his works
are valuable for their accurate learning, whichever side the reader may
take.)

MRS. ELIZABETH COTTLE.
1859. The Cottle Church.—For more than twenty years printed papers have
been sent about in the name of Elizabeth Cottle.[195] It is not so remarkable
that such papers should be concocted as that they should circulate for such a
length of time without attracting public attention. Eighty years ago Mrs.
Cottle might have rivalled Lieut. Brothers or Joanna Southcott.[196] Long
hence, when the now current volumes of our journals are well-ransacked

works of reference, those who look into them will be glad to see this feature
of our time: I therefore make a few extracts, faithfully copied as to type.
The Italic is from the New Testament; the Roman is the requisite
interpretation:
"Robert Cottle 'was numbered (5196) with the transgressors' at the back of
the Church in Norwood Cemetery, May 12, 1858—Isa. liii. 12. The Rev.
J. G. Collinson, Minister of St. James's Church, Chapham, the then district
church, before All Saints was built, read the funeral service over the
Sepulchre wherein never before man was laid.
"Hewn on the stone, 'at the mouth of the Sepulchre,' is his name,—Robert
Cottle, born at Bristol, June 2, 1774; died at Kirkstall Lodge, Clapham Park,
May 6, 1858. And that day (May 12, 1858) was the preparation (day and
year for 'the PREPARED place for you'—Cottleites—-by the widowed mother
of the Father's house, at Kirkstall Lodge—John xiv. 2, 3). And the Sabbath
(Christmas Day, Dec. 25, 1859) drew on (for the resurrection of the
Christian body on 'the third [Protestant Sun]-day'—1 Cor. xv. 35). Why seek
ye the living (God of the New Jerusalem—Heb. xii. 22; Rev. iii. 12) among
the dead (men): he (the God of Jesus) is not here (in the grave), but is risen
(in the person of the Holy Ghost, from the supper of 'the dead in the second
death' of Paganism). Remember how he spake unto you (in the church of the
Rev. George Clayton,[197] April 14, 1839). I will not drink henceforth (at
this last Cottle supper) of the fruit of this (Trinity) vine, until that day
(Christmas Day, 1859), when I (Elizabeth Cottle) drink it new with you
(Cottleites) in my Father's kingdom—John xv. If this (Trinitarian) cup may
not pass away from me (Elizabeth Cottle, April 14, 1839), except I drink it
('new with you Cottleites, in my Father's Kingdom'), thy will be done—
Matt. xxvi. 29, 42, 64. 'Our Father which art (God) in Heaven,' hallowed be
thy name, thy (Cottle) kingdom come, thy will be done in earth, as it is
(done) in (the new) Heaven (and new earth of the new name of Cottle—
Rev. xxi. 1; iii. 12).
"... Queen Elizabeth, from A.D. 1558 to 1566. And this WORD yet once more
(by a second Elizabeth—the WORD of his oath) signifieth (at John Scott's
baptism of the Holy Ghost) the removing of those things (those Gods and
those doctrines) that are made (according to the Creeds and
Commandments of men) that those things (in the moral law of God) which

cannot be shaken (as a rule of faith and practice) may remain, wherefore we
receiving (from Elizabeth) a kingdom (of God,) which cannot be moved (by
Satan) let us have grace (in his Grace of Canterbury) whereby we may serve
God acceptably (with the acceptable sacrifice of Elizabeth's body and blood
of the communion of the Holy Ghost) with reverence (for truth) and godly
fear (of the unpardonable sin of blasphemy against the Holy Ghost) for our
God (the Holy Ghost) is a consuming fire (to the nation that will not serve
him in the Cottle Church). We cannot defend ourselves against the
Almighty, and if He is our defence, no nation can invade us.
"In verse 4 the Church of St. Peter is in prison between four quaternions of
soldiers—the Holy Alliance of 1815. Rev. vii. i. Elizabeth, the Angel of the
Lord Jesus appears to the Jewish and Christian body with the vision of
prophecy to the Rev. Geo. Clayton and his clerical brethren, April 8th,
1839. Rhoda was the name of her maid at Putney Terrace who used to open
the door to her Peter, the Rev. Robert Ashton,[198] the Pastor of 'the little
flock' 'of 120 names together, assembled in an upper (school) room' at
Putney Chapel, to which little flock she gave the revelation (Acts. i. 13, 15)
of Jesus the same King of the Jews yesterday at the prayer meeting, Dec.
31, 1841, and to-day, Jan. 1, 1842, and for ever. See book of Life, page 24.
Matt. xviii. 19, xxi. 13-16. In verse 6 the Italian body of St. Peter is sleeping
'in the second death' between the two Imperial soldiers of France and
Austria. The Emperor of France from Jan. 1, to July 11, 1859, causes the
Italian chains of St. Peter to fall off from his Imperial hands.
"I say unto thee, Robert Ashton, thou art Peter, a stone, and upon this rock,
of truth, will I Elizabeth, the angel of Jesus, build my Cottle Church, and the
gates of hell, the doors of St. Peter, at Rome, shall not prevail against it—
Matt. xvi. 18. Rev. iii. 7-12."
This will be enough for the purpose. When any one who pleases can
circulate new revelations of this kind, uninterrupted and unattended to, new
revelations will cease to be a good investment of excentricity. I take it for
granted that the gentlemen whose names are mentioned have nothing to do
with the circulars or their doctrines. Any lady who may happen to be
intrusted with a revelation may nominate her own pastor, or any other
clergyman, one of her apostles; and it is difficult to say to what court the
nominees can appeal to get the commission abrogated.

March 16, 1865. During the last two years the circulars have continued. It is
hinted that funds are low: and two gentlemen who are represented as gone
"to Bethlehem asylum in despair" say that Mrs. Cottle "will spend all that
she hath, while Her Majesty's Ministers are flourishing on the wages of
sin." The following is perhaps one of the most remarkable passages in the
whole:
"Extol and magnify Him (Jehovah, the Everlasting God, see the Magnificat
and Luke i. 45, 46—68—73—79), that rideth (by rail and steam over land
and sea, from his holy habitation at Kirkstall Lodge, Psa. lxxvii. 19, 20),
upon the (Cottle) heavens, as it were (Sept. 9, 1864, see pages 21, 170),
upon an (exercising, Psa. cxxxi. 1), horse-(chair, bought of Mr. John Ward,
Leicester-square)."
I have pretty good evidence that there is a clergyman who thinks Mrs.
Cottle a very sensible woman.
[The Cottle Church. Had I chanced to light upon it at the time of writing, I
should certainly have given the following. A printed letter to the Western
Times, by Mr. Robert Cottle, was accompanied by a manuscript letter from
Mrs. Cottle, apparently a circular. The date was Novr. 1853, and the subject
was the procedure against Mr. Maurice[199] at King's College for doubting
that God would punish human sins by an existence of torture lasting
through years numbered by millions of millions of millions of millions
(repeat the word millions without end,) etc. The memory of Mr. Cottle has, I
think, a right to the quotation: he seems to have been no participator in the
notions of his wife:
"The clergy of the Established Church, taken at the round number of
20,000, may, in their first estate, be likened to 20,000 gold blanks, destined
to become sovereigns, in succession,—they are placed between the matrix
of the Mint, when, by the pressure of the screw, they receive the impress
that fits them to become part of the current coin of the realm. In a way
somewhat analogous this great body of the clergy have each passed through
the crucibles of Oxford and Cambridge,—have been assayed by the
Bishop's chaplain, touching the health of their souls, and the validity of
their call by the Divine Spirit, and then the gentle pressure of a prelate's
hand upon their heads; and the words—'Receive the Holy Ghost,' have, in a

brief space of time, wrought a change in them, much akin to the miracle of
transubstantiation—the priests are completed, and they become the current
ecclesiastical coin of our country. The whole body of clergy, here spoken of,
have undergone the preliminary induction of baptism and confirmation; and
all have been duly ordained, professing to hold one faith, and to believe in
the selfsame doctrines! In short, to be as identical as the 20,000 sovereigns,
if compared one with the other. But mind is not malleable and ductile, like
gold; and all the preparations of tests, creeds, and catechisms will not insure
uniformity of belief. No stamp of orthodoxy will produce the same impress
on the minds of different men. Variety is manifest, and patent, upon
everything mental and material. The Almighty has not created, nor man
fashioned, two things alike! How futile, then, is the attempt to shape and
mould man's apprehension of divine truth by one fallible standard of man's
invention! If proof of this be required, an appeal might be made to history
and the experience of eighteen hundred years."
This is an argument of force against the reasonableness of expecting tens of
thousands of educated readers of the New Testament to find the doctrine
above described in it. The lady's argument against the doctrine itself is very
striking. Speaking of an outcry on this matter among the Dissenters against
one of their body, who was the son of "the White Stone (Rev. ii. 17), or the
Roman cement-maker," she says—
"If the doctrine for which they so wickedly fight were true, what would
become of the black gentlemen for whose redemption I have been sacrificed
from April 8 1839."
There are certainly very curious points about this revelation. There have
been many surmises about the final restoration of the infernal spirits, from
the earliest ages of Christianity until our own day: a collection of them
would be worth making. On reading this in proof, I see a possibility that by
"black gentlemen" may be meant the clergy: I suppose my first
interpretation must have been suggested by context: I leave the point to the
reader's sagacity.]

JAMES SMITH, ARCH-PARADOXER.

The Problem of squaring the circle solved; or, the circumference
and area of the circle discovered. By James Smith.[200] London,
1859, 8vo.
On the relations of a square inscribed in a circle. Read at the
British Association, Sept. 1859, published in the Liverpool
Courier, Oct. 8, 1859, and reprinted in broadsheet.
The question: Are there any commensurable relations between a
circle and other Geometrical figures? Answered by a member of
the British Association ... London, 1860, 8vo.—[This has been
translated into French by M. Armand Grange, Bordeaux, 1863,
8vo.]
The Quadrature of the Circle. Correspondence between an
eminent mathematician and James Smith, Esq. (Member of the
Mersey Docks and Harbour Board), London, 1861, 8vo. (pp.
200).
Letter to the ... British Association ... by James Smith, Esq.
Liverpool, 1861, 8vo.
Letter to the ... British Association ... by James Smith, Esq.
Liverpool, 1862, 8vo.—[These letters the author promised to
continue.]
A Nut to crack for the readers of Professor De Morgan's 'Budget
of Paradoxes.' By James Smith, Esq. Liverpool, 1863, 8vo.
Paper read at the Liverpool Literary and Philosophical Society,
reported in the Liverpool Daily Courier, Jan. 26, 1864. Reprinted
as a pamphlet.
The Quadrature of the circle, or the true ratio between the
diameter and circumference geometrically and mathematically
demonstrated. By James Smith, Esq. Liverpool, 1865, 8vo.
[On the relations between the dimensions and distances of the
Sun, Moon, and Earth; a paper read before the Literary and

Philosophical Society of Liverpool, Jan. 25, 1864. By James
Smith, Esq.
The British Association in Jeopardy, and Dr. Whewell, the Master
of Trinity, in the stocks without hope of escape. Printed for the
authors (J. S. confessed, and also hidden under Nauticus). (No
date, 1865).
The British Association in Jeopardy, and Professor De Morgan in
the Pillory without hope of escape. London, 1866, 8vo.]

When my work appeared in numbers, I had not anything like an adequate
idea of Mr. James Smith's superiority to the rest of the world in the points in
which he is superior. He is beyond a doubt the ablest head at unreasoning,
and the greatest hand at writing it, of all who have tried in our day to attach
their names to an error. Common cyclometers sink into puny orthodoxy by
his side.
The behavior of this singular character induces me to pay him the
compliment which Achilles paid Hector, to drag him round the walls again
and again. He was treated with unusual notice and in the most gentle
manner. The unnamed mathematician, E. M. bestowed a volume of mild
correspondence upon him; Rowan Hamilton[201] quietly proved him wrong
in a way accessible to an ordinary schoolboy; Whewell,[202] as we shall see,
gave him the means of seeing himself wrong, even more easily than by
Hamilton's method. Nothing would do; it was small kick and silly fling at
all; and he exposed his conceit by alleging that he, James Smith, had placed
Whewell in the stocks. He will therefore be universally pronounced a
proper object of the severest literary punishment: but the opinion of all who
can put two propositions together will be that of the many strokes I have
given, the hardest and most telling are my republications of his own
attempts to reason.
He will come out of my hands in the position he ought to hold, the Supreme
Pontiff of cyclometers, the vicegerent of St. Vitus upon earth, the
Mamamouchi of burlesque on inference. I begin with a review of him
which appeared in the Athenæum of May 11, 1861. Mr. Smith says I wrote
it: this I neither affirm nor deny; to do either would be a sin against the

editorial system elsewhere described. Many persons tell me they know me
by my style; let them form a guess: I can only say that many have declared
as above while fastening on me something which I had never seen nor heard
of.

The Quadrature of the Circle: Correspondence between an
Eminent Mathematician and James Smith, Esq. (Edinburgh,
Oliver & Boyd; London, Simpkin, Marshall & Co.)

"A few weeks ago we were in perpetual motion. We did not then suppose
that anything would tempt us on a circle-squaring expedition: but the
circumstances of the book above named have a peculiarity which induces us
to give it a few words.
"Mr. James Smith, a gentleman residing near Liverpool, was some years
ago seized with the morbus cyclometricus.[203] The symptoms soon took a
defined form: his circumference shrank into exactly 3-1/8 times his
diameter, instead of close to 3-16/113, which the mathematician knows to
be so near to truth that the error is hardly at the rate of a foot in 2,000 miles.
This shrinking of the circumference remained until it became absolutely
necessary that it should be examined by the British Association. This body,
which as Mr. James Smith found to his sorrow, has some interest in
'jealously guarding the mysteries of their profession,' refused at first to
entertain the question. On this Mr. Smith changed his 'tactics' and the name
of his paper, and smuggled in the subject under the form of 'The Relations
of a Circle inscribed in a Square'! The paper was thus forced upon the
Association, for Mr. Smith informs us that he 'gave the Section to
understand that he was not the man that would permit even the British
Association to trifle with him.' In other words, the Association bore with
and were bored with the paper, as the shortest way out of the matter. Mr.
Smith also circulated a pamphlet. Some kind-hearted man, who did not
know the disorder as well as we do, and who appears in Mr. Smith's
handsome octavo as E. M.—the initials of 'eminent mathematician'—wrote
to him and offered to show him in a page that he was all wrong. Mr. Smith
thereupon opened a correspondence, which is the bulk of the volume. When
the correspondence was far advanced, Mr. Smith announced his intention to

publish. His benevolent instructor—we mean in intention—protested
against the publication, saying 'I do not wish to be gibbeted to the world as
having been foolish enough to enter upon what I feel now to have been a
ridiculous enterprise.'
"For this Mr. Smith cared nothing: he persisted in the publication, and the
book is before us. Mr. Smith has had so much grace as to conceal his kind
adviser's name under E. M., that is to say, he has divided the wrong among
all who may be suspected of having attempted so hopeless a task as that of
putting a little sense into his head. He has violated the decencies of private
life. Against the will of the kind-hearted man who undertook his case, he
has published letters which were intended for no other purpose than to clear
his poor head of a hopeless delusion. He deserves the severest castigation;
and he will get it: his abuse of confidence will stick by him all his days. Not
that he has done his benefactor—in intention, again—any harm. The
patience with which E. M. put the blunders into intelligible form, and the
perseverance with which he tried to find a cranny-hole for common
reasoning to get in at, are more than respectable: they are admirable. It is,
we can assure E. M., a good thing that the nature of the circle-squarer
should be so completely exposed as in this volume. The benefit which he
intended Mr. James Smith may be conferred upon others. And we should
very much like to know his name, and if agreeable to him, to publish it. As
to Mr. James Smith, we can only say this: he is not mad. Madmen reason
rightly upon wrong premises: Mr. Smith reasons wrongly upon no premises
at all.
"E. M. very soon found out that, to all appearance, Mr. Smith got a circle of
3-1/8 times the diameter by making it the supposition to set out with that
there was such a circle; and then finding certain consequences which, so it
happened, were not inconsistent with the supposition on which they were
made. Error is sometimes self-consistent. However, E. M., to be quite sure
of his ground, wrote a short letter, stating what he took to be Mr. Smith's
hypothesis, containing the following: 'On AC as diameter, describe the
circle D, which by hypothesis shall be equal to three and one-eighth times
the length of AC.... I beg, before proceeding further, to ask whether I have
rightly stated your argument.' To which Mr. Smith replied: 'You have stated
my argument with perfect accuracy.' Still E. M. went on, and we could not
help, after the above, taking these letters as the initials of Everlasting

Mercy. At last, however, when Mr. Smith flatly denied that the area of the
circle lies between those of the inscribed and circumscribed polygons,
E. M. was fairly beaten, and gave up the task. Mr. Smith was left to write
his preface, to talk about the certain victory of truth—which, oddly enough,
is the consolation of all hopelessly mistaken men; to compare himself with
Galileo; and to expose to the world the perverse behavior of the Astronomer
Royal, on whom he wanted to fasten a conversation, and who replied, 'It
would be a waste of time, Sir, to listen to anything you could have to say on
such a subject.'
"Having thus disposed of Mr. James Smith, we proceed to a few remarks on
the subject: it is one which a journal would never originate, but which is
rendered necessary from time to time by the attempts of the autopseustic to
become heteropseustic. To the mathematician we have nothing to say: the
question is, what kind of assurance can be given to the world at large that
the wicked mathematicians are not acting in concert to keep down their
superior, Mr. James Smith, the current Galileo of the quadrature of the
circle.
"Let us first observe that this question does not stand alone: independently
of the millions of similar problems which exist in higher mathematics, the
finding of the diagonal of a square has just the same difficulty, namely, the
entrance of a pair of lines of which one cannot be definitely expressed by
means of the other. We will show the reader who is up to the multiplication-
table how he may go on, on, on, ever nearer, never there, in finding the
diagonal of a square from the side.
"Write down the following rows of figures, and more, if you like, in the
way described:

1 2 5 12 29 70 169 408 985
1 3 7 17 41 99 239 577 1393

After the second, each number is made up of double the last increased by
the last but one: thus, 5 is 1 more than twice 2, 12 is 2 more than twice 5,
239 is 41 more than twice 99. Now, take out two adjacent numbers from the
upper line, and the one below the first from the lower: as

70 169

99.

Multiply together 99 and 169, giving 16,731. If, then, you will say that 70
diagonals are exactly equal to 99 sides, you are in error about the diagonal,
but an error the amount of which is not so great as the 16,731st part of the
diagonal. Similarly, to say that five diagonals make exactly seven sides does
not involve an error of the 84th part of the diagonal.
"Now, why has not the question of crossing the square been as celebrated as
that of squaring the circle? Merely because Euclid demonstrated the
impossibility of the first question, while that of the second was not
demonstrated, completely, until the last century.
"The mathematicians have many methods, totally different from each other,
of arriving at one and the same result, their celebrated approximation to the
circumference of the circle. An intrepid calculator has, in our own time,
carried his approximation to what they call 607 decimal places: this has
been done by Mr. Shanks,[204] of Houghton-le-Spring, and Dr.
Rutherford[205] has verified 441 of these places. But though 607 looks large,
the general public will form but a hazy notion of the extent of accuracy
acquired. We have seen, in Charles Knight's[206] English Cyclopædia, an
account of the matter which may illustrate the unimaginable, though
rationally conceivable, extent of accuracy obtained.
"Say that the blood-globule of one of our animalcules is a millionth of an
inch in diameter. Fashion in thought a globe like our own, but so much
larger that our globe is but a blood-globule in one of its animalcules: never
mind the microscope which shows the creature being rather a bulky
instrument. Call this the first globe above us. Let the first globe above us be
but a blood-globule, as to size, in the animalcule of a still larger globe,
which call the second globe above us. Go on in this way to the twentieth
globe above us. Now go down just as far on the other side. Let the blood-
globule with which we started be a globe peopled with animals like ours,
but rather smaller: and call this the first globe below us. Take a blood-
globule out of this globe, people it, and call it the second globe below us:
and so on to the twentieth globe below us. This is a fine stretch of
progression both ways. Now give the giant of the twentieth globe above us
the 607 decimal places, and, when he has measured the diameter of his

globe with accuracy worthy of his size, let him calculate the circumference
of his equator from the 607 places. Bring the little philosopher from the
twentieth globe below us with his very best microscope, and set him to see
the small error which the giant must make. He will not succeed, unless his
microscopes be much better for his size than ours are for ours.
"Now it must be remembered by any one who would laugh at the closeness
of the approximation, that the mathematician generally goes nearer; in fact
his theorems have usually no error at all. The very person who is
bewildered by the preceding description may easily forget that if there were
no error at all, the Lilliputian of the millionth globe below us could not find
a flaw in the Brobdingnagian of the millionth globe above. The three angles
of a triangle, of perfect accuracy of form, are absolutely equal to two right
angles; no stretch of progression will detect any error.
"Now think of Mr. Lacomme's mathematical adviser (ante, Vol. I, p. 46)
making a difficulty of advising a stonemason about the quantity of
pavement in a circular floor!
"We will now, for our non-calculating reader, put the matter in another way.
We see that a circle-squarer can advance, with the utmost confidence, the
assertion that when the diameter is 1,000, the circumference is accurately
3,125: the mathematician declaring that it is a trifle more than 3,141½. If
the squarer be right, the mathematician has erred by about a 200th part of
the whole: or has not kept his accounts right by about 10s. in every 100l. Of
course, if he set out with such an error he will accumulate blunder upon
blunder. Now, if there be a process in which close knowledge of the circle is
requisite, it is in the prediction of the moon's place—say, as to the time of
passing the meridian at Greenwich—on a given day. We cannot give the
least idea of the complication of details: but common sense will tell us that
if a mathematician cannot find his way round the circle without a relative
error four times as big as a stockbroker's commission, he must needs be
dreadfully out in his attempt to predict the time of passage of the moon.
Now, what is the fact? His error is less than a second of time, and the moon
takes 27 days odd to revolve. That is to say, setting out with 10s. in 100l. of
error in his circumference, he gets within the fifth part of a farthing in 100l.
in predicting the moon's transit. Now we cannot think that the respect in
which mathematical science is held is great enough—though we find it not

small—to make this go down. That respect is founded upon a notion that
right ends are got by right means: it will hardly be credited that the truth can
be got to farthings out of data which are wrong by shillings. Even the
celebrated Hamilton[207] of Edinburgh, who held that in mathematics there
was no way of going wrong, was fully impressed with the belief that this
was because error was avoided from the beginning. He never went so far as
to say that a mathematician who begins wrong must end right somehow.
"There is always a difficulty about the mode in which the thinking man of
common life is to deal with subjects he has not studied to a professional
extent. He must form opinions on matters theological, political, legal,
medical, and social. If he can make up his mind to choose a guide, there is,
of course, no perplexity: but on all the subjects mentioned the direction-
posts point different ways. Now why should he not form his opinion upon
an abstract mathematical question? Why not conclude that, as to the circle,
it is possible Mr. James Smith may be the man, just as Adam Smith[208] was
the man of things then to come, or Luther, or Galileo? It is true that there is
an unanimity among mathematicians which prevails in no other class: but
this makes the chance of their all being wrong only different in degree. And
more than this, is it not generally thought among us that priests and
physicians were never so much wrong as when there was most appearance
of unanimity among them? To the preceding questions we see no answer
except this, that the individual inquirer may as rationally decide a
mathematical question for himself as a theological or a medical question, so
soon as he can put himself into a position in mathematics, level with that in
which he stands in theology or medicine. The every-day thought and
reading of common life have a certain resemblance to the thought and
reading demanded by the learned faculties. The research, the balance of
evidence, the estimation of probabilities, which are used in a question of
medicine, are closely akin in character, however different the matter of
application, to those which serve a merchant to draw his conclusions about
the markets. But the mathematicians have methods of their own, to which
nothing in common life bears close analogy, as to the nature of the results or
the character of the conclusions. The logic of mathematics is certainly that
of common life: but the data are of a different species; they do not admit of
doubt. An expert arithmetician, such as is Mr. J. Smith, may fancy that
calculation, merely as such, is mathematics: but the value of his book, and

in this point of view it is not small, is the full manner in which it shows that
a practised arithmetician, venturing into the field of mathematical
demonstration, may show himself utterly destitute of all that distinguishes
the reasoning geometrical investigator from the calculator.
"And further, it should be remembered that in mathematics the power of
verifying results far exceeds that which is found in anything else: and also
the variety of distinct methods by which they can be attained. It follows
from all this that a person who desires to be as near the truth as he can will
not judge the results of mathematical demonstration to be open to his
criticism, in the same degree as results of other kinds. Should he feel
compelled to decide, there is no harm done: his circle may be 3⅛ times its
diameter, if it please him. But we must warn him that, in order to get this
circle, he must, as Mr. James Smith has done, make it at home: the laws of
space and thought beg leave respectfully to decline the order."

I will insert now at length, from the Athenæum of June 8, 1861, the easy
refutation given by my deceased friend, with the remarks which precede.
"Mr. James Smith, of whose performance in the way of squaring the circle
we spoke some weeks ago in terms short of entire acquiescence, has
advertised himself in our columns, as our readers will have seen. He has
also forwarded his letter to the Liverpool Albion, with an additional
statement, which he did not make in our journal. He denies that he has
violated the decencies of private life, since his correspondent revised the
proofs of his own letters, and his 'protest had respect only to making his
name public.' This statement Mr. James Smith precedes by saying that we
have treated as true what we well knew to be false: and he follows by
saying that we have not read his work, or we should have known the above
facts to be true. Mr. Smith's pretext is as follows. His correspondent E. M.
says, 'My letters were not intended for publication, and I protest against
their being published,' and he subjoins 'Therefore I must desire that my
name may not be used.' The obvious meaning is that E. M. protested against
the publication altogether, but, judging that Mr. Smith was determined to
publish, desired that his name should not be used. That he afterwards

corrected the proofs merely means that he thought it wiser to let them pass
under his own eyes than to leave them entirely to Mr. Smith.

"We have received from Sir W. Rowan Hamilton[209] a proof that the
circumference is more than 3⅛ diameters, requiring nothing but a
knowledge of four books of Euclid. We give it in brief as an exercise for our
juvenile readers to fill up. It reminds us of the old days when real geometers
used to think it worth while seriously to demolish pretenders. Mr. Smith's
fame is now assured: Sir W. R. Hamilton's brief and easy exposure will
procure him notice in connection with this celebrated problem.
"It is to be shown that the perimeter of a regular polygon of 20 sides is
greater than 3⅛ diameters of the circle, and still more, of course, is the
circumference of the circle greater than 3⅛ diameters.
"1. It follows from the 4th Book of Euclid, that the rectangle under the side
of a regular decagon inscribed in a circle, and that side increased by the
radius, is equal to the square of the radius. But the product 791 (791 +
1280) is less than 1280 × 1280; if then the radius be 1280 the side of the
decagon is greater than 791.
"2. When a diameter bisects a chord, the square of the chord is equal to the
rectangle under the doubles of the segments of the diameter. But the product
125 (4 × 1280 - 125) is less than 791 × 791. If then the bisected chord be a
side of the decagon, and if the radius be still 1280, the double of the lesser
segment exceeds 125.
"3. The rectangle under this doubled segment and the radius is equal to the
square of the side of an inscribed regular polygon of 20 sides. But the
product 125 × 1280 is equal to 400 × 400; therefore, the side of the last-
mentioned polygon is greater than 400, if the radius be still 1280. In other
words, if the radius be represented by the new member 16, and therefore the
diameter by 32, this side is greater than 5, and the perimeter exceeds 100.
So that, finally, if the diameter be 8, the perimeter of the inscribed regular
polygon of 20 sides, and still more the circumference of the circle, is greater
than 25: that is, the circumference is more than 3⅛ diameters."
The last work in the list was thus noticed in the Athenæum, May 27, 1865.

"Mr. James Smith appears to be tired of waiting for his place in the Budget
of Paradoxes, and accordingly publishes a long letter to Professor De
Morgan, with various prefaces and postscripts. The letter opens by a hint
that the Budget appears at very long intervals, and 'apparently without any
sufficient reason for it.' As Mr. Smith hints that he should like to see Mr. De
Morgan, whom he calls an 'elephant of mathematics,' 'pumping his brains'
'behind the scenes'—an odd thing for an elephant to do, and an odd place to
do it in—to get an answer, we think he may mean to hint that the Budget is
delayed until the pump has worked successfully. Mr. Smith is informed that
we have had the whole manuscript of the Budget, excepting only a final
summing-up, in our hands since October, 1863. [This does not refer to the
Supplement.] There has been no delay: we knew from the beginning that a
series of historical articles would be frequently interrupted by the things of
the day. Mr. James Smith lets out that he has never been able to get a
private line from Mr. De Morgan in answer to his communications: we
should have guessed it. He says, 'The Professor is an old bird and not to be
easily caught, and by no efforts of mine have I been able, up to the present
moment, either to induce or twit him into a discussion....' Mr. Smith curtails
the proverb: old birds are not to be caught with chaff, nor with twit, which
seems to be Mr. Smith's word for his own chaff, and, so long as the first
letter is sounded, a very proper word. Why does he not try a little grain of
sense? Mr. Smith evidently thinks that, in his character as an elephant, the
Professor has not pumped up brain enough to furnish forth a bird. In serious
earnest, Mr. Smith needs no answer. In one thing he excites our curiosity:
what is meant by demonstrating 'geometrically and mathematically?'"
I now proceed to my original treatment of the case.

Mr. James Smith will, I have no doubt, be the most uneclipsed circle-
squarer of our day. He will not owe this distinction to his being an
influential and respected member of the commercial world of Liverpool,
even though the power of publishing which his means give him should
induce him to issue a whole library upon one paradox. Neither will he owe
it to the pains taken with him by a mathematician who corresponded with
him until the joint letters filled an octavo volume. Neither will he owe it to
the notice taken of him by Sir William Hamilton, of Dublin, who refuted

him in a manner intelligible to an ordinary student of Euclid, which
refutation he calls a remarkable paradox easily explainable, but without
explaining it. What he will owe it to I proceed to show.
Until the publication of the Nut to Crack Mr. James Smith stood among
circle-squarers in general. I might have treated him with ridicule, as I have
done others: and he says that he does not doubt he shall come in for his
share at the tail end of my Budget. But I can make a better job of him than
so, as Locke would have phrased it: he is such a very striking example of
something I have said on the use of logic that I prefer to make an example
of his writings. On one point indeed he well deserves the scutica,[210] if not
the horribile flagellum.[211] He tells me that he will bring his solution to me
in such a form as shall compel me to admit it as un fait accompli [une faute
accomplie?][212] or leave myself open to the humiliating charge of
mathematical ignorance and folly. He has also honored me with some
private letters. In the first of these he gives me a "piece of information,"
after which he cannot imagine that I, "as an honest mathematician," can
possibly have the slightest hesitation in admitting his solution. There is a
tolerable reservoir of modest assurance in a man who writes to a perfect
stranger with what he takes for an argument, and gives an oblique threat of
imputation of dishonesty in case the argument be not admitted without
hesitation; not to speak of the minor charges of ignorance and folly. All this
is blind self-confidence, without mixture of malicious meaning; and I rather
like it: it makes me understand how Sam Johnson came to say of his old
friend Mrs. Cobb,[213]—"I love Moll Cobb for her impudence." I have now
done with my friend's suaviter in modo,[214] and proceed to his fortiter in
re[215]: I shall show that he has convicted himself of ignorance and folly,
with an honesty and candor worthy of a better value of π.
Mr. Smith's method of proving that every circle is 3⅛ diameters is to
assume that it is so,—"if you dislike the term datum, then, by hypothesis,
let 8 circumferences be exactly equal to 25 diameters,"—and then to show
that every other supposition is thereby made absurd. The right to this
assumption is enforced in the "Nut" by the following analogy:
"I think you (!) will not dare (!) to dispute my right to this hypothesis, when
I can prove by means of it that every other value of π will lead to the

grossest absurdities; unless indeed, you are prepared to dispute the right of
Euclid to adopt a false line hypothetically for the purpose of a 'reductio ad
absurdum'[216] demonstration, in pure geometry."

Euclid assumes what he wants to disprove, and shows that his assumption
leads to absurdity, and so upsets itself. Mr. Smith assumes what he wants to
prove, and shows that his assumption makes other propositions lead to
absurdity. This is enough for all who can reason. Mr. James Smith cannot be
argued with; he has the whip-hand of all the thinkers in the world. Montucla
would have said of Mr. Smith what he said of the gentleman who squared
his circle by giving 50 and 49 the same square root, Il a perdu le droit d'être
frappé de l'évidence.[217]
It is Mr. Smith's habit, when he finds a conclusion agreeing with its own
assumption, to regard that agreement as proof of the assumption. The
following is the "piece of information" which will settle me, if I be honest.
Assuming π to be 3⅛, he finds out by working instance after instance that
the mean proportional between one-fifth of the area and one-fifth of eight is
the radius. That is,

25 πr2 8
if π = , · = r.
8 5 5

This "remarkable general principle" may fail to establish Mr. Smith's
quadrature, even in an honest mind, if that mind should happen to know
that, a and b being any two numbers whatever, we need only assume—

a2 πr2 b
if π = , to get at · = r.
b a a

We naturally ask what sort of glimmer can Mr. Smith have of the subject
which he professes to treat? On this point he has given satisfactory
information. I had mentioned the old problem of finding two mean
proportionals, as a preliminary to the duplication of the cube. On this

mention Mr. Smith writes as follows. I put a few words in capitals; and I
write rq[218] for the sign of the square root, which embarrasses small type:
"This establishes the following infallible rule, for finding two mean
proportionals OF EQUAL VALUE, and is more than a preliminary, to the famous
old problem of 'Squaring the circle.' Let any finite number, say 20, and its
fourth part = ¼(20) = 5, be given numbers. Then rq(20 × 5) = rq 100 = 10,
is their mean proportional. Let this be a given mean proportional TO FIND
ANOTHER MEAN PROPORTIONAL OF EQUAL VALUE. Then

π 3.125
20 × = 20 × = 20 × .78125 = 15.625
4 4

will be the first number; as

π
25 : 16 :: rq 20 : rq 8.192: and (rq 8.192)2 = 8.192 × .78125 =
× 6.4
4

will be the second number; therefore rq(15.625 × 6.4) = rq 100 = 10, is the
required mean proportional.... Now, my good Sir, however competent you
may be to prove every man a fool [not every man, Mr. Smith! only some;
pray learn logical quantification] who now thinks, or in times gone by has
thought, the 'Squaring of the Circle' a possibility; I doubt, and, on the
evidence afforded by your Budget, I cannot help doubting, whether you
were ever before competent to find two mean proportionals by my unique
method."—(Nut, pp. 47, 48.) [That I never was, I solemnly declare!]
All readers can be made to see the following exposure. When 5 and 20 are
given, x is a mean proportional when in 5, x, 20, 5 is to x as x to 20. And x
must be 10. But x and y are two mean proportionals when in 5, x, y, 20, x is
a mean proportional between 5 and y, and y is a mean proportional between
x and 20. And these means are x = 5 ³√4, y = 5 ³√16. But Mr. Smith finds
one mean, finds it again in a roundabout way, and produces 10 and 10 as
the two (equal!) means, in solution of the "famous old problem." This is
enough: if more were wanted, there is more where this came from. Let it
not be forgotten that Mr. Smith has found a translator abroad, two, perhaps
three, followers at home, and—most surprising of all—a real mathematician

to try to set him right. And this mathematician did not discover the
character of the subsoil of the land he was trying to cultivate until a goodly
octavo volume of letters had passed and repassed. I have noticed, in more
quarters than one, an apparent want of perception of the full amount of Mr.
Smith's ignorance: persons who have not been in contact with the non-
geometrical circle-squarers have a kind of doubt as to whether anybody can
carry things so far. But I am an "old bird" as Mr. Smith himself calls me; a
Simorg, an "all-knowing Bird of Ages" in matters of cyclometry.
The curious phenomena of thought here exhibited illustrate, as above said, a
remark I have long ago made on the effect of proper study of logic. Most
persons reason well enough on matter to which they are accustomed, and in
terms with which they are familiar. But in unaccustomed matter, and with
use of strange terms, few except those who are practised in the abstractions
of pure logic can be tolerably sure to keep their feet. And one of the reasons
is easily stated: terms which are not quite familiar partake of the vagueness
of the X and Y on which the student of logic learns to see the formal force
of a proposition independently of its material elements.
I make the following quotation from my fourth paper on logic in the
Cambridge Transactions:
"The uncultivated reason proceeds by a process almost entirely material.
Though the necessary law of thought must determine the conclusion of the
ploughboy as much as that of Aristotle himself, the ploughboy's conclusion
will only be tolerably sure when the matter of it is such as comes within his
usual cognizance. He knows that geese being all birds does not make all
birds geese, but mainly because there are ducks, chickens, partridges, etc. A
beginner in geometry, when asked what follows from 'Every A is B,'
answers 'Every B is A.' That is, the necessary laws of thought, except in
minds which have examined their tools, are not very sure to work correct
conclusions except upon familiar matter.... As the cultivation of the
individual increases, the laws of thought which are of most usual
application are applied to familiar matter with tolerable safety. But
difficulty and risk of error make a new appearance with a new subject; and
this, in most cases, until new subjects are familiar things, unusual matter
common, untried nomenclature habitual; that is, until it is a habit to be
occupied upon a novelty. It is observed that many persons reason well in

some things and badly in others; and this is attributed to the consequence of
employing the mind too much upon one or another subject. But those who
know the truth of the preceding remarks will not have far to seek for what is
often, perhaps most often, the true reason.... I maintain that logic tends to
make the power of reason over the unusual and unfamiliar more nearly
equal to the power over the usual and familiar than it would otherwise be.
The second is increased; but the first is almost created."
Mr. James Smith, by bringing ignorance, folly, dishonesty into contact with
my name, in the way of conditional insinuation, has done me a good turn:
he has given me right to a freedom of personal remark which I might have
declined to take in the case of a person who is useful and respected in
matters which he understands.
Tit for tat is logic all the world over. By the way, what has become of the
rest of the maxim: we never hear it now. When I was a boy, in some parts of
the country at least, it ran thus:

"Tit for tat;
Butter for fat:
If you kill my dog,
I'll kill your cat."

He is a glaring instance of the truth of the observations quoted above. I will
answer for it that, at the Mersey Dock Board, he never dreams of proving
that the balance at the banker's is larger than that in the book by assuming
that the larger sum is there, and then proving that the other supposition—the
smaller balance—is upon that assumption, an absurdity. He never says to
another director, How can you dare to refuse me a right to assume the larger
balance, when you yourself, the other day, said,—Suppose, for argument's
sake, we had 80,000l. at the banker's, though you knew the book only
showed 30,000l.? This is the way in which he has supported his geometrical
paradox by Euclid's example: and this is not the way he reasons at the
board; I know it by the character of him as a man of business which has
reached my ears from several quarters. But in geometry and rational
arithmetic he is a smatterer, though expert at computation; at the board he is
a trained man of business. The language of geometry is so new to him that
he does not know what is meant by "two mean proportionals:" but all the

phrases of commerce are rooted in his mind. He is most unerasably booked
in the history of the squaring of the circle, as the speculator who took a
right to assume a proposition for the destruction of other propositions, on
the express ground that Euclid assumes a proposition to show that it
destroys itself: which is as if the curate should demand permission to
throttle the squire because St. Patrick drove the vermin to suicide to save
themselves from slaughter. He is conspicuous as a speculator who, more
visibly than almost any other known to history, reasoned in a circle by way
of reasoning on a circle. But what I have chiefly to do with is the force of
instance which he has lent to my assertion that men who have not had real
training in pure logic are unsafe reasoners in matter which is not familiar. It
is hard to get first-rate examples of this, because there are few who find the
way to the printer until practice and reflection have given security against
the grossest slips. I cannot but think that his case will lead many to take
what I have said into consideration, among those who are competent to
think of the great mental disciplines. To this end I should desire him to
continue his efforts, to amplify and develop his great principle, that of
proving a proposition by assuming it and taking as confirmation every
consequence that does not contradict the assumption.
Since my Budget commenced, Mr. Smith has written me notes: the portion
which I have preserved—I suppose several have been mislaid—makes a
hundred and seven pages of note-paper, closely written. To all this I have
not answered one word: but I think I cannot have read fewer than forty
pages. In the last letter the writer informs me that he will not write at
greater length until I have given him an answer, according to the "rules of
good society." Did I not know that for every inch I wrote back he would
return an ell? Surely in vain the net is spread in the eyes of anything that
hath a wing. There were several good excuses for not writing to Mr. J.
Smith: I will mention five. First, I distinctly announced at the beginning of
this Budget that I would not communicate with squarers of the circle.
Secondly, any answer I might choose to give might with perfect propriety
be reserved for this article; had the imputation of incivility been made after
the first note, I should immediately have replied to this effect: but I
presumed it was quite understood. Thirdly, Mr. Smith, by his publication of
E. M.'s letters against the wish of the writer, had put himself out of the pale
of correspondence. Fourthly, he had also gone beyond the rules of good

society in sending letter after letter to a person who had shown by his
silence an intention to avoid correspondence. Fifthly, these same rules of
good society are contrived to be flexible or frangible in extreme cases:
otherwise there would be no living under them; and good society would be
bad. Father Aldrovand has laid down the necessary distinction—"I tell thee,
thou foolish Fleming, the text speaketh but of promises made unto
Christians, and there is in the rubric a special exemption of such as are
made to Welchmen." There is also a rubric to the rules of good society; and
squarers of the circle are among those whom there is special permission not
to answer: they are the wild Welchmen of geometry, who are always
assailing, but never taking, the Garde Douloureuse[219] of the circle. "At this
commentary," proceeds the story, "the Fleming grinned so broadly as to
show his whole case of broad strong white teeth." I know not whether the
Welchman would have done the like, but I hope Mr. James Smith will: and I
hope he has as good a case to show as Wilkin Flammock. For I wish him
long life and long health, and should be very glad to see so much energy
employed in a productive way. I hope he wishes me the same: if not, I will
give him what all his judicious friends will think a good reason for doing
so. His pamphlets and letters are all tied up together, and will form a
curious lot when death or cessation of power to forage among book-shelves
shall bring my little library to the hammer. And this time may not be far off:
for I was X years old in A.D. X2; not 4 in A.D. 16, nor 5 in A.D. 25, but still in
one case under that law. And now I have made my own age a problem of
quadrature, and Mr. J. Smith may solve it. But I protest against his method
of assuming a result, and making itself prove itself: he might in this way, as
sure as eggs is eggs (a corruption of X is X), make me 1,864 years old,
which is a great deal too much.
April 5, 1864.—Mr. Smith continues to write me long letters, to which he
hints that I am to answer. In his last, of 31 closely written sides of note-
paper, he informs me, with reference to my obstinate silence, that though I
think myself and am thought by others to be a mathematical Goliath, I have
resolved to play the mathematical snail, and keep within my shell. A
mathematical snail! This cannot be the thing so called which regulates the
striking of a clock; for it would mean that I am to make Mr. Smith sound
the true time of day, which I would by no means undertake upon a clock
that gains 19 seconds odd in every hour by false quadrature. But he

ventures to tell me that pebbles from the sling of simple truth and common
sense will ultimately crack my shell, and put me hors de combat.[220] The
confusion of images is amusing: Goliath turning himself into a snail to
avoid π = 3⅛, and James Smith, Esq., of the Mersey Dock Board: and put
hors de combat—which should have been caché[221]—by pebbles from a
sling. If Goliath had crept into a snail-shell, David would have cracked the
Philistine with his foot. There is something like modesty in the implication
that the crack-shell pebble has not yet taken effect; it might have been
thought that the slinger would by this time have been singing—

"And thrice [and one-eighth] I routed all my foes,
And thrice [and one-eighth] I slew the slain."

But he promises to give the public his nut-cracker if I do not, before the
Budget is concluded, "unravel" the paradox, which is the mathematico-
geometrical nut he has given me to crack. Mr. Smith is a crack man: he will
crack his own nut; he will crack my shell; in the mean time he cracks
himself up. Heaven send he do not crack himself into lateral contiguity with
himself.
On June 27 I received a letter, in the handwriting of Mr. James Smith,
signed Nauticus. I have ascertained that one of the letters to the Athenæum
signed Nauticus is in the same handwriting. I make a few extracts:
"... The important question at issue has been treated by a brace of
mathematical birds with too much levity. It may be said, however, that
sarcasm and ridicule sometimes succeed, where reason fails.... Such a
course is not well suited to a discussion.... For this reason I shall for the
future [this implies there has been a past, so that Nauticus is not before me
for the first time] endeavor to confine myself to dry reasoning from
incontrovertible premises.
... It appears to me that so far as his theory is concerned he comes off
unscathed. You might have found "a hole in Smith's circle" (have you seen a
pamphlet bearing this title? [I never heard of it until now]), but after all it is
quite possible the hole may have been left by design, for the purpose of
entrapping the unwary."

[On the publication of the above, the author of the pamphlet obligingly
forwarded a copy to me of A Hole in Smith's Circle—by a Cantab:
Longman and Co., 1859, (pp. 15). "It is pity to lose any fun we can get out
of the affair," says my almamaternal brother: to which I add that in such a
case warning without joke is worse than none at all, as giving a false idea of
the nature of the danger. The Cantab takes some absurdities on which I have
not dwelt: but there are enough to afford a Cantab from every college his
own separate hunting ground.]
Does this hint that his mode of proof, namely, assuming the thing to be
proved, was a design to entrap the unwary? if so, it bangs Banagher. Was
his confounding two mean proportionals with one mean proportional found
twice over a trick of the same intent? if so, it beats cockfighting. That
Nauticus is Mr. Smith appears from other internal evidence. In 1819, Mr.
J. C. Hobhouse[222] was sent to Newgate for a libel on the House of
Commons which was only intended for a libel on Lord Erskine.[223] The ex-
Chancellor had taken Mr. Hobhouse to be thinking of him in a certain
sentence; this Mr. Hobhouse denied, adding, "There is but one man in the
country who is always thinking of Lord Erskine." I say that there is but one
man of our day who would couple me and Mr. James Smith as a "brace of
mathematical birds."
Mr. Smith's "theory" is unscathed by me. Not a doubt about it: but how does
he himself come off? I should never think of refuting a theory proved by
assumption of itself. I left Mr. Smith's π untouched: or, if I put in my thumb
and pulled out a plum, it was to give a notion of the cook, not of the dish.
The "important question at issue" was not the circle: it was, wholly and
solely, whether the abbreviation of James might be spelled Jimm.[224] This
is personal to the verge of scurrility: but in literary controversy the
challenger names the weapons, and Mr. Smith begins with charge of
ignorance, folly, and dishonesty, by conditional implication. So that the
question is, not the personality of a word, but its applicability to the person
designated: it is enough if, as the Latin grammar has it, Verbum personale
concordat cum nominativo.[225]
I may plead precedent for taking a liberty with the orthography of Jem. An
instructor of youth was scandalized at the abrupt and irregular—but very
effective—opening of Wordsworth's little piece:

"A simple child
That lightly draws its breath,
And feels its life in every limb,
What should it know of death?"

So he mended the matter by instructing his pupils to read the first line thus:

"A simple child, dear brother ——."

The brother, we infer from sound, was to be James, and the blank must
therefore be filled up with Jimb.
I will notice one point of the letter, to make a little more distinction between
the two birds. Nauticus lays down—quite correctly—that the sine of an
angle is less than its circular measure. He then takes 3.1416 for 180°, and
finds that 36' is .010472. But this is exactly what he finds for the sine of 36'
in tables: he concludes that either 3.1416 or the tables must be wrong. He
does not know that sines, as well as π, are interminable decimals, of which
the tables, to save printing, only take in a finite number. He is a six-figure
man: let us go thrice again to make up nine, and we have as follows:

Circular measure of 36' .010471975...
Sine of 36' .010471784...
Excess of measure over sine .000000191...

Mr. Smith invites me to say which is wrong, the quadrature, or the tables: I
leave him to guess. He says his assertions "arise naturally and necessarily
out of the arguments of a circle-squarer:" he might just as well lay down
that all the pigs went to market because it is recorded that "This pig went to
market." I must say for circle-squarers that very few bring their pigs to so
poor a market. I answer the above argument because it is, of all which Mr.
James Smith has produced, the only one which rises to the level of a
schoolboy: to meet him halfway I descend to that level.
Mr. Smith asks me to solve a problem in the Athenæum: and I will do it,
because the question will illustrate what is below schoolboy level.
"Let x represent the circular measure of an angle of 15°, and y half the sine
of an angle of 30° = area of the square on the radius of a circle of diameter

unity = .25. If x - y = xy, firstly, what is the arithmetical value of xy?
secondly, what is the angle of which xy represents the circular measure?"
If x represent 15° and y be ¼, xy represents 3° 45', whether x - y be xy or no.
But, y being ¼, x - y is not xy unless x be ⅓, that is, unless 12x or π be 4,
which Mr. Smith would not admit. How could a person who had just
received such a lesson as I had given immediately pray for further exposure,
furnishing the stuff so liberally as this? Is it possible that Mr. Smith,
because he signs himself Nauticus, means to deny his own very regular,
legible, and peculiar hand? It is enough to make the other members of the
Liverpool Dock Board cry, Mersey on the man!
Mr. Smith says that for the future he will give up what he calls sarcasm, and
confine himself, "as far as possible," to what he calls dry reasoning from
incontrovertible premises. If I have fairly taught him that his sarcasm will
not succeed, I hope he will find that his wit's end is his logic's beginning.
I now reply to a question I have been asked again and again since my last
Budget appeared: Why do you take so much trouble to expose such a
reasoner as Mr. Smith? I answer as a deceased friend of mine used to
answer on like occasions—A man's capacity is no measure of his power to
do mischief. Mr. Smith has untiring energy, which does something; self-
evident honesty of conviction, which does more; and a long purse, which
does most of all. He has made at least ten publications, full of figures which
few readers can criticize. A great many people are staggered to this extent,
that they imagine there must be the indefinite something in the mysterious
all this. They are brought to the point of suspicion that the mathematicians
ought not to treat "all this" with such undisguised contempt, at least. Now I
have no fear for π: but I do think it possible that general opinion might in
time demand that the crowd of circle-squarers, etc. should be admitted to
the honors of opposition; and this would be a time-tax of five per cent., one
man with another, upon those who are better employed. Mr. James Smith
may be made useful, in hands which understand how to do it, towards
preventing such opinion from growing. A speculator who expressly assumes
what he wants to prove, and argues that all which contradicts it is absurd,
because it cannot stand side by side with his assumption, is a case which
can be exposed to all. And the best person to expose it is one who has lived
in the past as well as the present, who takes misthinking from points of

view which none but a student of history can occupy, and who has
something of a turn for the business.
Whether I have any motive but public good must be referred to those who
can decide whether a missionary chooses his pursuit solely to convert the
heathen. I shall certainly be thought to have a little of the spirit of Col.
Quagg, who delighted in strapping the Grace-walking Brethren. I must
quote this myself: if I do not, some one else will, and then where am I? The
Colonel's principle is described as follows:
"I licks ye because I kin, and because I like, and because ye'se critters that
licks is good for. Skins ye have on, and skins I'll have off; hard or soft, wet
or dry, spring or fall. Walk in grace if ye like till pumpkins is peaches; but
licked ye must be till your toe-nails drop off and your noses bleed blue ink.
And—licked—they—were—accordingly."
I am reminded of this by the excessive confidence with which Mr. James
Smith predicted that he would treat me as Zephaniah Stockdolloger (Sam
Slick calls it slockdollager) treated Goliah Quagg. He has announced his
intention of bringing me, with a contrite heart, and clean shaved,—
4159265... razored down to 25,—to a camp-meeting of circle-squarers. But
there is this difference: Zephaniah only wanted to pass the Colonel's smithy
in peace; Mr. James Smith sought a fight with me. As soon as this Budget
began to appear, he oiled his own strap, and attempted to treat me as the
terrible Colonel would have treated the inoffensive brother.
He is at liberty to try again.

THE MOON HOAX.

The Moon-hoax; or the discovery that the moon has a vast
population of human beings. By Richard Adams Locke.[226] New
York, 1859, 8vo.

This is a reprint of the hoax already mentioned. I suppose R. A. Locke is
the name assumed by M. Nicollet.[227] The publisher informs us that when
the hoax first appeared day by day in a morning paper, the circulation

increased fivefold, and the paper obtained a permanent footing. Besides
this, an edition of 60,000 was sold off in less than one month.

The discovery was also published under the name of A. R. Grant.[228]
Sohncke's[229] Bibliotheca Mathematica confounds this Grant with Prof. R.
Grant[230] of Glasgow, the author of the History of Physical Astronomy, who
is accordingly made to guarantee the discoveries in the moon. I hope Adams
Locke will not merge in J. C. Adams,[231] the co-discoverer of Neptune.
Sohncke gives the titles of three French translations of the Moon hoax at
Paris, of one at Bordeaux, and of Italian translations at Parma, Palermo, and
Milan.
A Correspondent, who is evidently fully master of details, which he has
given at length, informs me that the Moon hoax appeared first in the New
York Sun, of which R. A. Locke was editor. It so much resembled a story
then recently published by Edgar A. Poe, in a Southern paper, "Adventures
of Hans Pfaal," that some New York journals published the two side by
side. Mr. Locke, when he left the New York Sun, started another paper, and
discovered the manuscript of Mungo Park;[232] but this did not deceive. The
Sun, however, continued its career, and had a great success in an account of
a balloon voyage from England to America, in seventy-five hours, by Mr.
Monck Mason,[233] Mr. Harrison Ainsworth,[234] and others. I have no doubt
that M. Nicollet was the author of the Moon hoax,[235] written in a way
which marks the practised observatory astronomer beyond all doubt, and by
evidence seen in the most minute details. Nicollet had an eye to Europe. I
suspect that he took Poe's story, and made it a basis for his own. Mr. Locke,
it would seem, when he attempted a fabrication for himself, did not
succeed.

The Earth we inhabit, its past, present, and future. By Capt.
Drayson.[236] London, 1859, 8vo.

The earth is growing; absolutely growing larger: its diameter increases
three-quarters of an inch per mile every year. The foundations of our
buildings will give way in time: the telegraph cables break, and no cause

ever assigned except ships' anchors, and such things. The book is for those
whose common sense is unwarped, who can judge evidence as well as the
ablest philosopher. The prospect is not a bad one, for population increases
so fast that a larger earth will be wanted in time, unless emigration to the
Moon can be managed, a proposal of which it much surprises me that
Bishop Wilkins has a monopoly.

IMPALEMENT BY REQUEST.
Athenæum, August, 19, 1865. Notice to Correspondents.
"R. W.—If you will consult the opening chapter of the Budget of
Paradoxes, you will see that the author presents only works in his own
library at a given date; and this for a purpose explained. For ourselves we
have carefully avoided allowing any writers to present themselves in our
columns on the ground that the Budget has passed them over. We gather
that Mr. De Morgan contemplates additions at a future time, perhaps in a
separate and augmented work; if so, those who complain that others of no
greater claims than themselves have been ridiculed may find themselves
where they wish to be. We have done what we can for you by forwarding
your letter to Mr. De Morgan."
The author of "An Essay on the Constitution of the Earth," published in
1844, demanded of the Athenæum, as an act of fairness, that a letter from
him should be published, proving that he had as much right to be "impaled"
as Capt. Drayson. He holds, on speculative grounds, what the other claims
to have proved by measurement, namely, that the earth is growing; and he
believes that in time—a good long time, not our time—the earth and other
planets may grow into suns, with systems of their own.
This gentleman sent me a copy of his work, after the commencement of my
Budget; but I have no recollection of having received it, and I cannot find it
on the (nursery? quarantine?) shelves on which I keep my unestablished
discoveries. Had I known of this work in time, (see the Introduction) I
should of course, have impaled it (heraldically) with the other work; but the
two are very different. Capt. Drayson professes to prove his point by results
of observation; and I think he does not succeed. The author before me only

speculates; and a speculator can get any conclusion into his premises, if he
will only build or hire them of shape and size to suit. It reminds me of a
statement I heard years ago, that a score of persons, or near it, were to dine
inside the skull of one of the aboriginal animals, dear little creatures!
Whereat I wondered vastly, nothing doubting; facts being stubborn and not
easy drove, as Mrs. Gamp said. But I soon learned that the skull was not a
real one, but artificially constructed by the methods—methods which have
had striking verifications, too—which enable zoologists to go the whole
hog by help of a toe or a bit of tail. This took off the edge of the wonder: a
hundred people can dine inside an inference, if you draw it large enough.
The method might happen to fail for once: for instance, the toe-bone might
have been abnormalized by therian or saurian malady; and the possibility of
such failure, even when of small probability, is of great alleviation. The
author before me is, apparently, the sole fabricator of his own premises.
With vital force in the earth and continual creation on the part of the
original Creator, he expands our bit of a residence as desired. But, as the
Newtoness of Cookery observed, First catch your hare. When this is done,
when you have a growing earth, you shall dress it with all manner of
proximate causes, and serve it up with a growing Moon for sauce, a
growing Sun, if it please you, at the other end, and growing planets for side-
dishes. Hoping this amount of impalement will be satisfactory, I go on to
something else.

THE HAILESEAN SYSTEM OF ASTRONOMY.

The Hailesean System of Astronomy. By John Davey Hailes[237]
(two pages duodecimo, 1860).

He offers to take 100,000l. to 1,000l. that he shows the sun to be less than
seven millions of miles from the earth. The earth in the center, revolving
eastward, the sun revolving westward, so that they "meet at half the circle
distance in the 24 hours." The diameter of the circle being 9839458303, the
circumference is 30911569920.
The following written challenge was forwarded to the Council of the
Astronomical Society: it will show the "general reader"—and help him

towards earning his name—what sort of things come every now and then to
our scientific bodies. I have added punctuation:

Challenge.
1,000 to 30,000.
"Leverrier's [238] name stand placed first. Do the worthy Frenchman justice.
By awarding him the medal in a trice.
Give Adams[239] an extra—of which neck and neck the race.
Now I challenge to meet them and the F.R.S.'s all,
For good will and one thousand pounds to their thirty thousand withall,
That I produce a system, which shall measure the time,
When the Sun was vertical to Gibeon, afterward to Syene.
To meet any time in London—name your own period,
To be decided by a majority of twelve persons—a President, odd.
That mean, if the twelve equally divide, the President decide,
I should prefer the Bishop of London, over the meeting to preside.
John Davy Hailes."
Feb. 17, 1847."

Mr. Hailes still issues his flying sheets. The last I have met with (October 7,
1863) informs us that the latitude of England is slowly increasing, which is
the true cause of the alteration in the variation of the magnet.
[Mr. Hailes continues his researches. Witness his new Hailesean system of
Astronomy, displaying Joshua's miracle-time, origin of time from science,
with Bible and Egyptian history. Rewards offered for astronomical
problems. With magnetism, etc. etc. Astronomical challenge to all the
world. Published at Cambridge, in 1865. The author agrees with Newton in
one marked point. Errores quam minimi non sunt contemnendi,[240] says
Isaac: meaning in figures, not in orthography. Mr. Hailes enters into the
spirit, both positive and negative, of this dictum, by giving the distance of
Sidius from the center of the earth at 163,162,008 miles 10 feet 8 inches 17-
28ths of an inch. Of course, he is aware that the center of figure of the earth
is 17.1998 inches from the center of gravity. Which of the two is he
speaking of?]

The Divine Mystery of Life. London [1861], 18mo. (pp.32).

The author has added one class to zoology, which is printed in capitals, as
derived from zoé, life, not from zôon, animal. That class is of Incorporealia,
order I., Infinitum, of one genus without plurality, Deus: order II., Finita,
angels good and evil. The rest is all about a triune system, with a diagram.
The author is not aware that ζωον is not animal, but living being. Aristotle
had classed gods under ζωα, and has been called to account for it by
moderns who have taken the word to mean animal.

A CHANCE FOR INVENTORS.

Explication du Zodiaque de Denderah, des Pyramides, et de
Genèse. Par le Capitaine au longcours Justin Roblin.[241] Caen,
1861. 8vo.

Capt. Roblin, having discovered the sites of gold and diamond mines by
help of the zodiac of Denderah, offered half to the shareholders of a
company which he proposed to form. One of our journals, by help of the
zodiac of Esné, offered, at five francs a head, to tell the shareholders the
exact amount of gold and diamonds which each would get, and to make up
the amount predicted to those who got less. There are moods of the market
in England in which this company could have been formed: so we must not
laugh at our neighbors.

JOHANNES VON GUMPACH.

A million's worth of property, and five hundred lives annually lost
at sea by the Theory of Gravitation. A letter on the true figure of
the earth, addressed to the Astronomer Royal, by Johannes von
Gumpach.[242] London, 1861, 8vo. (pp. 54).
The true figure and dimensions of the earth, in a letter addressed
to the Astronomer Royal. By Joh. von Gumpach. 2nd ed. entirely
recast. London, 1862, 8vo. (pp. 266).

Two issues of a letter published with two different title-pages, one
addressed to the Secretary of the Royal Society, the other to the
Secretary of the Royal Astronomical Society. It would seem that
the same letter is also issued with two other titles, addressed to
the British Association and the Royal Geographical Society. By
Joh. von Gumpach. London, 1862, 8vo.
Baby-Worlds. An essay on the nascent members of our solar
household. By Joh. von Gumpach. London, 1863, 8vo.

The earth, it appears, instead of being flattened, is elongated at the poles: by
ignorance of which the loss above mentioned occurs yearly. There is, or is
to be, a substitute for attraction and an "application hitherto neglected, of a
recognized law of optics to the astronomical theory, showing the true orbits
of the heavenly bodies to be perfectly circular, and their orbital motions to
be perfectly uniform." all irregularities being, I suppose, optical delusions.
Mr. Von Gumpach is a learned man; what else, time must show.

SLANDER PARADOXES.

Perpetuum Mobile: or Search for self-motive Power. By Henry
Dircks.[243] London, 1861, 8vo.

A useful collection on the history of the attempts at perpetual motion, that
is, at obtaining the consequences of power without any power to produce
them. September 7, 1863, a correspondent of the Times gave an anecdote of
George Stephenson,[244] which he obtained from Robert Stephenson.[245] A
perpetual motionist wanted to explain his method; to which George replied
—"Sir! I shall believe it when I see you take yourself up by the waistband,
and carry yourself about the room." Never was the problem better stated.
There is a paradox of which I ought to give a specimen, I mean the slander-
paradox; the case of a person who takes it into his head, upon evidence
furnished entirely by the workings of his own thoughts, that some other
person has committed a foul act of which the world at large would no more
suppose him guilty than they would suppose that the earth is a flat bordered

by ice. If I were to determine on giving cases in which the self-deluded
person imagines a conspiracy against himself, there would be no end of
choices. Many of the grosser cases are found at last to be accompanied by
mental disorder, and it is difficult to avoid referring the whole class to
something different from simple misuse of the reasoning power. The first
instance is one which puts in a strong light the state of things in which we
live, brought about by our glorious freedom of thought, speech, and writing.
The Government treated it with neglect, the press with silent contempt, and
I will answer for it many of my readers now hear of it for the first time,
when it comes to be enrolled among circle-squarers and earth-stoppers,
where, as the old philosopher said, it will not gravitate, being in proprio
loco.[246]
1862. On new year's day, 1862, when the nation was in the full tide of
sympathy with the Queen, and regret for its own loss, a paper called the
Free Press published a number devoted to the consideration of the causes of
the death of the Prince Consort. It is so rambling and inconsecutive that it
takes more than one reading to understand it. It is against the Times
newspaper. First, the following insinuation:
"To the legal mind, the part of [the part taken by] the Times will present a
prima facie case of the gravest nature, in the evident fore-knowledge of the
event, and the preparation to turn it to account when it should have
occurred. The article printed on Saturday must have been written on Friday.
That article could not have appeared had the Prince been intended to live."
Next, it is affirmed that the Times intended to convey the idea that the
Prince had been poisoned.
"Up to this point we are merely dealing with words which the Times
publishes, and these can leave not a shadow of doubt that there is an
intention to promulgate the idea that Prince Albert had been poisoned."
The article then goes on with a strange olio of insinuations to the effect that
the Prince was the obstacle to Russian intrigue, and that if he should have
been poisoned,—which the writer strongly hints may have been the case,—
some Minister under the influence of Russia must have done it. Enough for
this record. Un sot trouve toujours un plus sot qui l'admire:[247] who can he
be in this case?

THE NEPTUNE CONTROVERSY.
1846. At the end of this year arose the celebrated controversy relative to the
discovery of Neptune. Those who know it are well aware that Mr.
Adams's[248] now undoubted right to rank with Le Verrier[249] was made
sure at the very outset by the manner in which Mr. Airy,[250] the Astronomer
Royal, came forward to state what had taken place between himself and Mr.
Adams. Those who know all the story about Mr. Airy being arrested in his
progress by the neglect of Mr. Adams to answer a letter, with all the
imputations which might have been thrown upon himself for laxity in the
matter, know also that Mr. Airy's conduct exhibited moral courage, honest
feeling, and willingness to sacrifice himself, if need were, to the attainment
of the ends of private justice, and the establishment of a national claim. A
writer in a magazine, in a long and elaborate article, argued the supposition
—put in every way except downright assertion, after the fashion of such
things—that Mr. Airy had communicated Mr. Adams's results to M. Le
Verrier, with intention that they should be used. His presumption as to
motive is that, had Mr. Adams been recognized, "then the discovery must
have been indisputably an Englishman's, and that Englishman not the
Astronomer Royal." Mr. Adams's conclusions were "retouched in France,
and sent over the year after." The proof given is that it cannot be "imagined"
otherwise.
"Can it then be imagined that the Astronomer Royal received such results
from Mr. Adams, supported as they were by Professor Challis's[251] valuable
testimony as to their probable accuracy, and did not bring the French
astronomer acquainted with them, especially as he was aware that his friend
was engaged in matters bearing directly upon these results?"
The whole argument the author styles "evidence which I consider it difficult
to refute." He ends by calling upon certain persons, of whom I am one, to
"see ample justice done." This is the duty of every one, according to his
opportunities. So when the reputed author—the article being anonymous—
was, in 1849, proposed as a Fellow of the Astronomical Society, I joined—
if I remember right, I originated—an opposition to his election, until either
the authorship should be denied, or a proper retraction made. The friends of

the author neither denied the first, nor produced the second: and they judged
it prudent to withdraw the proposal. Had I heard of any subsequent
repentance, I would have taken some other instance, instead of this: should
I yet hear of such a thing, I will take care to notice it in the continuation of
this list, which I confidently expect, life and health permitting, to be able to
make in a few years. This much may be said, that the author, in a lecture on
the subject, given in 1849, and published with his name, did not repeat the
charge.

[The libel was published in the Mechanics' Magazine,[252] (vol. for 1846,
pp. 604-615): and the editor supported it as follows, (vol. for 1847, p. 476).
In answer to Mr. Sheepshanks's charitable hope that he had been hoaxed, he
says: "Mr. Sheepshanks cannot certainly have read the article referred to....
Severe and inculpatory it is—unjust some may deem it (though we
ourselves are out of the number.)... A 'hoax' forsooth! May we be often the
dupes of such hoaxes!" He then goes on to describe the article as directed
against the Astronomer Royal's alleged neglect to give Mr. Adams that
"encouragement and protection" which was his due, and does not hint one
word about the article containing the charge of having secretly and
fraudulently transmitted news of Mr. Adams's researches to France, that an
Englishman might not have the honor of the discovery. Mr. Sheepshanks
having called this a "deliberate calumny," without a particle of proof or
probability to support it, the editor says "what the reverend gentleman
means by this, we are at a loss to understand." He then proceeds not to
remember. I repeat here, what I have said elsewhere, that the management
of the journal has changed hands; but from 1846 to 1856, it had the collar of
S.S. (scientific slander). The prayer for more such things was answered (See
p. 349).]

JAMES IVORY.[253]
I have said that those who are possessed with the idea of conspiracy against
themselves are apt to imagine both conspirators and their bad motives and
actions. A person who should take up the idea of combination against
himself without feeling ill-will and originating accusations would be indeed
a paradox. But such a paradox has existed. It is very well known, both in

and beyond the scientific world, that the late James Ivory was subject to the
impression of which I am speaking; and the diaries and other sources of
anecdote of our day will certainly, sooner or later, make it a part of his
biography. The consequence will be that to his memory will be attached the
unfavorable impression which the usual conduct of such persons creates;
unless it should happen that some one who knows the real state of the case
puts the two sides of it properly together. Ivory was of that note in the
scientific world which may be guessed from Laplace's description of him as
the first geometer in Britain and one of the first in Europe. Being in
possession of accurate knowledge of his peculiarity in more cases than one;
and in one case under his own hand: and having been able to make full
inquiry about him, especially from my friend the late Thomas Galloway[254]
—who came after him at Sandhurst—one of the few persons with whom he
was intimate:—I have decided, after full deliberation, to forestall the future
biographies.
That Ivory was haunted by the fear of which I have spoken, to the fullest
extent, came to my own public and official knowledge, as Secretary of the
Astronomical Society. It was the duty of Mr. Epps,[255] the Assistant
Secretary, at the time when Francis Baily[256] first announced his discovery
of the Flamsteed Papers, to report to me that Mr. Ivory had called at the
Society's apartments to inquire into the contents of those papers, and to
express his hope that Mr. Baily was not attacking living persons under the
names of Newton and Flamsteed.[257] Mr. Galloway, to whom I
communicated this, immediately went to Mr. Ivory, and succeeded, after
some explanation, in setting him right. This is but one of many instances in
which a man of thoroughly sound judgment in every other respect seemed
to be under a complete chain of delusions about the conduct of others to
himself. But the paradox is this:—I never could learn that Ivory, passing his
life under the impression that secret and unprovoked enemies were at work
upon his character, ever originated a charge, imputed a bad motive, or
allowed himself an uncourteous expression. Some letters of his, now in my
possession, referring to a private matter, are, except in the main impression
on which they proceed, unobjectionable in every point: they might have
been written by a cautious friend, whose object was, if possible, to prevent
a difference from becoming a duel without compromising his principal's
rights or character. Knowing that in some quarters the knowledge of Ivory's

peculiarity is more or less connected with a notion that the usual
consequences followed, I think the preceding statement due to his memory.

THREE CLASSES OF JOURNALS.
In such a record as the present, which mixes up the grossest speculative
absurdities with every degree of what is better, an instance of another kind
may find an appropriate place. The faults of journalism, when merely
exposed by other journalism pass by and are no more regarded. A distinct
account of an undeniable meanness, recorded in a work of amusement and
reference both, may have its use: such a thing may act as a warning. An
editor who is going to indulge his private grudge may be prevented from
counting upon oblivion as a matter of certainty.
There are three kinds of journals, with reference to the mode of entrance of
contributors. First, as a thing which has been, but which now hardly exists,
there is the journal in which the editor receives a fixed sum to find the
matter. In such a journal, every article which the editor can get a friend to
give him is so much in his own pocket, which has a great tendency to lower
the character of the articles; but I am not concerned with this point.
Secondly, there is the journal which is supported by voluntary contributions
of matter, the editor selecting. Thirdly, there is the journal in which the
contributor is paid by the proprietors in a manner with which the literary
editor has nothing to do.
The third class is the safe class, as its editors know: and, as a usual rule,
they refuse unpaid contributions of the editorial cast. It is said that when
Canning[258] declined a cheque forwarded for an article in the Quarterly,
John Murray[259] sent it back with a blunt threat that if he did not take his
money he could never be admitted again. The great publisher told him that
if men like himself in position worked for nothing, all the men like himself
in talent who could not afford it would not work for the Quarterly. If the
above did not happen between Canning and Murray, it must have happened
between some other two. Now journals of the second class—and of the
first, if such there be—have a fault to which they alone are very liable, to
say nothing of the editorial function (see the paper at the beginning, p. 11 et

seq.), being very much cramped, a sort of gratitude towards effective
contributors leads the journal to help their personal likes and dislikes, and to
sympathize with them. Moreover, this sort of journal is more accessible
than others to articles conveying personal imputation: and when these
provoke discussion, the journal is apt to take the part of the assailant to
whom it lent itself in the first instance.

THE MECHANICS' MAGAZINE.
Among the journals which went all lengths with contributors whom they
valued, was the Mechanics' Magazine[260] in the period 1846-56. I cannot
say that matters have not mended in the last ten years: and I draw some
presumption that they have mended from my not having heard, since 1856,
of anything resembling former proceedings. And on actual inquiry, made
since the last sentence was written, I find that the property has changed
hands, the editor is no longer the same, and the management is of a different
stamp. This journal is chiefly supported by voluntary articles: and it is the
journal in which, as above noted, the ridiculous charge against the
Astronomer Royal was made in 1849. The following instance of attempt at
revenge is so amusing that I select it as the instance of the defect which I
intend to illustrate; for its puerility brings out in better relief the points
which are not so easily seen in more adult attempts.
The Mechanics' Magazine, which by its connection with engineering, etc.,
had always taken somewhat of a mathematical character, began, a little
before 1846, to have more to do with abstract science. Observing this, I
began to send short communications, which were always thankfully
received, inserted, and well spoken of. Any one who looks for my name in
that journal in 1846-49, will see nothing but the most respectful and even
laudatory mention. In May 1849 occurred the affair at the Astronomical
Society, and my share in forcing the withdrawal of the name of the alleged
contributor to the journal. In February 1850 occurred the opportunity of
payment. The Companion to the Almanac[261] had to be noticed, in which,
as then usual, was an article signed with my name. I shall give the review of
this article entire, as a sample of a certain style, as well as an illustration of
my point. The reader will observe that my name is not mentioned. This

would not have done; the readers of the Magazine would have stared to see
a name of not infrequent occurrence in previous years all of a sudden fallen
from the heaven of respect into the pit of contempt, like Lucifer, son of the
morning. But before giving the review, I shall observe that Mr. Adams, in
whose favor the attack on the Astronomer Royal was made, did not
appreciate the favor; and of course did not come forward to shield his
champion. This gave deadly offence, as appear from the following passage,
(February 16, 1850):
"It was our intention to enter into a comparison of the contents of our
Nautical Almanack with those of its rival, the Connaissance des Temps; but
we shall defer it for the present. The Nautical Almanack for 1851 will
contain Mr. Adams's paper 'On the Perturbation of Uranus'; and when it
comes, in due course, before the public, we are quite sure that that
gentleman will expect that we shall again enter upon the subject with
peculiar delight. Whilst we have a thorough loathing for mean, cowardly,
crawlers—we have an especial pleasure in maintaining the claims of men
who are truly grateful as well as highly talented: Mr. Adams, therefore, will
find that he cannot be disappointed—and the occasion will afford us an
opportunity for making the comparison to which we have adverted."
This passage illustrates what I have said on the editorial function (Vol. I, p.
15). What precedes and follows has some criticism on the Government, the
Astronomer Royal, etc., but reserved in allusion, oblique in sarcasm, and
not fiercely uncourteous. The coarseness of the passage I have quoted
shows editorial insertion, which is also shown by its blunder. The inserter is
waiting for the Almanac of 1851 that he may review Mr. Adams's paper,
which is to be contained in it. His own contributor, only two sentences
before the insertion, had said, "The Nautical Almanac, we believe, is
published three or four years in advance." In fact, the Almanac for 1851—
with Mr. Adams's paper at the end—was published at the end of 1847 or
very beginning of 1848; it had therefore been more than two years before
the public when the passage quoted was written. And probably every person
in the country who was fit to review Mr. Adams's paper—and most of those
who were fit to read it—knew that it had been widely circulated, in revise,
at the end of 1846: my copy has written on it, "2d revise, December 27,
1846, at noon," in the handwriting of the Superintendent of the Almanac;
and I know that there was an extensive issue of these revises, brought out

by the Le-Verrier-and-Adams discussion. I now give the review of myself,
(February 23, 1850):

"The British Almanack and Companion.
"The Companion to this Almanack, for some years after its first publication,
annually contained scientific articles by Sir J. Lubbock[262] and others of a
high order and great interest; we have now, however, closed the publication
as a scientific one in remembrance of what it was, and not in consequence
of what it is. Its list of contributors on science, has grown 'small by degrees
and beautifully less,' until it has dwindled down to one—'a last rose of
summer left withering alone.' The one contributor has contributed one paper
'On Ancient and Modern Usage in Reckoning.'
"The learned critic's chef d'œuvre, is considered, by competent judges, to be
an Essay on Old Almanacks printed a few years ago in this annual, and
supposed to be written with the view of surpassing a profound memoir on
the same subject by James O. Halliwell,[263] Esq., F.R. and A.S.S., but the
tremendous effort which the learned writer then made to excel many titled
competitors for honors in the antique line appears to have had a sad effect
upon his mental powers—at any rate, his efforts have since yearly become
duller and duller; happily, at last, we should suppose, 'the ancient and
modern usage in reckoning' indicates the lowest point to which the vis
inertia of the learned writer's peculiar genius can force him.
"We will give a few extracts from the article.
"The learned author says, 'Those who are accustomed to settle the meaning
of ancient phrases by self-examination will find some strange conclusions
arrived at by us.' The writer never wrote a more correct sentence—it admits
of no kind of dispute.
"'Language and counting,' says the learned author, 'both came before the
logical discussion of either. It is not allowable to argue that something is or
was, because it ought to be or ought to have been. That two negatives make
an affirmative, ought to be; if no man have done nothing, the man who has
done nothing does not exist, and every man has done something. But in
Greek, and in uneducated English, it is unquestionable that 'no man has
done nothing' is only an emphatic way of saying that no man has done

anything; and it would be absurd to reason that it could not have been so,
because it should not.'—p. 5.
"'But there is another difference between old and new times, yet more
remarkable, for we have nothing of it now: whereas in things indivisible we
count with our fathers, and should say in buying an acre of land, that the
result has no parts, and that the purchaser, till he owns all the ground, owns
none, the change of possession being instantaneous. This second difference
lies in the habit of considering nothing, nought, zero, cipher, or whatever it
may be called, to be at the beginning of the scale of numbers. Count four
days from Monday: we should now say Tuesday, Wednesday, Thursday,
Friday; formerly, it would have been Monday, Tuesday, Wednesday,
Thursday. Had we asked, what at that rate is the first day from Monday, all
would have stared at a phrase they had never heard. Those who were
capable of extending language would have said, Why it must be Monday
itself: the rest would have said, there can be no first day from Monday, for
the day after is Tuesday, which must be the second day: Monday, one;
Tuesday, two,'—p. 10.
"We assure our readers that the whole article is equally lucid, and its logic
alike formal.
"There are some exceedingly valuable footnotes; we give one of the most
interesting, taken from the learned Mr. Halliwell's profound book on
Nursery Rhymes[264]—a celebrated production, for which it is supposed the
author was made F.R.S.

"'One's nine,
Two's some,
Three's a many,
Four's a penny,
Five's a little hundred.'

'The last line refers to five score, the so-called hundred being more usually
six score. The first line, looked at etymologically, is one is not one, and the
change of thought by which nine, the decimal of one, aims to be associated
with the decimal of plurality is curious:'—Very.

"This valuable and profound essay will very probably be transferred to the
next edition of the learned Mr. Halliwell's rare work, of kindred worth,
entitled 'Rara Mathematica,' it will then be deservedly handed down to
posterity as a covering for cheap trunks—a most appropriate archive for
such a treasure."

In December, 1846, the Mechanics' Magazine published a libel on Airy in
the matter of the discovery of Neptune. In May, 1849, one * * * was to have
been brought forward for election at the Astronomical Society, and was
opposed by me and others, on the ground that he was the probable author of
this libel, and that he would not, perhaps could not, deny it. [N.B. I no more
doubt that he was the author then I doubt that I am the author of this
sentence.][265]
Accordingly, * * * was withdrawn, and a discussion took place, for which
see the Athenæum, No. 1126, May 26, 1849, p. 544. The Mechanics'
Magazine was very sore, but up to this day has never ventured beyond an
attack on Airy, private whisperings against Adams—(see ante, p. 147),—
and the above against myself. In due time, I doubt not my name will appear
as one of the âmes damnées[266] of the Mechanics' Magazine.[267]

T. S. DAVIES ON EUCLID.

First, as to Mr. Halliwell. The late Thomas Stephens Davies,[268] excellent
in geometry, and most learned in its history, was also a good hand at enmity,
though not implacable. He and Mr. Halliwell, who had long before been
very much one, were, at this date, very much two. I do not think T. S.
Davies wrote this article; and I think that by giving my reasons I shall do
service to his memory. It must have been written at the beginning of
February; and within three days of that time T. S. Davies was making over
to me, by his own free act, to be kept until claimed by the relatives, what all
who knew even his writings knew that he considered as the most precious
deposit he had ever had in his keeping—Horner's[269] papers. His letter
announcing the transmission is dated February 2, 1850. This is a strong

point; but there is another quite as strong. Euclid and his writings were
matters on which T. S. Davies knew neither fear nor favor: he could not
have written lightly about a man who stood high with him as a judge of
Euclid. Now in this very letter of Feb. 2, there is a sentence which I highly
value, because, as aforesaid, it is on a point on which he would never have
yielded anything, to which he had paid life-long attention, and on which he
had the bias of having long stood alone. In fact, knowing—and what I shall
quote confirms me,—that in the matter of Euclid his hand was against every
man, I expected, when I sent him a copy of my 22-column article,
"Eucleides" in Smith's Dictionary,[270] to have received back a criticism,
that would have blown me out of the water: and I thought it not unlikely
that a man so well up in the subject might have made me feel demolished
on some points. Instead of this, I got the following: "Although on one or
two minor points I do not quite accord with your views, yet as a whole and
without regard to any minor points, I think you are the first who has
succeeded in a delineation of Euclid as a geometer." All this duly
considered, it is utterly incredible that T. S. Davies should have written the
review in question. And yet Mr. Halliwell is treated just as T. S. Davies
would have treated him, as to tone and spirit. The inference in my mind is
that we have here a marked instance of the joining of hatreds which takes
place in journals supported by voluntary contributions of matter. Should
anything ever have revived this article—and no one ever knows what might
have been fished up from the forgotten mass of journals—the treatment of
Mr. Halliwell would certainly have thrown a suspicion on T. S. Davies, a
large and regular contributor to the Magazine. It is good service to his
memory to point out what makes it incredible that he should have written so
unworthy an article.
The fault is this. There are four extracts: the first three are perfectly well
printed. The printing of the Mechanics' Magazine was very good. I was
always exceedingly satisfied with the manner in which my articles
appeared, without my seeing proof. Most likely these extracts were printed
from my printed paper; if not the extractor was a good copier. I know this
by a test which has often served me. I use the subjunctive—"if no man have
done nothing," an ordinary transcriber, narrating a quotation almost always
lets his own habit write has. The fourth extract has three alterations, all
tending to make me ridiculous. None is altered, in two places, into nine,

denial into decimal, and comes into aims; so that "none, the denial of one,
comes to be associated with the denial of plurality," reads as "nine, the
decimal of one, aims to be associated with the decimal of plurality." This is
intentional; had it been a compositor's reading of bad handwriting, these
would not have been the only mistakes; to say nothing of the corrector of
the press. And both the compositor and reader would have guessed, from
the first line being translated into "one is not one," that it must have been
"one's none," not "one's nine." But it was not intended that the gem should
be recovered from the unfathomed cave, and set in a Budget of Paradoxes.
We have had plenty of slander-paradox. I now give a halfpennyworth of
bread to all this sack, an instance of the paradox of benevolence, in which
an individual runs counter to all the ideas of his time, and sees his way into
the next century. At Amiens, at the end of the last century, an institution was
endowed by a M. de Morgan, to whom I hope I am of kin, but I cannot trace
it; the name is common at Amiens. It was the first of the kind I ever heard
of. It is a Salle d'Asyle for children, who are taught and washed and taken
care of during the hours in which their parents must be at work. The
founder was a large wholesale grocer and colonial importer, who was made
a Baron by Napoleon I for his commercial success and his charities.

JAS. SMITH AGAIN.
1862. Mr. Smith replies to me, still signing himself Nauticus: I give an
extract:
"By hypothesis [what, again!] let 14° 24' be the chord of an arc of 15° [but I
wont, says 14° 24'], and consequently equal to a side of a regular polygon
of 24 sides inscribed in the circle. Then 4 times 14° 24' = 57° 36' = the
radius of the circle ..."
That is, four times the chord of an arc is the chord of four times the arc: and
the sum of four sides of a certain pentagon is equal to the fifth. This is the
capital of the column, the crown of the arch, the apex of the pyramid, the
watershed of the elevation. Oh! J. S.! J. S.! groans Geometry—Summum
J. S. summa injuria![271] The other J. S., Joseph Scaliger,[272] as already
mentioned, had his own way of denying that a straight line is always the

shortest distance between two points. A parallel might be instituted, but not
in half a column. And J. S. the second has been so tightly handled that he
may now be dismissed, with an inscription for his circular shield, obtained
by changing Lexica contexat into Circus quadrandus in an epigram of J. S.
the first:

"Si quem dura manet sententia judicis, olim
Damnatum ærumnis suppliciisque caput,
Hunc neque fabrili lassent ergastula massa,
Nec rigidas vexent fossa metalla manus.
Circus quadrandus: nam—cætera quid moror?—omnes
Pœnarum facies hic labor unus habet."[273]

I had written as far as damnatum when in came the letter of Nauticus as a
printed slip, with a request that I would consider the slip as a 'revised copy.'
Not a word of alteration in the part I have quoted! And in the evening came
a letter desiring that I would alter a gross error; but not the one above: this
is revising without revision! If there were cyclometers enough of this
stamp, they would, as cultivation progresses—and really, with John Stuart
Mill in for Westminster, it seems on the move, even though, as I learn while
correcting the proof, Gladstone be out from Oxford; for Oxford is no worse
than in 1829, while Westminster is far above what she ever has been:
election time excuses even such a parenthesis as this—be engaged to amuse
those who can afford it with paralogism at their meals, after the manner of
the other jokers who wore the caps and bells. The rich would then order
their dinners with panem et Circenses,—up with the victuals and the circle-
games—as the poor did in the days of old.
Mr. Smith is determined that half a column shall not do. Not a day without
something from him: letter, printed proof, pamphlet. In what is the last at
this moment of writing he tells me that part of the title of a work of his will
be "Professor De Morgan in the pillory without hope of escape." And where
will he be himself? This I detected by an effort of reasoning which I never
could have made except by following in his steps. In all matters connected
with π the letters l and g are closely related: this appears in the well-known
formula for the time of oscillation π √(l : g). Hence g may be written for l,
but only once: do it twice, and you require the time to be π √(l2 : g2). This

may be reinforced by observing that if as a datum, or if you dislike that
word, by hypothesis, the first l be a g, it is absurd that it should be an l.
Write g for the first l, and we have un fait accompli. I shall be in pillory;
and overhead, in a cloud, will sit Mr. James Smith on one stick laid across
two others, under a nimbus of 3⅛ diameters to the circumference—in π-
glory. Oh for a drawing of this scene! Mr. De Morgan presents his
compliments to Mr. James Smith, and requests the honor of an exchange of
photographs.
July 26.—Another printed letter.—Mr. James Smith begs for a distinct
answer to the following plain question: "Have I not in this communication
brought under your notice truths that were never before dreamed of in your
geometrical and mathematical philosophy?" To which, he having taken the
precaution to print the word truths in italics, I can conscientiously answer,
Yes, you have. And now I shall take no more notice of these truths, until I
receive something which surpasses all that has yet been done.

A FEW SMALL PARADOXERS.

The Circle secerned from the Square; and its area gauged in terms
of a triangle common to both. By Wm. Houlston,[274] Esq.
London and Jersey, 1862, 4to.

Mr. Houlston squares at about four poetical quotations in a page, and brings
out π = 3.14213.... His frontispiece is a variegated diagram, having parts
designated Inigo and Outigo. All which relieves the subject, but does not
remove the error.

Considerations respecting the figure of the Earth.... By C. F.
Bakewell.[275] London, 1862, 8vo.

Newton and others think that in a revolving sphere the loose surface matter
will tend to the equator: Mr. Bakewell thinks it will tend to the poles.

On eccentric and centric force: a new theory of projection. By
H. F. A. Pratt, M.D.[276] London, 1862, 8vo.

Dr. Pratt not only upsets Newton, but cuts away the very ground he stands
on: for he destroys the first law of motion, and will not have the natural
tendency of matter in motion to be rectilinear. This, as we have seen, was
John Walsh's[277] notion. In a more recent work "On Orbital Motion,"
London, 1863, 8vo., Dr. Pratt insists on another of Walsh's notions, namely,
that the precession of the equinoxes is caused by the motion of the solar
system round a distant central sun. In this last work the author refers to a
few notes, which completely destroy the theory of gravitation in terms
"perfectly intelligible as well to the unlearned as to the learned": to me they
are quite unintelligible, which rather tends to confirm a notion I have long
had, that I am neither one thing nor the other. There is an ambiguity of
phrase which delights a writer on logic, always on the look-out for
specimens of homonymia or æquivocatio. The author, as a physician, is
accustomed to "appeal from mere formulæ": accordingly, he sets at nought
the whole of the mathematics, which he does not understand. This
equivocation between the formula of the physician and that of the
mathematician is as good, though not so perceptible to the world at large, as
that made by Mr. Briggs's friend in Punch's picture, which I cut out to paste
into my Logic. Mr. Briggs wrote for a couple of bruisers, meaning to
prepare oats for his horses: his friend sent him the Whitechapel Chicken and
the Bayswater Slasher, with the gloves, all ready.

On matter and ether, and the secret laws of physical change. By
T. R. Birks, M.A.[278] Cambridge, 1862, 8vo.

Bold efforts are made at molecular theories, and the one before me is ably
aimed. When the Newton of this subject shall be seated in his place, books
like the present will be sharply looked into, to see what amount of
anticipation they have made.

DR. THORN AND MR. BIDEN.

The history of the 'thorn tree and bush' from the earliest to the
present time: in which is clearly and plainly shown the descent of
her most gracious Majesty and her Anglo-Saxon people from the
half tribe of Ephraim, and possibly from the half tribe of
Manasseh; and consequently her right and title to possess, at the
present moment, for herself and for them, a share or shares of the
desolate cities and places in the land of their forefathers! By
Theta, M.D.[279] (Private circulation.) London, 1862, 8vo.

This is much about Thorn, and its connected words, Thor, Thoth, Theta, etc.
It is a very mysterious vagary. The author of it is the person whom I have
described elsewhere as having for his device the round man in the three-
cornered hole, the writer of the little heap of satirical anonymous letters
about the Beast and 666. By accident I discovered the writer: so that if there
be any more thorns to crackle under the pot, they need not be anonymous.
Nor will they be anonymous. Since I wrote the above, I have received
onymous letters, as ominous as the rest. The writer, William Thorn, M.D., is
obliged to reveal himself, since it is his object to prove that he himself is
one 666. By using W for double Vau (or 12) he cooks the number out of his
own name. But he says it is the number not of a beast but of a man, and
adds, "Thereby hangs a tale!" which sounds like contradiction. He informs
me that he will talk the matter over with me: but I shall certainly have
nothing to say to a gentleman of his number; it is best to keep on the safe
side.
In one letter I am informed that not a line should I have had, but for my
"sneer at 666," which, therefore, I am well pleased to have given. I am also
told that my name means the "'garden of death,' that place in which the tree
of knowledge was plucked, and so you are like your name 'dead' to the fact
that you are an Israelite, like those in Ezekiel 37 ch." Some hints are given
that I shall not fare well in the next world, which any one who reads the
chapter in Ezekiel will see is quite against his comparison. The reader must
not imagine that my prognosticator means Morgan to be a corruption of
Mortjardin; he proves his point by Hebrew: but any philologist would tell
him the true derivation of the name, and how Glamorgan came to get it. It
will be of much comfort to those young men who have not got through to
know that the tree of knowledge itself was once in the same case. And so

good bye to 666 for the present, and the assumption that the enigma is to be
solved by the united numeral forces of the letters of a word.
It is worthy of note that, as soon as my Budget commenced, two guardian
spirits started up, fellow men as to the flesh, both totally unknown to me:
they have stuck to me from first to last. James Smith, Esq., finally Nauticus,
watches over my character in this world, and would fain preserve me from
ignorance, folly, and dishonesty, by inclosing me in a magic circle of 3⅛
diameters in circumference. The round man in the three-cornered hole,
finally William Thorn, M.D., takes charge of my future destiny, and tries to
bring me to the truth by unfolding a score of meanings—all right—of 666.
He hints that I, and my wife, are servants of Satan: at least he desires us
both to remember that we cannot serve God and Satan; and he can hardly
mean that we are serving the first, and that he would have us serve the
second. As becomes an interpreter of the Apocalypse, he uses seven
different seals; but not more than one to one letter. If his seals be all signet-
rings, he must be what Aristophanes calls a sphragidonychargocometical
fellow. But—and many thanks to him for the same—though an M.D., he
has not sent me a single vial. And so much for my tree of secular
knowledge and my tree of spiritual life: I dismiss them with thanks from
myself and thanks from my reader. The dual of the Pythagorean system was
Isis and Diana; of the Jewish law, Moses and Aaron; and of the City of
London, Gog and Magog; of the Paradoxiad, James Smith, Esq., and
William Thorn, M.D.

September, 1866. Mr. James Biden[280] has favored me with some of his
publications. He is a rival of Dr. Thorn; a prophet by name-right and crest-
right. He is of royal descent through the De Biduns. He is the watchman of
Ezekiel: God has told him so. He is the author of The True Church, a phrase
which seems to have a book-meaning and a mission-meaning. He shall
speak for himself:
"A crest of the Bidens has significance. It is a lion rampant between wings
—wings in Scripture denote the flight of time. Thus the beasts or living
creatures of the Revelations have each six wings, intimating a condition of
mankind up to and towards the close of six thousand years of Bible
teaching. The two wings of the crest would thus intimate power towards the
expiration of 2000 years, as time is marked in the history of Great Britain.

"In a recent publication, The Pestilence, Why Inflicted, are given many
reasons why the writer thinks himself to be the appointed watchman
foretold by Ezekiel, chapters iii. and xxxiii. Among the reasons are many
prophecies fulfilled in him. Of these it is now needful to note two as bearing
especially on the subject of the reign of Darius.
"1.—In Daniel it is said, 'Darius the Median took the kingdom, being about
threescore and two years old.'—Daniel v. 31.
"When 'Belshazzar' the king of the Chaldeans is found wanting, Darius
takes the kingdom. It is not given him by the popular voice; he asserts his
right, and this is not denied. He takes it when about sixty-two years of age.
The language of Daniel is prophetic, and Darius has in another an antitype.
The writer was born July 18th, 1803; and the claim was asserted at the close
of 1865, when he was about sixty-two years of age.
"The claims which have been asserted demand a settled faith, and which
could only be reached through a long course of divine teaching."
When I was a little boy at school, one of my school-fellows took it into his
head to set up a lottery of marbles: the thing took, and he made a stony
profit. Soon, one after another, every boy had his lottery, and it was, "I
won't put into yours unless you put into mine." This knocked up the
scheme. It will be the same with the prophets. Dr. Thorn, Mr. Biden, Mrs.
Cottle,[281] etc. will grow imitators, until we are all pointed out in the Bible:
but A will not admit B's claim unless B admits his. For myself, as elsewhere
shown, I am the first Beast in the Revelations.
Every contraband prophet gets a few followers: it is a great point to make
these sequacious people into Buridan's asses, which they will become when
prophets are so numerous that there is no choosing.

SIR G. C. LEWIS.

An historical survey of the Astronomy of the Ancients. By the Rt.
Hon. Sir G. C. Lewis.[282] 8vo. 1862.

There are few men of our day whom I admire more than the late Sir G.
Lewis: he was honest, earnest, sagacious, learned, and industrious. He
probably sacrificed his life to his conjunction of literature and politics: and
he stood high as a minister of state in addition to his character as a man of
letters. The work above named is of great value, and will be read for its
intrinsic merit, consulted for its crowd of valuable references, quoted for its
aid to one side of many a discussion, and opposed for its force against the
other. Its author was also a wit and a satirist. I know of three classical
satires of our day which are inimitable imitations: Mr. Malden's[283]
Pragmatized Legends, Mr. Mansel's[284] Phrontisterion, and Sir G.
Cornewall Lewis's Inscriptio Antiqua. In this last,
HEYDIDDLEDIDDLETHECATANDTHEFIDDLE etc. is treated as an Oscan
inscription, and rendered into Latin by approved methods. As few readers
have seen it, I give the result:

"Hejus dedit libenter, dedit libenter. Deus propitius [est], deus
[donatori] libenter favet. Deus in viarum juncturâ ovorum dape
[colitur], deus mundi. Deus in litatione voluit, benigno animo,
hædum, taurum intra fines [loci sacri] portandos. Deus, bis
lustratus, beat fossam sacræ libationis."[285]

How then comes the history of astronomy among the paradoxes? Simply
because the author, so admirably when writing about what he knew, did not
know what he did not know, and blundered like a circle-squarer. And why
should the faults of so good a writer be recorded in such a list as the
present? For three reasons: First, and foremost, because if the exposure be
not made by some one, the errors will gradually ooze out, and the work will
get the character of inaccurate. Nothing hurts a book of which few can
fathom the depths so much as a plain blunder or two on the surface.
Secondly, because the reviews either passed over these errors or treated
them too gently, rather implying their existence than exposing them.
Thirdly, because they strongly illustrate the melancholy truth, that no one
knows enough to write about what he does not know. The distinctness of the
errors is a merit; it proceeds from the clear-headedness of the author. The
suppression in the journals may be due partly to admiration of the talent and
energy which lived two difficult lives at once, partly to respect for high
position in public affairs, partly to some of the critics being themselves men

of learning only, unable to detect the errors. But we know that action and
reaction are equal and contrary. If our generation take no notice of defects,
and allow them to go down undetected among merits, the next generation
will discover them, will perhaps believe us incapable of detecting them, at
least will pronounce our judgment good for nothing, and will form an
opinion in which the merits will be underrated: so it has been, is, and will
be. The best thing that can be done for the memory of the author is to
remove the unsound part that the remainder may thrive. The errors do not
affect the work; they occur in passages which might very well have been
omitted: and I consider that, in making them conspicuous, I am but cutting
away a deleterious fungus from a noble tree.

(P. 154). The periodic times of the five planets were stated by Eudoxus,[286]
as we learn from Simplicius;[287] the following is his statement, to which
the true times are subjoined, for the sake of comparison:

STATEMENT OF EUDOXUS TRUE TIME
Mercury 1 year — 87d. 23h.
Venus 1 " — 224d. 16h.
Mars 2 " 1y. 321d. 23h.
Jupiter 12 " 11y. 315d. 14h.
Saturn 30 " 29y. 174d. 1h.

Upon this determination two remarks may be made. First, the error with
respect to Mercury and Venus is considerable; with respect to Mercury, it is,
in round numbers, 365 instead of 88 days, more than four times too much.
Aristotle remarks that Eudoxus distinguishes Mercury and Venus from the
other three planets by giving them one sphere each, with the poles in
common. The proximity of Mercury to the sun would render its course
difficult to observe and to measure, but the cause of the large error with
respect to Venus (130 days) is not apparent.
Sir G. Lewis takes Eudoxus as making the planets move round the sun; he
has accordingly compared the geocentric periods of Eudoxus with our
heliocentric periods. What greater blunder can be made by a writer on
ancient astronomy than giving Eudoxus the Copernican system? If Mercury
were a black spot in the middle of the sun it would of course move round

the earth in a year, or appear to do so: let it swing a little on one side and the
other of the sun, and the average period is still a year, with slight departures
both ways. The same for Venus, with larger departures. Say that a person
not much accustomed to the distinction might for once write down the
mistake; how are we to explain its remaining in the mind in a permanent
form, and being made a ground for such speculation as that of the difficulty
of observing Mercury leading to a period four times what it ought to be,
corrected in proof and published by an industrious and thoughtful person?
Only in one way: the writer was quite out of his depth. This one case is
conclusive; be it said with all respect for the real staple of the work and of
the author. He knew well the difference of the systems, but not the effect of
the difference: he is another instance of what I have had to illustrate by help
of a very different person, that it is difficult to reason well upon matter
which is not familiar.

(P. 254). Copernicus, in fact, supposed the axis of the earth to be always
turned towards the Sun.(169) [(169). See Delambre, Hist. Astr. Mod., Vol. I,
p. 96]. It was reserved to Kepler to propound the hypothesis of the constant
parallelism of the earth's axis to itself.

If there be one thing more prominent than another in the work of
Copernicus himself, in the popular explanations of it, and in the page of
Delambre[288] cited, it is that the parallelism of the earth's axis is a glaring
part of the theory of Copernicus. What Kepler[289] did was to throw away,
as unnecessary, the method by which Copernicus, per fas et nefas,[290]
secured it. Copernicus, thinking of the earth's orbital revolution as those
would think who were accustomed to the solid orbs—and much as the
stoppers of the moon's rotation do now: why do they not strengthen
themselves with Copernicus?—thought that the earth's axis would always
incline the same end towards the sun, unless measures were taken to
prevent it. He did take measures: he invented a compensating conical
motion of the axis to preserve the parallelism; and, which is one of the most
remarkable points of his system, he obtained the precession of the
equinoxes by giving the necessary trifle more than compensation. What

stares us in the face at the beginning of the paragraph to which the author
refers?
"C'est donc pour arriver à ce parallelisme, ou pour le conserver, que
Copernic a cru devoir recourir à ce mouvement égal et opposé qui détruit
l'effet qu'il attribue si gratuitement au premier, de déranger le parallelisme."
[291]

Parallelism at any price, is the motto of Copernicus: you need not pay so
dear, is the remark of Kepler.
The opinions given by Sir G. Lewis about the effects of modern astronomy,
which he does not understand and singularly undervalues, will now be seen
to be of no authority. He fancies that—to give an instance—for the
determination of a ship's place, the invention of chronometers has been far
more important than any improvement in astronomical theory (p. 254). Not
to speak of latitude,—though the omission is not without importance,—he
ought to have known that longitude is found by the difference between what
o'clock it is at Greenwich and at the ship's place, at one absolute moment of
time. Now if a chronometer were quite perfect—which no chronometer is,
be it said—and would truly tell Greenwich mean time all over the world, it
ought to have been clear that just as good a watch is wanted for the time at
the place of observation, before the longitude of that place with respect to
Greenwich can be found. There is no such watch, except the starry heaven
itself: and that watch can only be read by astronomical observation, aided
by the best knowledge of the heavenly motions.
I think I have done Sir G. Lewis's very excellent book more good than all
the reviewers put together.
I will give an old instance in which literature got into confusion about
astronomy. Theophrastus,[292] who is either the culprit or his historian,
attributes to Meton,[293] the contriver of the lunar calendar of nineteen
years, which lasts to this day, that his solstices were determined for him by
a certain Phaeinus of Elis on Mount Lycabettus. Nobody else mentions this
astronomer: though it is pretty certain that Meton himself made more than
one appointment with him for the purpose of observing solstices; and we
may be sure that if either were behind his time, it was Meton. For Phaeinus

Helius is the shining sun himself; and in the astronomical poet Aratus[294]
we read about the nineteen years of the shining sun:

Ἐννεακαιδέκα κύκλα φαεινοῦ ἠελίοιο.[295]

Some man of letters must have turned Apollo into Phaeinus of Elis; and
there he is in the histories of astronomy to this day. Salmasius[296] will have
Aratus to have meant him, and proposes to read ἠλείοιο: he did not observe
that Phaeinus is a very common adjective of Aratus, and that, if his
conjecture were right, this Phaeinus would be the only non-mythical man in
the poems of Aratus.
[When I read Sir George Lewis's book, the points which I have criticized
struck me as not to be wondered at, but I did not remember why at the time.
A Chancellor of the Exchequer and a writer on ancient astronomy are birds
of such different trees that the second did not recall the first. In 1855 I was
one of a deputation of about twenty persons who waited on Sir G. Lewis, as
Chancellor of the Exchequer, on the subject of a decimal coinage. The
deputation was one of much force: Mr. Airy, with myself and others,
represented mathematics; William Brown,[297] whose dealings with the
United States were reckoned by yearly millions, counted duodecimally in
England and decimally in America, was the best, but not the only,
representative of commerce. There were bullionists, accountants, retailers,
etc. Sir G. L. walked into the room, took his seat, and without waiting one
moment, began to read the deputation a smart lecture on the evils of a
decimal coinage; it would require alteration of all the tables, it would
impede calculation, etc. etc. Of those arguments against it which weighed
with many of better knowledge than his, he obviously knew nothing. The
members of the deputation began to make their statements, and met with
curious denials. He interrupted me with "Surely there is no doubt that the
calculations of our books of arithmetic are easier than those in the French
books." He was not aware that the universally admitted superiority of
decimal calculation made many of those who prefer our system for the
market and the counter cast a longing and lingering look towards decimals.
My answer and the smiles which he saw around, made him give a queer
puzzled look, which seemed to say, "I may be out of my depth here!" His
manner changed, and he listened. I saw both the slap-dash mode in which

he dealt with subjects on which he had not thought, and the temperament
which admitted suspicion when the means of knowledge came in his way.
Having seen his two phases, I wonder neither at his more than usual
exhibition of shallowness when shallow, nor at the intensity of the contrast
when he had greater depth.]

DECIMAL COINAGE.
Among the paradoxers are the political paradoxers who care not how far
they go in debate, their only object being to carry the House with them for
the current evening. What I have said of editors I repeat of them. The
preservation of a very marked instance, the association of political
recklessness with cyclometrical and Apocalyptic absurdity, may have a
tendency to warn, not indeed any hardened public-man and sinner, but some
young minds which have yearnings towards politics, and are in formation of
habits.

In the debate on decimal coinage of July 12, 1855, Mr. Lowe,[298] then
member for Kidderminster, an effective speaker and a smart man, exhibited
himself in a speech on which I wrote a comment for the Decimal
Association. I have seldom seen a more wretched attempt to distort the
points of a public question than the whole of this speech. Looking at the
intelligence shown by the speaker on other occasions, it is clear that if
charity, instead of believing all things, believed only all things but one, he
might tremble for his political character; for the honesty of his intention on
this occasion might be the incredible exception. I give a few paragraphs
with comments:
"In commenting on the humorous, but still argumentative speech of Mr.
Lowe, the member for Kidderminster, we may observe, in general, that it
consists of points which have been several times set forth, and several times
answered. Mr. Lowe has seen these answers, but does not allude to them,
far less attempt to meet them. There are, no doubt, individuals, who show in
their public speaking the outward and visible signs of a greater degree of
acuteness than they can summon to guide their private thinking. If Mr.
Lowe be not one of these, if the power of his mind in the closet be at all

comparable to the power of his tongue in the House, it may be suspected
that his reserve with respect to what has been put forward by the very
parties against whom he was contending, arises from one or both of two
things—a high opinion of the arguments which he ignored—a low opinion
of the generality of the persons whom he addressed. [Both, I doubt not].

"Did they calculate in florins ?" In the name of common sense,
how can it be objected to a
system that people do not use it
before it is introduced? Let the
decimal system be completed,
and calculation shall be made
in florins; that is, florins shall
take their proper place. If
florins were introduced now,
there must be a column for the
odd shilling.

"He was glad that some hon. If the hon. gentleman make this
gentleman had derived benefit assertion of himself, it is not for
from the issue of florins. His us to gainsay it. It only proves
only experience of their that he is one of that class of
convenience was, that when he men who are described in the
ought to have received half-a- old song, of which one couplet
crown, he had generally received runs thus:
a florin, and when he ought to
have paid a florin, he had I sold my cow to buy me a
generally paid half-a-crown." calf;
(Hear, hear, and laughter.) I never make a bargain but I
lose half,
With a etc. etc. etc.

But he cannot mean that Englishmen in general are so easily managed. And
as to Jonathan, who is but John lengthened out a little, he would see
creation whittled into chips before he would even split what may henceforth
be called the Kidderminster difference. The House, not unmoved—for it

laughed—with sly humor decided that the introduction of the florin had
been "eminently successful and satisfactory."
The truth is that Mr. Lowe here attacks nothing except the coexistence of
the florin and half-crown. We are endeavoring to abolish the half-crown.
Let Mr. Lowe join us; and he will, if we succeed, be relieved from the
pressure on his pocket which must arise from having the turn of the market
always against him.

"From a florin they get Note the sophism of expressing our coin
to 2 2-5ths of a penny, in terms of the penny, which we abandon,
but who ever bought instead of the florin, which we retain.
anything, who ever Remember that this 2 2-5ths is the
reckoned or wished to hundredth part of the pound, which is
reckon in such a coin called, as yet, a cent. Nobody buys
as that?" (Hear, hear.) anything at a cent, because the cent is not
yet introduced. Nobody reckons in cents
for the same reason. Everybody wishes to
reckon in cents, who wishes to combine
the advantage of decimal reckoning with
the preservation of the pound as the
highest unit of account; amongst others, a
majority of the House of Commons, the
Bank of England, the majority of London
bankers, the Chambers of Commerce in
various places, etc. etc. etc.

"Such a coin could Does 2½d. never pass from hand to
never come into hand? And is 2½d. so precisely the
general circulation modulus of popular wants, that an
because it represents alteration of 4 per cent. would make it
nothing which useless? Of all the values which 2½d.
corresponds with any measures, from three pounds of potatoes
of the wants of the down to certain arguments used in the
people." House of Commons, there is not one for
which a cent would not do just as well.
Mr. Lowe has fallen into the

misconception of the person who
admired the dispensation of Providence
by which large rivers are made to run
through cities so great and towns so
many. If the cent were to be introduced
to-morrow, straightway the buns and
cakes, the soda-water bottles, the short
omnibus fares, the bunches of radishes,
etc. etc. etc., would adapt themselves to
the coin.

"If the proposed system The confusion of ideas here exhibited is
were adopted, they most instructive. The speaker is under the
would all be compelled impression that we are introducing
to live in decimals for fractions: the truth is, that we only want
ever; if a man dined at to abandon the more difficult fractions
a public house he which we have got, and to introduce
would have to pay for easier fractions. Does he deny this? Let
his dinner in decimal us trace his denial to its legitimate
fractions. (Hear, hear.) consequences. A man ought to pay for his
He objected to that, for dinner in integers.
he thought that a man
ought to be able to pay
for his dinner in
integers." (Hear, hear,
and a laugh.)

Now, if Mr. Lowe insists on it that our integer is the pound, he is bound to
admit that the present integer is the pound, of which a shilling, etc., are
fractions. The next time he has a chop and a pint of stout in the city, the
waiter should say—"A pound, sir, to you," and should add, "Please to
remember the waiter in integers." Mr. Lowe fancies that when he pays one
and sixpence, he pays in integers, and so he does, if his integer be a penny
or a sixpence. Let him bring his mind to contemplate a mil as the integer,
the lowest integer, and the seven cents five mils which he would pay under
the new system would be payment in integers also. But, as it happens with

some others, he looks up the present system, with Cocker,[299] and
Walkingame,[300] and always looks down the proposed system. The word
decimal is obstinately associated with fractions, for which there is no need.
Hence it becomes so much of a bugbear, that, to parody the lines of Pope,
which probably suggested one of Mr. Lowe's phrases—

"Dinner he finds too painful an endeavor,
Condemned to pay in decimals for ever."

"The present system, A pleasant sum even for an
however, had not yet been accomplished mathematician. What
changed into decimal does divided by the decimal of a
system. That change might pound mean? Perhaps it means
appear very easy to reduced to the decimal of a pound!
accomplished Mr. Lowe supposes, as many others
mathematicians and men of do, that, after the change, all
science, but it was one calculations will be proposed in old
which it would be very money, and then converted into new.
difficult to carry out. (Hear, He cannot hit the idea that the new
hear). What would have to coins will take the place of the old.
be done? Every sum would This lack of apprehension will
have to be reduced into a presently appear further.
vulgar fraction of a pound,
and then divided by the
decimal of a pound—a
pleasant sum for an old
applewoman to work out!"
(Hear, hear, and laughter.)

"It would not be an Let the members be assured that nine
agreeable task, even for half-pence will be, for every
some members of that practical purpose, 18 mils. But now
House, to reduce 4½d., or to the fact asserted. Davies
nine half-pence, to mils." Gilbert[301] used to maintain that
(Hear, hear.) during the long period he sat in the
House, he never knew more than

three men in it, at one time, who had
a tolerable notion of fractions. [I
heard him give the names of three at
the time when he spoke: they were
Warburton,[302] Pollock,[303] and
Hume.[304] He himself was then out
of Parliament.] Joseph Hume
affirmed that he had never met with
more than ten members who were
arithmeticians. But both these
gentlemen had a high standard. Mr.
Lowe has given a much more
damaging opinion. He evidently
means that the general run of
members could not do his question.
It is done as follows: Since farthings
gain on mils, at the rate of a whole
mil in 24 farthings (24 farthings
being 25 mils), it is clear that 18
farthings being three-quarters of 24
farthings, will gain three-quarters of
a mil; that is, 18 farthings are
eighteen mils and three-quarters of a
mil. Any number of farthings is as
many mils and as many twenty-
fourths of a mil. To a certain extent,
we feel able to protest against the
manner in which Kidderminster has
treated the other constituencies. We
do not hold it impossible to give the
Members of the House in general a
sufficient knowledge of the meaning
and consequences of the decimal
succession of units, tens, hundreds,
thousands, etc.; and we believe that
there are in the House itself
competent men, in number enough

to teach all the rest. All that is
wanted is the power of starting from
the known to arrive at the unknown.
Now there is one kind of decimals
with which every member is
acquainted—the Chiltern Hundreds.
If public opinion would enable the
competent minority to start from this
in their teaching, not as a basis, but
as an alternative, in three weeks the
fundamentals would be acquired,
and members in general would be as
fit to turn 4½d. into mils, as any
boys on the lower forms of a
commercial school.
For a long period of years, allusion
to the general ignorance of
arithmetic, has been a standing mode
of argument, and has always been
well received: whenever one
member describes others as
knownothings, those others cry Hear
to the country in a transport of
delight. In the meanwhile the
country is gradually arriving at the
conclusion that a true joke is no
joke.

"The main objection was, if Fine words, wrongly used. The new
they went below 6d., that coins are commensurable with, and
the new scale of coins in a finite ratio to, the old ones. The
would not be commensurate farthing is to the mil as 25 to 24. The
in any finite ratio with speaker has something here in the
anything in this new bud, which we shall presently meet
currency of mils." with in the flower; and fallacies are

more easily nipped in flower than in
bud.

"No less than five of our This dreadful change of value
present coins must be called consists in sixpence farthing going
in, or else—which would be to the half-shilling instead of
worse—new values must be sixpence. Whether the new farthings
given to them." be called mils or not is of no
consequence.

"If a poor man put a penny Mr. Lowe, who cannot pass a half-
in his pocket, it would come crown for more than a florin, or get
out a coin of different in a florin at less than half-a-crown,
value, which he would not has such a high faith in the sterner
understand. Suppose he stuff of his fellow countrymen, that
owed another man a penny, he believes any two of them would
how was he to pay him ? go to fisty cuffs for the 25th part of a
Was he to pay him in mils? farthing. He reasons thus: He has
Four mils would be too often heard in the streets, "I'd fight
little, and five mils would you for the fiftieth part of a farden:"
be too much. The hon. and having (that is, for a Member) a
gentlemen said there would notion both of fractions and logic, he
be only a mil between them. infers that those who would fight for
That was exactly it. He the 50th of a farthing would, a
believed there would be a fortiori, fight for a 25th. His mistake
'mill' between them." arises from his not knowing that
(Much laughter.) when a person offers to fight another
for 1/200d., he really means to fight
for love; and that the stake is merely
a matter of form, a feigned issue, a
pro forma report of progress. Do the
Members of the House think they
have all the forms to themselves?

"What would be the present We should hardly believe all this to
expression for four-pence? be uttered in earnest, if we had not

Why, 0.166 (a laugh); for known that several persons who
threepence? .0125; for a have not Mr. Lowe's humor,
penny? .004166, and so on nevertheless have his impressions on
ad infinitum (a laugh); for a this point. It must therefore be
half-penny? .002083 ad answered; but how is this to be done
infinitum. (A laugh). What seriously?
would be the present
expression for a farthing? Dialogue between a member of
Why, .0010416 ad Parliament and an orange-boy, three
infinitum. (A laugh). And days after the introduction of the
this was the system which complete decimal system. The
was to cause such a saving member, going down to the House,
in figures, and these were wants oranges to sustain his voice in
the quantities into which the a two hours' speech on moving that
poor would have to reduce 100000l. be placed at the disposal of
the current coin of the Her Majesty, to supply the poor with
realm. (Cheers). With every ready-reckoners.
respect for decimal Boy. Fine oranges! two a penny! two
fractions, of which he a penny!
boasted no profound
knowledge, he doubted Member. Here boy, two! Now, how
whether the poor were am I to pay you?
equal to mental arithmetic
of this kind, (hear, hear) and Boy. Give you change, your honor.
he hoped the adoption of Member. Ah! but how? Where's your
the system would be ready-reckoner?
deferred until there were
some proof that they would Boy. I sells a better sort nor them.
be able to understand it; for, Mine's real Cheyny.
after all, this was the
question of the poor, and Member. But you see a farthing is
now .0014166666 ad infinitum, and
the whole weight of the
change would fall upon if we multiply this by 4——
them. Let the rich by all Boy. Hold hard, Guv'ner; I sees what
means have permission to you're arter. Now what'll you stand if
perplex themselves by any I puts you up to it? which Bill Smith
division of a pound they

pleased; but do not let them, he put me up in two minutes, cause
by any experiment like this, he goes to the Ragged School.
impose difficulties upon the
poor and compel men to Member. You don't mean that you do
carry ready-reckoners in without a book!
their pocket to give them all Boy. Book be blowed. Come now,
these fractional quantities." old un, here's summut for both on us.
(Hear, hear.) I got a florin, you gives me a half-a-
crown for it, and I larns you the new
money, gives you your oranges, and
calls you a brick into the bargain.
Member (to himself). Never had such
a chance of getting off half-a-crown
for value since that —— fellow
Bowring carried his crochet.
(Aloud.) Well, boy, it's a bargain.
Now!
Boy. Why, look 'e here, my trump, its
a farden more to the tizzy—that's
what it is.
Member. What's that?
Boy. Why, you knows a sixpence
when you sees it. (Aside). Blest if I
think he does! Well, its six browns
and a farden now. A lady buys two
oranges, and forks out a sixpence;
well in coorse, I hands over fippence
farden astead of fippence. I always
gives a farden more change, and
takes according.
Member (in utter surprise, lets his
oranges tumble into the gutter).
Never mind! They won't be wanted
now. (Walks off one way. Boy makes

a pass of naso-digital mesmerism,
and walks off the other way).

To the poor, who keep no books, the whole secret is "Sixpence farthing to
the half shilling, twelve pence halfpenny to the shilling." The new twopence
halfpenny, or cent, will be at once five to the shilling.
In conclusion, we remark that three very common misconceptions run
through the hon. Member's argument; and, combined in different
proportions, give variety to his patterns.
First, he will have it that we design to bring the uneducated into contact
with decimal fractions. If it be so, it will only be as M. Jourdain was
brought into contact with prose. In fact, Quoi! quand je dis, Nicole,
apportez-moi mes pantoufles, c'est de la prose?[305] may be rendered:
"What! do you mean that ten to the florin is a cent a piece must be called
decimal reckoning?" If we had to comfort a poor man, horror-struck by the
threat of decimals, we should tell him what manner of fractions had been
inflicted upon him hitherto; nothing less awful than quarto-duodecimo-
vicesimals, we should assure him.
Secondly, he assumes that the penny, such as it now is, will remain, as a
coin of estimation, after it has ceased to be a coin of exchange; and that the
mass of the people will continue to think of prices in old pence, and to
calculate them in new ones, or else in new mils. No answer is required to
this, beyond the mere statement of the nature of the assumption and denial.
Thirdly, he attributes to the uneducated community a want of perception
and of operative power which really does not belong to them. The evidence
offered to the Committee of the House shows that no fear is entertained on
this point by those who come most in contact with farthing purchasers. And
this would seem to be a rule,—that is, fear of the intelligence of the lower
orders in the minds of those who are not in daily communication with them,
no fear at all in the minds of those who are.
A remarkable instance of this distinction happened five-and-twenty years
ago. The Admiralty requested the Astronomical Society to report on the
alterations which should be made in the Nautical Almanac, the seaman's

guide-book over the ocean. The greatest alteration proposed was the
description of celestial phenomena in mean (or clock time), instead of
apparent (or sundial) time, till then always employed. This change would
require that in a great many operations the seaman should let alone what he
formerly altered by addition or subtraction, and alter by addition or
subtraction what he formerly let alone; provided always that what he
formerly altered by addition he should, when he altered at all, alter by
subtraction, and vice versa. This was a tolerably difficult change for
uneducated skippers, working by rules they had only learned by rote. The
Astronomical Society appointed a Committee of forty, of whom nine were
naval officers or merchant seamen [I was on this Committee]. Some men of
science were much afraid of the change. They could not trust an ignorant
skipper or mate to make those alterations in their routine, on the correctness
of which the ship might depend. Had the Committee consisted of men of
science only, the change might never have been ventured on. But the naval
men laughed, and said there was nothing to fear; and on their authority the
alteration was made. The upshot was, that, after the new almanacs
appeared, not a word of complaint was ever heard on the matter. Had the
House of Commons had to decide this question, with Mr. Lowe to quote the
description given by Basil Hall[306] (who, by the way, was one of the
Committee) of an observation on which the safety of the ship depended,
worked out by the light of a lantern in a gale of wind off a lee shore, this
simple and useful change might at this moment have been in the hands of
its tenth Government Commission.

[Aug. 14, 1866. The Committee was appointed in the spring of 1830: it
consisted of forty members. Death, of course, has been busy; there are now
left Lord Shaftesbury,[307] Mr. Babbage,[308] Sir John Herschel,[309] Sir
Thomas Maclear[310] (Astronomer Royal at the Cape of Good Hope), Dr.
Robinson[311] (of Armagh), Sir James South,[312] Lord Wrottesley,[313] and
myself].

THE TONAL SYSTEM.

Project of a new system of arithmetic, weight, measure, and
coins, proposed to be called the tonal system, with sixteen to the
base. By J. W. Mystrom.[314] Philadelphia, 1862, 8vo.

That is to say, sixteen is to take the place of ten, and to be written 10. The
whole language is to be changed; every man of us is to be sixteen-stringed
Jack and every woman sixteen-stringed Jill. Our old one, two, three, up to
sixteen, are to be (Noll going for nothing, which will please those who
dislike the memory of Old Noll) replaced by An, De, Ti, Go, Su, By, Ra,
Me, Ni, Ko, Hu, Vy, La, Po, Fy, Ton; and then Ton-an, Ton-de, etc. for 17,
18, etc. The number which in the system has the symbol

28(13)5(11)7(14)0(15)

(using our present compounds instead of new types) is to be pronounced

Detam-memill-lasan-suton-hubong-ramill-posanfy.

The year is to have sixteen months, and here they are:

Anuary, Debrian, Timander, Gostus,
Suvenary, Bylian, Ratamber, Mesudius,
Nictoary, Kolumbian, Husamber, Vyctorius,
Lamboary, Polian, Fylander, Tonborius.

Surely An-month, De-month, etc. would do as well. Probably the wants of
poetry were considered. But what are we to do with our old poets? For
example—

"It was a night of lovely June,
High rose in cloudless blue the moon."

Let us translate—

"It was a night of lovely Nictoary,
High rose in cloudless blue the (what, in the name of all that is absurd?)."

And again, Fylander thrown into our December! What is to become of
those lines of Praed, which I remember coming out when I was at
Cambridge,—

"Oh! now's the time of all the year for flowers and fun, the Maydays;
To trim your whiskers, curl your hair, and sinivate the ladies."

If I were asked which I preferred, this system or that of Baron Ferrari[315]
already mentioned, proceeding by twelves, I should reply, with Candide,
when he had the option given of running the gauntlet or being shot: Les
volontés sont libres, et je ne veux ni l'un ni l'autre.[316] We can imagine a
speculator providing such a system for Utopia as it would be in the mind of
a Laputan: but to explain how an engineer who has surveyed mankind from
Philadelphia to Rostof on the Don should for a moment entertain the idea of
such a system being actually adopted, would beat a jury of solar-system-
makers, though they were shut up from the beginning of Anuary to the end
of Tonborius. When I see such a scheme as this imagined to be practicable,
I admire the wisdom of Providence in providing the quadrature of the circle,
etc., to open a harmless sphere of action to the possessors of the kind of
ingenuity which it displays. Those who cultivate mathematics have a right
to speak strongly on such efforts of arithmetic as this: for, to my knowledge,
persons who have no knowledge are frequently disposed to imagine that
their makers are true brothers of the craft, a little more intelligible than the
rest.

SOME SMALL PARADOXERS.

Vis inertiae victa,[317] or Fallacies affecting science. By James
Reddie.[318] London, 1862, 8vo.

An attack on the Newtonian mechanics; revolution by gravitation
demonstrably impossible; much to be said for the earth being the
immovable center. A good analysis of contents at the beginning, a thing
seldom found. The author has followed up his attack in a paper submitted to
the British Association, but which it appears the Association declined to
consider. It is entitled—

Victoria Toto Cœlo; or, Modern Astronomy recast. London, 1863,
8vo.

At the end is a criticism of Sir G. Lewis's History of Ancient Astronomy.

On the definition and nature of the Science of Political Economy.
By H. Dunning Macleod,[319] Esq. Cambridge, 1862, 8vo.

A paper read—but, according to the report, not understood—at the British
Association. There is a notion that political economy is entirely
mathematical; and its negative quantity is strongly recommended for study:
it contains "the whole of the Funds, Credit, 32 parts out of 33 of the value
of Land...." The mathematics are described as consisting of—first, number,
or Arithmetic; secondly, the theory of dependent quantities, subdivided into
dependence by cause and effect, and dependence by simultaneous
variations; thirdly, "independent quantities or unconnected events, which is
the theory of probabilities." I am not ashamed, having the British
Association as a co-non-intelligent, to say I do not understand this: there is
a paradox in it, and the author should give further explanation, especially of
his negative quantity. Mr. Macleod has gained praise from great names for
his political economy; but this, I suspect, must have been for other parts of
his system.

On the principles and practice of just Intonation, with a view to
the abolition of temperament.... By General Perronet Thompson.
[320]
Sixth Edition. London, 1862, 8vo.

Here is General Thompson again, with another paradox: but always master
of the subject, always well up in what his predecessors have done, and
always aiming at a useful end. He desires to abolish temperament by
additional keys, and has constructed an enharmonic organ with forty sounds
in the octave. If this can be introduced, I, for one, shall delight to hear it:

but there are very great difficulties in the way, greater than stood even in the
way of the repeal of the bread-tax.
In a paper on the beats of organ-pipes and on temperament published some
years ago, I said that equal temperament appeared to me insipid, and not so
agreeable as the effect of the instrument when in progress towards being
what is called out of tune, before it becomes offensively wrong. There is
throughout that period unequal temperament, determined by accident.
General Thompson, taking me one way, says I have launched a declaration
which is likely to make an epoch in musical practice; a public musical
critic, taking me another way, quizzes me for preferring music out of tune. I
do not think I deserve either one remark or the other. My opponent critic, I
suspect, takes equally tempered and in tune to be phrases of one meaning.
But by equal temperament is meant equal distribution among all the keys of
the error which an instrument must have, which, with twelve sounds only in
the octave, professes to be fit for all the keys. I am reminded of the equal
temperament which was once applied to the postmen's jackets. The coats
were all made for the average man: the consequence was that all the tall
men had their tails too short; all the short men had them too long. Some one
innocently asked why the tall men did not change coats with the short ones.

A diagram illustrating a discovery in the relation of circles to
right-lined geometrical figures. London, 1863, 12mo.

The circle is divided into equal sectors, which are joined head and tail: but a
property is supposed which is not true.

An attempt to assign the square roots of negative powers; or what
is √ -1? By F.H. Laing.[321] London, 1863, 8vo.

If I understand the author, -a and +a are the square roots of -a2, as proved
by multiplying them together. The author seems quite unaware of what has
been done in the last fifty years.

BYRNE'S DUAL ARITHMETIC.

Dual Arithmetic. A new art. By Oliver Byrne.[322] London, 1863,
8vo.

The plan is to throw numbers into the form a(1.1)b (1.01)c (1.001)d... and to
operate with this form. This is an ingenious and elaborate speculation; and I
have no doubt the author has practised his method until he could surprise
any one else by his use of it. But I doubt if he will persuade others to use it.
As asked of Wilkins's universal language, Where is the second man to come
from?
An effective predecessor in the same line of invention was the late Mr.
Thomas Weddle,[323] in his "New, simple, and general method of solving
numeric equations of all orders," 4to, 1842. The Royal Society, to which
this paper was offered, declined to print it: they ought to have printed an
organized method, which, without subsidiary tables, showed them, in six
quarto pages, the solution (x=8.367975431) of the equation

1379.664 x622 + 2686034 × 10432 x152 - 17290224 × 10518 x60 + 2524156 ×
10574 = 0.

The method proceeds by successive factors of the form, a being the first
approximation, a × 1.b × 1.0c × 1.00d.... In my copy I find a few
corrections made by me at the time in Mr. Weddle's announcement. "It was
read before that learned body [the R. S.] and they were pleased [but] to
transmit their thanks to the author. The en[dis]couragement which he
received induces [obliges] him to lay the result of his enquiries in this
important branch of mathematics before the public [, at his own expense; he
being an usher in a school at Newcastle]." Which is most satirical, Mr.
Weddle or myself? The Society, in the account which it gave of this paper,
described it as a "new and remarkably simple method" possessing "several
important advantages." Mr. Rutherford's[324] extended value of π was read
at the very next meeting, and was printed in the Transactions; and very
properly: Mr. Weddle's paper was excluded, and very very improperly.

HORNER'S METHOD.
I think it may be admited that the indisposition to look at and encourage
improvements of calculation which once marked the Royal Society is no
longer in existence. But not without severe lessons. They had the luck to
accept Horner's[325] now celebrated paper, containing the method which is
far on the way to become universal: but they refused the paper in which
Horner developed his views of this and other subjects: it was printed by
T. S. Davies[326] after Horner's death. I make myself responsible for the
statement that the Society could not reject this paper, yet felt unwilling to
print it, and suggested that it should be withdrawn; which was done.

But the severest lesson was the loss of Barrett's Method,[327] now the
universal instrument of the actuary in his highest calculations. It was
presented to the Royal Society, and refused admission into the
Transactions: Francis Baily[328] printed it. The Society is now better
informed: "live and learn," meaning "must live, so better learn," ought to be
the especial motto of a corporation, and is generally acted on, more or less.
Horner's method begins to be introduced at Cambridge: it was published in
1820. I remember that when I first went to Cambridge (in 1823) I heard my
tutor say, in conversation, there is no doubt that the true method of solving
equations is the one which was published a few years ago in the
Philosophical Transactions. I wondered it was not taught, but presumed
that it belonged to the higher mathematics. This Horner himself had in his
head: and in a sense it is true; for all lower branches belong to the higher:
but he would have stared to have been told that he, Horner, was without a
European predecessor, and in the distinctive part of his discovery was heir-
at-law to the nameless Brahmin—Tartar—Antenoachian—what you please
—who concocted the extraction of the square root.
It was somewhat more than twenty years after I had thus heard a Cambridge
tutor show sense of the true place of Horner's method, that a pupil of mine
who had passed on to Cambridge was desired by his college tutor to solve a
certain cubic equation—one of an integer root of two figures. In a minute
the work and answer were presented, by Horner's method. "How!" said the
tutor, "this can't be, you know." "There is the answer, Sir!" said my pupil,
greatly amused, for my pupils learnt, not only Horner's method, but the

estimation it held at Cambridge. "Yes!" said the tutor, "there is the answer
certainly; but it stands to reason that a cubic equation cannot be solved in
this space." He then sat down, went through a process about ten times as
long, and then said with triumph: "There! that is the way to solve a cubic
equation!"
I think the tutor in this case was never matched, except by the country
organist. A master of the instrument went into the organ-loft during service,
and asked the organist to let him play the congregation out; consent was
given. The stranger, when the time came, began a voluntary which made the
people open their ears, and wonder who had got into the loft: they kept their
places to enjoy the treat. When the organist saw this, he pushed the
interloper off the stool, with "You'll never play 'em out this side Christmas."
He then began his own drone, and the congregation began to move quietly
away. "There," said he, "that's the way to play 'em out!"
I have not scrupled to bear hard on my own university, on the Royal
Society, and on other respectable existences: being very much the friend of
all. I will now clear the Royal Society from a very small and obscure
slander, simply because I know how. This dissertation began with the work
of Mr. Oliver Byrne, the dual arithmetician, etc. This writer published, in
1849, a method of calculating logarithms.[329] First, a long list of instances
in which, as he alleges, foreign discoverers have been pillaged by
Englishmen, or turned into Englishmen: for example, O'Neill,[330] so called
by Mr. Byrne, the rectifier of the semi-cubical parabola claimed by the
Saxons under the name of Neal: the grandfather of this mathematician was
conspicuous enough as Neal; he was archbishop of York. This list, says the
writer, might be continued without end; but he has mercy, and finishes with
his own case, as follows:—"About twenty years ago, I discovered this
method of directly calculating logarithms. I could generally find the
logarithm of any number in a minute or two without the use of books or
tables. The importance of the discovery subjected me to all sorts of prying.
Some asserted that I committed a table of logarithms to memory; others
attributed it to a peculiar mental property; and when Societies and
individuals failed to extract my secret, they never failed to traduce the
inventor and the invention. Among the learned Societies, the Royal Society
of London played a very base part. When I have more space and time at my
disposal, I will revert to this subject again."

Such a trumpery story as this remains unnoticed at the time; but when all
are gone, a stray copy from a stall falls into hands which, not knowing what
to make of it, make history of it. It is a very curious distortion. The reader
may take it on my authority, that the Royal Society played no part, good or
bad, nor had the option of playing a part. But I myself pars magna fui:[331]
and when the author has "space and time" at his disposal, he must not take
all of them; I shall want a little of both.

ARE ATOMS WORLDS?

The mystery of being; or are ultimate atoms inhabited worlds? By
Nicholas Odgers.[332] Redruth and London, 1863, 8vo.

This book, as a paradox, beats quadrature, duplication, trisection,
philosopher's stone, perpetual motion, magic, astrology, mesmerism,
clairvoyance, spiritualism, homœopathy, hydropathy, kinesipathy, Essays
and Reviews, and Bishop Colenso,[333] all put together. Of all the
suppositions I have given as actually argued, this is the one which is hardest
to deny, and hardest to admit. Reserving the question—as beyond human
discussion—whether our particles of carbon, etc. are clusters of worlds, the
author produces his reasons for thinking that they are at least single worlds.
Of course—though not mentioned—the possibility is to be added of the
same thing being true of the particles which make up our particles, and so
down, for ever: and, on the other hand, of our planets and stars as being
particles in some larger universe, and so up, for ever.

"Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on."[334]

I have often had the notion that all the nebulæ we see, including our own,
which we call the Milky Way, may be particles of snuff in the box of a giant
of a proportionately larger universe. Of course the minim of time—a
million of years or whatever the geologists make it[335]—which our little

affair has lasted, is but a very small fraction of a second to the great creature
in whose nose we shall all be in a few tens of thousands of millions of
millions of millions of years.
All this is quite possible, and the probabilities for and against are quite out
of reach. Perhaps also all the worlds, both above and below us, are fac-
similes of our own. If so, away goes free will for good and all; unless,
indeed, we underpin our system with the hypothesis that all the fac-simile
bodies of different sizes are actuated by a common soul. These acute
supplementary notions of mine go far to get rid of the difficulty which some
have found in the common theory that the soul inhabits the body: it has
been stated that there is, somewhere or another, a world of souls which
communicate with their bodies by wondrous filaments of a nature neither
mental nor material, but of a tertium quid fit to be a go-between; as it were
a corporispiritual copper encased in a spiritucorporeal gutta-percha. My
theory is that every soul is everywhere in posse, as the schoolmen said, but
not anywhere in actu, except where it finds one of its bodies. These a priori
difficulties being thus removed, the system of particle-worlds is reduced to
a dry question of fact, and remitted to the decision of the microscope. And a
grand field may thus be opened, as optical science progresses! For the
worlds are not fac-similes of ours in time: there is not a moment of our past,
and not a moment of our future, but is the present of one or more of the
particles. A will write the death of Cæsar, and B the building of the
Pyramids, by actual observation of the processes with a power of a
thousand millions; C will discover the commencement of the Millennium,
and D the termination of Ersch and Gruber's Lexicon,[336] as mere physical
phenomena. Against this glorious future there is a sad omen: the initials of
the forerunner of this discovery are—NO!

THE SUPERNATURAL.

The History of the Supernatural in all ages and nations, and in all
Churches, Christian and Pagan: demonstrating a universal faith.
By Wm. Howitt.[337] London, 2 vols. 8vo. 1863.

Mr. Howitt is a preacher of spiritualism. He cements an enormous
collection of alleged facts with a vivid outpouring of exhortation, and an
unsparing flow of sarcasm against the scorners of all classes. He and the
Rev. J. Smith[338] (ante, 1854) are the most thoroughgoing universalists of
all the writers I know on spiritualism. If either can insert the small end of
the wedge, he will not let you off one fraction of the conclusion that all
countries, in all ages, have been the theaters of one vast spiritual display.
And I suspect that this consequence cannot be avoided, if any part of the
system be of truly spiritual origin. Mr. Howitt treats the philosophers either
as ignorant babies, or as conscious spirit-fearers: and seems much inclined
to accuse the world at large of dreading, lest by the actual presence of the
other world their Christianity should imbibe a spiritual element which
would unfit it for the purposes of their lives.

FROM MATTER TO SPIRIT.

From Matter to Spirit. By C. D. With a preface by A. B.[339]
London, 1863, 8vo.

This is a work on Spiritual Manifestations. The author upholds the facts for
spiritual phenomena: the prefator suspends his opinion as to the cause,
though he upholds the facts. The work begins systematically with the lower
class of phenomena, proceeds to the higher class, and offers a theory,
suggested by the facts, of the connection of the present and future life. I
agree in the main with A. B.; but can, of course, make none but horrescent
reference to his treatment of the smaller philosophers. This is always the
way with your paradoxers: they behave towards orthodoxy as the thresher
fish behaves towards the whale. But if true, as is said, that the drubbing
clears the great fish of parasites which he could not otherwise get rid of, he
ought to bear no malice. This preface retorts a little of that contempt which
the "philosophical world" has bestowed with heaped measure upon those
who have believed their senses, and have drawn natural, even if hasty,
inferences. There is philosophercraft as well as priestcraft, both from one
source, both of one spirit. In English cities and towns, the minister of
religion has been tamed: so many weapons are bared against him when he
obtrudes his office in a dictatory manner, that, as a rule, there is no more

quiet and modest member of society than the urban clergyman. Domination
over religious belief is reserved for the exclusive use of those who admit the
right: the rare exception to this mode of behavior is laughed at as a bigot, or
shunned as a nuisance. But the overbearing minister of nature, who snaps
you with unphilosophical as the clergyman once frightened you with
infidel, is still a recognized member of society, wants taming, and will get
it. He wears the priest's cast-off clothes, dyed to escape detection: the better
sort of philosophers would gladly set him to square the circle.
The book just named appeared about the same time as this Budget began in
the Athenæum. It was commonly attributed, the book to my wife, the
preface to myself. Some time after, our names were actually announced by
the publisher, who ought to know. It will be held to confirm this statement
that I announce our having in our possession some twenty reviews of
different lengths, and of all characters: who ever collects a number of
reviews of a book, except the author?
A great many of these reviews settle the matter a priori. If there had been
spirits in the matter, they would have done this, and they would not have
done that. Jean Meslier[340] said there could be no God over all, for, if there
had been one, He would have established a universal religion. If J. M. knew
that, J. M. was right: but if J. M. did not know that, then J. M. was on the
"high priori road," and may be left to his course. The same to all who know
what spirits would do and would not do.
A. B. very distinctly said that he knew some of the asserted facts, believed
others on testimony, but did not pretend to know whether they were caused
by spirits, or had some unknown and unimagined origin. This he said as
clearly as I could have said it myself. But a great many persons cannot
understand such a frame of mind: their own apparatus is a kind of spirit-
level, and their conclusion on any subject is the little bubble, which is
always at one end or the other. Many of the reviewers declare that A. B. is a
secret believer in the spirit-hypothesis: and one of them wishes that he had
"endorsed his opinion more boldly." According to this reviewer, any one
who writes "I boldly say I am unable to choose," contradicts himself. In
truth, a person who does say it has a good deal of courage, for each side
believes that he secretly favors the other; and both look upon him as a
coward. In spite of all this, A. B. boldly repeats that he feels assured of

many of the facts of spiritualism, and that he cannot pretend to affirm or
deny anything about their cause.
The great bulk of the illogical part of the educated community—whether
majority or minority I know not; perhaps six of one and half-a-dozen of the
other—have not power to make a distinction, cannot be made to take a
distinction, and of course, never attempt to shake a distinction. With them
all such things are evasions, subterfuges, come-offs, loopholes, etc. They
would hang a man for horse-stealing under a statute against sheep-stealing;
and would laugh at you if you quibbled about the distinction between a
horse and a sheep. I divide the illogical—I mean people who have not that
amount of natural use of sound inference which is really not uncommon—
into three classes:—First class, three varieties: the Niddy, the Noddy, and
the Noodle. Second class, three varieties: the Niddy-Noddy, the Niddy-
Noodle, and the Noddy-Noodle. Third class, undivided: the Niddy-Noddy-
Noodle. No person has a right to be angry with me for more than one of
these subdivisions.
The want of distinction was illustrated to me, when a boy, about 1820, by
the report of a trial which I shall never forget: boys read newspapers more
keenly than men. Every now and then a bench of country magistrates rather
astonishes the town populations, accustomed to rub their brains[341] against
one another. Such a story as the following would, in our day, bring down
grave remarks from above: but I write of the olden (or Eldon[342]) time,
when nothing but conviction in a court of record would displace a
magistrate. In that day the third-class amalgamator of distinct things was
often on the bench of quarter-sessions.
An attorney was charged with having been out at night poaching. A clear
alibi was established; and perjury had certainly been committed. The whole
gave reason to suspect that some ill-willers thought the bench disliked the
attorney so much that any conviction was certain on any evidence. The
bench did dislike the attorney: but not to the extent of thinking he could
snare any partridges in the fields while he was asleep in bed, except the
dream-partridges which are not always protected by the dream-laws. So the
chairman said, "Mr. ——, you are discharged; but you should consider this
one of the most fortunate days of your life." The attorney indignantly
remonstrated, but the magistrate was right; for he said, "Mr. ——, you have

frequently been employed to defend poachers: have you been careful to
impress upon them the enormity of their practices?" It appeared in a
wrangling conversation that the magistrates saw little moral difference
between poaching and being a poacher's professional defender without
lecturing him on his wickedness: but they admitted with reluctance, that
there was a legal distinction; and the brain of N3 could no further go. This is
nearly fifty years ago; and Westernism was not quite extinct. If the present
lords of the hills and the valleys want to shine, let them publish a true
history of their own order. I am just old enough to remember some of the
last of the squires and parsons who protested against teaching the poor to
read and write. They now write books for the working classes, give them
lectures, and the like. There is now no class, as a class, more highly
educated, broadly educated, and deeply educated, than those who were, in
old times, best described as partridge-popping squireens. I have myself,
when a boy, heard Old Booby speaking with pride of Young Booby as
having too high a spirit to be confined to books: and I suspected that his
dislike to teaching the poor arose in fact from a feeling that they would, if
taught a little, pass his heir.
A. B. recommended the spirit-theory as an hypothesis on which to ground
inquiry; that is, as the means of suggestion for the direction of inquiry.
Every person who knows anything of the progress of physics understands
what is meant; but not the reviewers I speak of. Many of them consider
A. B. as adopting the spirit-hypothesis. The whole book was written, as
both the authors point out, to suggest inquiry to those who are curious;
C. D. firmly believing, A. B. as above. Neither C. D. nor A. B. make any
other pretence. Both dwell upon the absence of authentications and the
suppression of names as utterly preventive of anything like proof. And A. B.
says that his reader "will give him credit, if not himself a goose, for seeing
that the tender of an anonymous cheque would be of equal effect, whether
drawn on the Bank of England or on Aldgate Pump." By this test a number
of the reviewers are found to be geese: for they take the authors as offering
proof, and insist, against the authors, on the very point on which the authors
had themselves insisted beforehand.
Leaving aside imperceptions of this kind, I proceed to notice a clerical and
medical review. I have lived much in the middle ages, especially since the
invention of printing; and from thence I have brought away a high respect

for and grateful recollection of—the priest in everything but theology, and
the physician in everything but medicine. The professional harness was
unfavorable to all progress, except on a beaten road; the professional
blinkers prevented all but the beaten road from being seen: the professional
reins were pulled at the slightest attempt to quicken pace, even on the
permitted path; and the professional whip was heavily laid on at the
slightest attempt to diverge. But when the intelligent man of either class
turned his attention out of his ordinary work, he had, in most cases, the
freshness and vigor of a boy at play, and like the boy, he felt his freedom all
the more from the contrast of school-restraint.
In the case of medicine, and physics generally, the learned were, in some
essential points, more rational than many of their present impugners. They
pass for having put a priori obstacles in the way of progress: they might
rather be reproved for too much belief in progress obtained by a priori
means. They would have shouted with laughter at a dunce who—in a
review I read, but without making a note—declared that he would not
believe his senses except when what they showed him was capable of
explanation upon some known principle. I have seen such stuff as this
attributed to the schoolmen; but only by those who knew nothing about
them. The following, which I wrote some years ago, will give a notion of a
distinction worth remembering. It is addressed to the authorities of the
College of Physicians.
"The ignominy of the word empiric dates from the ages in which scholastic
philosophy deduced physical consequences a priori;—the ages in which,
because a lion is strong, rubbing with lion's fat would have been held an
infallible tonic. In those happy days, if a physician had given decoction of a
certain bark, only because in numberless instances that decoction had been
found to strengthen the patient, he would have been a miserable empiric.
Not that the colleges would have passed over his returns because they were
empirical: they knew better. They were as skilful in finding causes for facts,
as facts for causes. The president and the elects of that day would have
walked out into the forest with a rope, and would have pulled heartily at the
tree which yielded the bark: nor would they ever have left it until they had
pulled out a legitimate reason. If the tree had resisted all their efforts, they
would have said, 'Ah! no wonder now; the bark of a strong tree makes a
strong man.' But if they had managed to serve the tree as you would like to

serve homœopathy, then it would have been 'We might have guessed it; all
the virtus roborativa has settled in the bark.' They admitted, as we know
from Molière, the virtus dormitiva[343] of opium, for no other reason than
that opium facit dormire.[344] Had the medicine not been previously known,
they would, strange as it may seem to modern pharmacopœists, have
accorded a virtus dormitiva to the new facit dormire. On this point they
have been misapprehended. They were prone to infer facit from a virtus
imagined a priori; and they were ready in supplying facit in favor of an
orthodox virtus. They might have gone so far, for example, under pre-
notional impressions, as the alliterative allopath, who, when maintenance of
truth was busy opposing the progress of science called vaccination,
declared that some of its patients coughed like cows, and bellowed like
bulls; but they never refused to find virtus when facit came upon them, no
matter whence. They would rather have accepted Tenterden steeple than
have rejected the Goodwin Sands. They would have laughed their modern
imitators to scorn: but as they are not here, we do it for them.
"The man of our day—the a priori philosopher—tries the question whether
opium can cause sleep by finding out in the recesses of his own noddle
whether the drug can have a dormitive power: Well! but did not the
schoolman do the same? He did; but mark the distinction. The schoolman
had recourse to first principles, when there was no opium to try it by: our
man settles the point in the same way with a lump of opium before him. The
schoolman shifted his principles with his facts: the man of our drawing-
rooms will fight facts with his principles, just as an old physician would
have done in actual practice, with the rod of his Church at his back.
"The story about Galileo—which seems to have been either a joke made
against him, or by him—illustrates this. Nature abhors a vacuum was the
explanation of the water rising in a pump: but they found that the water
would not rise more than 32 feet. They asked for explanation: what does the
satirist make the schoolmen say? That the stoppage is not a fact, because
nature abhors a vacuum? No! but that the principle should be that nature
abhors a vacuum as far as 32 feet. And this is what would have been done.
"There are still among us both priests and physicians who would have
belonged, had they lived three or four centuries ago, to the glorious band of
whom I have spoken, the majority of the intelligent, working well for

mankind out of the professional pursuit. But we have a great many who
have helped to abase their classes. Go where we may, we find specimens of
the lower orders of the ministry of religion and the ministry of health
showing themselves smaller than the small of other pursuits. And how is
this? First, because each profession is entered upon a mere working smack
of its knowledge, without any depth of education, general or professional.
Not that this is the whole explanation, nor in itself objectionable: the great
mass of the world must be tended, soul and body, by those who are neither
Hookers[345] nor Harveys[346]: let such persons not venture ultra crepidam,
and they are useful and respectable. But, secondly, there is a vast upheaving
of thought from the depths of commonplace learning. I am a clergyman!
Sir! I am a medical man! Sir! and forthwith the nature of things is picked to
pieces, and there is a race, with the last the winner, between Philosophy
mounted on Folly's donkey, and Folly mounted on Philosophy's donkey.
How fortunate it is for Law that her battles are fought by politicians in the
Houses of Parliament. Not that it is better done: but then politics bears the
blame."
I now come to the medical review. After a quantity of remark which has
been already disposed of, the writer shows Greek learning, a field in which
the old physician would have had a little knowledge. A. B., for the joke's
sake, had left untranslated, as being too deep, a remarkably easy sentence of
Aristotle, to the effect that what has happened was possible, for if
impossible it would not have happened. The reviewer, in "simple
astonishment,"—it was simple—at the pretended incapacity—I was told by
A. B. that the joke was intended to draw out a reviewer—translates:—He
says that this sentence is A. B.'s summing up of the evidence of
Spiritualism. Now, being a sort of alter ego[347] of A. B., I do declare that
he is not such a fool as to rest the evidence of Spiritualism—the spirit
explanation—upon the occurrence of certain facts proving the possibility of
those very facts. In truth, A. B. refuses to receive spiritualism, while he
receives the facts: this is the gist of his whole preface, which simply admits
spiritualism among the qualified candidates, and does not know what others
there may be.
The reviewer speaks of Aristotle as "that clear thinker and concise writer." I
strongly suspect that his knowledge of Aristotle was limited to the single
sentence which he had translated or got translated. Aristotle is concise in

phrase, not in book, and is powerful and profound in thought: but no one
who knows that his writing, all we have of him, is the very opposite of
clear, will pretend to decide that he thought clearly. As his writing, so
probably was his thought; and his books are, if not anything but clear, at
least anything good but clear. Nobody thinks them clear except a person
who always clears difficulties: which I have no doubt was the reviewer's
habit; that is, if he ever took the field at all. The gentleman who read Euclid,
all except the As and Bs and the pictures of scratches and scrawls, is the
type of a numerous class.
The reviewer finds that the word amosgepotically, used by A. B., is utterly
mysterious and incomprehensible. He hopes his translation of the bit of
Greek will shield him from imputation of ignorance: and thinks the word
may be referred to the "obscure dialect" out of which sprung aneroid, kalos
geusis sauce, and Anaxyridian trousers. To lump the first two phrases with
the third smacks of ignorance in a Greek critic; for ἀναξυριδια, breeches,
would have turned up in the lexicon; and kalos geusis, though absurd, is not
obscure. And ἀμωσγεπως, somehow or other, is as easily found as
ἀναξυριδια. The word aneroid, I admit, has puzzled better scholars than the
critic: but never one who knows the unscholarlike way in which words
ending in ειδης have been rendered. The aneroid barometer does not use a
column of air in the same way as the old instrument. Now ἀεροειδης—
properly like the atmosphere—is by scientific non-scholarship rendered
having to do with the atmosphere; and ἀναεροειδης—say anaëroid—
denies having to do with the atmosphere; a nice thing to say of an
instrument which is to measure the weight of the atmosphere. One more
absurdity, and we have aneroid, and there you are. The critic ends with a
declaration that nothing in the book shakes his faith in a Quarterly reviewer
who said that suspension of opinion, until further evidence arrives, is
justifiable: a strange summing up for an article which insists upon utter
rejection being unavoidable.[348] The expressed aim of both A. B. and C. D.
was to excite inquiry, and get further evidence: until this is done, neither
asks for a verdict.
Oh where! and oh where! is old Medicine's learning gone! There was some
in the days of yore, when Popery was on! And it's oh! for some Greek, just
to find a word upon! The reviewer who, lexicon in hand, can neither make
out anaxyridical, amosgepotical, kalos geusis, nor distinguish them from

aneroid, cannot be trusted when he says he has translated a sentence of
Aristotle. He may have done it; but, as he says of spiritualism, we must
suspend our opinion until further evidence shall arrive.
We now come to the theological review. I have before alluded to the faults
of logic which are Protestant necessities: but I never said that Protestant
argument had nothing but paralogism. The writer before me attains this
completeness: from beginning to end he is of that confusion and perversion
which, as applied to interpretation of the New Testament, is so common as
to pass unnoticed by sermon-hearers; but which, when applied out of
church, is exposed with laughter in all subjects except theology. I shall take
one instance, putting some words in italics.

A. B. Theological Critic.
My state of mind, which refers the ... he proceeds to argue that
whole either to unseen he himself is outside its
intelligence, or something which sacred pale because he refers
man has never had any conception all these strange phenomena
of, proves me to be out of the pale to unseen spiritual
of the Royal Society. intelligence.

The possibility of a yet unimagined cause is insisted on in several places.
On this ground it is argued by A. B. that spiritualists are "incautious" for
giving in at once to the spirit doctrine. But, it is said, they may be justified
by the philosophers, who make the flint axes, as they call them, to be the
works of men, because no one can see what else they can be. This kind of
adoption, condemned as a conclusion, is approved as a provisional theory,
suggestive of direction of inquiry: experience having shown that inquiry
directed by a wrong theory has led to more good than inquiry without any
theory at all. All this A. B. has fully set forth, in several pages. On it the
reviewer remarks that "with infinite satisfaction he tries to justify his view
of the case by urging that there is no other way of accounting for it; after the
fashion of the philosophers of our own day, who conclude that certain flints
found in the drift are the work of men, because the geologist does not see
what else they can be." After this twist of meaning, the reviewer proceeds to
say, and A. B. would certainly join him, "There is no need to combat any

such mode of reasoning as this, because it would apply with equal force and
justice to any theory whatever, however fantastic, profane, or silly." And so,
having shown how the reviewer has hung himself, I leave him
funipendulous.
One instance more, and I have done. A reviewer, not theological, speaking
of the common argument that things which are derided are not therefore to
be rejected, writes as follows:—"It might as well be said that they who
laughed at Jenner[349] and vaccination were, in a certain but very
unsatisfactory way, witnesses to the possible excellence of the system of St.
John Long."[350] Of course it might: and of course it is said by all people of
common sense. In introducing the word "possible," the reviewer has hit the
point: I suspect that this word was introduced during revision, to put the
sentence into fighting order; hurry preventing it being seen that the sentence
was thus made to fight on the wrong side. Jenner, who was laughed at, was
right; therefore, it is not impossible—that is, it is possible—that a derided
system may be right. Mark the three gradations: in medio tutissimus ibis.
[351]

Reviewer.—If a system be derided, it is no ground of suspense that derided
systems have turned out true: if it were, you would suspend your opinion
about St. John Long on account of Jenner.—Ans. You ought to do so, as to
possibility; and before examination; not with the notion that J. proves St. J.
probable; only possible.
Common Sense.—The past emergence of truths out of derided systems
proves that there is a practical certainty of like occurrence to come. But,
inasmuch as a hundred speculative fooleries are started for one truth, the
mind is permitted to approach the examination of any one given novelty
with a bias against it of a hundred to one: and this permission is given
because so it will be, leave or no leave. Every one has licence not to jump
over the moon.
Paradoxer.—Great men have been derided, and I am derided: which proves
that my system ought to be adopted. This is a summary of all the degrees in
which paradoxers contend for the former derision of truths now established,
giving their systems probability. I annex a paragraph which D [e &c.]
inserted in the Athenæum of October 23, 1847.

"Discoverers and Discoveries.
"Aristotle once sent his servant to the cellar to fetch wine:—and the fellow
brought him back small beer. The Stagirite (who knew the difference) called
him a blockhead. 'Sir,' said the man, 'all I can say is, that I found it in the
cellar.' The philosopher muttered to himself that an affirmative conclusion
could not be proved in the second figure,—and Mrs. Aristotle, who was by,
was not less effective in her remark, that small beer was not wine because it
was in the same cellar. Both were right enough: and our philosophers might
take a lesson from either—for they insinuate an affirmative conclusion in
the second figure. Great discoverers have been little valued by established
schools,—and they are little valued. The results of true science are strange
at first,—and so are their's. Many great men have opposed existing notions,
—and so do they. All great men were obscure at first,—and they are
obscure. Thinking men doubt,—and they doubt. Their small beer, I grant,
has come out of the same cellar as the wine; but this is not enough. If they
had let it stand awhile in the old wine-casks, it might have imbibed a little
of the flavor."

There are better reviews than I have noticed; which, though entirely
dissenting, are unassailable on their own principles. What I have given
represents five-sixths of the whole. But it must be confessed that the
fraction of fairness and moderation and suspended opinion which the
doctrine of Spirit Manifestations has met with—even in the lower reviews
—is strikingly large compared to what would have been the case fifty years
ago. It is to be hoped that our popular and periodical literatures are giving
us one thinker created for twenty geese double-feathered: if this hope be
realized, we shall do! Seeing all that I see, I am not prepared to go the
length of a friend of mine who, after reading a good specimen of the lower
reviewing, exclaimed—Oh! if all the fools in the world could be rolled up
into one fool, what a reviewer he would make!

Calendrier Universel et Perpétuel; par le Commandeur P. J.
Arson.[352] Publié par ses Enfans (Œuvre posthume). Nice, 1863,

4to.

I shall not give any account of this curious calendar, with all its changes and
symbols. But there is one proposal, which, could we alter the general
notions of time—a thing of very dubious possibility—would be convenient.
The week is made to wax and wane, culminating on the Sunday, which
comes in the middle. Thursday, Friday, Saturday, are ascending or waxing
days; Monday, Tuesday, Wednesday, are descending or waning days. Our
six days, lumped together after the great distinguishing day, Sunday, are too
many to be distinctly thought of together: a division of three preceding and
three following the day of most note would be much more easily used. But
all this comes too late. It may be, nevertheless, that some individuals may
be able to adjust their affairs with advantage by referring Thursday, Friday,
Saturday, to the following Sunday, and Monday, Tuesday, Wednesday, to
the preceding Sunday. But M. Arson's proposal to alter the names of the
days is no more necessary than it is practicable.

CYCLOMETRY.
I am not to enter anything I do not possess. The reader therefore will not
learn from me the feats of many a man-at-arms in these subjects. He must
be content, unless he will bestir himself for himself, not to know how Mr.
Patrick Cody trisects the angle at Mullinavat, or Professor Recalcati squares
the circle at Milan. But this last is to be done by subscription, at five francs
a head: a banker is named who guarantees restitution if the solution be not
perfectly rigorous; the banker himself, I suppose, is the judge. I have heard
of a man of business who settled the circle in this way: if it can be reduced
to a debtor and creditor account, it can certainly be done; if not, it is not
worth doing. Montucla will give the accounts of the lawsuits which wagers
on the problem have produced in France.
Neither will I enter at length upon the success of the new squarer who
advertises (Nov. 1863) in a country paper that, having read that the circular
ratio was undetermined, "I thought it very strange that so many great
scholars in all ages should have failed in finding the true ratio, and have
been determined to try myself.... I am about to secure the benefit of the

discovery, so until then the public cannot know my new and true ratio." I
have been informed that this trial makes the diameter to the circumference
as 64 to 201, giving π = 3.140625 exactly. The result was obtained by the
discoverer in three weeks after he first heard of the existence of the
difficulty. This quadrator has since published a little slip, and entered it at
Stationers' Hall. He says he has done it by actual measurement; and I hear
from a private source that he uses a disk of 12 inches diameter, which he
rolls upon a straight rail. Mr. James Smith did the same at one time; as did
also his partisan at Bordeaux. We have, then, both 3.125 and 3.140625, by
actual measurement. The second result is more than the first by about one
part in 200. The second rolling is a very creditable one; it is about as much
below the mark as Archimedes was above it. Its performer is a joiner, who
evidently knows well what he is about when he measures; he is not wrong
by 1 in 3,000.
The reader will smile at the quiet self-sufficiency with which "I have been
determined to try myself" follows the information that "so many great
scholars in all ages" have failed. It is an admirable spirit, when
accompanied by common sense and uncommon self-knowledge. When I
was an undergraduate there was a little attendant in the library who gave me
the following,—"As to cleaning this library, Sir, if I have spoken to the
Master once about it, I have spoken fifty times: but it is of no use; he will
not employ littery men; and so I am obliged to look after it myself."
I do not think I have mentioned the bright form of quadrature in which a
square is made equal to a circle by making each side equal to a quarter of
the circumference. The last squarer of this kind whom I have seen figures in
the last number of the Athenæum for 1855: he says the thing is no longer a
problem, but an axiom. He does not know that the area of the circle is
greater than that of any other figure of the same circuit. This any one might
see without mathematics. How is it possible that the figure of greatest area
should have any one length in its circuit unlike in form to any other part of
the same length?
The feeling which tempts persons to this problem is that which, in romance,
made it impossible for a knight to pass a castle which belonged to a giant or
an enchanter. I once gave a lecture on the subject: a gentleman who was
introduced to it by what I said remarked, loud enough to be heard by all

around, "Only prove to me that it is impossible, and I will set about it this
very evening."
This rinderpest of geometry cannot be cured, when once it has seated itself
in the system: all that can be done is to apply what the learned call
prophylactics to those who are yet sound. When once the virus gets into the
brain, the victim goes round the flame like a moth; first one way and then
the other, beginning where he ended, and ending where he begun: thus
verifying the old line

"In girum imus nocte, ecce! et consumimur igni."[353]

Every mathematician knows that scores of methods, differing altogether
from each other in process, all end in this mysterious 3.14159..., which
insists on calling itself the circumference to a unit of diameter. A reader
who is competent to follow processes of arithmetic may be easily satisfied
that such methods do actually exist. I will give a sketch, carried out to a few
figures, of three: the first two I never met with in my reading; the third is
the old method of Vieta.[354] [I find that both the first and second methods
are contained in a theorem of Euler.]
What Mr. James Smith says of these methods is worth noting. He says I
have given three "fancy proofs" of the value of π: he evidently takes me to
be offering demonstration. He proceeds thus:—
"His first proof is traceable to the diameter of a circle of radius 1. His
second, to the side of any inscribed equilateral triangle to a circle of radius
1. His third, to a radius of a circle of diameter 1. Now, it may be frankly
admitted that we can arrive at the same result by many other modes of
arithmetical calculation, all of which may be shown to have some sort of
relation to a circle; but, after all, these results are mere exhibitions of the
properties of numbers, and have no more to do with the ratio of diameter to
circumference in a circle than the price of sugar with the mean height of
spring tides. (Corr. Oct. 21, 1865)."
I quote this because it is one of the few cases—other than absolute
assumption of the conclusion—in which Mr. Smith's conclusions would be
true if his premise were true. Had I given what follows as proof, it would
have been properly remarked, that I had only exhibited properties of
numbers. But I took care to tell my reader that I was only going to show
him methods which end in 3.14159.... The proofs that these methods
establish the value of π are for those who will read and can understand.

200000000 31415 3799
66666667 2817
26666667 1363
11428571 661

5079365 321
2308802 156
1065601 76
497281 37
234014 18
110849 9
52785 5
25245 2
12118 1
5834
————— ——— ——
314153799 31415 9265

1. Take any diameter, double it, take 1-3d of that double, 2-5ths of the last,
3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so on. The sum
of all is the circumference of that diameter. The preceding is the process
when the diameter is a hundred millions: the errors arising from rejection of
fractions being lessened by proceeding on a thousand millions, and striking
off one figure. Here 200 etc. is double of the diameter; 666 etc. is 1-3rd of
200 etc.; 266 etc. is 2-5ths of 666 etc.; 114 etc. is 3-7ths of 266 etc.; 507
etc. is 4-9ths of 114 etc.; and so on.
2. To the square root of 3 add its half. Take half the third part of this; half 2-
5ths of the last; half 3-7ths of the last; and so on. The sum is the
circumference to a unit of diameter.

Square root of 3.... 1.73205081
.86602540
—————
2.59807621
.43301270
.08660254
1855768
412393

93726
21629
5047
1188
281
67
16
4
1
—————
3.14159265

3. Take the square root of ½; the square root of half of one more than this;
the square root of half of one more than the last; and so on, until we come
as near to unity as the number of figures chosen will permit. Multiply all the
results together, and divide 2 by the product: the quotient is an
approximation to the circumference when the diameter is unity. Taking aim
at four figures, that is, working to five figures to secure accuracy in the
fourth, we have .70712 for the square root of ½; .92390 for the square root
of half one more than .70712; and so on, through .98080, .99520, .99880,
.99970, .99992, .99998. The product of the eight results is .63667; divide 2
by this, and the quotient is 3.1413..., of which four figures are correct. Had
the product been .636363... instead of .63667..., the famous result of
Archimedes, 22-7ths, would have been accurately true. It is singular that no
cyclometer maintains that Archimedes hit it exactly.
A literary journal could hardly admit as much as the preceding, if it stood
alone. But in my present undertaking it passes as the halfpennyworth of
bread to many gallons of sack. Many more methods might be given, all
ending in the same result, let that result mean what it may.
Now since dozens of methods, to which dozens more might be added at
pleasure, concur in giving one and the same result; and since these methods
are declared by all who have shown knowledge of mathematics to be
demonstrated: it is not asking too much of a person who has just a little
knowledge of the first elements that he should learn more, and put his hand

upon the error, before he intrudes his assertion of the existence of error
upon those who have given more time and attention to it than himself, and
who are in possession, over and above many demonstrations, of many
consequences verifying each other, of which he can know nothing. This is
all that is required. Let any one square the circle, and persuade his friends,
if he and they please: let him print, and let all read who choose. But let him
abstain from intruding himself upon those who have been satisfied by
existing demonstration, until he is prepared to lay his finger on the point in
which existing demonstration is wrong. Let him also say what this
mysterious 3.14159... really is, which comes in at every door and window,
and down every chimney, calling itself the circumference to a unit of
diameter. This most impudent and successful impostor holds false title-
deeds in his hands, and invites examination: surely those who can find out
the rightful owner are equally able to detect the forgery. All the quadrators
are agreed that, be the right what it may, 3.14159... is wrong. It would be
well if they would put their heads together, and say what this wrong result
really means. The mathematicians of all ages have tried all manner of
processes, with one object in view, and by methods which are admitted to
yield demonstration in countless cases. They have all arrived at one result.
A large number of opponents unite in declaring this result wrong, and all
agree in two points: first, in differing among themselves; secondly, in
declining to point out what that curious result really is which the
mathematical methods all agree in giving.
Most of the quadrators are not aware that it has been fully demonstrated that
no two numbers whatsoever can represent the ratio of the diameter to the
circumference with perfect accuracy. When therefore we are told that either
8 to 25 or 64 to 201 is the true ratio, we know that it is no such thing,
without the necessity of examination. The point that is left open, as not fully
demonstrated to be impossible, is the geometrical quadrature, the
determination of the circumference by the straight line and circle, used as in
Euclid. The general run of circle-squarers, hearing that the quadrature is not
pronounced to be demonstratively impossible, imagine that the arithmetical
quadrature is open to their ingenuity. Before attempting the arithmetical
problem, they ought to acquire knowledge enough to read Lambert's[355]
demonstration (last given in Brewster's[356] translation of Legendre's[357]
Geometry) and, if they can, to refute it. [It will be given in an Appendix.]

Probably some have begun this way, and have caught a Tartar who has
refused to let them go: I have never heard of any one who, in producing his
own demonstration, has laid his finger on the faulty part of Lambert's
investigation. This is the answer to those who think that the mathematicians
treat the arithmetical squarers too lightly, and that as some person may
succeed at last, all attempts should be examined. Those who have so
thought, not knowing that there is demonstration on the point, will probably
admit that a person who contradicts a theorem of which the demonstration
has been acknowledged for a century by all who have alluded to it as read
by themselves, may reasonably be required to point out the error before he
demands attention to his own result.
Apopempsis of the Tutelaries.—Again and again I am told that I spend too
much time and trouble upon my two tutelaries: but when I come to my
summing-up I shall make it appear that I have a purpose. Some say I am too
hard upon them: but this is quite a mistake. Both of them beat little Oliver
himself in the art and science of asking for more; but without Oliver's
excuse, for I had given good allowance. Both began with me, not I with
them: and both knew what they had to expect when they applied for a
second helping.
On July 31, the Monday after the publication of my remarks on my 666
correspondent, I found three notes in separate envelopes, addressed to me at
"7A, University College." When I saw the three new digits I was taken
rhythmopoetic, as follows—

Here's the Doctor again with his figs, and by Heavens!
He was always at sixes, and now he's at sevens.

To understand this fully the reader must know that the greater part of
Apocalyptic interpretation has long been condensed, in my mind, into the
Turkish street-cry—In the name of the Prophet! figs! I make a few extracts.
The reader will observe that Dr. Thorn grumbles at his private letters being
publicly ridiculed. A man was summoned for a glutolactic assault; he
complained of the publication of his proceeding: I kicked etc. in confidence,
he said.

"After reading your last, which tries in every way to hold me up to public
ridicule for daring to write you privately ['that you would be d——d,'
omitted by accident] one would say, Why have anything to do with such a
testy person? [Wrong word; no testy person can manage cool and
consecutive ridicule. Quære, what is this word? Is it anything but a
corruption of the obsolete word tetchy of the same meaning? Some think
touchy is our modern form of tetchy, which I greatly doubt]. My answer is,
the poor man is lamentably ignorant; he is not only so, but 'out of the way'
[quite true; my readers know me by this time for an out-of-the-way person.
What other could tackle my squad of paradoxers? What other would
undertake the job?] Can he be brought back and form one of those who in
Ezekiel 37 ch. have the Spirit breathed into them and live.... Have I any
other feeling towards you except that of peace and goodwill? [Not to your
distinct knowledge; but in all those who send people to 'the other place' for
contempt of their interpretations, there is a lurking wish which is father to
the thought; 'you will be d——d' and 'you be d—d' are Siamese twins]. Of
course your sneer at 666 brought plain words; but when men meddle with
what they do not understand (not having the double Vahu) they must be
dealt with faithfully by those who do.... [They must; which justifies the
Budget of Paradoxes: but no occasion to send them anywhere; no preachee
and floggee too, as the negro said]. Many will find the text Prov. i. 26 fully
realized. [All this contains distinct assumption of a right 'of course' to
declare accursed those who do not respect the writer's vagary].... If I could
but get the ‫א‬, the Ox-head, which in Old Hebrew was just the Latin
Digamma, F, out of your name, and could then Thau you with the Thau of
Ezekiel ix, 4, the χ, then you would bear the number of a man! But this is
too hard for me, although not so for the Lord! Jer. xxxii. 17.... And now a
word: is ridicule the right thing in so solemn a matter as the discussion of
Holy Writ? [Is food for ridicule the right thing? Did I discuss Holy Writ? I
did not: I concussed profane scribble. Even the Doctor did not discuss; he
only enunciated and denunciated out of the mass of inferences which a
mystical head has found premises for in the Bible]."

M 40
O 70
R 100
G 6

N 50
——
266
‫ =ת‬χ 400

[That ill opinions are near relations of ill wishes, will be detected by those
who are on the look out. The following was taken down in a Scotch Church
by Mr. Cobden,[358] who handed it to a Roman friend of mine, for his
delectation (in 1855): "Lord, we thank thee that thou hast brought the Pope
into trouble; and we pray that thou wouldst be mercifully pleased to
increase the same."]
Here is a martyr who quarrels with his crown; a missionary who reviles his
persecutor: send him to New Zealand, and he would disagree with the
Maoris who ate him. Man of unilateral reciprocity! have you, who write to a
stranger with hints that that stranger and his wife are children of perdition,
the bad taste to complain of a facer in return? As James Smith[359]—the
Attorney-wit, not the Dock-cyclometer—said, or nearly said,

"A pretty thing, forsooth!
Is he to burn, all scalding hot,
Me and my wife, and am I not
To job him out a tooth?"

Those who think parody vulgar will be pleased to substitute for the above a
quotation from Butler[360]:—

"There's nothing so absurd or vain
Or barbarous or inhumane,
But if it lay the least pretence
To piety and godliness,
Or tender-hearted conscience,
And zeal for gospel truths profess,—
Does sacred instantly commence,
And all that dare but question it are straight
Pronounced th' uncircumcised and reprobate,
As malefactors that escape and fly

Into a sanctuary for defence,
Must not be brought to justice thence,
Although their crimes be ne'er so great and high.
And he that dares presume to do't
Is sentenced and delivered up
To Satan that engaged him to't."

THE NUMBER OF THE BEAST.
Of all the drolleries of controversy none is more amusing than the manner
in which those who provoke a combat expect to lay down the laws of
retaliation. You must not strike this way! you must not parry that way! If
you don't take care, we shall never meddle with you again! We were not
prepared for such as this! Why did we have anything to do with such a testy
person? M. Jourdain must needs show Nicole, his servant-maid, how good a
thing it was to be sure of fighting without being killed, by care and tierce.
[361] "Et cela n'est il pas beau d'être assuré de son fait quand on se bat contre

quelqu'un? Là, pousse moi un peu, pour voir. Nicole. Eh bien! quoi? M.
Jourdain. Tout beau. Hola! Ho! doucement. Diantre soit la coquine! Nicole.
Vous me dites de pousser. M. Jourdain. Oui; mais tu me pousses en tierce,
avant que de pousser en quarte, et tu n'as pas la patience que je pare."
His colleague, my secular tutelary, who also made an anachronistic onset,
with his repartees and his retorts, before there was anything to fire at, takes
what I give by way of subsequent provocation with a good humor which
would make a convert of me if he could afford .01659265 ... of a grain of
logic. He instantly sent me his photograph for the asking, and another letter
in proof. The Thor-hammerer does nothing but grumble, except when he
tells a good story, which he says he had from Dr. Abernethy.[362] A Mr.
James Dunlop was popping at the Papists with a 666-rifled gun, when Dr.
Chalmers[363] quietly said, "Why, Dunlop, you bear it yourself," and handed
him a paper on which the numerals in

I A C O B V S D V N L O P V S
1 100 5 500 5 50 5

were added up. This is almost as good as the Filii Dei Vicarius, the
numerical letters of which also make 666. No more of these crazy—I first
wrote puerile, but why should young cricketers be libelled?—attempts to
extract religious use from numerical vagaries, and to make God over all a
proposer of salvation conundrums: and no more of the trumpery hints about
future destiny which is too great a compliment to call blasphemous. If the
Doctor will cipher upon the letter in ἐν ᾡ μετρῳ μετρειτε μετρηθησεται
ὑμιν[364] with double Vahu cubic measure, he will perhaps learn to leave off
trying to frighten me into gathering grapes from thorns.
Mystical hermeneutics may be put to good use by out-of-the-way people.
They may be made to call the attention of the many to a distinction well
known among the learned. The books of the New Testament have been for
1,500 years divided into two classes: the acknowledged (ὁμολογουμενα),
which it has always been paradox not to receive; and the controverted
(ἀντιλεγομενα), about which there has always been that difference of
opinion which no scholar overlooks, however he may decide for himself
after balance of evidence. Eusebius,[365] who first (l. 3, c. 25) recorded the
distinction—which was much insisted on by the early Protestants—states
the books which are questioned as doubtful, but which yet are approved and
acknowledged by many—or the many, it is not easy to say which he means
—to be the Epistles of James and Jude, the second of Peter and the second
and third of John. In other places he speaks doubtingly of the Epistle to the
Hebrews. The Apocalypse he does not even admit into this class, for he
proceeds as follows—I use the second edition of the English folio
translation (1709), to avert suspicion of bias from myself:—
"Among the spurious [νοθοι] let there be ranked both the work entitled the
Acts of Paul, and the book called Pastor, and the Revelation of Peter: and
moreover, that which is called the Epistle of Barnabas, and that named the
Doctrines of the Apostles: and moreover, as I said, the Revelation of John (if
you think good), which some, as I have said, do reject, but others allow of,
and admit among those books which are received as unquestionable and
undoubted."
Eusebius, though he will not admit the Apocalypse even into the
controverted list, but gives permission to call it spurious, yet qualifies his
permission in a manner which almost annihilates the distinctive force of

νοθος, and gives the book a claim to rank (if you think good, again) in the
controverted list. And this is the impression received by the mind of
Lardner, who gives Eusebius fully and fairly, but when he sums up,
considers his author as admitting the Apocalypse into the second list. A
stick may easily be found to beat the father of ecclesiastical history. There
are whole faggots in writers as opposite as Baronius and Gibbon, who are
perhaps his two most celebrated sons. But we can hardly imagine him
totally misrepresenting the state of opinion of those for whom and among
whom he wrote. The usual plan, that of making an author take the views of
his readers, is more easy in his case than in that of any other writer: for, as
the riddle says, he is You-see-by-us; and to this reading of his name he has
often been subjected. Dr. Nathaniel Lardner,[366] who, though heterodox in
doctrine, tries hard to be orthodox as to the Canon, is "sometimes apt to
think" that the list should be collected and divided as in Eusebius. He would
have no one of the controverted books to be allowed, by itself, to establish
any doctrine. Even without going so far, a due use of early opinion and long
continued discussion would perhaps prevent rational people from being
induced by those who have the double Vahu to place the Apocalypse above
the Gospels, which all the Bivahuites do in effect, and some are said to have
done in express words. But my especial purpose is to point out that an easy
way of getting rid of 665 out of 666 of the mystics is to require them to
establish the Apocalypse before they begin. See if they even know so much
as that there is a crowd of testimonies for and against, running through the
first four centuries, which makes this book the most difficult of the whole
Canon. Try this method, and you will escape beautiful, as the French say.
Dean Alford,[367] in Vol. IV, p. 8, of his New Testament, gives an elaborate
handling of this question. He concludes by saying that he cannot venture to
refuse his consent to the tradition that the Apostle is the author. This
modified adherence, or non-nonadherence, pretty well represents the feeling
of orthodox Protestants, when learning and common sense come together.
I have often, in former days, had the attempt made to place the Apocalypse
on my neck as containing prophecies yet unfulfilled. The preceding method
prevents success; and so does the following. It may almost be taken for
granted that theological system-fighters do not read the New Testament:
they hunt it for detached texts; they listen to it in church in that state of
quiescent nonentity which is called reverent attention: but they never read

it. When it is brought forward, you must pretend to find it necessary to turn
to the book itself: you must read "The revelation ... to show unto his
servants things which must shortly come to pass.... Blessed is he that
readeth ... for the time is at hand." You must then ask your mystic whether
things deferred for 1800 years were shortly to come to pass, etc.? You must
tell him that the Greek ἐν ταχει, rendered "shortly," is as strong a phrase as
the language has to signify soon. The interpreter will probably look as if he
had never read this opening: the chances are that he takes up the book to see
whether you have been committing a fraud. He will then give you some
exquisite evasion: I have heard it pleaded that the above was a mere
preamble. This word mere is all-sufficient: it turns anything into nothing.
Perhaps he will say that the argument is that of the Papists: if so, tell him
that there is no Christian sect but bears true witness against some one or
more absurdities in other sects.
An anonyme suggests that ἐν ταχει may not be "soon," it may be "quickly,
without reference to time when:" he continues thus, "May not time be 'at
hand' when it is ready to come, no matter how long delayed?" I now
understand what *** and *** meant when they borrowed my books and
promised to return them quickly, it was "without reference to time when."
As to time at hand—provided you make a long arm—I admire the quirk,
but cannot receive it: the word is ἐγγυς, which is a word of closeness in
time, in place, in reckoning, in kindred, etc.
Another gentleman is not surprised that Apocalyptic reading leads to a
doubt of the "canonicity" of the book: it ought not to rest on church
testimony, but on visible miracle. He offers me, or any reader of the
Athenæum, the "sight of a miracle to that effect, and within forty-eight
hours' journey (fare paid)." I seldom travel, and my first thought was
whether my carpet-bag would be found without a regular hunt: but, on
reading further, I found that it was only a concordance that would be
wanted. Forty hours' collection and numerical calculation of Greek nouns
would make it—should I happen to agree with the writer—many hundred
millions to one that Revelation xiii is superhuman. There is but one verse
(the fifth) which the writer does not see verified. I looked at this verse, and
was much startled. The Budget began in October 1863: should it last until
March 1867—it is now August 1866—it is clear that I am the first Beast,
and my paradoxers are the saints whom I persecute.

[The Budget did terminate in March 1867: I hope the gentleman will be
satisfied with the resulting interpretation.]
The same opponent is surprised that I should suppose a thing which "comes
to pass" must be completed, and cannot contain what is to happen 1800
years after. All who have any knowledge of English idiom know that a thing
comes to pass when it happens, and came to pass afterwards. But as the
original is Greek, we must look at the Greek: it is δει γενεσθαι for "must
come to pass," and we know that ἐγενετο is what is usually translated
"came to pass." No word of more finished completion exists in Greek.
And now for a last round of biter-bit with the Thor-hammerer, of whom, as
in the other case, I shall take no more notice until he can contrive to surpass
himself, which I doubt his being able to do. He informs me that by
changing A into ‫ ת‬in my name he can make a 666 of me; adding, "This is
too hard for me, although not so for the Lord!" Sheer nonsense! He could
just as easily have directed to "Prof. De Morg‫ת‬n" as have assigned me
apartment 7A in University College. It would have been seen for whom it
was intended: and if not, it would still have reached me, for my colleagues
have for many a year handed all out-of-the-way things over to me. There is
no 7A: but 7 is the Museum of Materia Medica. I took the only hint which
the address gave: I inquired for hellebore, but they told me it was not now
recognized, that the old notion of its value was quite obsolete, and that they
had nothing which was considered a specific in senary or septenary cases.
The great platitude is the reference of such a difficulty as writing ‫ ת‬for A to
the Almighty! Not childish, but fatuous: real childishness is delightful. I
knew an infant to whom, before he could speak plain, his parents had
attempted to give notions of the Divine attributes: a wise plan, many think.
His father had dandled him up-side-down, ending with, There now! Papa
could not dance on his head! The mannikin made a solemn face, and said,
But Dod tood! I think the Doctor has rather mistaken the way of becoming
as a little child, intended in Matt. xviii. 3: let us hope the will may be taken
for the deed.
Two poets have given images of transition from infancy to manhood:
Dryden,—for the Hind is Dryden himself on all fours! and Wordsworth, in
his own character of broad-nailed, featherless biped:

"The priest continues what the nurse began,
And thus the child imposes on the man."
"The child's the father of the man,
And I could wish my days to be
Bound each to each by natural piety."

In Wordsworth's aspiration it is meant that sense and piety should grow
together: in Dryden's description a combination of Mysticism And Bigotry
(can this be the double Vahu?), personified as "the priest,"—who always
catches it on this score, though the same spirit is found in all associations,—
succeeds the boguey-teaching of the nurse. Never was the contrast of smile
and scowl, of light and darkness, better seen than in the two pictures. But an
acrostic distinction may be drawn. When mysticism predominates over
bigotry, we have the grotesque picturesque, and the natural order of words
gives us Mab, an appropriate suggestion. But when bigotry has the upper
hand, we see Bam, which is just as appropriate; for bigotry nearly always
deals with facts and logic so as to require the application of at least one of
the minor words by which dishonesty is signified. I think that M is the
Doctor's initial, and that Queen Mab tickles him in his sleep with the sharp
end of a 6.
(Monday, August 21.) Three weeks having elapsed without notice from me
of the Doctor, I receive a reminder of his existence, in which I find that as I
am the Daniel who judges the Magi of Babylon, it is to be pointed out that
Daniel "bore a certain number, that of a man (beloved), Daniel, ch. 10. v.
11, and which you certainly do not." Then, "by Greek power," Belteshazzar
is made = 666. Here is another awkward imitation of the way of a baby
child. When you have sported with the tiny creature until it runs away
offended, by the time you have got into conversation again you will find the
game is to be renewed: a little head peeps out from a hiding-place with "I
don't love you." The proper rejoinder is, "Very well! then I'll have pussy."
But in the case before me there is a rule of three sums to do; as baby : Pussy
Dr. :: 666 : the answer required. I will work it out, if I can.
The squaring of the circle and the discovery of the Beast are the two goals
—and goals also—of many unbalanced intellects, and of a few instances of
the better kind. I might have said more of 666, but I am not deep in its
bibliography. A work has come into my hands which contains a large

number of noted cases: to some of my readers it will be a treat to see the
collection; and the sight will perhaps be of some use to those who have read
controversy on the few celebrated cases which are of general notoriety. It is
written by a learned decipherer, a man who really knew the history of the
subject, the Rev. David Thom,[368] of Bold Street Chapel, Liverpool, who
died, I am told, a few years ago.
Anybody who reads his book will be inclined to parody a criticism which
was once made on Paley's[369] Evidences—"Well! if there be anything in
Christianity, this man is no fool." And, if he should chance to remember it,
he will be strongly reminded of a sentence in my opening chapter,—"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."
And this is reinforced by the fact that Mr. Thom, though a scholar, was not
conspicuous for learning, except in this his great pursuit. He was a
paradoxer on other points. He reconciled Calvinism and eternal reprobation
with Universalism and final salvation; showing these two doctrines to be all
one.
This gentleman must not be confounded with the Rev. John Hamilton
Thom[370] (no relation), at or near the same time and until recently, of
Renshaw Street Chapel, Liverpool who was one of the minority in the
Liverpool controversy when, nearly thirty years ago, three heretical
Unitarian schooners exchanged shotted sermons with thirteen Orthodox
ships of the line, and put up their challengers' dander—an American
corruption of d—d anger—to such an extent, by quiet and respectful
argument, that those opponents actually addressed a printed intercession to
the Almighty for the Unitarian triad, as for "Jews, Turks, Infidels, and
Heretics." So much for the distinction, which both gentlemen would thank
me for making very clear: I take it quite for granted that a guesser at 666
would feel horrified at being taken for a Unitarian, and that a Unitarian
would feel queerified at being taken for a guesser at 666. Mr. David Thom's
book is The Number and Names of the Apocalyptic Beasts, Part I, 1848,
8vo.: I think the second part was never published. I give the Greek and
Latin solutions, omitting the Hebrew: as usual, all the Greek letters are

numeral, but only M D C L X V I of the Latin. I do not give either the
decipherers or their reasons: I have not room for this; nor would I, if I
could, bias my reader for one rather than another.

D. F. Julianus Cæsar Atheus (or Aug.[371]); Diocles Augustus; Ludovicus;
Silvester Secundus; Linus Secundus; Vicarius Filii Dei; Doctor et Rex
Latinus; Paulo V. Vice-Deo; Vicarius Generalis Dei in Terris; Ipse
Catholicæ Ecclesiæ Visibile Caput; Dux Cleri; Una, Vera, Catholica,
Infallibilis Ecclesia; Auctoritas politica ecclesiasticaque Papalis (Latina will
also do); Lutherus Ductor Gregis; Calvinus tristis fidei interpres; Dic Lux ;
Ludvvic; Will. Laud; Λατεινος;[372] ἡ λατινη βασιλεια; ἐκκλησια ἰταλικα;
εὐανθας; τειταν; ἀρνουμε; λαμπετις; ὁ νικητης; κακος ὁδηγος; ἀληθης
βλαβερος; παλαι βασκανος; ἀμνος ἀδικος; ἀντεμος; γενσηρικος;
εὐινας; Βενεδικτος; Βονιβαζιος γ. παπα ξ. η. ε. ε. α., meaning Boniface
III. Pope 68th, bishop of bishops the first! οὐλπιος; διος εἰμι ἡ ἡρας; ἡ
μισσα ἡ παπικη; λουθερανα; σαξονειος; Βεζζα ἀντιθεος (Beza); ἡ
ἀλαζονεια βιου; Μαομετις; Μαομετης β.; θεος εἰμι ἐπι γαιης; ἰαπετος;
παπεισκος; διοκλασιανος; χεινα; βρασκι; Ιον Παυνε; κουποκς;
(cowpox, ς being the vau; certainly the vaccinated have the mark of the
Beast); Βοννεπαρτη; Ν. Βονηπαρτε; εὐπορια; παραδοσις; το
μεγαθηριον.
All sects fasten this number on their opponents. It is found in Martin
Lauter, affirmed to be the true way of writing the name, by carrying
numbers through the Roman Alphabet. Some Jews, according to Mr. Thorn,
found it in ‫ ישו נצרי‬Jesus of Nazareth. I find on inquiry that this satire was
actually put forth by some medieval rabbis, but that it is not idiomatic: it
represents quite fairly "Jesus Nazarene," but the Hebrew wants an article
quite as much as the English wants "the."
Mr. David Thom's own solution hits hard at all sides: he finds a 666 for
both beasts; ἡ φρην (the mind) for the first, and ἐκκλησιαι σαρκικαι
(fleshly churches) for the second. A solution which embodies all mental
philosophy in one beast and all dogmatic theology in the other, is very
tempting: for in these are the two great supports of Antichrist. It will not,
however, mislead me, who have known the true explanation a long time.
The three sixes indicate that any two of the three subdivisions, Roman,
Greek, and Protestant, are, in corruption of Christianity, six of one and half

a dozen of the other: the distinctions of units, tens, hundreds, are nothing
but the old way (1 Samuel xviii. 7, and Concordance at ten, hundred,
thousand) of symbolizing differences of number in the subdivisions.
It may be good to know that, even in speculations on 666, there are different
degrees of unreason. All the diviners, when they get a colleague or an
opponent, at once proceed to reckon him up: but some do it in play and
some in earnest. Mr. David Thom found a young gentleman of the name St.
Claire busy at the Beast number: he forthwith added the letters in στ κλαιρε
and found 666: this was good fun. But my spiritual tutelary, when he found
that he could not make a beast of me, except by changing ‫ א‬into ‫ת‬,
solemnly referred the difficulty to the Almighty: this was poor earnest.
I am glad I did not notice, in time to insert it in the Athenæum, a very
remarkable paradoxer brought forward by Mr. Thom, his friend Mr.
Wapshare[373]: it is a little too strong for the general public. In the
Athenæum they would have seen and read it: but this book will be avoided
by the weaker brethren. It is as follows:
"God, the Elohim, was six days in creating all things, and having made MAN
he entered into his rest. He is no more seen as a Creator, as Elohim, but as
Jehovah, the Lord of the Sabbath, and the Spirit of life in Man, which Spirit
worketh sin in the flesh; for the Spirit of Love, in all flesh, is Lust, or the
spirit of a beast, So Rom. vii. And which Spirit is crucified in the flesh. He
then, as Jehovah—as the power of the Law, in and over all flesh, John viii.
44—increases that which he has made as the Elohim, and his power shall
last for 6 days, or 6 periods of time, computed at a millennium of years; and
at the end of which six days, he who is the Spirit of all flesh shall manifest
himself as the Holy Spirit of Almighty Love, and of all truth; and so shall
the Church have her Sabbath of Rest—all contention being at an end. This
is, as well as I may now express it, my solution of the mystery in Hebrew,
and in Greek, and also in Latin, IHS. For he that was lifted up is King of the
Jews, and is the Lord of all Life, working in us, both to will and to do; as is
manifest in the Jews—they slaying him that his blood might be good for the
healing of the nations, of all people and tongues. As the Father of all
natural flesh, he is the Spirit of Lust, as in all beasts; as the Father, or King
of the Jews, he is the Devil, as he himself witnesseth in John viii., already
referred to. As lifted up, he is transformed into the Spirit of Love, a light to

the Gentiles, and the glory of his people Israel.... For there is but ONE God,
ONE Lord, ONE Spirit, ONE body, etc. and he who was Satan, the Spirit of life
in that body, is, in Christ crucified, seen in the Spirit that is in all, and
through all and over all, God blessed for ever."
All this seems well meant, and Mr. Thom prints it as convinced of its piety,
and "pronounces no opinion." Mystics of all sorts! see what you may come
to, or what may come to you! I have inserted the above for your good.
There is nothing in this world so steady as some of the paradoxers. They are
like the spiders who go on spinning after they have web enough to catch all
the flies in the neighborhood, if the flies would but come. They are like the
wild bees who go on making honey which they never can eat, proving sic
vos non vobis to be a physical necessity of their own contriving. But
nobody robs their hives: no, unlike the bees, they go about offering their
ware to any who will take it as a gift. I had just written the last sentence
(Oct. 30, 1866, 8.45 A.M.) when in comes the second note received this
morning from Dr. Thorn: at 1.30 P.M. came in a third. These arise out of the
above account of the Rev. D. Thom, published Oct. 27: three notes had
arrived before.
For curiosity I give one day's allowance, supposing these to be all: more
may arrive before night.
29th Oct. 1866.
"Dear Sir,—

In re .[374]
"So that 'Zaphnath Paaneah' may be after all the revealer of the 'Northern
Tau' Φανεροω—To make manifest, shew, or explain; and this may satisfy
the House of Joseph in Amos 5c. While Belteshazzar = 666 may be also
satisfactory to the House of David, and so we may have Zech. 10c. 6v. in
operation when Ezekiel 37c. 16v. has been realised;—but there, what is the
use of writing, it is all Coptic to a man who has not , The Thau of the
North, the double Vahu ‫ָו ו‬. Look at Jeremiah 3c. 8v. and then to Psalm 83 for
'hidden ones' ‫—ְצ פּוֶנ י ְי הָו ה‬The Zephoni Jehovah, and say whether they have

any connection with the Zephon Thau. The Hammer of Thor of Jeremiah
23c. 29v. as I gave you in No. 3 of my present edition.

Yours truly

Le Chevalier Au Cin."

By Greek Power.

C = 20
H= 8
E= 5
V= 6
A= 1
L= 30
I= 10
E= 5
R = 100

A= 1
U = 400

C= 20
I= 10
N= 50
——
666

There will be thousands of Morgans who will be among the wise and
prudent of Hosea 14c. 9v. when the Seventh Angel sounds, let me number
that One by Greek, Rev. 17c. 1v:

S = 200
E= 5

×V= 6
E= 5
N= 50
T = 300
H= 8

A= 1
N= 50
×G= 6
E= 5
L= 30
——
666

V and G = 12 ought to be equal to one Gammadion or 3 3 × 4 =
12, what say you?
London, October 29, 1866.
"Dear Sir,—

In re versus .
However pretentious the X or may be, and it is peculiarly so just now in
this land; after all it is only made of two Roman V's—and so is only = (10)
—and therefore is not the perfect number 12 of Reveln, but is the mark of
the goddess Decima!

Yours truly

Wm. Thorn."
Had the one who sent forth a pastoral (Romish) the other day, remained
amongst the faithful expectants, see how he would have numbered, whereas
he sold himself for the privilege of signing

Henry E. Manning.[375]

Transcriber's note.

By English Key. H = 8
E= 5
N= 40
R= 80
Y = 140

E= 5
D= 4
W = 120
A= 1
R= 80
D= 4

M= 30
A= 1
N= 40
N= 40
I= 9
N= 40
G= 7
= 12
——
666

Can you now understand the difference between and or X?
Look to my challenge.

Cutting from newspaper:—
ITALY.
Rome (via Marseilles), October
Mr. Gladstone has paid a visit to the Pope.

By Greek Power. G = 6
L= 30
A= 1
D= 4
S = 200
T = 300
O= 70
N= 50
E= 5
——
666

And what then ?
In other letters John Stuart Mill is 666 if the a be left out; Chasuble is
perfect. John Brighte[376] is a fait accompli; and I am asked whether
intellect can account for the final e. Very easily: this Beast is not the M. P.,
but another person who spells his name differently. But if John Sturt Mill
and John Brighte choose so to write themselves, they may.
A curious collection; a mystical phantasmagoria! There are those who will
try to find meaning: there are those who will try to find purpose.

"And some they said—What are you at?
And some—What are you arter?"

My account of Mr. Thom and his 666 appeared on October 27: and on the
29th I received from the editor a copy of Mr. Thom's sermons published in
1863 (he died Feb. 27, 1862) with best wishes for my health and happiness.
The editor does not name himself in the book; but he signed his name in my
copy: and may my circumference never be more than 3⅛ of my diameter if
the signature, name and writing both, were not that of my ing friend Mr.
James Smith! And so I have come in contact with him on 666 as well as on
π! I should have nothing left to live for, had I not happened to hear that he
has a perpetual motion on hand. I returned thanks and kind regards: and
Miss Miggs's words—"Here's forgivenesses of injuries! here's

amicablenesses!"—rang in my ears. But I was made slightly uncomfortable:
how could the war go on after this armistice? Could I ever make it
understood that the truce only extended to the double Vahu and things
thereunto relating? It was once held by seafaring men that there was no
peace with Spaniards beyond the line: I was determined that there must be
no concord with J. S. inside the circle; that this must be a special exception,
like Father Huddleston and old Grouse in the gun-room. I was not long in
anxiety; twenty-four hours after the book of sermons there came a copy of
the threatened exposure—The British Association in Jeopardy, and
Professor De Morgan in the Pillory without hope of escape. By James
Smith, Esq. London and Liverpool, 8vo., 1866 (pp. 94). This exposure
consists of reprints from the Athenæum and Correspondent: of things new
there is but one. In a short preface Mr. J. S. particularly recommends to
"read to the end." At the end is an appendix of two pages, in type as large as
the work; a very prominent peroration. It is an article from the Athenæum,
left out of its place. In the last sentence Mr. J. Smith, who had asked
whether his character as an honest Geometer and Mathematician was not at
stake, is warned against the fallacia plurium interrogationum.[377] He is told
that there is not a more honest what's-his-name in the world: but that as to
the counter which he calls his character as a mathematician, he is assured
that it has been staked years ago, and lost. And thus truth has the last word.
There is no occasion to say much about reprints. One of them is a letter
[that given above] of August 25, 1865, written by Mr. J. S. to the
Correspondent. It is one of his quadratures; and the joke is that I am made
to be the writer: it appears as what Mr. J. S. hopes I shall have the sense to
write in the Athenæum and forestall him. When I saw myself thus quoted—
yes! quoted! double commas, first person—I felt as I suppose did Wm.
Wilberforce[378] when he set eyes on the affectionate benediction of the
potato which waggish comrades had imposed on a raw Irish reporter as part
of his speech. I felt as Martin[379] of Galway—kind friend of the poor dumb
creatures!—when he was told that the newspapers had put him in Italics. "I
appeal to you, Mr. Speaker! I appeal to the House! Did I speak in Italics?
Do I ever speak in Italics?" I appeal to editor and readers, whether I ever
squared the circle until a week or two ago, when I gave my charitable mode
of reconciling the discrepant cyclometers.

The absurdity of the imitation of symbolic reasoning is so lusciously rich,
that I shall insert it when I make up my final book. Somebody mastered
Spanish merely to read Don Quixote: it would be worth while to learn a
little algebra merely to enjoy this a b-istical attack on the windmills. The
principle is, Prove something in as roundabout a way as possible, mention
the circle once or twice irrelevantly in the course of your proof, and then
make an act of Q. E. D. in words at length. The following is hardly
caricature:—
To prove that 2 and 2 make 5. Let a = 2, b = 5: let c = 658, the number of
the House: let d = 666, the number of the Beast. Then of necessity d = a + b
+ c + 1; so that 1 is a harmonious and logical quantification of the number
of which we are to take care. Now, b, the middle of our digital system, is,
by mathematical and geometrical combination, a mean between 5 + 1 and 2
+ 2. Let 1 be removed to be taken care of, a thing no real mathematician can
refuse without serious injury to his mathematical and geometrical
reputation. It follows of necessity that 2 + 2 = 5, quod erat
demonstrumhorrendum. If Simpkin & Marshall have not, after my notice, to
account for a gross of copies more than would have gone off without me,
the world is not worthy of its James Smith!
The only fault of the above is, that there is more connection than in the
process of Faber Cyclometricus: so much, in fact, that the blunders are
visible. The utter irrelevance of premises to conclusion cannot be exhibited
with the requisite obscurity by any one who is able to follow reasoning: it is
high art displayed in a certain toning down of the ægri somnia, which
brings them to a certain look of reproach to reasoning which I can only
burlesque. Mr. J. S. produces something which resembles argument much as
a chimpanzee in dolor, because balked of his dinner, resembles a thinking
man at his studies. My humble attempt at imitation of him is more like a
monkey hanging by his tail from a tree and trying to crack a cocoa-nut by
his chatter.
I could forgive Mr. J. S. anything, properly headed. I would allow him to
prove—for himself—that the Quadrature of the Circle is the child of a
private marriage between the Bull Unigenitus and the Pragmatic Sanction,
claiming tithe of onions for repeal of the Mortmain Act, before the Bishops
in Committee under the kitchen table: his mode of imitating reason would

do this with ease. But when he puts his imitation into my mouth, to make
me what he calls a "real mathematician," my soul rises in epigram against
him. I say with the doll's dressmaker—such a job makes me feel like a
puppet's tailor myself—"He ought to have a little pepper? just a few grains?
I think the young man's tricks and manners make a claim upon his friends
for a little pepper?" De Fauré[380] and Joseph Scaliger[381] come into my
head: my reader may look back for them.

"Three circlesquarers to the manner born,
Switzerland, France, and England did adorn,
De Fauré in equations did surpass,
Joseph at contradictions was an ass.
Groaned Folly, I'm used up! What shall I do
To make James Smith? Grinned Momus, Join the two!"

As to my locus pœnitentiæ,[382] the reader who is fit to enjoy the letter I
have already alluded to will see that I have a soft and easy position; that the
thing is really a pillowry; and that I am, like Perrette's pot of milk,

"Bien posé sur un coussinet."[383]

Joanna Southcott[384] never had a follower who believed in her with more
humble piety than Mr. James Smith believes in himself. After all that has
happened to him, he asks me with high confidence to "favor the writer with
a proof" that I still continue of opinion that "the best of the argument is in
my jokes, and the best of the joke is in his arguments." I will not so favor
him. At the very outset I told him in plain English that he has the whiphand
of all the reasoners in the world, and in plain French that il a perdu le droit
d'être frappé de l'évidence[385]; I might have said pendu.[386] To which I
now add, in plain Latin, Sapienti pauca, indocto nihil.[387] The law of
Chancery says that he who will have equity must do equity: the law of
reasoning says that he who will have proof must see proof.
The introduction of things quite irrelevant, by way of reproach, is an
argument in universal request: and it often happens that the argument so
produced really tells against the producer. So common is it that we forget
how boyish it is; but we are strikingly reminded when it actually comes

from a boy. In a certain police court, certain small boys were arraigned for
conspiring to hoot an obnoxious individual on his way from one of their
school exhibitions. This proceeding was necessary, because there seemed to
be a permanent conspiracy to annoy the gentleman; and the masters did not
feel able to interfere in what took place outside the school. So the boys were
arraigned; and their friends, as silly in their way as themselves, allowed one
of them to make the defence, instead of employing counsel; and did not
even give them any useful hints. The defence was as follows; and any one
who does not see how richly it sets off the defences of bigger boys in bigger
matters has much to learn. The innocent conviction that there was answer in
the latter part is delightful. Of course fine and recognizance followed.
A—— said the boys had received great provocation from B——. He was
constantly threatening them with a horsewhip which he carried in his hand
[the boy did not say what had passed to induce him to take such a weapon],
and he had repeatedly insulted the master, which the boys could not stand.
B—— had in his own drawing-room told him (A——) that he had drawn
his sword against the master and thrown away the scabbard. B—— knew
well that if he came to the college he would catch it, and then he went off
through a side door—which was no sign of pluck; and then he brought Mrs.
B—— with him, thinking that her presence would protect him.
My readers may expect a word on Mr. Thom's sermons, after my account of
his queer doings about 666. He is evidently an honest and devout man,
much wanting in discrimination. He has a sermon about private judgment,
in which he halts between the logical and legal meanings of the word. He
loathes those who apply their private judgment to the word of God: here he
means those who decide what it ought to be. He seems in other places
aware that the theological phrase means taking right to determine what it is.
He uses his own private judgment very freely, and is strong in the
conclusion that others ought not to use theirs except as he tells them how;
he leaves all the rest of mankind free to think with him. In this he is not
original: his fame must rest on his senary tripod.

JAMES SMITH ONCE MORE.

Mr. James Smith's procedures are not caricature of reasoning; they are
caricature of blundering. The old way of proving that 2 = 1 is solemn
earnest compared with his demonstrations. As follows:[388]

Let x=1
Then x2 = x
And x2 - 1 = x - 1
Divide both sides by x - 1; then
x + 1 = 1; but x = 1, whence 2 = 1.

When a man is regularly snubbed, bullied, blown up, walked into, and put
down, there is usually some reaction in his favor, a kind of deostracism,
which cannot bear to hear him always called the blunderer. I hope it will be
so in this case. There is nothing I more desire than to see sects of
paradoxers. There are fully five thousand adults in England who ought to be
the followers of some one false quadrature. And I have most hope of 3⅛,
because I think Mr. James Smith better fitted to be the leader of an
organized infatuation than any one I know of. He wants no pity, and will get
none. He has energy, means, good humor, strong conviction, character, and
popularity in his own circle. And, most indispensable point of all, he sticks
at nothing;

"In cœlum jusseris, ibit."[389]

When my instructor found I did not print an acceptance of what I have
quoted, he addressed me as follows (Corr., Sept 23):—
"In this life, however, we must do our duty, and, when necessary, use the
rod, not in a spirit of revenge, but for the benefit of the culprit and the good
of society. Now, Sir, the opportunity has been thrown in your way of
slipping out of the pillory without risk of serious injury; but, like an
obstinate urchin, you have chosen to quarrel with your opportunity and
remain there, and thus you compel me to deal with you as schoolmasters
used to do with stupid boys in bygone days—that is to say, you force me to
the use of the critic's rod, compel me to put you where little Jack Horner sat,
and, as a warning to other naughty boys, to ornament you with a dunce's

cap. The task I set you was a very simple one, as I shall make manifest at
the proper time."
In one or more places, as well as this, Mr. Smith shows that he does not
know the legend of little Jack Horner, whom he imagines to be put in the
corner as a bad boy. This is curious; for there had been many allusions to
the story in the journal he was writing in, and the Christmas pie had become
altered into the Seaforth π.
Mr. Smith is satisfied at last that—what between argument and punishment
he has convinced me. He says (Corr., Jan. 27, 1866): "I tell him without
hesitation that he knows the true ratio of diameter to circumference as well
as I do, and if he be wise he will admit it." I should hope I do, and better;
but there is no occasion to admit what everybody knows.
I have often wished that we could have a slight glimpse of the reception
which was given to some of the old cyclometers: but we have nothing,
except the grave disapprobation of historians. I am resolved to give the New
Zealander a chance of knowing a little more than this about one of them at
least; and, by the fortunate entrance into life of the Correspondent, I am
able to do it. I omit sober mathematical answers, of which there were
several. The following letter is grave earnest:
"Sir,—I have watched Mr. James Smith's writings on this subject from the
first, and I did hope that, as the more he departs from truth the more easy it
must be to refute him, [this by no means always true] some of your
correspondents would by this time have done so. I own that I am unable to
detect the fallacy of his argument; and I am quite certain that 'Π' is wrong,
in No. 23, where he declares that Mr. Smith is 'ignorant of the very elements
of mathematical truth.' I have observed an immense amount of geometrical
reasoning on his part, and I cannot see that it is either fair or honest to deny
this, which may be regarded as the 'elements' of mathematical truth. Would
it not be better for 'Π' to answer Mr. Smith, to refute his arguments, to point
out their fallacies, and to save learners from error, than to plunge into gross
insult and unmanly abuse? Would it not be well, also, that Professor De
Morgan should favour us with a little reasoning?
"I have hitherto seen no attempt to overthrow Mr. Smith's arguments; I trust
that this will not continue, since the subject is one of immense importance

to science in general, especially to nautical science, and all that thereto
belongs.

Yours, etc.,

A Captain, R.N."
On looking at this homœopathic treatment of the 3⅛ quadrature—
remember, homœopathic, similia similibus,[390] not infinitesimal—and at
the imputation thrown upon it, I asked myself, what is vulgarity? No two
agree, except in this, that every one sees vulgarity in what is directed
against himself. Mark the world, and see if anything be so common as the
description of the other side's remarks as "vulgar attempt at wit." "I suppose
you think that very witty:" the answer is "No my friend! your remark shows
that you feel it as wit, so that the purpose is answered; I keep my razor for
something else than cutting blocks;" I am inclined to think that "out of
place" is a necessary attribute of true vulgarity. And further, it is to be
noticed that nothing is unproducible—salvo pudore[391]—which has
classical authority, modern or ancient, in its favor. "He is a vulgar fellow; I
asked him what he was upon, and what do you think he answered, My
legs!"—"Well, and has he not justification? what do you find in Terence?
Quid agitur? Statur."[392] I do not even blench from my principle where I
find that it brings what is called "taking a sight" within permissible forms of
expression: Rabelais not only establishes its antiquity, but makes it English.
Our old translation[393] has it thus (book 2. ch. 19):
"Then made the Englishman this sign. His left hand, all open, he lifted up
into the air, then instantly shut into his fist the four fingers thereof; and his
thumb extended at length he placed upon the tip of his nose. Presently after
he lifted up his right hand all open and abased and bent it downwards,
putting the thumb thereof in the very place where the little finger of the left
hand did close in the fist, and the four right hand fingers he softly moved in
the air. Then contrarily he did with the right hand what he had done with the
left, and with the left what he had done with the right."
An impressive sight! The making of a fist of the left hand is a great addition
of power, and should be followed in modern practice. The gentle sullation
of the front fingers, with the clenched fist behind them, says as plainly as

possible, Put suaviter in modo in the van, but don't forget to have fortiter in
re[394] in the rear.
My Budget was announced (March 23, 1867) for completion on the 30th.
Mr. James Smith wrote five letters, one before the completion, four after it;
the five contained 68 pages of quarto letter paper. Mr. J. S. had picked up a
clerical correspondent, with whom he was in the heat of battle.
"March 27.—Dear Sir. Very truly yours. Duty; for my own sake; just time
left to retrieve my errors; sends copy of letter to clergyman; new proof
never before thought of; merest tyro would laugh if I were to stifle it,
whether by rhodomontade or silent contempt; keep your temper. I shall be
convinced; and if world be right in supposing me incapable of a foul act, I
shall proclaim glorious discovery in the Athenæum.
"April 15.—Sir,... My dear Sir, Your sincere tutelary. Copy of another letter
to clergyman; discovery tested by logarithms; reasons such as none but a
knave or a sinner can resist. Let me advise you to take counsel before it is
too late! Keep your temper. Let not your pride get the better of your
discretion! Screw up your courage, my good friend, and resolve to show the
world that you are an honest man....
"April 20.—Sir ... Your very sincere and favorite tutelary. I have long
played the cur, snapping and snarling...; suddenly lost my power, and
became half-starved dog without spirit to bark; try if air cannot restore me;
calls himself the thistle in allusion to my other tutelary, the thorn; Would I
prefer his next work to be, 'A whip for the Mathematical Cur, Prof. De M.'
In some previous letter which I have mislaid, he told me his next would be
'a muzzle for the Mathematical Bull dog, Prof. De M.'
"April 23.—Sir. Very sincerely yours. More letters to clergyman; you may
as well knock your head against a stone wall to improve your intellect as
attempt to controvert my proofs. [I thought so too; and tried neither].
"May 6.—My dear Sir. Very sincerely yours. All to myself, and nothing to
note.
"July 2.—No more in this interval. All that precedes is a desperate attempt
to induce me to continue my descriptions: notoriety at any price."

I dare say the matter is finished: the record of so marked an instance of self-
delusion will be useful.

I append to the foregoing a letter from Dr. Whewell[395] to Mr. James
Smith. The Master of Trinity was conspicuous as a rough customer, an
intellectual bully, an overbearing disputant: the character was as well
established as that of Sam Johnson. But there was a marked difference. It
was said of Johnson that if his pistol missed fire, he would knock you down
with the butt end of it: but Whewell, in like case, always acknowledged the
miss, and loaded again or not, as the case might be. He reminded me of
Dennis Brulgruddery, who says to Dan, Pacify me with a good reason, and
you'll find me a dutiful master. I knew him from the time when he was my
teacher at Cambridge, more than forty years. As a teacher, he was anything
but dictatorial, and he was perfectly accessible to proposal of objections. He
came in contact with me in his slashing way twice in our after joint lives,
and on both occasions he acknowledged himself overcome, by that change
of manner, and apologetic mode of continuance, which I had seen him
employ towards others under like circumstances.
I had expressed my wish to have a thermometer of probability, with
impossibility at one end, as 2 and 2 make 5, and necessity at the other, as 2
and 2 make 4, and a graduated rise of examples between them. Down came
a blow: "What! put necessary and contingent propositions together! It's
absurd!" I pointed out that the two kinds of necessity are but such extremes
of probability as 0 and ∞ are of number, and illustrated by an urn with 1
white and n black balls, n increasing without limit. It was frankly seen, and
the point yielded; a large company was present.
Again, in a large party, after dinner, and politics being the subject, I was
proceeding, in discussion with Mr. Whewell, with "I think"...—"Ugh! you
think!" was the answer. I repeated my phrase, and gave as a reason the
words which Lord Grey[396] had used in the House of Lords the night before
(the celebrated advice to the Bishops to set their houses in order). He had
not heard of this, and his manner changed in an instant: he was the rational
discutient all the rest of the evening, having previously been nothing but a
disputant with all the distinctions strongly marked.

I have said that Whewell was gentle with his pupils; it was the same with all
who wanted teaching: it was only on an armed enemy that he drew his
weapon. The letter which he wrote to Mr. J. Smith is an instance: and as it
applies with perfect fidelity to the efforts of unreasoning above described, I
give it here. Mr. James Smith is skilfully exposed, and felt it; as is proved
by "putting the writer in the stocks."
"The Lodge, Cambridge, September 14th, 1862.
"Sir,—I have received your explanation of your proposition that the
circumference of the circle is to its diameter as 25 to 8. I am afraid I shall
disappoint you by saying that I see no force in your proof: and I should
hope that you will see that there is no force in it if you consider this: In the
whole course of the proof, though the word cycle occurs, there is no
property of the circle employed. You may do this: you may put the word
hexagon or dodecagon, or any other word describing a polygon in the place
of Circle in your proof, and the proof would be just as good as before. Does
not this satisfy you that you cannot have proved a property of that special
figure—a circle?
"Or you may do this: calculate the side of a polygon of 24 sides inscribed in
a circle. I think you are a Mathematician enough to do this. You will find
that if the radius of the circle be one, the side of this polygon is .264 etc.
Now, the arc which this side subtends is according to your proposition
3.125/12 = .2604, and therefore the chord is greater than its arc, which you
will allow is impossible.
"I shall be glad if these arguments satisfy you, and

"I am, Sir, your obedient Servant,

"W. Whewell."

AN M.P.'S ARITHMETIC.
In the debate of May, 1866, on Electoral Qualifications, a question arose
about arithmetical capability. Mr. Gladstone asked how many members of
the House could divide 1330l. 7s. 6d. by 2l. 13s. 8d. Six hundred and fifty-

eight, answered one member; the thing cannot be done, answered another.
There is an old paradox to which this relates: it arises out of the ignorance
of the distinction between abstract and concrete arithmetic. Magnitude may
be divided by magnitude; and the answer is number: how often does 12d.
contain 4d.; answer three times. Magnitude may be divided by number, and
the answer is magnitude: 12d. is divided in four equal parts, what is each
part? Answer three pence. The honorable objector, whose name I suppress,
trusting that he has mended his ways, gave the following utterance:
"With regard to the division sum, it was quite possible to divide by a sum,
but not by money. How could any one divide money by 2l. 16s. 8d.?
(Laughter.) The question might be asked, 'How many times 2s. will go into
1l.?' but that was not dividing by money; it was simply dividing 20 by 2. He
might be asked, 'How many times will 6s. 8d. go into a pound?' but it was
only required to divide 240 by 80. If the right hon. gentleman were to ask
the hon. member for Brighton (Professor Fawcett),[397] or any other
authority, he would receive the same answer—viz., that it was possible to
divide by a sum, but not by money. (Hear.)"

I shall leave all comment for the second edition, if I publish one.[398] I shall
be sure to have something to laugh at. Anything said from a respectable
quarter, or supposed to be said, is sure to find defenders. Sam Johnson, a
sound arithmetician, comparing himself, and what he alone had done in
three years, with forty French Academicians and their forty years, said it
proved that an Englishman is to a Frenchman as 40 × 40 to 3, or as 1600 to
3. Boswell, who was no great hand at arithmetic, made him say that an
Englishman is to a Frenchman as 3 to 1600. When I pointed this out, the
supposed Johnson was defended through thick and thin in Notes and
Queries.
I am now curious to see whether the following will find a palliator. It is
from "Tristram Shandy," book V. chapter 3. There are two curious idioms,
"for for" and "half in half"; but these have nothing to do with my point:
"A blessing which tied up my father's tongue, and a misfortune which set it
loose with a good grace, were pretty equal: sometimes, indeed, the
misfortune was the better of the two; for, for instance, where the pleasure of
harangue was as ten, and the pain of the misfortune but as five, my father

gained half in half; and consequently was as well again off as if it had never
befallen him."
This is a jolly confusion of ideas; and wants nothing but a defender to make
it perfect. A person who invests five with a return of ten, and one who loses
five with one hand and gains ten with the other, both leave off five richer
than they began, no doubt. The first gains "half in half," more properly "half
on half," that is, of the return, 10, the second 5 is gain upon the first 5
invested. "Half in half" is a queer way of saying cent. per cent. If the 5l.
invested be all the man had in the world, he comes out, after the gain, twice
as well off as he began, with reference to his whole fortune. But it is very
odd to say that balance of 5l. gain is twice as good as if nothing had
befallen, either loss or gain. A mathematician thinks 5 an infinite number of
times as great as 0. The whole confusion is not so apparent when money is
in question: for money is money whether gained or lost. But though
pleasure and pain stand to one another in the same algebraical relation as
money gained and lost, yet there is more than algebra can take account of in
the difference.

Next, Ri. Milward[399] (Richard, no doubt, but it cannot be proved) who
published Selden's[400] Table Talk, which he had collected while serving as
amanuensis, makes Selden say, "A subsidy was counted the fifth part of a
man's estate; and so fifty subsidies is five and forty times more than a man
is worth." For times read subsidies, which seems part of the confusion, and
there remains the making all the subsidies equal to the first, though the
whole of which they are to be the fifths is perpetually diminished.
Thirdly, there is the confusion of the great misomath of our own day, who
discovered two quantities which he avers to be identically the same, but the
greater the one the less the other. He had a truth in his mind, which his
notions of quantity were inadequate to clothe in language. This erroneous
phraseology has not found a defender; and I am almost inclined to say, with
Falstaff, The poor abuses of the time want countenance.

ERRONEOUS ARITHMETICAL NOTIONS.

"Shallow numerists," as Cocker[401] is made to call them, have long been at
work upon the question how to multiply money by money. It is, I have
observed, a very common way of amusing the tedium of a sea voyage: I
have had more than one bet referred to me. Because an oblong of five
inches by four inches contains 5 × 4 or 20 square inches, people say that
five inches multiplied by four inches is twenty square inches: and, thinking
that they have multiplied length by length, they stare when they are told that
money cannot be multiplied by money. One of my betters made it an
argument for the thing being impossible, that there is no square money:
what could I do but suggest that postage-stamps should be made legal
tender. Multiplication must be repetition: the repeating process must be
indicated by number of times. I once had difficulty in persuading another of
my betters that if you repeat five shillings as often as there are hairs in a
horse's tail, you do not multiply five shillings by a horsetail.[402]
I am very sorry to say that these wrong notions have found support—I think
they do so no longer—in the University of Cambridge. In 1856 or 1857, an
examiner was displaced by a vote of the Senate. The pretext was that he
was too severe an examiner: but it was well known that great dissatisfaction
had been expressed, far and wide through the Colleges, at an absurd
question which he had given. He actually proposed such a fraction as

6s. 3d.
.
17s. 4d.

As common sense gained a hearing very soon, there is no occasion to say
more. In 1858, it was proposed at a college examination, to divide 22557
days, 20 hours, 20 minutes, 48 seconds, by 57 minutes, 12 seconds, and also
to explain the fraction

32l. 18s. 8d.
.
62l. 12s. 9d.

All paradoxy, in matters of demonstration, arises out of muddle about first
principles. Who can say how much of it is to be laid at the door of the

University of Cambridge, for not taking care of the elements of arithmetical
thought?

ON LITERARY BARGAINS.
The phenomena of the two ends of society, when brought together, give
interesting comparisons: I mean the early beginnings of thought and
literature, and our own high and finished state, as we think it. There is one
very remarkable point. In the early day, the letter was matter of the closest
adherence, and implied meanings were not admitted.
The blessing of Isaac meant for Esau, went to false Jacob, in spite of the
imposition; and the writer of Genesis seems to intend to give the notion that
Isaac had no power to pronounce it null and void. And "Jacob's policy,
whereby he became rich"—as the chapter-heading puts it—in speckled and
spotted stock, is not considered as a violation of the agreement, which
contemplated natural proportions. In the story of Lycurgus the lawgiver is
held to have behaved fairly when he bound the Spartans to obey his laws
until he returned—intimating a short absence—he intending never to return.
And Vishnoo, when he asked the usurper for three steps of territory as a
dwarf, and then enlarged himself until he could bring heaven and earth
under the bargain, was thought clever, certainly, but quite fair.
There is nothing of this kind recognized in our day: so far good. But there is
a bad contrary: the age is apt, in interpretation, to upset the letter in favor of
the view—very often the after thought—of one side only. The case of John
Palmer,[403] the improver of the mail coach system, is smothered. He was to
have an office and a salary, and 2½ per cent for life on the increased
revenue of the Post-Office. His rights turned out so large, that Government
would not pay them. For misconduct, real or pretended, they turned him out
of his office: but his bargain as to the percentage had nothing to do with his
future conduct; it was payment for his plan. I know nothing, except from
the debates of 1808 in the two Houses: if any one can redeem the credit of
the nation, the field is open. When I was young, the old stagers spoke of this
transaction sparingly, and dismissed it speedily.

The government did not choose to remember what private persons must
remember, and are made to remember, if needful. When Dr. Lardner[404]
made his bargain with the publishers for the Cabinet Cyclopædia he
proposed that he, as editor, should have a certain sum for every hundred
sold above a certain number: the publishers, who did not think there was
any chance of reaching the turning sale of this stipulation, readily
consented. But it turned out that Dr. Lardner saw further than they: the
returns under this stipulation gave him a very handsome addition to his
other receipts. The publishers stared; but they paid. They had no idea of
standing out that the amount was too much for an editor; they knew that,
though the editor had a percentage, they had all the rest; and they would not
have felt aggrieved if he had received ten times as much. But governments,
which cannot be brought to book before a sworn jury, are ruled only by
public opinion. John Palmer's day was also the day of Thomas Fyshe
Palmer,[405] and the governments, in their prosecutions for sedition, knew
that these would have a reflex action upon the minds of all who wrote about
public affairs.

DECLARATION OF BELIEF
1864-65.—It often happens that persons combine to maintain and enforce
an opinion; but it is, in our state of society, a paradox to unite for the sole
purpose of blaming the opposite side. To invite educated men to do this, and
above all, men of learning or science, is the next paradoxical thing of all.
But this was done by a small combination in 1864. They got together and
drew up a declaration, to be signed by "students of the natural sciences,"
who were to express their "sincere regret that researches into scientific truth
are perverted by some in our own times into occasion for casting doubt
upon the truth and authenticity of the Holy Scriptures." In words of
ambiguous sophistry, they proceeded to request, in effect, that people would
be pleased to adopt the views of churches as to the complete inspiration of
all the canonical books. The great question whether the Word of God is in
the Bible, or whether the Word of God is all the Bible, was quietly taken for
granted in favor of the second view; to the end that men of science might be
induced to blame those who took the first view. The first public attention
was drawn to the subject by Sir John Herschel,[406] who in refusing to sign

the writ sent to him, administered a rebuke in the Athenæum, which would
have opened most eyes to see that the case was hopeless. The words of a
man whose suaviter in modo makes his fortiter in re[407] cut blocks with a
razor are worth preserving:
"I consider the act of calling upon me publicly to avow or disavow, to
approve or disapprove, in writing, any religious doctrine or statement,
however carefully or cautiously drawn up (in other words, to append my
name to a religious manifesto) to be an infringement of that social
forbearance which guards the freedom of religious opinion in this country
with especial sanctity.... I consider this movement simply mischievous,
having a direct tendency (by putting forward a new Shibboleth, a new
verbal test of religious partisanship) to add a fresh element of discord to the
already too discordant relations of the Christian world.... But no nicety of
wording, no artifice of human language, will suffice to discriminate the
hundredth part of the shades of meaning in which the most world-wide
differences of thought on such subjects may be involved; or prevent the
most gentle worded and apparently justifiable expression of regret, so
embodied, from grating on the feelings of thousands of estimable and well-
intentioned men with all the harshness of controversial hostility."

Other doses were administered by Sir J. Bowring,[408] Sir W. Rowan
Hamilton,[409] and myself. The signed declaration was promised for
Christmas, 1864: but nothing presentable was then ready; and it was near
Midsummer, 1865, before it was published. Persons often incautiously put
their names without seeing the character of a document, because they
coincide in its opinions. In this way, probably, fifteen respectable names
were procured before printing; and these, when committed, were hawked as
part of an application to "solicit the favor" of other signatures. It is likely
enough no one of the fifteen saw that the declaration was, not maintenance
of their own opinion, but regret (a civil word for blame) that others should
think differently.
When the list appeared, there were no fewer than 716 names! But analysis
showed that this roll was not a specimen of the mature science of the
country. The collection was very miscellaneous: 38 were designated as
"students of the College of Chemistry," meaning young men who attended
lectures in that college. But as all the Royal Society had been applied to, a

test results as follows. Of Fellows of the Royal Society, 600 in number, 62
gave their signatures; of writers in the Philosophical Transactions, 166 in
number, 19 gave their signatures. Roughly speaking, then, only one out of
ten could be got to express disapprobation of the free comparison of the
results of science with the statements of the canonical books. And I am
satisfied that many of these thought they were signing only a declaration of
difference of opinion, not of blame for that difference. The number of
persons is not small who, when it comes to signing printed documents,
would put their names to a declaration that the coffee-pot ought to be taken
down-stairs, meaning that the teapot ought to be brought up-stairs. And
many of them would defend it. Some would say that the two things are not
contradictory; which, with a snort or two of contempt, would be very
effective. Others would, in the candid and quiet tone, point out that it is all
one, because coffee is usually taken before tea, and it keeps the table clear
to send away the coffee-pot before the teapot is brought up.
The original signatures were decently interred in the Bodleian Library: and
the advocates of scattering indefinite blame for indefinite sins of opinion
among indefinite persons are, I understand, divided in opinion about the
time at which the next attempt shall be made upon men of scientific studies:
some are for the Greek Calends, and others for the Roman Olympiads. But,
with their usual love of indefiniteness, they have determined that the choice
shall be argued upon the basis that which comes first cannot be settled, and
is of no consequence.
I give the declaration entire, as a curiosity: and parallel with it I give a
substitute which was proposed in the Athenæum, as worthy to be signed
both by students of theology, and by students of science, especially in past
time. When a new attempt is made, it will be worth while to look at both:

Declaration. Proposed Substitute.
We, the undersigned Students We, the undersigned Students of
of the Natural Sciences, desire Theology and of Nature, desire to
to express our sincere regret, express our sincere regret, that
that researches into scientific common notions of religious truth
truth are perverted by some in are perverted by some in our own

our own times into occasion times into occasion for casting
for casting doubt upon the reproach upon the advocates of
Truth and Authenticity of the demonstrated or highly probable
Holy Scriptures. scientific theories.

We conceive that it is We conceive that it is impossible
impossible for the Word of for the Word of God, as correctly
God, as written in the book of read in the Book of Nature, and
nature, and God's Word the Word of God, as truly
written in Holy Scripture, to interpreted out of the Holy
contradict one another, Scripture, to contradict one
however much they may another, however much they may
appear to differ. appear to differ.

We are not forgetful that We are not forgetful that neither
Physical Science is not theological interpretation nor
complete, but is only in a physical knowledge is yet
condition of progress, and that complete, but that both are in a
at present our finite reason condition of progress; and that at
enables us only to see as present our finite reason enables
through a glass darkly, us only to see both one and the
other as through a glass darkly
[the writers of the original
declaration have distinctively
applied to physical science the
phrase by which St. Paul denotes
the imperfections of theological
vision, which they tacitly assume
to be quite perfect],

and we confidently believe, and we confidently believe, that a
that a time will come when the time will come when the two
two records will be seen to records will be seen to agree in
agree in every particular. We every particular. We cannot but
cannot but deplore that deplore that Religion should be
Natural Science should be looked upon with suspicion by

looked upon with suspicion by some and Science by others, of
many who do not make a the students of either who do not
study of it, merely on account make a study of the other, merely
of the unadvised manner in on account of the unadvised
which some are placing it in manner in which some are placing
opposition to Holy Writ. Religion in opposition to Science,
and some are placing Science in
opposition to Religion.

We believe that it is the duty We believe that it is the duty of
of every Scientific Student to every theological student to
investigate nature simply for investigate the Scripture, and of
the purpose of elucidating every scientific student to
truth, investigate Nature, simply for the
purpose of elucidating truth.

and that if he finds that some And if either should find that
of his results appear to be in some of his results appear to be in
contradiction to the Written contradiction, whether to
Word, or rather to his own Scripture or to Nature, or rather to
interpretations of it, which his own interpretation of one or
may be erroneous, he should the other, which may be
not presumptuously affirm erroneous, he should not affirm as
that his own conclusions must with certainty that his own
be right, and the statements of conclusion must be right, and the
Scripture wrong; other interpretation wrong:

rather, leave the two side by but should leave the two side by
side till it shall please God to side for further inquiry into both,
allow us to see the manner in until it shall please God to allow
which they may be reconciled; us to arrive at the manner in
which they may be reconciled.

and, instead of insisting upon In the mean while, instead of
the seeming differences insisting, and least of all with

between Science and the acrimony or injurious statements
Scriptures, it would be as well about others, upon the seeming
to rest in faith upon the points differences between Science and
in which they agree. the Scriptures, it would be a
thousand times better to rest in
faith as to our future state, in hope
as to our coming knowledge, and
in charity as to our present
differences.

The distinctness of the fallacies is creditable to the composers, and shows
that scientific habits tend to clearness, even to sophistry. Nowhere does it so
plainly stand out that the Written Word means the sense in which the
accuser takes it, while the sense of the other side is their interpretation. The
infallible church on one side, arrayed against heretical pravity on the other,
is seen in all subjects in which men differ. At school there were various
games in which one or another advantage was the right of those who first
called for it. In adult argument the same thing is often attempted: we often
hear—I cried Church first!
I end with the answer which I myself gave to the application: its revival
may possibly save me from a repetition of the like. If there be anything I
hate more than another it is the proposal to place any persons, especially
those who allow freedom to me, under any abridgment of their liberty to
think, to infer, and to publish. If they break the law, take the law; but do not
make the law: ἀγοραιοι ἀγονται ἐγκαλειτωσαν ἀλληλοις.[410] I would
rather be asked to take shares in an argyrosteretic company (with limited
liability) for breaking into houses by night on fork and spoon errands. I
should put aside this proposal with nothing but laughter. It was a joke
against Sam Rogers[411] that his appearance was very like that of a corpse.
The John Bull newspaper—suppose we now say Theodore Hook[412]—
averred that when he hailed a coach one night in St. Paul's Churchyard, the
jarvey said, "Ho! ho! my man; I'm not going to be taken in that way: go
back to your grave!" This is the answer I shall make for the future to any
relics of a former time who shall want to call me off the stand for their own
purposes. What obligation have I to admit that they belong to our world?

"SCRIPTURE AND SCIENCE.

"The Writ De Hæretico Commiserando.[413]
Nov. 14, 1864.
"This document was sent to me four days ago. It 'solicits the favor'—I
thought at first it was a grocer's supplication for tea and sugar patronage—
of my signature to expression of 'sincere regret' that some persons unnamed
—general warrants are illegal—differ from what I am supposed—by
persons whom it does not concern—to hold about Scripture and Science in
their real or alleged discrepancies.
"No such favor from me: for three reasons. First, I agree with Sir. J.
Herschel that the solicitation is an intrusion to be publicly repelled.
Secondly, I do not regret that others should differ from me, think what I
may: those others are as good as I, and as well able to think, and as much
entitled to their conclusions. Thirdly, even if I did regret, I should be
ashamed to put my name to bad chemistry made to do duty for good
reasoning. The declaration is an awkward attempt to saturate sophism with
truism; but the sophism is left largely in excess.
"I owe the inquisitors a grudge for taking down my conceit of myself. For
two months I have crowed in my own mind over my friend Sir J. Herschel,
fancying that the promoters instinctively knew better than to bring their
fallacies before a writer on logic. Ah! my dear Sir John! thought I, if you
had shown yourself to be well up in Barbara Celarent,[414] and had ever
and anon astonished the natives with the distinction between simpliciter and
secundum quid, no autograph-hunters would have baited a trap with non
sequitur[415] to catch your signature. What can I say now? I hide my
diminished head, diminished by the horns which I have been compelled to
draw in.
"Those who make personal solicitation for support to an opinion about
religion are bound to know their men. The king had a right to Brother
Neale's money, because Brother Neale offered it. Had he put his hand into
purse after purse by way of finding out all who were of Brother Neale's

mind, he would have been justly met by a rap on the knuckles whenever he
missed his mark.
"The kind of test before me is the utmost our time will allow of that
inquisition into opinion which has been the curse of Christianity ever since
the State took Providence under its protection. The writ de hæretico
commiserando is little more than the smell of the empty cask: and those
who issue it may represent the old woman with her

"O suavis anima, quale in te dicam bonum
Antehac fuisse; tales cum sint reliquiæ."[416]

It is no excuse that the illegitimate bantling is a very little one. Its parents
may think themselves hardly treated when they are called lineal successors
of Tony Fire-the-faggot: but, degenerate though they be, such is their
ancestry. Let every allowance be made for them: but their unholy fire must
be trodden out; so long as a spark is left, nothing but fuel is wanted to make
a blaze. If this cannot be done, let the flame be confined to theology, though
even there it burns with diminished vigor: and let charity, candor, sense, and
ridicule, be ready to play upon it whenever there is any chance of its
extending to literature and science.
"What would be the consequence if this test-signing absurdity were to
grow? Deep would call unto deep; counter-declaration would answer
declaration, each stronger than the one before. The moves would go on like
the dispute of two German students, of whom each is bound to a sharper
retort on a graduated scale, until at last comes dummer Junge![417]—and
then they must fight. There is a gentleman in the upper fifteen of the signers
of the writ—the hawking of whose names appears to me very bad taste—
whom I met in cordial cooperation for many a year at a scientific board. All
I knew about his religion was that he, as a clergyman, must in some sense
or other receive the 39 Articles:—all that he could know about mine was
that I was some kind of heretic, or so reputed. If we had come to signing
opposite manifestoes, turn-about, we might have found ourselves in the
lowest depths of party discussion at our very council-table. I trust the list of
subscribers to the declaration, when it comes to be published, will show that
the bulk of those who have really added to our knowledge have seen the
thing in its true light.

"The promoters—I say nothing about the subscribers—of the movement
will, I trust, not feel aggrieved at the course I have taken or the remarks I
have made. Walter Scott says that before we judge Napoleon by the
temptation to which he yielded, we ought to remember how much he may
have resisted: I invite them to apply this rule to myself; they can have no
idea of the feeling with which I contemplate all attempts to repress freedom
of inquiry, nor of the loathing with which I recoil from the proposal to be
art and part. They have asked me to give a public opinion upon a certain
point. It is true that they have had the kindness to tender both the opinion
they wish me to form, and the shape in which they would have it appear: I
will let them draw me out, but I will not let them take me in. If they will put
an asterisk to my name, and this letter to the asterisk, they are welcome to
my signature. As I do not expect them to relish this proposal, I will not
solicit the favor of its adoption. But they have given a right to think, for
they have asked me to think; to publish, for they have asked me to allow
them to publish; to blame them, for they have asked me to blame their
betters. Should they venture to find fault because my direction of
disapproval, publicly given, is half a revolution different from theirs, they
will be known as having presented a loaded document at the head of a
traveler in the highway of discussion, with—Your signature or your
silence!"

THE FLY-LEAF PARADOX.
The paradox being the proposition of something which runs counter to what
would generally be thought likely, may present itself in many ways. There
is a fly-leaf paradox, which puzzled me for many years, until I found a
probable solution. I frequently saw, in the blank leaves of old books,
learned books, Bibles of a time when a Bible was very costly, etc., the name
of an owner who, by the handwriting and spelling, must have been an
illiterate person or a child, followed by the date of the book itself.
Accordingly, this uneducated person or young child seemed to be the first
owner, which in many cases was not credible. Looking one day at a
Barker's[418] Bible of 1599, I saw an inscription in a child's writing, which
certainly belonged to a much later date. It was "Martha Taylor, her book,
giuen me by Granny Scott to keep for her sake." With this the usual verses,

followed by 1599, the date of the book. But it so chanced that the blank
page opposite the title, on which the above was written, was a verso of the
last leaf of a prayer book, which had been bound before the Bible; and on
the recto of this leaf was a colophon, with the date 1632. It struck me
immediately that uneducated persons and children, having seen dates
written under names, and not being quite up in chronology, did frequently
finish off with the date of the book, which stared them in the face.
Always write in your books. You may be a silly person—for though your
reading my book is rather a contrary presumption, yet it is not conclusive—
and your observations may be silly or irrelevant, but you cannot tell what
use they may be of long after you are gone where Budgeteers cease from
troubling.

I picked up the following book, printed by J. Franklin[419] at Boston, during
the period in which his younger brother Benjamin was his apprentice. And
as Benjamin was apprenticed very early, and is recorded as having learned
the mechanical art very rapidly, there is some presumption that part of it
may be his work, though he was but thirteen at the time. As this set of
editions of Hodder[420] (by Mose[421]) is not mentioned, to my knowledge, I
give the title in full:

"Hodder's Arithmetick: or that necessary art made most easy:
Being explained in a way familiar to the capacity of any that
desire to learn it in a little time. By James Hodder, Writing-
master. The Five and twentieth edition, revised, augmented, and
above a thousand faults amended, by Henry Mose, late servant
and successor to the author. Boston: printed by J. Franklin, for S.
Phillips, N. Buttolph, B. Elliot, D. Henchman, G. Phillips, J.
Elliot, and E. Negus, booksellers in Boston, and sold at their
shops. 1719."

The book is a very small octavo, the type and execution are creditable, the
woodcut at the beginning is clumsy. It is a perfect copy, page for page, of
the English editions of Mose's Hodder, of which the one called seventeenth
is of London, 1690. There is not a syllable to show that the edition above
described might not be of Boston in England. Presumptions, but not very
strong ones, might be derived from the name of Franklin, and from the

large number of booksellers who combined in the undertaking. It chanced,
however, that a former owner had made the following note in my copy:

"Wednessday, July ye 14, 1796, att ten in ye forenoon we saild
from Boston, came too twice, once in King Rode, and once in ye
Narrows. Saild by ye lighthouse in ye eveng."

No ordinary map would decide these points: so I had to apply to my friend
Sir Francis Beaufort,[422] and the charts at the Admiralty decided
immediately for Massachusetts.

PARADOXES OF ORTHOGRAPHY AND COMPUTATION.
The French are able paradoxers in their spelling of foreign names. The
Abbé Sabatier de Castres,[423] in 1772, gives an account of an imaginary
dialogue between Swif, Adisson, Otwai, and Bolingbrocke. I had hoped that
this was a thing of former days, like the literal roasting of heretics; but the
charity which hopeth all things must hope for disappointments. Looking at
a recent work on the history of the popes, I found referred to, in the matter
of Urban VIII[424] and Galileo, references to the works of two Englishmen,
the Rev. Win Worewel and the Rev. Raden Powen. [Wm. Whewell and
Baden Powell].[425]
I must not forget the "moderate computation" paradox. This is the way by
which large figures are usually obtained. Anything surprisingly great is got
by the "lowest computation," anything as surprisingly small by the "utmost
computation"; and these are the two great subdivisions of "moderate
computation." In this way we learn that 70,000 persons were executed in
one reign, and 150,000 persons burned for witchcraft in one century.
Sometimes this computation is very close. By a card before me it appears
that all the Christians, including those dispersed in heathen countries, those
of Great Britain and Ireland excepted, are 198,728,000 people, and pay their
clergy 8,852,000l. But 6,400,000 people pay the clergy of the Anglo-Irish
Establishment 8,896,000l.; and 14,600,000 of other denominations pay
1,024,000l. When I read moderate computations, I always think of Voltaire
and the "mémoires du fameux évêque de Chiapa, par lesquels il paraît qu'il

avait égorgé, ou brulé, ou noyé dix millions d'infidèles en Amérique pour
les convertir. Je crus que cet évêque exaggérait; mais quand on réduisait ces
sacrifices à cinq millions de victimes, cela serait encore admirable."[426]

CENTRIFUGAL FORCE.
My Budget has been arranged by authors. This is the only plan, for much of
the remark is personal: the peculiarities of the paradoxer are a large part of
the interest of the paradox. As to subject-matter, there are points which
stand strongly out; the quadrature of the circle, for instance. But there are
others which cannot be drawn out so as to be conspicuous in a review of
writers: as one instance, I may take the centrifugal force.
When I was about nine years old I was taken to hear a course of lectures,
given by an itinerant lecturer in a country town, to get as much as I could of
the second half of a good, sound, philosophical omniscience. The first half
(and sometimes more) comes by nature. To this end I smelt chemicals,
learned that they were different kinds of gin, saw young wags try to kiss the
girls under the excuse of what was called laughing gas—which I was sure
was not to blame for more than five per cent of the requisite assurance—
and so forth. This was all well so far as it went; but there was also the
excessive notion of creative power exhibited in the millions of miles of the
solar system, of which power I wondered they did not give a still grander
idea by expressing the distances in inches. But even this was nothing to the
ingenious contrivance of the centrifugal force. "You have heard what I have
said of the wonderful centripetal force, by which Divine Wisdom has
retained the planets in their orbits round the Sun. But, ladies and gentlemen,
it must be clear to you that if there were no other force in action, this
centripetal force would draw our earth and the other planets into the Sun,
and universal ruin would ensue. To prevent such a catastrophe, the same
wisdom has implanted a centrifugal force of the same amount, and directly
opposite," etc. I had never heard of Alfonso X of Castile,[427] but I ventured
to think that if Divine Wisdom had just let the planets alone it would come
to the same thing, with equal and opposite troubles saved. The paradoxers
deal largely in speculation conducted upon the above explanation. They
provide external agents for what they call the centrifugal force. Some make

the sun's rays keep the planets off, without a thought about what would
become of our poor eyes if the push of the light which falls on the earth
were a counterpoise to all its gravitation. The true explanation cannot be
given here, for want of room.

CAMBRIDGE POETS.
Sometimes a person who has a point to carry will assert a singular fact or
prediction for the sake of his point; and this paradox has almost obtained
the sole use of the name. Persons who have reputation to care for should
beware how they adopt this plan, which now and then eventuates a spanker,
as the American editor said. Lord Byron, in "English Bards, etc." (1809),
ridiculing Cambridge poetry, wrote as follows:

"But where fair Isis rolls her purer wave,
The partial muse delighted loves to lave;
On her green banks a greener wreath she wove,
To crown the bards that haunt her classic grove;
Where Richards[428] wakes a genuine poet's fires,
And modern Britons glory in their sires."[429]

There is some account of the Rev. Geo. Richards, Fellow of Oriel and Vicar
of Bampton, (M.A. in 1791) in the Living Authors by Watkins[430] and
Shoberl[431] (1816). In Rivers's Living Authors, of 1798, which is best fitted
for citation, as being published before Lord Byron wrote, he is spoken of in
high terms. The Aboriginal Britons was an Oxford (special) prize poem, of
1791. Charles Lamb mentions Richards as his school-fellow at Christ's
Hospital, "author of the Aboriginal Britons, the most spirited of the Oxford
Prize Poems: a pale, studious Grecian."

As I never heard of Richards as a poet,[432] I conclude that his fame is
defunct, except in what may prove to be a very ambiguous kind of
immortality, conferred by Lord Byron. The awkwardness of a case which
time has broken down is increased by the eulogist himself adding so
powerful a name to the list of Cambridge poets, that his college has placed
his statue in the library, more conspicuously than that of Newton in the

chapel; and this although the greatness of poetic fame had some serious
drawbacks in the moral character of some of his writings. And it will be
found on inquiry that Byron, to get his instance against Cambridge, had to
go back eighteen years, passing over seven intermediate productions, of
which he had either never heard, or which he would not cite as waking a
genuine poet's fires.
The conclusion seems to be that the Aboriginal Britons is a remarkable
youthful production, not equalled by subsequent efforts.
To enhance the position in which the satirist placed himself, two things
should be remembered. First, the glowing and justifiable terms in which
Byron had spoken,—a hundred and odd lines before he found it convenient
to say no Cambridge poet could compare with Richards,—of a Cambridge
poet who died only three years before Byron wrote, and produced greatly
admired works while actually studying in the University. The fame of Kirke
White[433] still lives; and future literary critics may perhaps compare his
writings and those of Richards, simply by reason of the curious relation in
which they are here placed alongside of each other. And it is much to
Byron's credit that, in speaking of the deceased Cambridge poet, he forgot
his own argument and its exigencies, and proved himself only a paradoxer
pro re nata.
Secondly, Byron was very unfortunate in another passage of the same
poem:

"What varied wonders tempt us as they pass!
The cow-pox, tractors, galvanism, and gas.
In turns appear, to make the vulgar stare,
Till the swoln bubble bursts—and all is air!"

Three of the bubbles have burst to mighty ends. The metallic tractors are
disused; but the force which, if anything, they put in action, is at this day,
under the name of mesmerism, used, prohibited, respected, scorned,
assailed, defended, asserted, denied, declared utterly obscure, and
universally known. It was hard lines to select for candidates for oblivion not
one of whom got in. I shall myself, I am assured, be some day cited for
laughing at the great discovery of ——: the blank is left for my reader to fill
up in his own way; but I think I shall not be so unlucky in four different
ways.

FALSIFIED PREDICTION.
The narration before the fact, as prophecy has been called, sometimes quite
as true as the narration after the fact, is very ridiculous when it is wrong.
Why, the pre-narrator could not know; the post-narrator might have known.
A good collection of unlucky predictions might be made: I hardly know one
so fit to go with Byron's as that of the Rev. Daniel Rivers, already quoted,
about Johnson's biographers. Peter Pindar[434] may be excused, as personal
satire was his object, for addressing Boswell and Mrs. Piozzi[435] as
follows:

"Instead of adding splendor to his name,
Your books are downright gibbets to his fame;
You never with posterity can thrive,
'Tis by the Rambler's death alone you live."

But Rivers, in prose narrative, was not so excusable. He says:
"As admirers of the learning and moral excellence of their hero, we glow at
almost every page with indignation that his weaknesses and his failings
should be disclosed to public view.... Johnson, after the luster he had

reflected on the name of Thrale ... was to have his memory tortured and
abused by her detested itch for scribbling. More injury, we will venture to
affirm, has been done to the fame of Johnson by this Lady and her late
biographical helpmate, than his most avowed enemies have been able to
effect: and if his character becomes unpopular with some of his successors,
it is to those gossiping friends he is indebted for the favor."
Poor dear old Sam! the best known dead man alive! clever, good-hearted,
logical, ugly bear! Where would he have been if it had not been for Boswell
and Thrale, and their imitators? What would biography have been if
Boswell had not shown how to write a life?
Rivers is to be commended for not throwing a single Stone at Mrs. Thrale's
second marriage. This poor lady begins to receive a little justice. The
literary world seems to have found out that a blue-stocking dame who keeps
open house for a set among them has a right, if it so please her, to marry
again without taking measures to carry on the cake-shop. I was before my
age in this respect: as a boy-reader of Boswell, and a few other things that
fell in my way, I came to a clearness that the conduct of society towards
Mrs. Piozzi was blackguard. She wanted nothing but what was in that day a
woman's only efficient protection, a male relation with a brace of pistols,
and a competent notion of using them.

BYRON AND WORDSWORTH.
Byron's mistake about Hallam in the Pindar story may be worth placing
among absurdities. For elucidation, suppose that some poet were now to
speak—

"Of man's first disobedience, and the fruit
Eve gave to Adam in his birthday suit—"

and some critic were to call it nonsense, would that critic be laughing at
Milton? Payne Knight,[436] in his Taste, translated part of Gray's Bard into
Greek. Some of his lines are

θερμὰ δ' ὁ τὲγγων δάκρυα στοναχαῖς

οὖλον μέλος φοβερᾷ
ηἔιδε φωνᾷ.

Literally thus:

"Wetting warm tears with groans,
Continuous chant with fearful
Voice he sang."

On which Hallam remarks: "The twelfth line [our first] is nonsense." And
so it is, a poet can no more wet his tears with his groans than wet his ale
with his whistle. Now this first line is from Pindar, but is only part of the
sense; in full it is:

θερμὰ δὲ τέγγων δάκρυα στοναχαῖς
ὅρθιον φώνασε.

Pindar's τέγγων must be Englished by shedding, and he stands alone in this
use. He says, "shedding warm tears, he cried out loud, with groans." Byron
speaks of

"Classic Hallam, much renowned for Greek:"

and represents him as criticising the Greek of all Payne's lines, and not
discovering that "the lines" were Pindar's until after publication. Byron was
too much of a scholar to make this blunder himself: he either accepted the
facts from report, or else took satirical licence. And why not? If you want to
laugh at a person, and he will not give occasion, whose fault is it that you
are obliged to make it? Hallam did criticise some of Payne Knight's Greek;
but with the caution of his character, he remarked that possibly some of
these queer phrases might be "critic-traps" justified by some one use of
some one author. I remember well having a Latin essay to write at
Cambridge, in which I took care to insert a few monstrous and unusual
idioms from Cicero: a person with a Nizolius,[437] and without scruples may
get scores of them. So when my tutor raised his voice against these oddities,
I was up to him, for I came down upon him with Cicero, chapter and verse,
and got round him. And so my own solecisms, many of them, passed
unchallenged.

Byron had more good in his nature than he was fond of letting out: whether
he was a soured misanthrope, or whether his vein lay that way in poetry,
and he felt it necessary to fit his demeanor to it, are matters far beyond me.
Mr. Crabb Robinson[438] told me the following story more than once. He
was at Charles Lamb's chambers in the Temple when Wordsworth came in,
with the new Edinburgh Review in his hand, and fume on his countenance.
"These reviewers," said he, "put me out of patience! Here is a young man—
they say he is a lord—who has written a volume of poetry; and these
fellows, just because he is a lord, set upon him, laugh at him, and sneer at
his writing. The young man will do something, if he goes on as he has
begun. But these reviewers seem to think that nobody may write poetry,
unless he lives in a garret." Crabb Robinson told this long after to Lady
Byron, who said, "Ah! if Byron had known that, he would never have
attacked Wordsworth. He went one day to meet Wordsworth at dinner;
when he came home I said, 'Well, how did the young poet get on with the
old one?' 'Why, to tell you the truth,' said he, 'I had but one feeling from the
beginning of the visit to the end, and that was—reverence!'" Lady Byron
told my wife that her husband had a very great respect for Wordsworth. I
suppose he would have said—as the Archangel said to his Satan—"Our
difference is po[li = e]tical."
I suspect that Fielding would, if all were known, be ranked among the
unlucky railers at supposed paradox. In his Miscellanies (1742, 8vo) he
wrote a satire on the Chrysippus or Guinea, an animal which multiplies
itself by division, like the polypus. This he supposes to have been drawn up
by Petrus Gualterus, meaning the famous usurer, Peter Walter. He calls it a
paper "proper to be read before the R——l Society": and next year, 1743, a
quarto reprint was made to resemble a paper in the Philosophical
Transactions. So far as I can make out, one object is ridicule of what the
zoologists said about the polypus: a reprint in the form of the Transactions
was certainly satire on the Society, not on Peter Walter and his knack of
multiplying guineas.
Old poets have recognized the quadrature of the circle as a well-known
difficulty. Dante compares himself, when bewildered, to a geometer who
cannot find the principle on which the circle is to be measured:

"Quale è 'l geometra che tutto s' affige

Per misurar lo cerchio, e non ritruova,
Pensando qual principio ond' egli indige."[439]

And Quarles[440] speaks as follows of the summum bonum:

"Or is't a tart idea, to procure
An edge, and keep the practic soul in ure,
Like that dear chymic dust, or puzzling quadrature?"

The poetic notion of the quadrature must not be forgotten. Aristophanes, in
the Birds, introduces a geometer who announces his intention to make a
square circle. Pope, in the Dunciad, delivers himself as follows, with a
Greek pronunciation rather strange in a translator of Homer. Probably Pope
recognized, as a general rule, the very common practice of throwing back
the accent in defiance of quantity, seen in o´rator, au´ditor, se´nator, ca
´tenary, etc.

"Mad Mathesis alone was unconfined,
Too mad for mere material chains to bind,—
Now to pure space lifts her ecstatic stare,
Now, running round the circle, finds it square."

The author's note explains that this "regards the wild and fruitless attempts
of squaring the circle." The poetic idea seems to be that the geometers try to
make a square circle. Disraeli quotes it as "finds its square," but the
originals do not support this reading.

DE BECOURT.
I have come in the way of a work, entitled The Grave of Human
Philosophies (1827), translated from the French of R. de Bécourt[441] by A.
Dalmas. It supports, but I suspect not very accurately, the views of the old
Hindu books. That the sun is only 450 miles from us, and only 40 miles in
diameter, may be passed over; my affair is with the state of mind into which
persons of M. Bécourt's temperament are brought by a fancy. He fully
grants, as certain, four millions of years as the duration of the Hindu race,