A BUDGET OF PARADOXES
BY
AUGUSTUS DE MORGAN,
F.R.A.S. AND C.P.S. OF TRINITY COLLEGE, CAMBRIDGE.
REPRINTED. WITH THE AUTHOR'S ADDITIONS. FROM THE ATHBN2ECM
SECOND EDITION
EDITED BY
DAVID EUGENE SMITH.
"UT AGENDO SURGAMCS ARGUENDO GUSTAMUS."
-PTOCHODOKIARCHUS ANAGRAMMATISTES.
VOLUME II.
THE OPEN COURT PUBLISHING CO.
CHICAGO LONDON
1915
AUTHORIZED EDITION
COPYRIGHT IN GREAT BRITAIN UNDER THE ACT OF IpII
AND COPYRIGHT IN THE UNITED STATES BY
THE OPEN COURT PUBLISHING COMPANY
1915
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 some-
what which went by more names than one, might be per-
sonal, intelligent, and superintendent. In the works of La-
place, 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 So-
ciety 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 "Systeme
du Monde" to the First Consul, or Emperor. Napoleon,
whom some wags had told that this book contained no men-
tion of the name of God, and who was fond of putting em-
barrassing 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
1 See Vol. I, page 255, note 6.
33?85-i
2 A BUDGET OF PARADOXES.
bluntly, "J e n'avais pas besoin de cette hypothese-la." 2 Na-
poleon, greatly amused, told this reply to Lagrange, who
exclaimed, "Ah! c'est une belle hypothese; c.a 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."* This looks like a parody on New-
ton's pebbles: 5 the following is the true account; it conies
to me through one remove from Poisson. 6 After the pub-
lication (in 1825) of the fifth volume of the Mecanique
Celeste, Laplace became gradually weaker, and with it mus-
ing and abstracted. He thought much on the great prob-
lems of existence, and often muttered to himself, Qu'est ce
que c'est que tout celal 7 After many alternations, he ap-
peared 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 a vous
annoncer: on a rec.u au Bureau des Longitudes une lettre
d'Allemagne annongant que M. Bessel a verifie par 1'obser-
vation vos decouvertes theoriques sur les satellites de Jupi-
ter." 8 Laplace opened his eyes and answered with deep
*"I have no need for this hypothesis."
8 "Ah, it is a beautiful hypothesis ; it explains many things."
'"What we know is very slight; what we don't know is im-
mense."
"Brewster relates (Life of Sir Isaac Newton, Vol. II, p. 407)
that, a short time before his death, Newton remarked: "I do not
know what I may appear to the world, but to myself I seem to have
been only like a boy playing on the seashore, and diverting myself
in now and then finding a smoother pebble or a prettier shell than
ordinary, whilst the great ocean of truth lay all undiscovered be-
fore me."
See Vol. I, p. 292, note 1.
7 "What is all that!"
*"I have some good news to tell you: at the Bureau of Longi-
tudes they have just received a letter from Germany announcing that
M. Bessel has verified by observation your theoretical discoveries on
the satellites of Jupiter."
ON SOME PHILOSOPHICAL ATHEISTS. 3
gravity, "L'homme ne poursuit que des chimeres." 9 He
never spoke again. His death took place March 5, 1827.
The language used by the two great geometers illus-
trates 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 straight-
forward. The following story is told by Thiebault, 11 in
his Souvenirs de vingt ans de sejour a Berlin, published in
his old age, about 1804. This volume was fully received as
trustworthy ; and Marshall Mollendorff 13 told the Due de
Bassano 14 in 1807 that it was the most veracious of books
written by the most honest of men. Thiebault says that he
has no personal knowledge of the truth of the story, but
'"Man follows only phantoms."
19 See Vol. I, page, 382, note 13.
"Dieudonne Thiebault (1733-1807) was a Jesuit in his early
life, but he left the order and took up the study of law. In 1765 he
went to Prussia and became a favorite of Frederick the Great. He
returned to France in 1785 and became head of the Lycee at Ver-
sailles.
Memories of Twenty Years of Residence in Berlin. There
was a second French and an English edition in 1805.
"Richard Joachim Heinrich von Mollendorff (1724-1816) began
his career as a page of Frederick the Great (1740) and became field
marshal (1793) and commander of the Prussian army on the Rhine
(1794).
14 Hugiies Bernard Maret (1763-1839) was not Due de Bassano
in 1807, this title not being conferred upon him until 1809. He was
ambassador to England in 1792 and to Naples in 1793. Napoleon
made him head of the cabinet and his special confidant. The Bour-
bons exiled him in 1816.
4 A BUDGET OF PARADOXES.
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 + b n )/n = x, done Dieu existe ; repondez!
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. 1 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.
"Denis Diderot (1713-1784), whose Lettre sur les aveugles
(1749) introduced him to the world as a philosopher, and whose
work on the Encyclopedie is so well known.
""Sir, (a-f fc n )/n = jr, whence God exists; answer!"
1 This was one James Laurie of Musselburgh.
ROTATION OF THE MOON. D
A writer on astronomy said of Mr. Jellinger Symons, 2 "Of
course he convinced no one who knew anything of the
subject." This "ungenerous slur" on the speculator's mem-
ory appears to have been keenly felt; but its truth is ad-
mitted. 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 pres-
byter-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 Phari-
sees 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 ab-
surd 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, in-
geniously astronomizing upon ignorant geometry and false
logic, and comparing to blockheads those who expose his
nonsense. Their comparison is as foolish as supposing
'Jelinger Cookson Symons (1809-1860) was an office-holder with
a decided leaning towards the improvement of education and social
conditions. He wrote A Plea for Schools (1847), The Industrial
Capacities of South Wales (1855), and Lunar Motion (1856), to
which last work the critic probably refers.
6 A BUDGET OF PARADOXES.
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 propa-
gated 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 learn-
ing: 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 sub-
stance is whole again in a moment.
Miracles versus Nature: being an application of certain propo-
sitions in the theory of chances to the Christian miracles. By
Protimalethes. 3 Cambridge, 1847, 8vo.
The theory, as may be supposed, is carried further than
most students of the subject would hold defensible.
'"Protimalethes" followed this by another work along the same
line the following year, The Independence of the Testimony of St.
Matthew and St. John tested and vindicated by the theory of chances.
ROTATION OF THE MOON. 7
An astronomical Lecture. By the Rev. R. Wilson. 4 Greenock,
1847, 12mo.
Against the moon's rotation on her axis.
[Handed about in the streets in 1847: I quote the whole:] Im-
portant discovery in astronomy, communicated to the Astron-
omer Royal, December 21st, 1846. That the Sun revolve round
the Planets in 25748V 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, 5 of Shrewsbury, published some re-
marks tending to impeach the fact that Neptune, the planet
found by Galle, 6 really was the planet which Le Verrier
and Adams 7 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. Lever rier's
Exposition." Several persons, when the remarkable dis-
covery was made, contended that the planet actually dis-
covered was an intruder; and the future histories of the
discovery must contain some account of this little after-
piece. 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
4 Wilson had already taken up the lance against science in his
Strictures on Geology and Astronomy, in reference to a supposed
want of harmony between these sciences and some parts of Divine
Revelation, Glasgow, 1843. He had also ventured upon poetry in his
Pleasures of Piety, Glasgow, 1837.
8 Mrs. Borron was Elizabeth Willesford Mills before her mar-
riage. She made an attempt at literature in her Sibyfs Leaves,
London (printed at Devonport), 1826.
9 See Vol. I, page 386, note 10.
7 See Vol. I, page 43, notes 7 and 8.
g A BUDGET OF PARADOXES.
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 Daedalus Britannicus. Lon-
don, 1847, 8vo.
In 1842-43 a Mr. Henson 1 had proposed what he called
an aeronaut steam-engine, and a Bill was brought in to in-
corporate an "Aerial Transit Company." The present plan
is altogether different, the moving power being the explo-
sion 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 difficul-
ties will at last be overcome. Darwin, 2 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, 3 when he spoke of dragging the slow barge :
it is only very recently that the steam-tug has been em-
ployed on the canals. The car was to be driven, not drawn,
and on the common roads. Perhaps, the flying chariot will
1 His flying machine, designed in 1843, was one of the earliest
attempts at aviation on any extensive scale.
'Erasmus Darwin (1731-1802) was the grandfather of Charles
Darwin. The work here mentioned had great influence, being trans-
lated into French, Portuguese, and Italian. Canning parodied it in
his Loves of the Triangles
8 See Vol. I, page 147, note 1.
THE SECRET OF THE UNIVERSE DIVULGED.
be something of a character which we cannot imagine,
even with the two prophecies and their fulfilments to help
us. 4
THE SECRET OF THE UNIVERSE DIVULGED.
A book for the public. New Discovery. The causes of the cir-
culation 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 perjudice 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 1 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 Lord-
ship for introducing me to Mr. ; he has convinced me
4 The notes on this page were written on the day of the funeral of
Wilbur Wright, June 1, 1912, the man who realized all of these
prophecies, and then died a victim of municipal crime, of typhoid
fever.
1 John Charles, third Earl Spencer (1782-1845), to whose efforts
the Reform Bill was greatly indebted for its final success.
10 A BUDGET OF PARADOXES.
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
THE TRISECTION AND QUADRATURE AGAIN. 11
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) .*
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," 2 and "Dangers along a coast
by correcting (as it is called) a ship's reckoning by bear-
ings 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 circum-
scribed square: proved on an assumption which it is pur-
posed to explain in a longer essay. 3 The author, as Q. E. D.,
was in controversy with the Athenceum journal, and criti-
cised a correspondent, D., who wrote against a certain class
of discoverers. He believed the common theories of hydro-
statics 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 Athenceum published but without some Italics,
for which the editor was sharply reproved, as a sufficient
1 This was published in London in 1851 instead of 1848.
* This appeared in 1846.
"This was done in The Circle Squared, published at Brighton in
1865.
12 A BUDGET OF PARADOXES.
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.*
This is the almanac of a sect of Christians who keep
the Jewish Sabbath, having a chapel at Mill Yard, Good-
man'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 geometri-
cally solved. By W. Upton, B. A. 6 Bath (circa 1849). 8vo.
The author published two tracts under this title, con-
taining 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 pro-
duction. 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
It first appeared in 1847, under the title, The Scriptural Calen-
dar and Chronological Reformer, 1848. Including a review of tracts
by Dr. iVardlaw and others on the Sabbath question. By W. H.
Black. The one above mentioned, for 1849, was printed in 1848, and
was also by Black (1808-1872). He was pastor of the Seventh Day
Baptists and was interested in archeology and in books. He cata-
logued the manuscripts of the Ashmolean Museum at Oxford.
' William Upton, a Trinity College man, Dublin. He also wrote
Upton's Physioglyphics, London, 1844 ; Pars prima. Geometria vindl-
cata; antiquorumque Problematum, ad hoc tempus desperatorum,
Trisectionis Anguli, Circulique Quadraturae, Solutio, per Eucliden
effecta, London (printed at Southampton), 1847; The Uptonian
section, London, 1866; and The Circle Squared, London,
THE TRISECTION AND QUADRATURE AGAIN. 13
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 dupli-
cation of the cube.
The trisector of an angle, if he demand attention from
any mathematician, is bound to produce, from his construc-
tion, an expression for the sine or cosine of the third part
of any angle, in terms of the sine or cosine of the angle it-
self, 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 pro-
duce 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 pre-
sents 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 con-
spiracy 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:
which is certainly false. 6
* For example, if & = 90 we should have 3 cos 30 = 1 -|-
V4 sin* 90, or 3.^V3 = 1 + V3, or
14 A BUDGET OF PARADOXES.
In 1852 I examined a terrific construction, at the request
of the late Dr. Wallich, 7 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, 6 being any angle, the cosine
of its third part is
sin 30. cos (SO/2) + sin 2 sin (SO/2)
divided by the square root of
sin 2 30.cos 2 (50/2)+sin 4 + sin30.sin50.sin 2 0.
This is from my rough notes, and I believe it is correct. 8 It
is so nearly true, unless the angle be very obtuse, that com-
mon 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 con-
tent.
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
'Nathaniel Wallich (1786-1854) was surgeon at the Danish
settlement at Serampore when the East India Company took over the
control in 1807. He entered the British medical service and was
invalided to England in 1828. His Plantae Asiaticae Rariores (3
vpls., London, 1830-1832) was recognized as a standard. He became
vice-president of the Linnean Society, F. R. S., and fellow of the
Royal Asiatic Society.
' But if = 90 this asserts that
sin 270 . cos 225 + sin90 . sin 225
cos 30 = ,
Vsm a 270 .cos 2 225 + sin* 90 -f- sin 270" . sin 450 U . sin a 90
or that
-l(
VI. '/S-f 1 1.1.1
so that De Morgan must have made some error in copying.
THE TRISECTION AND QUADRATURE AGAIN. 15
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 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 trouble-
some 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
16 A BUDGET OF PARADOXES.
of Bonnycastle 9 into Turkish. 10 This Englishman was
Richard Baily, brother of Francis Baily 11 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 curiosi-
ties; 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 man 8 merit & ability aught to be
appreciated and valued In proportion to its worth & utility
"In whatever State or Circumstances they may for-
tunately 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
9 John Bonnycastle (died in 1821) was professor of mathematics
at Woolwich. His edition of Bossut's History of Mathematics
(1803), and his works on elementary mathematics were well known.
19 The bibliographies give Husain Rifki as the translator, a prac-
tical geometry as the work, and 1802 as the date.
u See Vol. I, page 309, note 2.
THE TRISECTION AND QUADRATURE AGAIN. 17
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 knowl-
edge 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
18 A BUDGET OF PARADOXES.
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/ 12 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 at-
tempted this (the quadrature of the circle) for your mathe-
matical 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 acknowl-
edge 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
u Probably in The Improvement of the Mind which Isaac Watts
(1674-1748) published in 1741. His Horae Lyricae appeared in 1706,
and the Hymns, by which he is still well known, in 1707.
THE MOON'S ROTATION. 19
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 / 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 re-
ward offered by the government of this country for the dis-
covery of the quadrature of the circle.' I beg to inform
you that there was but that it having been deemed an im-
possibility the government has withdrawn it. I do this
upon no less an authority than the Marquis of Northamp-
ton. 18
"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 Rota-
tion and Revolution, owing to the double meaning improperly
u Spencer Joshua Alwyne Compton, second Marquis of North-
ampton (1790-1851), was a poet, a scientist, and a statesman. He
was president of the Royal Society from 1838 to 1849.
20 A BUDGET OF PARADOXES.
attributed to each of the words. (No date nor place, but by
Mr. Perigal, 1 I have no doubt, and containing letters of 1849
and 1850.)
The moon controversy. Facts v. Definitions. By H. P., Jua
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 Cyclopedia: 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; 2 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 3 and an anonymous oppo-
nent ; and I think there have been others.
1 Besides the writings here mentioned Perigal published a work
on Geometric Maps (London, 1853), and Graphic Demonstrations of
Geometric Problems (1891).
3 See Vol. II, page 5, note 2.
"James Ferguson (1710-1776) was a portrait painter, an astron-
omer, and a popular writer and lecturer on various subjects.
THE MOON'S ROTATION. 21
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 doc-
trines 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 proof less ! 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 per-
son who can give and a person who can receive. I feel in-
spired 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 ; accord-
ingly, 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
22 A BUDGET OF PARADOXES.
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 sev-
erally appropriated by parties. Whig and Tory are unob-
jectionable names: the first which occurs in English ballad
as well as in Scotland is sour milk j 1 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 2 ) 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 dis-
puted it, as they would have done in later times if they had
had fair play. The Jews of our day, I see by their news-
papers, speak of Jesus Christ as the Rabbi Joshua. But the
*In the old ballad of King Alfred and the Shepherd, when the
latter is tempting the disguised king into his service, he says :
"Of whig and whey we have good store,
And keep good pease-straw fire."
Whig is then a preparation of milk. But another commonly cited
derivation ^ay be suspected from the word whiggamor being used
before whig, as applied to the political party; whig may be a con-
traction. Perhaps both derivations conspired : the word whiggamor,
said to be a word of command to the horses, might contract into
whig, and the contraction might be welcomed for its own native
meaning. A. De M.
' This was p. 147 in the first edition.
ON THE NAMES OF RELIGIOUS BODIES. 23
heathens, who knew little or nothing about the Jewish hope,
would naturally apply the term Christians to the only fol-
lowers 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, 3
a freakish arguer, or, to put it in the way of an old writer,
lectorem ne multiloquii tadio fastidiat, Punicis quibusdam
argutiis re ere are solet* 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, 5 in a work (first published in 1801 or 1802) which
I suppose still circulates, "The End of Religious Con-
troversy" : a startling title which, so far as its truth is con-
cerned, 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 Protes-
tants to the other marks of the Church, if they are capable
of keeping them shut to this? Every time they address the
'St. Augustine (354-430) was bishop of Hippo. His Confes-
siones, in 13 books, was written in 397, and his De Civitate Dei in
426.
* "He was wont to indulge in certain Punic subtleties lest he
should weary the reader by much speaking."
John Milner (1751-1826), bishop of Castabala, a well-known
antiquarian.
24 A BUDGET OF PARADOXES.
God of Truth, either in solemn worship or in private de-
votion [stretch of rhetoric], they are forced, each of them,
to repeat: / 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 s'elf-
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 writ-
ten, 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 emitter 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 9 is not assur-
tt 'It will be said that when the 'final happiness is spoken of in
sure and certain hope," it is the Resurrection, generally; but when
afterwards application is made to the individual, simple "hope" is all
that is predicated which merely means "wish?" I know it: but
just before the general declaration, it is declared that it has pleased
God of his great mercy to take unto Himself, the soul of our dear
brother: and between the "hopes" hearty thanks are given that it
has pleased God to deliver our dear brother out of the miseries of
ON THE NAMES OF RELIGIOUS BODIES. 25
ance." 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 T
(lib. i. c. 12, de nomine S 'acre? Ecclesice, p. 87 of the Venice
this wicked world, with an additional prayer that the number of the
elect may shortly be accomplished. All which means, that our dear
brother is declared to be taken to God, to be in a place not so mis-
erable as this world a description which excludes the "wicked
place" and to be of the elect. Yes, but it will be said again ! do
you not know that when this Liturgy was framed, all who were not
in the road to Heaven were excomunicated, and could not have the
burial service read over them. Supposing the fact to have been true
in old time, which is a very spicy supposition, how does that excuse
the present practice? Have you a right always to say what you
believe cannot always be true, because you think it was once always
true? Yes, but, choose whom you please, you cannot be certain He
is not gone to Heaven. True, and choose which Bishop you please,
you cannot be demonstratively certain, he is not a concealed unbe-
liever : may I therefore say of the whole bench, singulatim et seria-
tim, that they are unbelievers ? No ! No ! The voice of common
sense, of which common logic is a part, is slowly opening the eyes
of the multitude to the unprincipled reasoning of theologians. Re-
member 1819. What chance had Parliamentary Reform when the
House of Commons thanked the Manchester sabre-men? If you do
not reform your Liturgy, it will be reformed for you, and sooner
than you think! The dishonest interpretations, by defence of which
even the minds of children are corrupted, and which throw their
shoots into literature and commerce, will be sent to the place whence
they came: and over the door of the established organization for
teaching religion will be posted the following notice:
"Shift and Subterfuge, Shuffle and Dodge,
No longer here allowed to lodge !"
All this ought to be written by some one who belongs to the Estab-
lishment: in him, it would be quite prudent and proper; in me, it is
kind and charitable. A. De M.
T But few do have access to it, for the work is not at all common,
and this Piscator is rarely mentioned.
26 A BUDGET OF PARADOXES.
folio of 1537). I am told that there is a Rituale in the In-
dex 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. 8
It amuses me to give, at a great distance of time, a small
Rowland for a small Oliver, which I received, de par
I'Eglise, 10 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 ety-
mological meaning, and applied to those who give the higher
and final authority to the declaration ex cathedra^ of the
Pope. See Dr. Wiseman's 12 article, Catholic Church, in the
Penny Cyclopaedia.
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
8 This derivation has been omitted. S. E. De M.
9 A blow for a blow. Roland and Oliver were two of the pala-
dins of Charlemagne whose exploits were so alike that each was
constantly receiving credit for what the other did. Finally they met
and fought for five days on an island in the Rhine, but even at the
end of that period it was merely a drawn battle.
10 "In the name of the church."
11 "From the chair," officially.
"Nicholas Patrick Stephen Wiseman (1802-1865), whose ele-
vation to the archbishopric of Westminster and the cardinalate
(1850) led to the act prohibiting Roman Catholics from assuming
episcopal titles in England, a law that was never enforced.
ON THE NAMES OF RELIGIOUS BODIES. 27
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 re-
cords 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 oc-
curs 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 ex-
clusiveness, 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 ad-
herents 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 mathe-
28 A BUDGET OF PARADOXES.
matics 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, 13 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 14 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.
"He was born in 1812 and was converted to Catholicism in
1839. He founded the Tablet in London in 1840, removing its office
to Dublin in 1849. He became M. P. in 1852, and at the time of his
death (1855) he was preparing a memorial to the Pope asking him
to annul the proclamation of an Irish bishop prohibiting his priests
from taking part in politics.
"John Guillim (1565-1621) was the first to systematize and
illustrate the whole science of heraldry. He published A display of
Heraldrie : manifesting a more easie accesse to the knowledge thereof
in 1610.
ON THE NAMES OF RELIGIOUS BODIES. 29
The mention of Dr. Wiseman reminds me of another
word, appropriated by Christians to themselves : fides; 1 * the
Roman faith is fides, and nothing else; and the ad-
herents are fideies. 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 dis-
cussion 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 author-
ity, whom I forget) approved of the legend. At last pro
fide vindicata 17 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. 16 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 Sui-
das, 19 o-KivSaTro-os 20 a word meaning a four stringed instru-
ment played with a quill was an exclamation of con-
temptuous dissent. How the wits of different races jump I
15 "Faith."
" "Faithful."
" "For the faith vindicated."
18 The words are of the same root, and hence our word fiddle.
Some suppose this root means a rope, which, as that to which you
trust, becomes, in one divergence, confidence itself just as a rock,
and other words, come to mean reliance and in another, a little
string. A. De M.
"The Greek lexicographer, a Christian, living after 1000 A. D.
His lexicon was first printed at Milan in 1499.
20 Skindapsos.
30 A BUDGET OF PARADOXES.
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 Uni-
versity 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 re-
member, 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 ! 21
THE WORD CHURCH.
To return to Notes and Queries. The substitution in
the (editorial) index of "Unitarian teacher," for the con-
tributor'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 ques-
tion when the establishment was first called the "Church
of England and Ireland":
91 This was John William Burgon (1813-1888), Gresham pro-
fessor of theology (1867) and dean of Chichester. He was an ultra-
conservative, opposing the revised version of the New Testament, and
saying of the admission of women to the university examinations
that it was "a thing inexpedient and immodest."
ON THE NAMES OF RELIGIOUS BODIES. 31
"That unmeaning clause, The United Church of Eng-
land and Ireland,' which occurs on the title-page of The
Book of Common Prayer, was first used at the commence-
ment 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 Eng-
land and Ireland/" Of course, churchmen are not respon-
sible 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 sup-
port 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 corpora-
tion, 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 mean-
ing. The following dialogue between Ecclesiastes and
Haereticus, which I cannot vouch for, has often taken
place in spirit, if not in letter: E. The word Church (0^X77-
o-ta) 22 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.
23 Ekklesia, or ecclesia.
32 A BUDGET OF PARADOXES.
H. Indeed! E. It is beyond a doubt (here he quoted half
a dozen texts in support). H. Do you mean that any doc-
trine or ordinance which was solemnly practised by the
KK\.rj<na 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 e/cKATjo-ta (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 excep-
tion! H. Why, the Recorder's sermon itself contains an-
other, the ewo/xos KK\r)ma, 2Z 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 aternum peribo ; 24 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 I
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." 25 But they do not
mean it personally I Every universal proposition is per-
* Ennomos ekklesia.
84 "Without doubt I shall perish forever.*
""Every man is an animal." "Sortes is a man." "Sortes is an
animal."
PROTESTANT AND PAPAL CHRISTENDOM. 33
sonal to every instance of the subject. If this be not con-
ceded, then I retort, in their own sense and manner, "Who-
soever would serve God, before all things he must not pro-
nounce 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, 29 at another. "Before
we proceed to consider any question involving physical
principles, we should set out with clear ideas of the nat-
urally possible and impossible." The eminent man who
said this, when wanting it for his views of mental educa-
tion ( !) 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 hav-
ing 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 ob-
jections. 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 theol-
ogies 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 false-
* "For a special purpose."
34 A BUDGET OF PARADOXES.
hood 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 com-
pound of everything that could make Heraclitus 1 sob and
Democritus 2 snigger. But not the only one. The Protes-
tants, 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 conse-
quence 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 quern, 3 would be as remarkable to the
general eye, as the Roman manufacture of termini a quo, 4
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 evi-
dence: two or three additional shiffle-shuffles towards de-
fence of saying the Athanasian curse in church and un-
saying 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,
1 Heraclitus of Ephesus, the weeping philosopher, 6th century
B.C.
2 Democritus, the laughing philosopher, founder of the atomistic
theory, 5th century B. C.
'"Ends to which."
*"Ends from which."
PROTESTANT AND PAPAL CHRISTENDOM. 35
when he cannot find it totidem verbis. 5 This is Protestant
method: the Roman plan is mam faciam; the Protestant
plan is viam inveniam? 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 Athana-
sian 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 an-
other: 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
'"In just as many syllables," "With just as many letters," "la
just as many words."
6 "I shall make a way," "I shall find a way."
36 A BUDGET OF PARADOXES.
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 phi-
losopher: and if any one should hold the first word offen-
sive, 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 philos-
ophers, 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 unintelli-
gible 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. 37
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 misbe-
have. 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 f ormulized 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 la-
menting, 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 bat-
tery; 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 re-
signed or been 1 turned out? Has he been put under restric-
1 The notion that the Evil Spirit is a functionary liable to be dis-
missed for not attending to his duty, is, so far as my reading goes,
utterly unknown in theology. My first wrinkle on the subject was
the remark of the Somersetshire farmer upon Palmer the poisoner
"Well ! if the Devil don't take he, he didn't ought to be allowed to be
devil no longer." A. De M.
William Palmer (1824-1856) was a member of the Royal Col-
lege of Surgeons and practised medicine at London. He was hanged
in 1856 for having poisoned a friend and was also suspected of having
poisoned his wife and brother for their insurance money, besides
being guilty of numerous other murders. His trial was very much
in the public attention at the time.
38 A BUDGET OF PARADOXES.
tion? 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? 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 hold-
ing. 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 3 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 4
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
'Advantages and dangers.
8 The old priory of St. Mary of Bethlehem in London, was used
as an asylum for the insane. The name was corrupted to Bedlam.
4 Referring to the common English pronunciation of St. John,
almost Sinjin. John St. John Long (1798-1834), an Irishman by
birth, practised medicine in London. He claimed to have found a
specific for rheumatism and tuberculosis, but upon the death of one
of his patients in 1830 he was tried for manslaughter. He died of
tuberculosis four years later, refusing to take his own treatment.
RELIGION AND PHILOSOPHY. 39
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 an-
cient 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, fol-
lowed by organizations gradually emerging from some cu-
rious 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 obedi-
ence are due, and who has declared himself, as with a blind
Nature of Things. A pure materialist, as to all things vis-
ible, 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 psycho-
logical 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
40 A BUDGET OF PARADOXES.
without any such necessity. With Occam 5 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 some-
thing 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 per-
sonal 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 im-
possibility"? 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
'William of Occam (d. 1349), so called from his birthplace,
Ockham, in Surrey. He was a Franciscan, and lectured on philos-
ophy in the Sorbonne.
THE SUN AN ELECTRIC SPACE. 41
may be more vital and more powerful. Where is this to
stop? Is it impossible that a finite quantity, rarefied ad in-
tinitum, may be an Omnipotent ? Perhaps the true Genesis,
when written, will open with "In the beginning was an im-
perial quart of oxygen at 60 of Fahrenheit, and the pres-
sure of the atmosphere; and this oxygen was infinitely
rarefied; and this oxygen became God." For myself, my
aspirations as to this system are Manichsean. 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 hence-
forward 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 har-
mony 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. 1 London, 1849, 8vo.
The author says:
"I am satisfied that I have given the true laws consti-
tuting 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
*He signs himself "James Hopkins, schoolmaster," and this
seems to have been his only published effort.
42 A BUDGET OF PARADOXES.
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 icontinuous 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 1 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 un-
claimed dividends, and disclosing them to their right own-
ers, 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 clergy-
man 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 2 and all other aldermen" ; which was nearly true,
1 Joseph Ady (1770-1852) was a famous swindler. One of his
best-known schemes was to send out letters informing the recipients
that they would learn something to their advantage on payment of a
certain sum. He spent some time in prison.
2 Sir Peter Laurie (c. 1779-1861) was worth referring to, for he
was prominent as a magistrate and was honored because of his in-
terest in all social reforms. He made a fortune as a contractor,
became sheriff of London in 1823, and was knighted in the following
year He became Lord Mayor of London in 1832.
ON MODERN ASTROLOGY. 43
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 dis-
pleased 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 01 anybody, my
voluntary referee, the Rt. Hon. Sir Peter Laurie, Kt., per-
petual Deputy Lord Mayor, will see justice done you with-
out any charge whatever : he and his toady, .
The accursed of Moses can hang any man : thus, by catch-
ing 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, 1 N. N. London
(s. a.) 12mo.
1 See Vol. I, page 321, note 2. The Astronomy in a nutshell appeared
in 1860. The Herald of Astrology was first published in London
in 1831, "by Zadkiel the Seer." It was continued as The Astrological
Almanac (London, 1834), as Zadkiel's Almanac and Herald of As-
trology (ibid., 1835, edited by R. J. Morrison, and subsequently by
A. J. Pearce), and as Raphael's Prophetic Almanac (1840-1855).
44 A BUDGET OF PARADOXES.
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 heav-
enly 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 appa-
ritions : the two things differ in precisely the way in which
a science of observation differs from a science of experi-
ment. Many make the mistake which M. le Marquis made
when he came too late, and hoped M. Cassini 2 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 prophe-
sying 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 Astronom-
1 See Vol. I, page 172, note 3.
ON MODERN ASTROLOGY. 45
ical 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 3 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 4
received a letter from Pons, 5 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
3 See Vol. I, page 87, note 4.
4 Franz Xaver, Freiherr von Zach (1754-1832) was director of
the observatory at Seeberge near Gotha. He wrote the Tabulae spe-
ciales aberrationis et mutationis (1806-7), Novae et correctae tabulae
solis (1792), and L 'attraction des montagnes et ses effets sur le fil
aplomb (1814).
5 Jean Louis Pons (1761-1831) was connected with the observa-
tory at Marseilles for thirty years (1789-1819). He later became
director of the observatory at Marlia, near Lucca, and subsequently
filled the same office at Florence. He was an indefatigable searcher
for comets, discovering 37 between 1801 and 1827, among them being
the one that bears Encke's name.
46 A BUDGET OF PARADOXES.
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 exceed-
ingly if some day a real relation should be established be-
tween comets and solar spots: of late years good reason
has been shown for advancing a connection between these
spots and the earth's magnetism. 6 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 extraordi-
nary. The great paradox of coincidence is that of Leibnitz,
known as the pre-established harmony, or law of coinci-
dences, 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 coin-
cident 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 What-
ever 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 fail-
ings, seldom revive Leibnitz's fantasy: they seem to act
upon the maxim quoted by Father Eustace 7 from the Decre-
* This hypothesis has now become an established fact.
T John Chetwode Eustace (c. 1762-1815) was born in Ireland.
Although a Roman Catholic priest he lived for a time at Cambridge
where he did some tutoring. His Classical Tour appeared in 1813
and went through several editions.
ON MODERN ASTROLOGY. 47
tals, Facinora ostendi dum puniuntur, flagitia autem ab-
scondi debent. 8
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 phenom-
enon 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 con-
nected 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 ex-
plained, as a connection in time of the death, and the
'"Crimes should be exposed when they are punished, but dis-
graceful acts should be hidden."
48 A BUDGET OF PARADOXES.
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, re-
quires 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, 9 of the French Institute,
wrote to me to the effect that Fresnel 10 had sent to Eng-
land, 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,^ 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)
"Henri Hureau de Senarmont (1808-1862) was professor of
mineralogy at the Ecole dcs mines and examiner at the Ecole poly-
technique at Paris.
10 Augtistin Jean Fresnel (1788-1827), "Ingenieur des ponts et
chaussees," gave the first experimental proofs of the wave theory of
light. He studied the questions of interference and polarization, and
determined the approximate velocity of light.
u "As is my custom."
ON MODERN ASTROLOGY. 49
of the European Review" I thus got the clue by which
I ascertained that there was no chance of recovering Fres-
nel'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 Inde-
pendence. 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 pam-
phlets 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 per-
mission it was published." I immediately saw that my con-
fusion 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 Hey wood's 12 Analysis of Kant's Critic k, 1844.
"Francis Heywood (1796-1858) made the first English trans-
lation of Kant's Critick of Pure Reason (1838, reprinted in 1848).
The Analysis came out, as here stated, in 1844.
50 A BUDGET OF PARADOXES.
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 13 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 Chifnnch. 14 Now the
letters are a verbal acrostic of Pere Mansuete a Cordelier
Friar, and a syllabic acrostic of PortsMouth and Chif Finch.
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 Eng-
lish readers would use Pere 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 sur-
" Louise Renee de Keroualle, Duchess of Portsmouth and Au-
bigny (1649-1734), was a favorite of Charles II. She used her in-
fluence to keep him under the control of Louis XIV.
"William Chiffinch (c. 1602-1688) was page of the king's bed-
chamber and keeper of the private closet to Charles II. He was one
of the king's intimates and was an unscrupulous henchman.
ON MODERN ASTROLOGY. 51
vivors, at the taking of Pondicherry, Captain John Fletcher,
Captain De Morgan, and Lieutenant Bosanquet, each dis-
tinctly foretold his own death on the morning of his fate."
I have no doubt of all three; and I knew it of my grand-
father 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 con-
sider any danger short of one like the above, sufficient rea-
son 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,
52 A BUDGET OF PARADOXES.
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, but not the bundle. It is also useful
to establish some of the good jokes which all take for in-
ventions. My friend Mr. J. Bellingham Inglis, 16 before
1800, saw the tobacconist's carriage with a sample of to-
bacco in a shield, and the motto Quid rides (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 18 remembers the King's Counsel (Sam-
uel Marryat) who took the motto Causes produce effects,
when his success enabled him to start a carriage.
The coincidences of errata are sometimes very remark-
able: it may be that the misprint has a sting. The death
of Sir W. Hamilton 19 of Edinburgh was known in London
on a Thursday, and the editor of the Athenceum wrote to
10 "Well devised."
16 John Bellingham Inglis. His Philobiblion "translated from the
first edition (of Ricardus d'Aungervile, Bishop of Durham), 1473,"
appeared at London in 1832. It was republished in America (Al-
bany, N.Y.) in 1864.
" "What are you laughing at ?"
18 See Vol. I, page 314, note 4.
19 See Vol. I, page 112, note 7.
ON MODERN ASTROLOGY. 53
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 rea-
sons for believing in my entire innocence. Of course I
could not see a proof : and two errata occurred. The words
"addition to Stewart" 20 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, 21 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 Hamil-
ton'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
"Referring to Hamilton's edition of the Collected Works of
Dugald Stewart, 10 volumes, Edinburgh, 1854-58. It is not com-
monly remembered that Stewart (1753-1828) taught mathematics at
the University of Edinburgh before he took up philosophy.
81 This was Hamilton's edition of the Works of Thomas Reid
(2 vols., Edinburgh, 1846-1863). Reid (1710-1796) included mathe-
matics in his work in philosophy at Aberdeen. In 1764 he suc-
ceeded Adam Smith at Glasgow.
54 A BUDGET OF PARADOXES.
pass for Irving's 22 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 speci-
mens 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, 1 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
23 Edward Irving (1792-1834), the famous preacher. At first he
assisted Dr. Chalmers at Glasgow, but in 1822 he went to London
where he met with great success. A few years later he became
mentally unbalanced and was finally expelled from his church (1832)
for heresy. He was a great friend of Carlyle.
1 He also wrote a number of other paradoxes, including An
Essay towards a Science of Consciousness (1838), Instinctive Nat-
ural Religion (1858), Popular Treatise on the structure, diseases,
and treatment of the human teeth (1837), and On Headache (1859).
ON SPIRITUALISM. 55
do not pronounce insane. But in this case the second sen-
tence 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 gra-
ciously 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. 1 London, 1854, 8vo.
I have several books on that great paradox of our day,
Spiritualism, but I shall exclude all but three. The bib-
liography of this subject is now very large. The question
is one both of evidence and speculation ; Are the facts
/James Smith (1801-1857), known as Shepherd Smith, was a
socialist and a mystic, with a philosophy that was wittily described
as "Oriental pantheism translated into Scotch." He was editor of
several journals.
56 A BUDGET OF PARADOXES.
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 follow-
ing. A person was invited to name a rule without excep-
tion, 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 prop-
erly 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 "re-
ferring 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 en-
force "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.
ON SPIRITUALISM. 57
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 Eng-
land, it is evident that no country in the world is better pre-
pared 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 Ba-
ronial 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 orig-
inally founded. There is a complete series of spiritual
revelations in England and the United States, besides mes-
meric 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 con-
cedes 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 fol-
lows:
58 A BUDGET OF PARADOXES.
(P. 592.) "Joanna Southcott 2 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 enter-
tained 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 Di-
vine 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
* Joanna Southcott (1750-1814) was known for her rhyming
prophecies in which she announced herself as the woman spoken of
in Revelations xii. She had at one time as many as 100,000 disciples,
and she established a sect that long survived her.
A CONDENSED HISTORY OF MATHEMATICS. 59
of Thales, 1 the Milesian, they came into Greece, where they
were improved very much by Pythagoras, 2 Anaxagoras, 3
and Anopides 4 of Chios. These were followed by Briso, 5
Antipho, [two circle-squarers ; where is Euclid?] and Hip-
pocrates, 6 but the excellence of the algebraic art was begun
by Geber, 7 an Arabian astronomer, and was carried on by
Cardanus, 8 Tartaglia, 9 Clavius, 10 , Stevinus, 11 Ghetaldus, 12
Herig^nius, 13 Fran, Van Schooten [meaning Francis Van
Schooten 14 ], Florida de Beauwe/ 5 etc."
Bryso was a mistaken man. Antipho had the disad-
vantage of being in advance of his age. He had the notion
of which the modern geometry has made so much, that of
I Thales, c. 640-548 B. C
* Pythagoras, 580-501 B. C.
* Anaxagoras, 499-428 B. C., the last of the Ionian school, teacher
of Euripides and Pericles. Plutarch speaks of him as having squared
the circle.
*Oinopides of Chios, contemporary of Anaxagoras. Proclus
tells us that Oinopides was the first to show how to let fall a perpen-
dicular to a line from an external point.
8 Bryson and Antiphon, contemporaries of Socrates, invented the
so-called method of exhaustions, one of the forerunners of the cal-
culus.
4 He wrote, c. 440 B. C, the first elementary textbook on mathe-
matics in the Greek language. The "lunes of Hippocrates" are well
known in geometry.
T Jabir ben Aflah. He lived c. 1085, at Seville, and wrote on
astronomy and spherical trigonometry. The Gebri filii Affla Hispa-
lensis de astronomia libri IX was published at Nuremberg in 1533.
"Hieronymus Cardanus, or Girolamo Cardano (1501-1576), the
great algebraist. His Artis magnae sive de regulis Algebrae was
published at Nuremberg in 1545.
'Nicolo Tartaglia (c. 1500-1557), the great rival of Cardan.
10 See note 5, Vol. I, page 69.
II See note 10, Vol. I, page 83.
11 See note 9, Vol. I, page 83.
13 Pierre Herigone lived in Paris the first half of the 17th cen-
tury. His Cours mathentatique (6 vols., 1634-1644) had some stand-
ing but was not at all original.
14 Franciscus van Schooten (died in 1661) was professor of
mathematics at Leyden. He edited Descartes's La Geometric.
"Florimond de Beaune (1601-1652) was the first Frenchman to
write a commentary on Descartes's La Geometrie. He did some note-
worthy work in the theory of curves.
60 A BUDGET OF PARADOXES.
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, 16 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 in-
ventor.
Any person who meddles with the circle may find him-
self the crane who was netted among the geese : as Antipho
for one, and Olivier de Serres 17 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 approxi-
mation; but Montucla and others misunderstood him, and,
still worse, misunderstood their own misunderstanding, and
made him say the circle was exactly double of the equi-
lateral 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 Anghera, 1 *
Malta, 1854, 8vo.
16 See note 3, Vol. I, page 41.
" Olivier de Serres (b. in 1539) was a writer on agriculture.
Montucla speaks of him in his Quadrature du cercle (page 227) as
having asserted that the circle is twice the inscribed equilateral tri-
angle, although, as De Morgan points out, this did not fairly inter-
pret his position.
** Anghera wrote not only the three works here mentioned, but
also the Problemi del piu alto interesse scientifico, geometricamente
risoluti e dimostrati, Naples, 1861. His quadrature was defended
by Giovanni Motti in a work entitled Matematica Vera. Falsitd del
sistema ciclometrico d'Archimede, quadratura del cerchio d' An-
ghera, ricerca algebraica dei lati di qualunque poligono regolare in-
scritto in un circolo, Voghera, 1877. The Problemi of 1861 contains
ST. VITUS, PATRON OF CYCLOMETERS. 61
Equazioni geometriche, estratte dalla lettera del Rev. Arciprete . .
al Professore Pullicino lb sulla quadratura del cerchio. Milan,
1855 or 1856, 8vo.
II 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. Anghera. Malta, 1857,
12mo.
Quadrature of the circle... by the Rev. D. Anghera, 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, 2 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 con-
taining St. Pudentiana, 3 who shares a day with St. Dunstan.
The Archpriest of St. Vitus will have it that the square in-
scribed in a semicircle is half of the semicircle, or the cir-
cumference 3 l / 5 diameters. He is active and able, with
Anghera's portrait, and states that he lived at Malta from 1849 to
1861. It further states that the Malta publications are in part re-
produced in this work.
lb This was his friend Paolo Pullicino whose Elogio was pro-
nounced by L. Farrugia at Malta in 1890. He wrote a work La
Santa Effegie delta Blata Vergine Maria, published at Valetta in
1868.
*St. Vitus, St. Modestus, and St. Crescentia were all martyred
the same day, being torn limb from limb after lions and molten lead
had proved of no avail. At least so the story runs.
"The reference is to Cardinal Wiseman. See Vol. II, page 26,
note 12.
62 A BUDGET OF PARADOXES.
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* The Vice-Chancellor of Oxford a blunt Eng-
lishman 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 vic-
tory 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 5 in his lives of Saints, and that Baronius, 8 in
4 "Worthy of esteem."
"Pedro de Ribadeneira (Ribadeneyra, Rivadeneira), was born
at Toledo in 1526 and died in 1611. He held high position in the
Jesuit order. The work referred to is the Flos Sanctorum o libro de
las vidas de los santos, of which there was an edition at Barcelona
in 1643. His life of Loyola (1572) and Historia ecclesidstica del
Cisma del reino de Inglaterra were well known.
Caesar Baronius (1538-1607) was made a cardinal in 1595 and
"became librarian at the Vatican in 1597. The work referred to ap-
peared at Rome in 1589.
CELEBRATED APPROXIMATIONS OF TT. 63
his Martyr ologium Romanum, refers to several authors who
have written concerning him. There is an account in Mrs.
Jameson's 7 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 mak-
ing him the protector of the cyclometers. Why he is repre-
sented with a cock is a disputed point, which is now made
clear: next after gallus gallinaceus 8 himself, there is no
crower like the circle-squarer.
CELEBRATED APPROXIMATIONS OF .
The following is an extract from the English Cyclo-
pcedia, Art. TABLES:
"1853. William Shanks, 1 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 calcula-
tion of the reciprocal of 601 . 5 601 ; 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
T Mrs. Jameson's (1794-1860) works were very popular half a
century ago, and still have some circulation among art lovers. The
first edition of the work mentioned appeared in 1848.
8 The barnyard cock.
1 Shanks did nothing but computing. The title should, of course,
read "to 607 Places of Decimals." He later carried the computation
to 707 decimal places. (Proc. Roy. Society, XXI, p. 319.) He also
prepared a table of prime numbers up to 60,000. (Proc. Roy. So-
ciety, XXII, p. 200.)
64 A BUDGET OF PARADOXES.
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 be-
lieve 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 TT 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, 2 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 re-
mains 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 an-
nouncement of the following table, undated, as open to in-
spection 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, con-
taining 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 an-
nouncement. The powers of 2 have been calculated for
many purposes. In Vol. II of his Magia Universalis Na-
tures et Artis, Herbipoli, 1658, 4to, the Jesuit Caspar
Schott 3 having discovered, on some grounds of theological
2 See Vol. I, page 42, note 4.
1 See Vol. I, page 64, note 1.
CELEBRATED APPROXIMATIONS OF TT. 65
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 TT which attracts attention, perhaps without deserv-
ing 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 ;
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 de-
prived 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 mys-
tic number seven \ If the cyclometers and the apocalyptics
would lay their heads together until they come to a unani-
mous verdict on this phenomenon, and would publish noth-
ing until they are of one mind, they would earn the grati-
tude of their race. I was wrong: it is the Pyramid-specu-
lator who should have been appealed to. A correspondent
of my friend Prof. Piazzi Smyth 4 notices that 3 is the
number of most frequency, and that 3% 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
of which will be made available by those who do not receive
4 See Vol. I, page 328, note 1.
66 A BUDGET OF PARADOXES.
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, 1 M.A., and Mr. J. R. Lunn, 2 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
x^-2x^, the example given of Newton's method, on
which all improvements have been tested. In 1831, Fou-
rier's 3 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,* not yet known in France, and not much known in
1 George Suffield published Synthetic Division in Arithmetic, to
which reference is made, in 1863.
"John Robert Lunn wrote chiefly on Church matters, although
he published a work on motion in 1859.
3 Jean Baptiste Joseph, Baron Fourier (1768-1830), sometime
professor in the Military School at Paris, and later at the Ecole
poly technique. He is best known by his Theorie analytique de la
chaleur (Paris, 1822), in which the Fourier series is used. The
work here referred to is the Analyse des equations determinees
(Paris, 1831).
4 William George Horner (1786-1837) acquired a name for him-
self in mathematics in a curious manner. He was not a university
man nor was he a mathematician of any standing. He taught school
near Bristol and at Bath, and seems to have stumbled upon his in-
genious method for finding the approximate roots of numerical
higher equations, including as a special case the extracting of the
various roots of numbers. Davies Gilbert presented the method to
the Royal Society in 1819, and it was reprinted in the Ladies' Diary
for 1838, and in the Mathematician in 1843. The method was orig-
inal as far as Horner was concerned, but it is practically identical
with the one used by the Chinese algebraist Ch'in Chiu-shang, in his
Su-shu Chiu-chang of 1247. But even Ch'in Chiu-shang can hardly
CURIOUS CALCULATIONS. 67
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, 5 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 ex-
plain. His solution verified the former one, but he was
unable to see the connection, even when his result was ob-
tained. My reader may be as much at a loss : the two solu-
tions are:
2.0945514815423265...
9.0544851845767340...
The results are published in the Mathematician, Vol. Ill,
p. 290. In 1851, another pupil of mine, Mr. J. Power
Hicks, 6 carried the result to 152 decimal places, without
knowing what Mr. Johnston had done. The result is in the
English Cyclopedia, 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
be called the discoverer of the method since it is merely the exten-
sion of a process for root extracting that appeared in the Chiu-
chang Suan-shu of the second century B. C.
8 He afterwards edited Lofttis's Inland Revenue Officers' Manual
(London, 1865). The two equations mentioned were x* 2x = 5
and y 3 90/ + 2500y 16,000 = 0, in which y = 30 10*. Hence
each place of y is the complement of the following place of x with
respect to 9.
8 Probably the John Power Hicks who wrote a memoir on T. H.
Key, London, 1893.
68 A BUDGET OF PARADOXES.
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 7 of Birkenhead verified this by actual mul-
tiplication, and produced
2580413
10 117
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: 8 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, 1 of Norbury
Booths Hall, Knutsford, who published for eight or ten
7 Possibly the one who wrote on the quadrature of the circle in
1881.
"As it is. But what a pity that we have not 12 fingers, with
duodecimal fractions instead of decimals! We should then have 0.6
for V* 0.4 for V,, 0.8 for /., 0.3 for l /<, 0.9 for 3 A, and 0.16 for %,
instead of 0.5, 0.333-f, 0.666+, 0.25, 0.75, and 0.125 as we now
have with our decimal system. In other words, the most frequently
used fractions in business would be much more easily represented
on the duodecimal scale than on the decimal scale that we now use.
*He wrote Hints for an Essay on Anemology and Ombrology
(London, 1839-40) and The Music of the Eye (London, 1831).
A NEW PHASE OF MORMONISM. 69
years the Ombrological Almanac, a work of asserted dis-
covery 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 j" 1 on the right, "Given
by inspiration of God. Joseph Smith." 2 A leading article
on the discoveries of Prof. Orson Pratt 8 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
1 Brigham Young (1801-1877) was born at Whitingham, Ver-
mont, and entered the Mormon church in 1832. In 1840 he was sent
as a missionary to England. After the death of Joseph Smith he be-
came president of the Mormons (1847), leading the church to Salt
Lake City (1848).
'Joseph Smith (1805-1844) was also born in Vermont, and was
four years the junior of Brigham Young. The Book of Mormon
appeared in 1827, and the church was founded in 1830. He was
murdered in 1844.
"Orson Pratt (1811-1881) was one of the twelve apostles of the
Mormon church (1835), and made several missionary journeys to
England. He was professor of mathematics in the University of
Deseret (the Mormon name for Utah). Besides the paper mentioned
Pratt wrote the Divine Authenticity of the Book of Mormon (1849),
Cubic and Biquadratic Equations (1866), and a Key to the Universe
(1866).
70 A BUDGET OF PARADOXES.
and commented on. Dated G. S. L. City, Utah Ter., Aug.
1, 1855. If the creed, as above, be correctly given, no won-
der 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 mathemat-
ically 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 happi-
ness), 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 dis-
coveries."
There has been a moderate quantity of well-meant at-
tempt to enforce, sometimes motive, sometimes doctrine,
by arguments drawn from mathematics, the proponents be-
ing 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 re-
quires 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 be-
ing 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
MATHEMATICAL ILLUSTRATIONS OF DOCTRINE. 71
the other becomes infinite. In fact, the argument is a perfect
non sequitur. 1 Those who propose it have in their minds,
though in a cloudy and indefinite form, the idea of the in-
crease of guilt being proportionate to the increase of great-
ness 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% times as great as an-
other is exactly, no more and no less, 4% 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 Laid, 2 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, 3 who was
a sound and learned mathematician, adopted this dangerous
kind of illustration in his Letters on the Christian Religion.
J "It does not follow."
'Dryden (1631-1700) published his Religio Laid in 1682. The
use of the word "proportion" in the sense of ratio was common be-
fore his time, but he uses it in the sense of having four terms ; that
is, that price is to price as offence is to offence.
'Olinthus Gilbert Gregory (1774-1841) succeeded Hutton as pro-
fessor of mathematics at Woolwich. He was, with De Morgan,
much interested in founding the University of London. He wrote on
astronomy (1793), mechanics (1806), practical mathematics (1825),
and Christian evidences (1811).
72 A BUDGET OF PARADOXES.
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 doc-
trines 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 dis-
cussed by a person who treats heaven as a deferred per-
petual 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 in-
finitely great, then, even if the probability of their argu-
ments 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 mathe-
MATHEMATICAL ILLUSTRATIONS OF DOCTRINE. 73
maticians, 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 (Pansees, ch. 7) 4 that "le juste est de ne point
parier," he answers, "Oui: mais il faut parier: vous etes
embarque; et ne parier point que Dieu est, c'est parier qu'il
n'est pas." 5 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, 6 who, as
cited by Bayle, 7 speaks thus:
"Sed et ipse [Christus] quse pollicetur, non probat. Ita
est. Nulla enim, ut dixi, futurorum potest existere com-
probatio. Cum ergo haec sit conditio futurorum, ut teneri et
comprehendi nullius possint anticipationis attactu; nonne
4 See Vol. I, page 220, note 6. The Pensees appeared posthumously
in 1670.
"The right thing to do is not to wager at all." "Yes, but you
ought to wager; you have started out; and not to wager at all that
God exists is to wager that he does not exist."
8 He lived about 300 A. D., in Africa, and wrote Libri septem ad-
versus Gentes. This was printed at Rome in 1542-3.
T Pierre Bayle (1647-1706) was professor of philosophy at the
Protestant University at Sedan from 1675 until its dissolution in 1681.
He then became professor at Rotterdam (1681-1693). In 1684 he
began the publication of his journal of literary criticism Nouvelles
de la Republique des Lettrcs. He is best known for his erudite
Dictionnaire historique et critique (1697).
74 A BUDGET OF PARADOXES.
purior ratio est, ex duobus incertis, et in ambigua expec-
tatione pendentibus, id potius credere, quod aliquas spes
f erat, 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." 8
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 addi-
tion 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 Mora-
Hum. 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,
8 "But Christ himself does not prove what he promises. It is
true. For, as I have said, there cannot be any absolute proof of
future events. Therefore since it is a condition of future events that
they cannot be grasped or comprehended by any efforts of antici-
pation, is it not more reasonable, out of two alternatives that are
uncertain and that are hanging in doubtful expectation, to give
credence to the one that gives some hope rather than to the one that
offers none at all? For in the former case there is no danger if, as
is said to threaten, it becomes empty and void; while in the latter
case the danger is greatest, that is, the loss of salvation, if when the
time comes it is found that it was not a falsehood."
NOVUM ORGANUM MORALIUM. 75
political and ecclesiastical affairs. By Tresham Dames Gregg, 1
Chaplain of St. Mary's, within the church of St. Nicholas intra
muros, Dublin. London, 1859, 8vo. (pp. xl-f-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, 2 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 jeal-
ousy as to a matter so vast. If De Morgan and Boole have
had a priority in the case, to them we cheerfully shall re-
sign 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
1 Gregg wrote several other paradoxes, including the following:
The Authentic Report of the extraordinary case of Tresham Dames
Gregg. .. .his committal to Bridewell for refusing to give his recog-
nisance (Dublin, 1841), An Appeal to Public Opinion upon a Case of
Injury and Wrong. .. .in the case of a question of prerogative that
arose between [R. Whately] Archbishop of Dublin and the author
(London, 1861), The Cosmology of Sir Isaac Newton proved to be in
accordance with the Bible (London, 1871), The Steam Locomotive
as revealed in the Bible (London, 1863) and On the Sacred Law of
1866, conferring perpetual life with immunity from decay and dis-
ease. A cento of decisive scriptural oracles strangely discovered
(London and Dublin, 1875). These titles will help the reader to
understand the man whom De Morgan so pleasantly satirizes.
a See Vol. I, page 261, note 2.
76 A BUDGET OF PARADOXES.
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 ! // 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 discov-
ery, by our newspaper. Our cry shall be evpryKao-i ! 3 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, simultane-
ity, and posteriority, and request that nothing may be trum-
peted from the mountain top except our abjuration of all
community of thought or operation with this Novum Or-
ganum.
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
cvprjKCLcri, and not even for IvprjKaa-i. For self and Boole, I
point out what would have convinced either of us that this
house is divided against itself.
A being an apostolic element, 8 the doctrinal element,
and X the body of the faithful, the church is A 8 X, we are
told. Also, that if A become negative, or the Apostolicity
become Diabolicity [my words] ; or if 8 become negative,
and doctrine become heresy ; or if X 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 A and 8 should both become negative, diabolical origin
8 "They have found it."
NOVUM ORGANUM MORALIUM. 77
and heretical doctrine, then the church, A8X, is still posi-
tive, what it ought to be, unless X 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 cex 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 xf'- 4 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 Apos-
tacy? 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:
4 The late Greeks used the letters of their alphabet as numerals,
adding three early alphabetic characters. The letter x represented
600, represented 60, and f stood for 6. This gives 666, the number
of the Beast given in the Revelation.
78 A BUDGET OF PARADOXES.
"And the whole tells us just this, that David did what
he could. He augmented those elements of his constitu-
tion which were (exceptis excipiendis) 5 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 aug-
mented, and ex rose proportionally. The law of the varia-
tion, according to our theory, would be thus expressed. The
resultant was David the king cex [c = r?] (who had been
David the shepherd boy), and from the conditions of the
theorem we have
du dx dc
ce-i+ex
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." 6
The "solution of the family problem" is of high inter-
est. 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 cex be the father; c^e^x^ 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) ;
8 "Allowing for necessary exceptions."
"Mr. Gregg is not alone in his efforts to use the calculus in
original lines, as any one who has read Herbart's application of the
subject to psychology will recall
A TRIBUTE TO BOOLE. 79
and this expression will represent his relation to the servant.
Consequently,
(mz\ ( mz\
a+ \e x; otherwise! a+ Jex
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 un-
assisted 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 meas-
ure 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 justi-
fication.
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.
80 A BUDGET OF PARADOXES.
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 obitu-
ary 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 admira-
tion 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 fur-
nish the grammar and dictionary of an all-containing sys-
tem of logic, would not have been believed until it was
proved. When Hobbes, 1 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 sepa-
rated, will one day be matter of notoriety and common
wonder: and Boole's name will be remembered in connec-
tion 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. 1 London
and Liverpool, 1856, 8vo.
'See Vol. I, page 105, note 4; page 109, note I.
*The full title shows the plan, The Decimal System as a whole,
in its relation to time, measure, weight, capacity, and money, in uni-
son with each other. But why is this so much worse than the French
plan of which we have only the metric system and the decimal divi-
sion of the angle left ?
ON PHONETIC SPELLING. 81
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 apos-
tles! 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, 1
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. 2
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 re-
*One of the brothers of Sir Isaac Pitman (1813-1897), the in-
ventor of modern stenography. Of these brothers, Benjamin taught
the art in America, Jacob in Australia, and Joseph, Henry, and Fred-
erick in England.
'For example, The Phonographic Lecturer (London, 1871 etc.),
The Phonographic Student (1867, etc.), and The Shorthand Maga-
zine (1866, etc.).
82 A BUDGET OF PARADOXES.
solve 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 pronun-
ciation 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 promul-
gated 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. 83
A HANDFUL OF LITTLE PARADOXERS.
Ombrological Almanac. Seventeenth year. An essay on Ane-
mology and Ombrology. By Peter Legh, 1 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. 2
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 per-
fectly acquainted with the works of Thales, Euclid, Archi-
medes, ..." I had some thought of asking whether he had
used the Elzevir edition of Thales, 3 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
1 See Vol. II, page 68, note I.
a lt involves the theory of non-Euclidean geometry, Euclid's
postulate of parallels being used in proving this theorem.
* Referring to the fact that none of the works of Thales is extant
84 A BUDGET OF PARADOXES.
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
T he Longitude. 4 (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 be-
comes 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, 1 inspector of schools,
which commenced a controversy of many letters and pam-
phlets. This dispute comes on at intervals, and will con-
tinue to do so. It sometimes arises from inability to under-
stand the character of simple rotation, geometrically ; some-
times from not understanding the mechanical doctrine of
rotation.
4 The author was one B. Bulstrode. Parts 4 and 5 were printed
at Calcutta.
1 See Vol. II, page 5, note 2.
LUNAR MOTION AGAIN. 85
Lunar Motion. The whole argument stated, and illustrated by
diagrams; with letters from the Astronomer Royal. By Jel-
linger C. Symons. London, 1856, 8vo.
The Astronomer Royal endeavored to disentangle Mr. J.
C. Symons, but failed. Mr. Airy 2 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 per-
suaded 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 3 taught his Russians at Is-
mail 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,
a See Vol. I, page 85, note 2.
'Alexander Vasilievich Suvaroff (1729-1800), a Russian general
who fought against the Turks, in the Polish wars, and in the early
Napoleonic campaigns. When he took Ismail in 1790 he sent this
couplet to Empress Catherine.
86 A BUDGET OF PARADOXES.
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 dis-
putations, 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 New-
tonus* said the opponent. This was repeated the requisite
number of times, and counted for as many acts and oppo-
nencies. 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 re-
peated with every pair of candidates.
The real disputations were very severe exercises. I was
badgered for two hours with arguments given and an-
swered in Latin, or what we called Latin against New-
ton's first section, Lagrange's 5 derived functions, and Locke 6
on innate principles. And though I took off everything, and
was pronounced by the moderator to have disputed magno
honore, 7 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.
4 "Newton hath determined rightly," "Newton hath not deter-
mined rightly."
1 See Vol. I, page 288, note 3.
See Vol. I, page 326, note 1.
T "With great honor."
LUNAR MOTION AGAIN. 87
The Doctrine of the Moon's Rotation, considered in a letter to
the Astronomical Censor of the Athenaum. By Jones L. Mac-
Elshender. 8 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 "culti-
vated 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 oppo-
sition 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 in-
tended 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.'
"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
1 Apparently unknown to biographers. He seems to have written
nothing else.
'Captain Marryat (1792-1848) published Snarley-yow, or tht
Dog Fiend in 1837.
88 A BUDGET OF PARADOXES.
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 provin-
cial 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 astron-
omy," 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 him-
self Parallax: but at Trowbridge, in 1849, he was S. Goul-
den. 1 In this last advertisement is the following announce-
ment: "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. Her-
schel, 2 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 argu-
ments 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
1 He is not known to biographers, and published nothing else
under this name.
1 See Vol. I, page 80, note 5. .
ZETETIC ASTRONOMY. 89
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 ex-
plain why the large hull of a ship disappeared before the
sails. The persons present and waiting for the second lec-
ture 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 cir-
cumstantial: scores of phenomena ask, separately and in-
dependently, what other explanation can be imagined ex-
cept 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 mathemat-
ical demonstration.
The Zetetic system still lives in lectures and books; as
it ought to do, for there is no way of teaching a truth com-
parable 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 fenow.
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
90 A BUDGET OF PARADOXES.
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 Longi-
tude 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 3 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, 4 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 be-
longed to Scipio Africanus, whose family vault was dis-
covered, it is supposed, in 1780. Mr. Archer is of note as
'He published a Family and Commercial Illustrated Almanack
and Year Book for 1861 (Bath, 1860).
4 Louis Dutens (1730-1812) was born at Tours, but went to Eng-
land as a young man. He made the first collection of the works of
Leibnitz, against the advice of Voltaire, who wrote to him: "Les
ecrits de Leibnitz sont epars comme les feuilles de la Sybille, et aussi
obscurs que les ecrits de cette vieille." The work appeared at Ge-
neva, in six volumes, in 1769.
ZETETIC ASTRONOMY. 91
the suggester of the perforated border of the postage-
stamps, and, I think, of the way of doing it ; for this he got
4,000/. 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 fool-
ish. 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 perspec-
tive, 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 as-
tronomy. The manner in which the sun dips into the sea,
especially in tropical climates, upsets the whole. Mungo
Park, 5 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 ac-
' Mungo Park (1771-1806), the first European to explore the
Niger (1795-6). His Travels in the Interior of Africa appeared in
1799. He died in Africa.
92 A BUDGET OF PARADOXES.
curate 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 dedi-
cated 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 re-
torted "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 9 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
'Gerhard Mercator (1512-1594) the well-known map maker of
Louvain. The "Mercator's Projection" was probably made as early
as 1550, but the principle of its construction was first set forth by
Edward Wright (London, 1599).
ZETETIC ASTRONOMY. 93
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 argu-
ment 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, Num-
bers, Stars, on the Neo-Christian Religion. . .VoL i. London,
1858, 1859, 1860. 8vo.
The name of the author is Filopanti. 7 He announces
himself as the 49th and last Emanuel : his immediate prede-'
graphs.
T Quirico Barilli Filopanti wrote a number of works and mono-
)hs. He succeeded in getting his Cesare al Rubicone and Degli
94 A BUDGET OF PARADOXES.
cessors 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, 8 in retribution
for the massacre of St. Bartholomew, was hanged in Lon-
don under the name of Barthelemy for the murder of Col-
lard : 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.' 1 (Broadsheet.)
This gentleman is well known to the readers of the
Athenaum, in which, for nearly twenty years, he has in-
serted, 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 con-
secutive, but may have any time millions of years be-
tween 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
usi idraulici delta Tela in the Memoria letta. . . all' Accadentia delle
Stienze in Bologna (1847, 1866). He also wrote Dio esiste (1881),
Dio Liberate (1880), and Sunto delta memoria suite geuranie ossia
di alcune singolari relazioni cosmiche della terra e del cielo (1862).
8 The periods of disembodiment may be interesting. They will be
seen from the following dates: Descartes (1596-1650), William III
(1650-1702) ; Roger Bacon (1214 to c. 1294), Boccaccio (1313-1375).
Charles IX was born in 1550 and died in 1574.
1 His real name was Frederick Parker, and he wrote several
works on the Greek language and on religion. Among these were
a translation of the New Testament from the Vatican MS. (1864),
The Revealed History of Man (1854), An Enquiry respecting the
Punctuation of Ancient Greek (1841), and Rules for Ascertaining the
sense conveyed in Ancient Greek Manuscripts (1848, the seventh
edition appearing in 1862).
THE SABBATH THE GREAT PYRAMID. 95
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, 2 12mo.
This work is very learned, and may be referred to for
the history of previous speculations. It professes to con-
nect the dimensions of the Pyramid with a system of metrol-
ogy which is supposed to have left strong traces in the sys-
tems 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 3 noticed this work, and gave several
coincidences, in the Athenaum, 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 sys-
tem 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 satisfac-
tory 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.
9 See Vol. I, page 352, second note 1.
The literature on the subject of the Great Pyramid, considered
from the standpoint of metrology, is extensive.
8 See Vol. I, page 80, note 5.
96 A BUDGET OF PARADOXES.
My old friend Mr. Taylor is well known as the author
of the argument which has convinced many, even most, that
Sir Philip Francis* was Junius : pamphlet, 1813 ; supple-
ment, 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 conver-
sation 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 ques-
tion, "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 re-
markable : 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 use-
fully 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
4 Sir Philip Francis (1740-1818) was a Whig politician. The
evidence that he was the author of the Letters of Junius (1769-1772)
is purely circumstantial. He was clerk in the war office at the time
of their publication . In 1774 he was made a member of the Supreme
Council of Bengal, and was a vigorous opponent of Warren Hastings,
the two fighting a duel in 1780. He entered parliament in 1784 and
was among the leaders in the agitation for parliamentary reform.
MRS. ELIZABETH COTTLE. 97
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 tem-
perament, he had a curious turn for vexed questions. But
he reflected very long and very patiently before he pub-
lished: 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 Eliza-
beth Cottle. 1 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. 2 Long hence, when the now current
volumes of our journals are well-ransacked works of ref-
erence, those who look into them will be glad to see this
1 Mrs. Cottle published a number of letters that attracted atten-
tion at the time. Among these were letters to the emperor of France
and king of Sardinia (1859) relating to the prophecies of the war
between France and Austria; to G. C. Lavis and Her Majesty's
Ministers (1859) relating to her claims as a prophetess; and to the
"Crowned Heads" at St. James, the King of Prussia, and others
(1860), relating to certain passages of Scripture. She also wrote
The Lamb's Book of Life for the New Jerusalem Church and King-
dom, interpreted for all nations (1861).
8 See Vol. I, page 315, note 2, and Vol. II, page 58, note 2.
98 A BUDGET OF PARADOXES.
feature of our time : I therefore make a few extracts, faith-
fully copied as to type. The Italic is from the New Testa-
ment; the Roman is the requisite interpretation:
"Robert Cottle 'was numbered (5196) with the trans-
gressors' 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 wid-
owed 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, 3 April 14, 1839). /
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 zvith you
(Cottleites) in my Father's kingdom John xv. // 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
* A Congregational minister, who published a number of ser-
mons, chiefly obituaries, between 1804 and 1851. His Frailty of
Human Life, two sermons delivered on the occasion of the death of
Princess Charlotte, went through at least three editions.
MRS. ELIZABETH COTTLE. 99
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 Eliza-
beth) 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 Al-
mighty, 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 proph-
ecy 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, 4 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 reve-
lation (Acts. i. 13, 15) of Jesus the same King of the Jews
yesterday at the prayer meeting, Dec. 31, 1841, and to-day,
4 He was secretary of the Congregational Board and editor of
the Congregational Year Book (from 1846) and the Congregational
Manual.
100 A BUDGET OF PARADOXES.
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, un-
interrupted 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 revela-
tion 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 asy-
lum 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, 46687379),
that rideth (by rail and steam over land and sea, from his
holy habitation at Kirkstall Lodge, Psa. Ixxvii. 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)."
MRS. ELIZABETH COTTLE. 101
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 fol-
lowing. 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 5 at King's College for doubting that God
would punish human sins by an existence of torture last-
ing through years numbered by millions of millions of mil-
lions 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 suc-
cession, 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 Cam-
bridge, have been assayed by the Bishop's chaplain, touch-
ing the health of their souls, and the validity of their call
by the Divine Spirit, and then the gentle pressure of a pre-
late's hand upon their heads ; and the words 'Receive the
Holy Ghost/ have, in a brief space of time, wrought a
"Frederick Denison Maurice (1805-1872) began his preaching as
a Unitarian but entered the Established Church in 1831, being or-
dained in 1834. He was professor of English and History at King's
College, London, from 1840 to 1853. He was one of the founders of
Queen's College for women, and was the first principal of the Work-
ing Men's College, London. The subject referred to by De Morgan
is his expression of opinion in his Theological Essays (1853) that
future punishment is not eternal. As a result of this expression he
lost his professorship at King's College. In 1866 he was made
Knightbridge Professor of Casuistry, Moral Theology, and Moral
Philosophy at Cambridge.
102 A BUDGET OF PARADOXES.
change in them, much akin to the miracle of transub-
stantiation 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 mate-
rial. 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 fal-
lible standard of man's invention! If proof of this be
required, an appeal might be made to history and the ex-
perience 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 reve-
lation. 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 possi-
bility that by "black gentlemen" may be meant the clergy.
JAMES SMITH, ARCH-PARADOXER. 103
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. 1 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 emi-
nent 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. Liver-
pool, 1861, 8vo.
Letter to the. .British Association. . .by James Smith, Esq. Liver-
pool, 1862, 8vo. [These letters the author promised to con-
tinue.]
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. Re-
printed 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.
1 See Vol. I, page 46, note 1. Besides the books mentioned in
this list he wrote The Ratio between Diameter and Circumference
demonstrated by angles, and Euclid's Theorem, Proposition 32, Book
I, proved to be fallacious (Liverpool, 1870). This is the theorem
which asserts that the exterior angle of a triangle is equal to the sum
of the two opposite interior angles, and that the sum of the interior
angles equals two right angles. He also published his Curiosities of
Mathematics in 1870, a work containing an extensive correspondence
with every one who would pay any attention to him. De Morgan
was then too feeble to show any interest in the final effort of the
subject of some of his keenest satire.
104 A BUDGET OF PARADOXES.
[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 Mas-
ter of Trinity, in the stocks without hope of escape. Printed
for the authors (J. S. confessed, and also hidden under Nauti-
cus). (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 any-
thing 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 2 quietly proved
him wrong in a way accessible to an ordinary schoolboy;
Whewell, 3 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 there-
fore 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
9 See Vol. I, page 332, note 4.
3 See Vol. I, page 101, note 4.
JAMES SMITH, ARCH-PARADOXER. 105
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 Athenaum 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. 4
The symptoms soon took a defined form: his circum-
ference shrank into exactly 3% times his diameter, instead
of close to 3 1 % 13 , 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 exam-
ined 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/ re-
fused at first to entertain the question. On this Mr. Smith
changed his 'tactics' and the name of his paper, and smug-
gled 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
4 "The circle-squaring disease"; literally, "the circle-measuring
disease."
106 A BUDGET OF PARADOXES.
'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 pub-
lished letters which were intended for no other purpose
than to clear his poor head of a hopeless delusion. He de-
serves 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 in-
telligible 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
JAMES SMITH, ARCH-PARADOXER. 107
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% 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 hap-
pened, were not inconsistent with the supposition on which
they were made. Error is sometimes self-consistent. How-
ever, 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 pro-
ceeding 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 vic-
tory of truth which, oddly enough, is the consolation of
all hopelessly mistaken men ; to compare himself with Gali-
leo; 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 hetero-
108 A BUDGET OF PARADOXES.
pseustic. 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 diag-
onal 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
JAMES SMITH, ARCH-PARADOXER. 109
question, while that of the second was not demonstrated,
completely, until the last century.
"The mathematicians have many methods, totally dif-
ferent 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, 5 of Houghton-
le-Spring, and Dr. Rutherford 8 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 7 English Cyclop&dia, an
account of the matter which may illustrate the unimagin-
able, though rationally conceivable, extent of accuracy ob-
tained.
"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:
6 See Vol. II, page 63, note 1.
'William Rutherford (c. 1798-1871), teacher of mathematics at
Woolwich, secretary of the Royal Astronomical Society, editor of
The Mathematician, and author of various textbooks. The Extension
of if to 440 places, appeared in the Proceedings of the Royal Society
in 1853 (p. 274).
T Charles Knight (1791-1873) was associated with De Morgan
for many years. After 1828 he superintended the publications of the
Society for the Diffusion of Useful Knowledge, to which De Morgan
contributed, and he edited the Penny Cyclopedia (1833-1844) for
which De Morgan wrote the articles on mathematics.
110 A BUDGET OF PARADOXES.
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 ac-
curacy worthy of his size, let him calculate the circum-
ference 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 mathe-
matician 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 stone-
mason 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 3,141%. 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 10^. in every 100/. Of
course, if he set out with such an error he will accumulate
blunder upon blunder. Now, if there be a process in which
JAMES SMITH, ARCH-PARADOXER. Ill
close knowledge of the circle is requisite, it is in the pre-
diction 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 com-
mon 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 re-
volve. That is to say, setting out with Ws. in 100/. of error
in his circumference, he gets within the fifth part of a
farthing in 100/. 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 Hamil-
ton 8 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
' Sir William Hamilton. See Vol. I, page 112, note 7.
112 A BUDGET OF PARADOXES.
as Adam Smith 9 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 una-
nimity 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 resem-
blance to the thought and reading demanded by the learned
faculties. The research, the balance of evidence, the esti-
mation 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 mathe-
maticians 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 arith-
metician, venturing into the field of mathematical demon-
stration, may show himself utterly destitute of all that dis-
tinguishes the reasoning geometrical investigator from the
calculator.
Adam Smith (1723-1790) was not only known for his Wealth
of Nations (1776), but for his Theory of Moral Sentiments (1759),
published while he was professor of moral philosophy at Glasgow
(1752-1764). He was Lord Rector of the university in 1787.
JAMES SMITH, ARCH-PARADOXER. 113
"And further, it should be remembered that in mathe-
matics 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 demon-
stration 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 3% times its diam-
eter, 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 Athenaum 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 for-
warded his letter to the Liverpool Albion, with an addi-
tional 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
114 A BUDGET OF PARADOXES.
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 10 a
proof that the circumference is more than 3% 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 pre-
tenders. 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 poly-
gon of 20 sides is greater than 3% diameters of the circle,
and still more, of course, is the circumference of the circle
greater than 3% 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 f 1280)
is less than 1280 x 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 (4x 1280-
125) is less than 791x791. 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 x 1280 is
equal to 400 x 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 mem-
" See Vol. I, page 332, note 4.
JAMES SMITH, ARCH-PARADOXER. 115
her 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 3% diameters/'
The last work in the list was thus noticed in the Athe-
naum, May 27, 1865.
"Mr. James Smith appears to be tired of waiting for
his place in the Budget of Paradoxes, and accordingly pub-
lishes 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 histor-
ical 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
116 A BUDGET OF PARADOXES.
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 in-
duce 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 Dub-
lin, 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 writ-
ings. On one point indeed he well deserves the scutica* 1
if not the horribile flagellum. 12 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?]^
1 "Whip."
""Terrible lash."
13 <
'An accomplished fact [an accomplished fault]."
JAMES SMITH, ARCH-PARADOXER. 117
or leave myself open to the humiliating charge of mathe-
matical 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, 14
"I love Moll Cobb for her impudence." I have now done
with my friend's suaviter in modo, and proceed to his
fortiter in re 16 : I shall show that he has convicted himself
of ignorance and folly, with an honesty and candor worthy
of a better value of TT.
Mr. Smith's method of proving that every circle is 3%
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 TT 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
"See Extracts from the Diary and Letters of Mrs. Mary Cobb,
London, 1805.
""Gentle in manner."
* "Brave in action." The motto of Earl Newborough was "Sua-
viter in modo, fortiter in re."
118 A BUDGET OF PARADOXES.
of a 'reductio ad absurdum'^ demonstration, in pure geom-
etry."
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 ab-
surdity. 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, // a perdu
le droit d'etre frappe de I' evidence.
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. As-
suming TT to be 3%, 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 I fa,* 8\
if TT = , ^ I ] = r.
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
a 2
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 men-
tioned the old problem of finding two mean proportionals,
'"Reduction to an absurdity," a method of proof occasionally
used in geometry and in logic.
""He has lost the right of being moved (struck) by evidence."
JAMES SMITH, ARC^-PARADOXER. 119
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 for the sign of the square root,
which embarrasses small type:
"This establishes the following infallible rule, for find-
ing two mean proportionals OF EQUAL VALUE, and is more
than a preliminary, to the famous old problem of 'Squar-
ing the circle/ Let any finite number, say 20, and its fourth
part = %(20)=5, be given numbers. Then rg(20x5)-
rq 100 = 10, is their mean proportional. Let this be a given
mean proportional TO FIND ANOTHER MEAN PROPORTIONAL OF
EQUAL VALUE. Then
= 2 X -78125 = 15. 625
4 4
will be the first number; as
25:16::r<720:r<78.192: and (r?8-192) 2 X ^=8-192
X -78125 = 6. 4
will be the second number; therefore rq (15.625x6.4) -
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 possi-
bility ; I doubt, and, on the evidence afforded by your Bud-
get, 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 sol-
emnly 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
"For radix quadratus. The usual root sign is supposed to be
derived from r (for radix), and at one time q was commonly used
for square, as in Viete's style of writing Aq for A a .
120 A BUDGET OF PARADOXES.
is a mean proportional between 5 and y, and y is a mean
proportional between x and 20. And these means are
x = 5 ^ 4, y = 5 ^/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 mathe-
matician 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 illus-
trate, 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 unaccus-
tomed 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 propo-
sition 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
JAMES SMITH, ARCH-PARADOXER. 121
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 in-
creases, the laws of thought which are of most usual appli-
cation 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, un-
tried nomenclature habitual; that is, until it is a habit to
be occupied upon a novelty. It is observed that many per-
sons 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, dishon-
esty 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
122 A BUDGET OF PARADOXES.
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 80,000/. at the banker's, though
you knew the book only showed 30,000/. ? 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 busi-
ness 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 pro-
portionals :" 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 propo-
sitions, on the express ground that Euclid assumes a propo-
sition to show that it destroys itself: which is as if the
curate should demand permission to throttle the squire be-
cause St. Patrick drove the vermin to suicide to save them-
selves 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
JAMES SMITH, ARCH-PARADOXER. 123
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 dis-
ciplines. 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 con-
firmation 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 sev-
eral have been mislaid makes a hundred and seven pages
of note-paper, closely written. To all this I have not an-
swered 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 pre-
sumed 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
124 A BUDGET OF PARADOXES.
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 fran-
gible in extreme cases: otherwise there would be no living
under them ; and good society would be bad. Father Aldro-
vand 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 Dou-
loureuse 20 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 pam-
phlets 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. X 2 ; 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.
* The Garde Douloureuse was a castle in the marches of Wales
and received its name because of its exposure to attacks by the
Welsh.
JAMES SMITH, ARCH-PARADOXER. 125
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 2 *
The confusion of images is amusing: Goliath turning him-
self into a snail to avoid 7r = 3%, and James Smith, Esq.,
of the Mersey Dock Board: and put hors de combat
which should have been cache 2 * 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 para-
dox, 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
a "Out of the fight/
""Hidden."
126 A BUDGET OF PARADOXES.
*
that one of the letters to the Athenaum 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 pam-
phlet 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 Can-
tab 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 23 was sent to Newgate for a
18 John Cam Hobhouse (1786-1869), Baron Broughton, was com-
mitted to Newgate for two months in 1819 for his anonymous pam-
phlet, A Trifling Mistake. This was a great advertisement for him,
and upon his release he was at once elected to parliament for West-
JAMES SMITH, ARCH-PARADOXER.
127
libel on the House of Commons which was only intended
for a libel on Lord Erskine. 24 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 mathemat-
ical 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 TT untouched: or, if I put in
my thumb und 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. 2S This is
personal to the verge of scurrility: but in literary contro-
versy 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 personate concordat cum nominative.
I may plead precedent for taking a liberty with the
orthography of Jem. An instructor of youth was scan-
dalized at the abrupt and irregular but very effective
opening of Wordsworth's little piece:
minster. He was a strong supporter of all reform measures, and
was Secretary for War in 1832. He was created Baron Broughton
de Gyfford in 1851.
"Thomas Erskine (1750-1823), the famous orator. He became
Lord Chancellor in 1806, but sat in the House of Commons most of
his life.
25 The above is explained in the MS. by a paragraph referring to
some anagrams, in one of which, by help of the orthography sug-
gested, a designation for this cyclometer was obtained from the let-
ters of his name. S. E. De M.
""A personal verb agrees with its subject."
128 A BUDGET OF PARADOXES.
"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 TT, 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 Athenaum:
JAMES SMITH, ARCH-PARADOXER. 129
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 xyl
secondly, what is the angle of which xy represents the cir-
cular measure?"
If x represent 15 and y be %, xy represents 3 45',
whether x-y be xy or no. But, y being %, x-y is not xy
unless x be %, that is, unless \2x or TT 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 prem-
ises. 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
130 A BUDGET OF PARADOXES.
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 con-
tempt, at least. Now I have no fear for TT: 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 fiv
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 as-
sumes 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 re-
ferred 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 slockdol-
lager) treated Goliah Quagg. He has announced his in-
THE MOON HOAX. . 131
tention 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. 1
New York, 1859, 8vo.
This is a reprint of the hoax already mentioned. I sup-
pose R. A. Locke is the name assumed by M. Nicollet. 2
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. Be-
sides 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. 8 Sohncke's 4 Bibliotheca Mathematica con-
founds this Grant with Prof. R. Grant 5 of Glasgow, the
author of the History of Physical Astronomy, who is ac-
cordingly made to guarantee the discoveries in the moon.
I hope Adams Locke will not merge in J. C. Adams, 8 the
co-discoverer of Neptune. Sohncke gives the titles of
1 See Vol. I, page 326, note 1.
8 See Vol. I, page 326, note 2.
8 Apparently unknown to biographers.
*The Bibliotheca Mathematica of Ludwig Adolph Sohncke (1807-
1853), professor of mathematics at Konigsberg and Halle, covered
the period from 1830 to 1854, being completed by W. Engelmann.
It appeared in 1854.
5 See Vol. I, page 392, note 2.
6 See Vol. I, page 43, note 7.
132 A BUDGET OF PARADOXES.
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 dis-
covered the manuscript of Mungo Park; 7 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, 8 Mr. Harrison Ainsworth, 9 and others. I have
no doubt that M. Nicollet was the author of the Moon
hoax, 10 written in a way which marks the practised ob-
servatory 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 at-
tempted a fabrication for himself, did not succeed.
The Earth we inhabit, its past, present, and future. By Capt.
Drayson. 11 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
7 See Vol. II, page 91, note 5.
* Mason made a notable balloon trip from London to Weilburg,
in the Duchy of Nassau, in November, 1836, covering 500 miles in
18 hours. He published an account of this trip in 1837, and a work
entitled Aeronautica in 1838.
'William Harrison Ainsworth (1805-1885) the novelist.
10 On this question see Vol. I, page 326, note 2.
11 Major General Alfred Wilks Drayson, author of various works
on geology, astronomy, military surveying, and adventure.
IMPALEMENT BY REQUEST. 133
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
Athenaum, 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 Athenaum, 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?
134 A BUDGET OF PARADOXES.
quarantine?) shelves on which I keep my unestablished dis-
coveries. Had I known of this work in time, (see the
Introduction) I should of course, have impaled it (herald-
ically) 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 state-
ment 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 allevia-
tion. The author before me is, apparently, the sole fabri-
cator 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. 135
THE HAILESEAN SYSTEM OF ASTRONOMY.
The Hailesean System of Astronomy. By John Davey Hailes 1
(two pages duodecimo, 1860).
He offers to take 100,000/. to 1,000/. 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 re-
volving westward, so that they "meet at half the circle dis-
tance 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 2 name stand placed first. Do the worthy Frenchman
j ustice.
By awarding him the medal in a trice.
Give Adams 3 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
1 Hailes also wrote several other paradoxes on astronomy and
circle squaring during the period 1843-1872.
3 See Vol. I, page 43, note 8.
a See Vol. I, page 43, note 7.
136 A BUDGET OF PARADOXES.
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 mir-
acle-time, origin of time from science, with Bible and
Egyptian history. Rewards offered for astronomical prob-
lems. 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* 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 zoe, life, not from
zoon, animal. That class is of I nc or pore alia, order I., Infini-
tum, 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 wov is not
animal, but living being. Aristotle had classed gods under
o>a, 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
Genese. Par le Capitaine au longcours Justin Roblin. 1 Caen,
1861. 8vo.
4 "Very small errors are not to be condemned."
1 He seems to have written nothing else.
JOHANNES VON GUMPACH. 137
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
Esne, 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. 1 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 Geograph-
ical 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
1 Besides the paradoxes here mentioned by De Morgan he wrote
several other works, including the following: Abriss der Babylonisch-
Assyrischen Geschichte (Mannheim, 1854), A Popular Inquiry into
the Moon's rotation on her axis (London, 1856), Practical Tables
for the reduction of the Mahometan dates to the Christian kalendar
(London, 1856), Grundziige einer neuen Weltlehre (Munich, 1860),
and On the historical Antiquity of the People of Egypt (London,
1863).
138 A BUDGET OF PARADOXES.
recognized law of optics to the astronomical theory, show-
ing 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. 1 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, 2 which he obtained from Robert
Stephenson. 3 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
(1806-1873) was a civil engineer of prominence, and a
member of the British Association and the Royal Society of Edin-
burgh. He wrote (1863) on "Pepper's Ghost," an ingenious optical
illusion invented by him. There was a second edition of the Per-
petuum Mobile in 1870.
'George Stephenson (1781-1848), the inventor of the first suc-
cessful steam locomotive. His first engine was tried in 1814.
'Robert Stephenson (1803-1859), the only son of George. Most
of the early improvements in locomotive manufacture were due
to him. He was also well known for his construction of great
bridges.
SLANDER PARADOXES. 139
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. 4 "
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 in-
consecutive that it takes more than one reading to under-
stand 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 prepa-
ration 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 insinua-
4 "In its proper place."
140 A BUDGET OF PARADOXES.
tions 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 I' admire : 5 who can he be in this case ?
THE NEPTUNE CONTROVERSY.
1846. At the end of this year arose the celebrated con-
troversy relative to the discovery of Neptune. Those who
know it are well aware that Mr. Adams's 1 now undoubted
right to rank with Le Verrier 2 was made sure at the very
outset by the manner in which Mr. Airy, 8 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
1 "A fool always finds a bigger fool to admire him."
1 See Vol. I, page 43, note 7.
* See Vol. I, page 43, note 8.
1 See Vol. I, page 85, note 2.
THE NEPTUNE CONTROVERSY. 141
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 ChallisV 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 op-
portunities. 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 pro-
duced 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?
(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,
4 See Vol. I, page 390, note 1.
' From 1823 to 1852 it was edited by I. C. Robertson ; from 1852
to 1857 by R. A. Brooman; and from 1857 to 1863 by Brooman and
E. J. Reed.
142 A BUDGET OF PARADOXES.
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 pro-
tection" 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 re-
searches 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. 1
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 him-
self without feeling ill-will and originating accusations
would be indeed a paradox. But such a paradox has ex-
isted. It is very well known, both in and beyond the scien-
tific world, that the late James Ivory was subject to the
1 Sir James Ivory (1765-1842) was, as a young man, manager of
a flax mill in Scotland. In 1804 he was made professor of mathe-
matics at the Royal Military College, then at Marlow and later at
Sandhurst He was deeply interested in mathematical physics, and
there is a theorem on the attraction of ellipsoids that bears his
name. He was awarded three medals of the Royal Society, and was
knighted together with Herschel and Brewster, in 1831.
JAMES IVORY. 143
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, espe-
cially from my friend the late Thomas Galloway 2 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 So-
ciety. It was the duty of Mr. Epps, 8 the Assistant Secre-
tary, at the time when Francis Baily 4 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. 5 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 thor-
oughly sound judgment in every other respect seemed to be
under a complete chain of delusions about the conduct of
8 See Vol. I, page 56, note 1.
See Vol. I, page 153, note 5.
4 See Vol. I, page 309, note 2.
6 See Vol. I, page 87, note 4.
144 A BUDGET OF PARADOXES.
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 writ-
ten by a cautious friend, whose object was, if possible, to
prevent a difference from becoming a duel without com-
promising 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 con-
sequences 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 appro-
priate place. The faults of journalism, when merely ex-
posed by other journalism pass by and are no more re-
garded. 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
THE MECHANICS' MAGAZINE. 145
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 1 declined a
cheque forwarded for an article in the Quarterly, John
Murray 2 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 jour-
nal to help their personal likes and dislikes, and to sym-
pathize with them. Moreover, this sort of journal is more
accessible than others to articles conveying personal im-
putation: 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 con-
tributors whom they valued, was the Mechanics' Magazine*
in the period 1846-56. I cannot say that matters have not
mended in the last ten years: and I draw some presump-
1 George Canning (1770-1857), the Tory statesman and friend
of Scott, was much interested in founding the Quarterly Review
(1808) and was a contributor to its pages.
* See Vol. I, page 186, note 14.
1 See Vol. II, page 141, note 5.
146 A BUDGET OF PARADOXES.
tion 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 vol-
untary 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 mathe-
matical 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 re-
ceived, 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 oc-
curred the opportunity of payment. The Companion to the
Almanac 2 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
*De Morgan had a number of excellent articles in this publi-
cation.
THE MECHANICS' MAGAZINE. 147
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 for-
word to shield his champion. This gave deadly offence, as
will 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. 1 5 ) . 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 blun-
der. 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
148 A BUDGET OF PARADOXES.
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 3 and others of a high order and great interest ;
we have now, however, closed the publication as a scien-
tific one in remembrance of what it was, and not in con-
sequence 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'ceuvre, 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, 4 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
' See Vol. I, page 279, note 1.
/James Orchard Halliwell (182O-1889), afterwards Halliwell-
Phillips, came into prominence as a writer at an early age. When he
was seventeen he wrote a series of lives of mathematicians for the
Parthenon. His Rara Mathematica appeared when he was but nine-
teen. He was a great bibliophile and an enthusiastic student of
Shakespeare.
THE MECHANICS' MAGAZINE. 149
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-examina-
tion will find some strange conclusions arrived at by us. f
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, Wednes-
day, Thursday, Friday ; formerly, it would have been Mon-
day, 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
150 A BUDGET OF PARADOXES.
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 5 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 ety-
mologically, 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. Halli-
well's rare work, of kindred worth, entitled 'KARA MATHE-
MATICA/ it will then be deservedly handed down to pos-
terity 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
* This was written at the age of twenty-two.
T. S. DAVIES ON EUCLID. 151
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.] 8
"Accordingly, * * * was withdrawn, and a discussion
took place, for which see the Athenaum, 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 antes damnees 7 of
the Mechanics' Magazine?
T. S. DAVIES ON EUCLID.
First, as to Mr. Halliwell. The late Thomas Stephens
Davies, 1 excellent in geometry, and most learned in its his-
tory, 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 con-
sidered as the most precious deposit he had ever had in his
keeping Horner's 2 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
* The subject of this criticism is of long past date, and as it has
only been introduced by the author as an instance of faulty editor-
ship, I have omitted the name of the writer of the libel, and a few
lines of further detail. S. E. De M.
7 "Condemned souls."
'The editor of the Mechanics' Magazine died soon after the
above was written. S. E. De M.
1 Thomas Stephens Davies (1795-1851) was mathematical master
at Woolwich and F. R. S. He contributed a series of "Geometrical
Notes" to the Mechanics' Magazine and edited the Mathematician.
He also published a number of text-books.
* See Vol. II, page 66, note 4.
152 A BUDGET OF PARADOXES.
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 Dic-
tionary? to have received back a criticism, that would
have blown me out of the water: and I thought it not un-
likely 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 ques-
tion. And yet Mr. Halliwell is treated just as T. S. Davies
would have treated him, as to tone and spirit. The in-
ference 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 ser-
vice 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
'The Dictionary of Greek and Roman Biography (1849), edited
by Sir William Smith (1813-1893), whose other dictionaries on
classical and biblical matters are well known.
T. S. DAVIES ON EUCLID. 153
three are perfectly well printed. The printing of the Me-
chanics' 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 un fathomed 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 coun-
ter 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 com-
mon 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 whole-
sale grocer and colonial importer, who was made a Baron
by Napoleon I for his commercial success and his charities.
154 A BUDGET OF PARADOXES.
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 injurial 1 The other
J. S., Joseph Scaliger, 3 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 insti-
tuted, 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 quern dura manet sententia judicis, olim
Damnatum aerumnis suppliciisque caput,
Hunc neque fabrili lassent ergastula massa,
Nee rigidas vexent fossa metalla manus.
Circus quadrandus: nam caetera quid moror? omnes
Pcenarum facies hie labor unus habet" 8
1U O J. S. ! This is the worst! the greatest possible injury!"
8 See Vol. I, page 44, note 9 and page 110, note 5.
'"If there's a man whom the judge's pitiless sentence awaiteth,
' His head condemned to penalties and tribulations,
Let neither penitentiaries tire him with laborer's burdens
Nor let his stiffened hands be harrassed by work in the mines.
He must square the circle ! For what else do I care ? all
Known punishments this one task hath surely included."
J. S. SMITH AGAIN. 155
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 de-
tected by an effort of reasoning which I never could have
made except by following in his steps. In all matters con-
nected with TT the letters / and g are closely related : this
appears in the well-known formula for the time of oscilla-
tion 7r\/(l:g}. Hence g may be written for /, but only
once : do it twice, and you require the time to be ir\/ (l*:g 2 ).
This may be reinforced by observing that if as a datum,
or if you dislike that word, by hypothesis, the first / be a g,
it is absurd that it should be an /. Write g for the first /,
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 3% diameters to
156 A BUDGET OF PARADOXES.
the circumference in ?r-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, 1 Esq.
London and Jersey, 1862, 4to.
Mr. Houlston squares at about four poetical quotations
in a page, and brings out 7r = 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.2 London, 1862, 8vo.
Newton and others think that in a revolving sphere the
1 Houlston was in the customs service. He also published Ink-
lings of Areal Autometry, London, 1874.
9 This is Frederick C. Bakewell. He had already published
Natural Evidence of a Future Life (London, 1835), Philosophical
Conversations (London, 1833, with other editions), and Electric
Science (London, 1853, with other editions).
A FEW SMALL PARADOXERS.
157
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.s 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 4 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 equi-
noxes 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 gravi-
tation in terms "perfectly intelligible as well to the un-
learned as to the learned": to me they are quite unintelli-
gible, 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
aquivocatio. The author, as a physician, is accustomed
to "appeal from mere formulae": 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.
* Henry F. A. Pratt had already published A Dissertation on the
power of the intercepted pressure of the Atmosphere (London, 1844)
and The Genealogy of Creation (1861). Later he published a work
On Orbital Motion (1863), and Astronomical Investigations (1865).
4 See Vol. I, page 260, note 1.
158 A BUDGET OF PARADOXES.
On matter and ether, and the secret laws of physical change.
By T. R. Birks, M.A. 6 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 antici-
pation 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 pos-
sess, 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. 1 (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 else-
where as having for his device the round man in the three-
cornered hole, the writer of the little heap of satirical anon-
ymous letters about the Beast and 666. By accident I dis-
covered 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 him-
' Thomas Rawson Birks (1810-1883), a theologian and contro-
versialist, fellow of Trinity College, Cambridge, and (1872) pro-
fessor of moral philosophy in that university. He wrote Modern
Rationalism (1853), The Bible and Modern Thought (1861), The
First Principles of Moral Science (1873), and Modern Physical
Fatalism and the Doctrine of Evolution (1876), the last being an
attack on Herbert Spencer's First Principles.
1 Pseudonym for William Thorn. In the following year (1863)
he published a second work, The Thorn-Tree : being a History of
Thorn Worship, a reply to Bishop Colenso's work entitled The Pen-
tateuch and the Book of Joshua critically examined.
DR. THORN AND MR. BIDEN. 159
self, 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 cer-
tainly 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 knowl-
edge 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 com-
menced, 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 in-
closing me in a magic circle of 3% diameters in circum-
ference. The round man in the three-cornered hole, finally
William Thorn, M.D., takes charge of my future destiny,
160 A BUDGET OF PARADOXES.
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 sphragidonychargoco-
metical 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 my-
self and thanks from my reader. The dual of the Pythag-
orean 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 2 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
Ezekielr.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.
"Besides The Pestilence (1866) he published The True Church
(1851), The Church and her destinies (1855), Religious reformation
imperatively demanded (1864), and The Bible plan unfolded (second
edition, 1872).
DR. THORN AND MR. BIDEN. 161
"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 lan-
guage 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, 3 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 else-
where 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 numer-
ous that there is no choosing.
* See Vol. II, page 97, note 1.
162 A BUDGET OF PARADOXES.
SIR G. C. LEWIS.
An historical survey of the Astronomy of the Ancients. By the
Rt. Hon. Sir G. C. Lewis.* 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 imi-
tations : Mr. Maiden's 2 Pragmatized Legends, Mr. Mansel's 3
Phrontisterion, and Sir G. Cornewall Lewis's Inscriptio
Antigua. ' In this last, HEYDIDDLEDIDDLETHECATANDTHEFID-
DLE 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
'Sir George Cornewall Lewis (1806-1863) also wrote an Essay
on the Origin and Formation of the Romance Languages (1835), an
Essay on the Government of Dependencies (1841), and an Essay on
Foreign Jurisdiction and the Extradition of Criminals (1859). He
was Chancellor of the Exchequer in 1855 and Home Secretary in
1859.
2 Henry Maiden (1800-1876), a classical scholar, fellow of Trin-
ity College, Cambridge, and professor of Greek at University College
(1831-1876), then (1831) the University of London. He wrote a
History of Rome to 390 B. C. (1830), and On the Origin of Uni-
versities and Academical Degrees (1835).
'Henry Longueville Mansel (1820-1871), theologian and meta-
physician, reader in theology at Magdalen College, Oxford (1855),
and professor of ecclesiastical history and Dean of St. Paul's (1866).
He wrote on metaphysics, and his Bampton Lectures (1858) were
reprinted several times.
SIR G. C. LEWIS. 163
junctura ovorum dape [colitur], deus mundi. Deus in lita-
tione voluit, benigno animo, haedum, taurum intra fines [loci
sacri] portandos. Deus, bis lustratus, beat fossam sacrse
libationis." 4
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, be-
cause 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 imply-
ing 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 pro-
nounce our judgment good for nothing, and will form an
'"Hejus gave freely, gave freely. God is propitious, God is
favorable to him who gives freely. God is honored with a banquet of
eggs at the cross roads, the god of the world. God, with benignant
spirit, desired in sacrifice a goat, a bull to be carried within the pre-
cincts of the holy place. God, twice propitiated, blesses the pit of
the sacred libation."
164 A BUDGET OF PARADOXES.
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 con-
spicuous, 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, 5 as we learn from Simplicius; 6 the
following is his statement, to which the true times are sub-
joined, for the sake of comparison :
STATEMENT OF EUDOXUS TRUE TIME
Mercury ... 1 year ... 87d. 23h.
Venus .... 1 " ... 224d. 16h.
Mars .... 2 " . . . ly. 321d. 23h.
Jupiter ... 12 " . . lly. 315d. 14h.
Saturn .... 30 4< . . 29y. 174d. Ih.
Upon this determination two remarks may be made. First,
the error with respect to Mercury and Venus is consider-
able; 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 ob-
serve and to measure, but the cause of the large error with
respect to Venus (130 days) is not apparent.
'Eudoxus of Cnidus (408-355 B.C.) had much to do with the
early scientific astronomy of the Greeks. The fifth book of Euclid
is generally attributed to him. His astronomical works are known
chiefly through the poetical version of Aratus mentioned in note 13,
page 167.
6 Simplicius, a native of Cilicia, lived in the 6th century of our
era. He was driven from Athens by Justinian and went to Persia
(531), but he returned later and had some fame as a teacher.
SIR G. C. LEWIS. 165
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 astron-
omy than giving Eudoxus the Copernican system? If Mer-
cury 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 de-
partures both ways. The same for Venus, with larger de-
partures. 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 diffi-
cult 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. <lw) [(169).
See Delambre, Hist. Astr. Mod., Vol. I, p. 96]. It was
reserved to Kepler to propound the hypothesis of the con-
stant 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 7 cited, it is that the
parallelism of the earth's axis is a glaring part of the
1 See Vol. I, page 160, note 3.
166 A BUDGET OF PARADOXES.
theory of Copernicus. What Kepler 8 did was to throw
away, as unnecessary, the method by which Copernicus,
per fas et nefas* 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?
"Cest done pour arriver a ce parallelisme, ou pour le
conserver, que Copernic a cru devoir recourir a ce mouve-
ment egal et oppose qui detruit 1'effet qu'il attribue si
gratuitement au premier, de deranger le parallelisme." 10
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 author-
ity. He fancies that to give an instance for the deter-
mination of a ship's place, the invention of chronometers
has been far more important than any improvement in astro-
nomical 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
8 See Vol. I, page 76, note 3.
' "Through right and wrong."
"It is therefore to arrive at this parallelism, or to preserve it,
that Copernicus feared to be obliged to have recourse to this equal
and opposite movement which destroys the effect which he attributed
so freely to the first, of deranging the parallelism."
SIR G. C. LEWIS. 167
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 ob-
servation, 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, 11 who is either
the culprit or his historian, attributes to Meton, 12 the con-
triver 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 13 we read about the nineteen
years of the shining sun:
*Ei/i>eaKcu8eKa KVK\O. <aeivov ^eAioto. 14
Some man of letters must have turned Apollo into Phaeinus
of Elis; and there he is in the histories of astronomy to
"A contemporary of Plato and a disciple of Aristotle.
12 Meton's solstice, the beginning of the Metonic cycles, has been
placed at 432 B. C. Ptolemy states that he made the length of the
year 36574 + V 72 days.
13 Aratus lived about 270 B. C., at the court of Antigonus of
Macedonia, and probably practiced medicine there. He was the
author of two astronomical poems, the Qaivofieva, apparently based
on the lost work of Eudoxus, and the Atoo-Tjeia based on Aristotle's
Meteorologica and De Signis Ventorum of Theophrastus.
""The nineteen (-year) cycle of the shining sun."
168 A BUDGET OF PARADOXES.
this day. Salmasius 15 will have Aratus to have meant him,
and proposes to read qAei'oto : he did not observe that Phaei-
nus 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, 1 '
whose dealings with the United States were reckoned by
yearly millions, counted duodecimally in England and deci-
mally in America, was the best, but not the only, represen-
tative 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 ob-
viously knew nothing. The members of the deputation
began to make their statements, and met with curious de-
nials. He interrupted me with "Surely there is no doubt
that the calculations of our books of arithmetic are easier
"Claudius Salmasius (1588-1653), or Claude Saumaise, was a
distinguished classicist, and professor at the University of Leyden.
The word ^Xe/oio means Elian, thus making the phrase refer to the
brilliant one of Elis.
"Sir William Brown (1784-1864). In 1800 the family moved
to Baltimore, and there the father, Alexander Brown, became prom-
inent in the linen trade. William went to Liverpool where he ac-
quired great wealth as a merchant and banker. He was made a
baronet in 1863.
DECIMAL COINAGE. 169
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 con-
trast 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 reck-
lessness 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 yearn-
ings towards politics, and are in formation of habits.
In the debate on decimal coinage of July 12, 1855, Mr.
Lowe, 1 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,
1 Robert Lowe (1811-1892), viscount Sherbrooke, was a fellow
of Magdalen College, Oxford (1835). He went to Australia in 1842
and was very successful at the bar. He returned to England in 1850
and became leader writer on the Times. He was many years in parlia-
ment, and in 1880 was raised to the peerage.
170 A BUDGET OF PARADOXES.
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 argumenta-
tive 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 an-
swered. 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 acute-
ness 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 In the name of common
florins?" 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 nozv, there must be a column for the odd shil-
ling.
"He was glad that some If the hon. gentleman
hon. gentleman had derived make this assertion of him-
benefit from the issue of self, it is not for us to gain-
florins. His only experience say it. It only proves that
of their convenience was, he is one of that class of
DECIMAL COINAGE. 171
that when he ought to have men who are described in
received half-a-crown, he the old song, of which one
had generally received a couplet runs thus:
florin, and when he ought I sold my cow to buy me a
to have paid a florin, he calf;
had generally paid half-a- I never make a bargain but I
crown." (Hear, hear, and lose half,
laughter.) 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 un-
moved 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 en-
deavoring 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 ex-
to 2 2-5ths of a penny, but pressing our coin in terms of
who ever bought anything, the penny, which we aban-
vvho ever reckoned or wished don, instead of the florin,
to reckon in such a coin as which we retain. Remem-
that?" (Hear, hear.) her that this 2 2-5ths is the
hundredth part of the pound,
which is called, as yet, a cent. Nobody buys anything at a
cent, because the cent is not yet introduced. Nobody reck-
ons 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
172
A BUDGET OF PARADOXES.
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 never
come into general circula-
lation, because it represents
nothing which corresponds
with any of the wants of
the people."
Does 2^d. never pass
from hand to hand? And
is 2d. so precisely the modu-
lus of popular wants, that
an alteration of 4 per cent,
would make it useless? Of
all the values which 2d.
measures, from three pounds of potatoes down to certain
arguments used in the 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 omni-
bus fares, the bunches of radishes, etc. etc. etc., would
adapt themselves to the coin.
"If the proposed system
were adopted, they would
all be compelled to live in
decimals for ever; if a man
dined at a public house he
would have to pay for his
dinner in decimal fractions.
(Hear, hear.) He objected
to that, for he thought that
a man ought to be able to
pay for his dinner in in-
tegers." (Hear, hear, and a
laugh.)
The confusion of ideas
here exhibited is most in-
structive. The speaker is
under the impression that we
are introducing fractions :
the truth is, that we only
want to abandon the more
difficult fractions which he
have got, and to introduce
easier fractions. Does he
deny this? Let us trace his
denial to its legitimate con-
sequences. A man ought to
pay for his dinner in integers.
DECIMAL COINAGE. 173
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, 2 and Walkingame, 3 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, how- A pleasant sum even for
ever, had not yet been an accomplished mathemati-
changed into decimal system, cian. What does divided by
That change might appear the decimal of a pound
very easy to accomplished mean ? Perhaps it means re-
mathematicians and men of duced to the decimal of a
science, but it was one which pound ! Mr. Lowe supposes,
it would be very difficult to as many others do, that, after
carry out. (Hear, hear), the change, all calculations
What would have to be will be proposed in old
done ? Every sum would have money, and then converted
to be reduced into a vulgar into new. He cannot hit the
a See Vol. I, page 42, note 4.
'Francis Walkingame (fl. about 1751-1785), whose Tutor's Assis-
tant went through many editions from 1751-1854.
174 A BUDGET OF PARADOXES.
fraction of a pound, and idea that the new coins will
then divided by the decimal take the place of the old.
of a pound a pleasant sum This lack of apprehension
for an old applewoman to will presently appear further,
work out !" ( Hear, hear, and
laughter.)
"It would not be an agree- Let the members be as-
able task, even for some sured that nine half-pence
members of that House, to will be, for every practical
reduce 4Jd., or nine half- purpose, 18 mils. But now
pence, to mils." (Hear, to the fact asserted. Davies
hear.) Gilbert 4 used to maintain
that 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, 5 Pollock, 6 and Hume. 7 He
himself was then out of Parliament.] Joseph Hume af-
firmed 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 dam-
aging 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
4 Davies Gilbert (1767-1839). His family name was Giddy, but
he assumed his wife's name. He sat in parliament from 1806 to 1832.
In 1819 he secured the establishment of the Cape of Good Hope
observatory. He was Treasurer (1820-1827) and President (1827-
1830) of the Royal Society.
B See Vol. I, page 55, note 2.
'Sir Jonathan Frederick Pollock (1783-1870) entered parlia-
ment in 1831 and was knighted in 1834.
'Joseph Hume (1777-1855) entered parliament in 1812 and for
thirty years was leader of the Radical party.
DECIMAL COINAGE. 175
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, hun-
dreds, 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 4Jd. into mils, as any boys on the
lower forms of a commercial school.
For a long period of years, allusion to the general ig-
norance of arithmetic, has been a standing mode of argu-
ment, 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 mean-
while the country is gradually arriving at the conclusion that
a true joke is no joke.
"The main objection was, Fine words, wrongly used,
if they went below 6d., that The new coins are commen-
the new scale of coins would surable with, and in a finite
not be commensurate in any ratio to, the old ones. The
finite ratio with anything in farthing is to the mil as 25
this new currency of mils." to 24. The speaker has some-
thing here in the bud, which
we shall presently meet with
in the flower; and fallacies
are more easily nipped in
flower than in bud.
176
A BUDGET OF PARADOXES.
"No less than five of our This dreadful change of
present coins must be called value consists in sixpence
in, or else which would be farthing going to the half-
worse new values must be shilling instead of sixpence,
given to them." Whether the new farthings
be called mils or not is of no
consequence.
"If a poor man put a Mr. Lowe, who cannot
penny in his pocket, it would pass a half-crown for more
come out a coin of different than a florin, or get in a
value, which he would not florin at less than half-a-
understand. Suppose he owed crown, has such a high faith
another man a penny, how
was he to pay him ? Was he
in the sterner stuff of his
fellow countrymen, that he
to pay him in mils? Four believes any two of them
mils would be too little, and would go to fisty cuffs for
five mils would be too much.
The hon. gentlemen said
would be a 'mill' between
them." (Much laughter.)
the 25th part of a farthing.
He reasons thus: He has
there would be only a mil often heard in the streets,
between them. That was ex- "I'd fight you for the fiftieth
actly it. He believed there part of a farden:" and hav-
ing (that is, for a Member)
a notion both of fractions
and logic, he infers that those
who would fight for the 50th
of a farthing would, a for-
tiori, fight for a 25th. His mistake arises from his not
knowing that when a person offers to fight another for
%ood., ne 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 pres- We should hardly believe
sent expression for four- all this to be uttered in ear-
pence? Why, 0.166 (a nest, if we had not known
DECIMAL COINAGE.
177
laugh) ; for threepence?
.0125; for a penny? .004-
166, and so on ad infinitum
(a laugh) ; for a half-penny?
.002083 ad infinitum. (A
laugh). What would be the
present expression for a far-
thing? Why, .0010416 ad
infinitum. (A laugh). And
this was the system which
was to cause such a saving
in figures, and these were the
quantities into which the
poor would have to reduce
the current coin of the realm.
(Cheers). With every re-
spect for decimal fractions,
of which he boasted no pro-
found knowledge, he doubted
whether the poor were equal
to mental arithmetic of this
kind, (hear, hear) and he
hoped the adoption of the
system would be deferred
until there were some proof
that they would be able to
understand it; for, after all,
this was the question of the
poor, and the whole weight
of the change would fall
upon them. Let the rich by
all means have permission
to perplex themselves by any
division of a pound they
pleased ; but do not let them,
by any experiment like this,
that several persons who
have not Mr. Lowe's hu-
mor, nevertheless have his
impressions on this point. It
must therefore be answered ;
but how is this to be done
seriously ?
Dialogue between a mem-
ber of Parliament and an
orange-boy, three days after
the introduction of the com-
plete decimal system. The
member, going down to the
House, wants oranges to sus-
tain his voice in a two hours'
speech on moving that 100-
OOO/. be placed at the dis-
posal of Her Majesty, to
supply the poor with ready-
reckoners.
Boy. Fine oranges! two
a penny ! two a penny !
178
A BUDGET OF PARADOXES.
impose difficulties upon the
poor and compel men to carry
ready - reckoners in their
pocket to give them all these
fractional quantities. "(Hear,
hear.)
Member. Here boy, two !
Now, how am I to pay you?
Boy. Give you change,
your honor.
Member. Ah! but how?
Where's your ready-reck-
oner?
Boy. I sells a better sort
nor them. Mine's real
Cheyny.
Member. But you see a
farthing is now .0014166-
666 ad infinitum, and if we
multiply this by A
Boy. Hold hard, Guv'-
ner ; I sees what you're arter.
Now what'll you stand if I
puts you up to it? which
Bill Smith he put me up in
two minutes, cause he goes
to the Ragged School.
Member. You don't mean that you do without a book !
Boy. Book be blowed. Come now, old un, here's
summut for both on us. 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
DECIMAL COINAGE. 179
out a sixpence ; well in coorse, I hands over fippence f arden
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 half-
penny 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 mis-
conceptions 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 unedu-
cated 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 prosef 8 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 in-
flicted 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 re-
quired to this, beyond the mere statement of the nature of
the assumption and denial.
""What! when I say, 'Nicole, bring me my slippers,' is that
prose?"
180 A BUDGET OF PARADOXES.
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 far-
thing 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 Astro-
nomical 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 em-
ployed. 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 Astro-
nomical 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 Com-
mittee 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
DECIMAL COINAGE. 181
decide this question, with Mr. Lowe to quote the descrip-
tion given by Basil Hall 9 (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 Shaftes-
bury, 10 Mr. Babbage, 11 Sir John Herschel, 12 Sir Thomas
Maclear 13 (Astronomer Royal at the Cape of Good Hope),
Dr. Robinson 14 (of Armagh), Sir James South, 15 Lord
Wrottesley, 16 and myself].
'Captain Basil Hall (1788-1844), a naval 9fficer, carried on a
series of pendulum observations in 1820-1822, while on a cruise of the
west coast of North America. The results were published in 1823
in the Philosophical Transactions. He also wrote two popular works
on travel that went through numerous editions.
"Anthony Ashley Cooper (1801-1885), Earl of Shaftesbury. His
name is connected with philanthropic work and factory legislation.
11 See Vol. I, page 207, note 12.
13 See Vol. I, page 80, note 5.
"Sir Thomas Maclear (1794-1879), an Irishman by birth, be-
came Astronomer Royal at the Cape of Good Hope in 1833. He
was an indefatigable observer. He was knighted in 1860.
"Thomas Romney Robinson (1792-1882), another Irish astron-
omer of prominence. He was a deputy professor at Trinity College,
Dublin, but took charge of the Armagh observatory in 1823 and re-
mained there until his death.
"Sir James South (1785-1867) was in early life a surgeon, but
gave up his practice in 1816 and fitted up a private observatory. He
contributed to the science of astronomy, particularly with respect to
the study of double stars.
"Sir John Wrottesley (1798-1867), second Baron Wrottesley.
Like Sir James South, he took up the study of astronomy after a
professional career, in his case in law. He built a private observa-
tory in 1829 and made a long series of observations, publishing three
star catalogues. He was president of the Astronomical Society from
1841 to 1843, and of the Royal Society from 1854 to 1857.
182 A BUDGET OF PARADOXES.
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. 1 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 six-
teen, 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. Prob-
ably 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
1 He seems to have written nothing else.
SOME SMALL PARADOXERS. 183
to become of those lines of Praed, which I remember com-
ing out when I was at Cambridge,
"Oh! now's the time of all the year for flowers and fun, the May-
days;
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 2 already mentioned, proceeding by twelves,
I should reply, with Candide, when he had the option given
of running the gauntlet or being shot: Les volontes sont
libres, et je ne veux ni Tun ni 1'autre. 3 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 quad-
rature 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, 1 or Fallacies affecting science. By James
Reddie. 2 London, 1862, 8vo.
a See Vol. II, page 68, note 8.
"The wills are free, and I wish neither the one nor the other."
'"The force of inertia conquered."
'Reddie also wrote The Meclianics of the Heavens, referred to
later in this work. He must not be confused with Judge James
Reddie (1773-1852), of Glasgow, who wrote on international law,
although this is done in the printed edition of the British Museum
catalogue, for he is mentioned by De Morgan somewhat later as
being alive in 1862.
184 A BUDGET OF PARADOXES.
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 Associa-
tion declined to consider. It is entitled
Victoria Toto Ccelo', 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 Econ-
omy. By H. Dunning Macleod, 3 Esq. Cambridge, 1862, 8vo.
A paper read but, according to the report, not under-
stood 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 varia-
tions; thirdly, "independent quantities or unconnected
events, which is the theory of probabilities." I am not
ashamed, having the British Association as a co-non-intel-
ligent, to say I do not understand this : there is a paradox
in it, and the author should give further explanation, espe-
cially of his negative quantity. Mr. Macleod has gained
'Henry Dunning Macleod (1821-1902), a lawyer and writer on
political economy, was a Scotchman by birth. He wrote on econom-
ical questions, and lectured on banking at Cambridge (1877) and at
King's College, London (1878). He was a free lance in his field,
and was not considered orthodox by the majority of economists
of his time. He was an unsuccessful candidate for the chairs of
political economy at Cambridge (1863), Edinburgh (1871), and
Oxford (1888).
SOME SMALL PARADOXERS. 185
praise from great names for his political economy; but
this, I suspect, must have been for other parts of his sys-
tem.
On the principles and practice of just Intonation, with a view to
the abolition of temperament.. . By General Perronet Thomp-
son. 4 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 tempera-
ment published some years ago, I said that equal tempera-
ment 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 tempera-
ment, 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 re-
mark 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 tem-
perament which was once applied to the postmen's jackets.
The coats were all made for the average man: the conse-
* See Vol. I, page 252, note 2.
186 A BUDGET OF PARADOXES.
quence 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 V 1 ? By F. H. Laing. 5 London, 1863, 8vo.
If I understand the author, -a and +a are the square
roots of - a 2 , 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. 1 London, 1863,
8vo.
The plan is to throw numbers into the form a ( 1 . 1 ) b
(1.01) c (1.001) rf 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 uni-
versal language, Where is the second man to come from?
An effective predecessor in the same line of invention
6 Francis Henry Laing (1816-1889) was a graduate of Queen's
College, Cambridge, and a clergyman in the Church of England
until 1846, when he entered the Church of Rome. He taught in
various Jesuit colleges until 1862, when his eccentricity was too
marked to warrant the Church in allowing him to continue. He
published various controversial writings during his later years. Of
course if he had known the works of Wessel, Gaus, Buee, Argand,
and others, he would not have made such a sorry exhibition of his
ignorance of mathematics.
1 See Vol. I, page 329, note 1. The book went into a second edi-
tion in 1864.
HORNER'S METHOD. 187
was the late Mr. Thomas Weddle, 2 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. 367975-
431) of the equation
1379 . 664:r C22 + 2686034 x lO 432 * 153 - 17290224 x 10 51 V +
2524156 x!0 574 = 0.
The method proceeds by successive factors of the form, a
being the first approximation, axl-frxl-Ocx l-OOd
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]cour-
agement which he received induces [obliges] him to lay the
result of his enquiries in this important branch of mathe-
matics 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 remark-
ably simple method" possessing "several important advan-
tages." Mr. Rutherford's 3 extended value of TT 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
"Thomas Weddle (1817-1853) was, at the time of publishing
this paper, a teacher in a private school. In 1851 he became pro-
fessor of mathematics at Sandhurst. He contributed several papers
to the Cambridge and Dublin Mathematical Journal, chiefly on geom-
etry.
8 See Vol. II, page 109, note 6.
188 A BUDGET OF PARADOXES.
marked the Royal Society is no longer in existence. But
not without severe lessons. They had the luck to accept
Horner's 4 now celebrated paper, containing the method
which is far on the way to become universal: but they re-
fused the paper in which Horner developed his views of
this and other subjects: it was printed by T. S. Davies 5
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, 9
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 7
printed it. The Society is now better informed: "live and
learn/ 9 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 conversa-
tion, there is no doubt that the true method of solving equa-
tions 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 mathe-
matics. 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,
4 See Vol. II, page 66, note 4
' See Vol. II, page 151, note 1.
'George Barrett (1752-1821) worked from 1786 to 1811 on a
set of life insurance and annuity tables. He invented a plan known
as the "columnar method" for the construction of such tables, and
as De Morgan states, this was published by Francis Baily, appearing
in the appendix to his work on annuities, in the edition of 1813.
Some of his tables were used in Babbage's Comparative View of the
various Institutions for the Assurance of Lives (1826).
7 See Vol. I, page 309, note 2.
HORNER'S METHOD. 189
was without a European predecessor, and in the distinctive
part of his discovery was heir-at-law to the nameless Brah-
min Tartar Antenoachian what you please who con-
cocted 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
190 A BUDGET OF PARADOXES.
the work of Mr. Oliver Byrne, the dual arithmetician, etc.
This writer published, in 1849, a method of calculating
logarithms. 8 First, a long list of instances in which, as he
alleges, foreign discoverers have been pillaged by English-
men, or turned into Englishmen : for example, O'Neill, 9 so
called by Mr. Byrne, the rectifier of the semi-cubical parab-
ola 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 in-
ventor 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.
"This was his Practical short and direct Method of Calculating
the Logarithm of any given Number, and the Number corresponding
to any given Logarithm (1849).
'This is William Neile (1637-1670), grandson of Richard Neile
(not Neal), Archbishop of York. At the age of 19, in 1657, he gave
the first rectification of the semicubical parabola. Although he com-
municated it to Brouncker, Wren, and others, it was not published
until 1639, when it appeared in John Wallis's De Cycloide.
ARE ATOMS WORLDS? 191
But I myself pars magna fui: w 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. 1 Redruth and London, 1863, 8vo.
This book, as a paradox, beats quadrature, duplication,
trisection, philosopher's stone, perpetual motion, magic, as-
trology, mesmerism, clairvoyance, spiritualism, homoeop-
athy, hydropathy, kinesipathy, Essays and Reviews, and
Bishop Colenso, 2 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 ques-
tion 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 par-
ticles 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." s
I have often had the notion that all the nebulae 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
" I myself "was a considerable part."
J He also wrote A Glance at the Universe ("2d thousand" in
1862), and The Resurrection Body (1869).
J See Vol. I, page 63, note 1.
* As Swift gave it in his Poetry. A Rhapsody, it is as follows :
"So, naturalists observe, a flea
Has smaller fleas that on him prey;
And these have smaller still to bite 'em.
And so proceed ad infinitum! 1
192 A BUDGET OF PARADOXES.
larger universe. Of course the minim of time a million
of years or whatever the geologists make it 4 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 mil-
lions 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
started 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 corpori-
spiritual 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 Caesar, and B
the building of the Pyramids, by actual observation of the
processes with a power of a thousand millions ; C will dis-
cover the commencement of the Millennium, and D the ter-
4 Perhaps 1,600,000,000 years, if Boltwood's recent computations
based on radium disintegration stand the test. This would mean,
according to MacCurdy's estimate, 60,000,000 years since life first
appeared on the earth.
THE SUPERNATURAL. 193
mination of Ersch and Gruber's Lexicon, 5 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 1 London, 2 vols. 8vo. 1863.
Mr. Howitt is a preacher of spiritualism. He cements
an enormous collection of alleged facts with a vivid out-
pouring of exhortation, and an unsparing flow of sarcasm
against the scorners of all classes. He and the Rev. J.
Smith 2 (ante, 1854) are the most thoroughgoing universal-
ists 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 con-
scious 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.
5 De Morgan wrote better than he knew, for this work, the All-
gemeine Encyclop'ddie der IVissenschaften und Kunste, begun at
Leipsic in 1818, is still (1913) unfinished. Section I, A-G, consists
of 99 parts in 56 volumes; Section II, H-N, consists of 43 volumes
and is not yet completed; and Section III, O-Z, consists of 25 vol-
umes thus far, with most of the work still to be done. Johann
Samuel Ersch (1766-1828), the founder, was head librarian at Halle.
Johann Gottfried Gruber (1774-1851), his associate, was professor of
philosophy at the same university.
1 William Howitt (1792-1879) was a poet, a spiritualist, and a
miscellaneous writer. He and his wife became spiritualists about
1850. He wrote numerous popular works on travel, nature and his-
tory.
9 See Vol. II, page 55, note 1.
194 A BUDGET OF PARADOXES.
FROM MATTER TO SPIRIT.
From Matter to Spirit. By C. D. With a preface by A. B. 1
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 ortho-
doxy 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 dic-
tatory manner, that, as a rule, there is no more quiet and
modest member of society than the urban clergyman. Domi-
nation 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 fright-
ened you with infidel, is still a recognized member of society,
wants taming, and will get it. He wears the priest's cast-off
1 As will be inferred from the text, C. D. was Mrs. De Morgan,
and A. B. was De Morgan.
FROM MATTER TO SPIRIT. 195
clothes, dyed to escape detection: the better sort of philos-
ophers would gladly set him to square the circle.
The book just named appeared about the same time as
this Budget began in the Athenceum. 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 char-
acters: 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*
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
'Jean Meslier (1678-1733), cure of Estrepigny, in Champagne,
was a skeptic, but preached only strict orthodoxy to his people.
It was only in his manuscript, Mon Testament, that was published
after his death, and that caused a great sensation in France, that his
antagonism to Christianity became known.
196 A BUDGET OF PARADOXES.
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, sub-
terfuges, 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 uncom-
mon 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 aston-
ishes the town populations, accustomed to rub their brains 3
against one another. Such a story as the following would,
'Baron Zach relates that a friend of his, in a writing intended
for publication, said Un esprit doit se frotter centre un autre. The
censors struck it out. The Austrian police have a keen eye for con-
sequences. A. De M.
"One mind must rub against another." On Baron Zach, see Vol.
II, page 45, note 4.
FROM MATTER TO SPIRIT. 197
in our day, bring down grave remarks from above: but I
write of the olden (or Eldon 4 ) time, when nothing but con-
viction 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 sus-
pect 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-par-
tridges 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 lectur-
ing him on his wickedness: but they admitted with reluc-
tance, that there was a legal distinction; and the brain of
N 3 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 lec-
tures, and the like. There is now no class, as a class, more
highly educated, broadly educated, and deeply educated,
4 Referring to the first Lord Eldon (1751-1838), who was Lord
Chancellor from 1799 to 1827, with the exception of one year.
198 A BUDGET OF PARADOXES.
than those who were, in old times, best described as par-
tridge-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 sug-
gestion 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 pre-
vented all but the beaten road from being seen: the pro-
fessional reins were pulled at the slightest attempt to
quicken pace, even on the permitted path; and the pro-
FROM MATTER TO SPIRIT. 199
fessional 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 con-
trast 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 remem-
bering. 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 conse-
quences 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 number-
less 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 be-
cause 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
200 A BUDGET OF PARADOXES.
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 homoeopathy,
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 Moliere, the virtus dormitiva 5 of opium,
for no other reason than that opium facit dormire* Had
the medicine not been previously known, they would, strange
as it may seem to modern pharmacopoeists, 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 main-
tenance 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 school-
man 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 draw-
ing-rooms will fight facts with his principles, just as an old
6 "Sleeping power."
6 "Causes sleep."
FROM MATTER TO SPIRIT. 201
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 stop-
page 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 work-
ing smack of its knowledge, without any depth of education,
general or professional. Not that this is the whole explana-
tion, nor in itself objectionable: the great mass of the
world must be tended, soul and body, by those who are
neither Hookers 7 nor Harveys 8 : let such persons not ven-
ture 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
'Richard Hooker (c. 1554-1600), a theologian, "the ablest liv-
ing advocate of the Church of England as by law established."
' See Vol. I, page 76, note 3.
202 A BUDGET OF PARADOXES.
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 hap-
pened 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 trans-
lates : He says that this sentence is A. B.'s summing up
of the evidence of Spiritualism. Now, being a sort of alter
ego g 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 any-
thing 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
"Other I," other self.
FROM MATTER TO SPIRIT. 203
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 igno-
rance in a Greek critic ; for dvaiyu8ia, breeches, would have
turned up in the lexicon; and kalos geusis, though absurd,
is not obscure. And djLuooycTrws, somehow or other, is as
easily found as dvaupi8ta. 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
1877? have been rendered. The aneroid barometer does not
use a column of air in the same way as the old instrument.
Now aepoeiSr)? properly like the atmosphere is by scien-
tific non-scholarship rendered having to do with the at-
mosphere; and ava.epoet.Sr)? say anaeroid denies having to
do with the atmosphere ; a nice thing to say of an instru-
ment 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 in-
sists upon utter rejection being unavoidable. 10 The ex-
pressed 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
E Ut De M^ "" ^ * fepeated (1872) by the sarae
204 A BUDGET OF PARADOXES.
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 sus-
pend 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 necessi-
ties : but I never said that Protestant argument had nothing
but paralogism. The writer before me attains this com-
pleteness: 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 ... he proceeds to argue
refers the whole either to that he himself is outside its
unseen intelligence, or some- sacred pale because he refers
thing which man has never all these strange phenomena
had any conception of, proves to unseen spiritual intelli-
me to be out of the pale of gence.
the Royal Society.
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 in-
FROM MATTER TO SPIRIT. 205
quiry 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 account-
ing 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 11 and vaccination were, in a certain but very un-
satisfactory way, witnesses to the possible excellence of
the system of St. John Long." 12 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 re-
vision, to put the sentence into fighting order, hurry pre-
venting 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. 13
"Edward Jenner (1749-1823) was a physician and biologist His
was pubfohSffn 1 1 n 7 9g accination were made in 1796 > and h 's discovery
" See Vol. II, page 38, note 4.
'"You will go most safely in the middle (way)."
206 A BUDGET OF PARADOXES.
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 Athenceum 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 block-
head. '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 effec-
tive 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 in-
sinuate an affirmative conclusion in the second figure. Great
discoverers have been little valued by established schools,
FROM MATTER TO SPIRIT. 207
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 fair-
ness and moderation and suspended opinion which the doc-
trine 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- f eathered : 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, ex-
claimed Oh! if all the fools in the world could be rolled
up into one fool, what a reviewer he would make!
Calendrier Universe! et Perpetuel; par le Commandeur P. J.
Arson. 14 Public par ses Enfans (OEuvre 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,
14 Pierre Joseph Arson was known early in the 19th century for
his controversy with Hoene Wronski the mathematician, whom he
attacked in his Document pour Phistoire des grands fourbes qui ont
figure sur la terre (1817-1818).
208 A BUDGET OF PARADOXES.
which comes in the middle. Thursday, Friday, Saturday,
are ascending or waxing days ; Monday, Tuesday, Wednes-
day, 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 law-
suits 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
CYCLOMETRY. 209
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 TT = 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 pub-
lished 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 meas-
urement. 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 com-
mon 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 Athenceum 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
210 A BUDGET OF PARADOXES.
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 im-
possible, 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." 1
Every mathematician knows that scores of methods, dif-
fering 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 com-
petent to follow processes of arithmetic may be easily satis-
fied 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. 2 [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 TT : he evidently takes me to be offering demonstra-
tion. He proceeds thus :
"His first proof is traceable to the diameter of a circle
1 "We enter the course by night and are consumed by fire."
8 See Vol. I, page 51, note 3.
CYCLOMETRY. 211
of radius 1. His second, to the side of any inscribed equi-
lateral 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 TT 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
212
A BUDGET OF PARADOXES.
1. Take any diameter, double it, take l-3d of that double,
2-5ths of the last, 3-7ths of the last, 4-9ths of the last,
5-llths 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 pro-
ceeding on a thousand millions, and striking off one figure.
Here 200 etc. is double of the diameter; 666 etc. is l-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 ; the square root of half of
one more than this; the square root of half of one more
CYCLOMETRY. 213
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 ; . 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 Ar-
chimedes 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 demon-
strated : 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
214 A BUDGET OF PARADOXES.
to lay his finger on the point in which existing demonstra-
tion 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 circum-
ference 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 man-
ner 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 im-
possible, imagine that the arithmetical quadrature is open
to their ingenuity. Before attempting the arithmetical prob-
lem, they ought to acquire knowledge enough to read Lam-
bert's 3 demonstration (last given in Brewster's 4 translation
8 See Vol. I, page 336, note 8.
'See Vol. I, page 137, note 8.
CYCLOMETRY. 215
of Legendre's 5 Geometry) and, if they can, to refute it. [It
will be given in an Appendix.] Probably some have begun
in this way, and have caught a Tartar who has refused to
let them go: I have never heard of any one who, in pro-
ducing 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 arith-
metical 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 con-
tradicts 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 1
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
' See Vol. I, page 229, note 2.
216 A BUDGET OF PARADOXES.
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. Quaere, what is this word? Is it
anything but a corruption of the obsolete word tetchy of the
same meaing? 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 Vdhu) 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 real-
ized. [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 8, the Ox-head,
which in Old Hebrew was just the Latin Digamma, F, out
CYCLOMETRY.
217
of your name, and could then Thau you with the Thau of
Ezekiel ix, 4, the x , then you would bear the number of a
man! But this is too hard for me, although
M 40 not so for the Lord! Jer. xxxii. 17... And
O 70 now a word: is ridicule the right thing in so
R 100 solemn a matter as the discussion of Holy
G 6 Writ? [Is food for ridicule the right thing?
N 50 Did I discuss Holy Writ? I did not: I con-
cussed profane scribble. Even the Doctor did
not discuss', he only enunciated and denun-
= X 400 c j ate( j ou t of the mass of inferences which
a mystical head has found premises for in the Bible]."
[That ill opinions are near relations of ill wishes, will
be detected by those who are on the look out. The follow-
ing was taken down in a Scotch Church by Mr. Cobden, 8
who handed it to a Roman friend of mine, for his delecta-
tion (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 mis-
sionary who reviles his persecutor: send him to New Zea-
land, 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 chil-
dren of perdition, the bad taste to complain of a facer in
return ? As James Smith 7 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?"
"Richard Cobden (1804-1865), the cotton manufacturer and
statesman who was prominent in his advocacy of the repeal of the
Corn Laws.
T James Smith (1775-1839), solicitor to the Board of Ordnance.
With his brother Horatio he wrote numerous satires. His Horace
in London (1813) imitated the Roman poet. His works were col-
lected and published in 1840.
218 A BUDGET OF PARADOXES.
Those who think parody vulgar will be pleased to sub-
stitute for the above a quotation from Butler 8 :
"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 amus-
ing 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.* "Et
cela n'est il pas beau d'etre assure de son fait quand on se
bat centre quelqu'un? La, pousse moi un peu, pour voir.
NICOLE. Eh bien! quoi? M. JOURDAIN. Tout beau. Hola!
'Samuel Butler (1612-1680), the poet and satirist, author of
Hudibras (1663-1678).
* "Is it not fine to be sure of one's action when entering in a
combat with another? There, push me a little in order to see.
NICOLE. Well ! what's the matter ? M. JOURDAIN. Slowly. Ho there !
Ho! gently. Deuce take the rascal! NICOLE. You told me to push.
M. JOURDAIN. Yes, but you pushed me en tierce, before you pushed
en quarte, and you did not give me time to parry."
THE NUMBER OF THE BEAST. 219
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, be-
fore 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-ham-
merer does nothing but grumble, except when he tells a
good story, which he says he had from Dr. Abernethy. 1
A Mr. James Dunlop was popping at the Papists with a
666-rifled gun, when Dr. Chalmers 2 quietly said, "Why,
Dunlop, you bear it yourself," and handed him a paper
on which the numerals in
IACOBVS DVNLOPVS
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 ev o> /ner/ow /XCT/JCITC peTprjOrjcrtTai v/xiv 3 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
a john Abernethy (1764-1831), the famous physician and surgeon.
' See Vol. I, paee 102, note 5.
*"With what measure ye mete, it shall be measured to you
again."
220 A BUDGET OF PARADOXES.
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 (6/xoAoyov/uva),
which it has always been paradox not to receive; and the
controverted (avTiAcyo/xera), about which there has always
been that difference of opinion which no scholar overlooks,
however he may decide for himself after balance of evi-
dence. Eusebius,* who first (1. 3, c. 25) recorded the dis-
tinction which was much insisted on by the early Prot-
estants 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 doubt-
ingly of the Epistle to the Hebrews. The Apocalypse he
does not even admit into this class, for he proceeds as fol-
lows I use the second edition of the English folio trans-
lation (1709), to avert suspicion of bias from myself:
"Among the spurious [voOoi] 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 un-
doubted."
Eusebjus, 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 voOos, and gives
the book a claim to rank (if you think good, again) in the
controverted list. And this is the impression received by
4 Eusebius of Caesarea (c. 260-340), leader of the moderate party
at the Council of Nicaea, and author of a History of the Christian
Church in ten books (c. 324 A. D.).
THE NUMBER OF THE BEAST. 221
the mind of Lar drier, 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, 5 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, 8 in Vol. IV,
p. 8, of his New Testament, gives an elaborate handling
of tliis question. He concludes by saying that he cannot
"Nathaniel Lardner (1684-1768), a non-conformist minister and
one of the first to advocate the scientific study of early Christian
literature.
'Henry Alford (1810-1871) Dean of Canterbury (1857-1871)
and editor of the Greek Testament (1849-1861).
222 A BUDGET OF PARADOXES.
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 ortho-
dox 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 cv raxct, rendered
"shortly," is as strong a phrase as the language has to sig-
nify 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. Per-
haps 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 lv rax 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 ref-
THE NUMBER OF THE BEAST. 223
erence 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 eyyvs, 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 Athenaum,
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 can-
not 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 after-
wards. But as the original is Greek, we must look at the
Greek: it is 8 yeveo-0cu for "must come to pass," and we
know that eyevcro 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
,
224 A BUDGET OF PARADOXES.
more notice until he can contrive to surpass himself, which
I doubt his being able to do. He informs me that by chan-
ging A into n in 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 hdve directed to
"Prof. De Morgnn" as have assigned me apartment 7 A 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 7 A: 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
n for 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 toodl
I think the Doctor has rather mistaken the way of becom-
ing 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."
THE NUMBER OF THE BEAST. 225
In Wordsworth's aspiration it is meant that sense and
piety should grow together : in Dryden's description a com-
bination of Mysticism And Bigotry (can this be the double
Vahut), personified as "the priest," who always catches
it on this score, though the same spirit is found in all asso-
ciations, 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 dis-
tinction may be drawn. When mysticism predominates over
bigotry, we have the grotesque picturesque, and the natural
order of words gives us Mob, 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 con-
versation 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 unbal-
anced intellects, and of a few instances of the better kind.
226 A BUDGET OF PARADOXES.
I might have said more of 666, but I am not deep in its
bibliography. A work has come into my hands which con-
tains a large number of noted cases : to some of my readers
it will be a treat to see the collection ; and the sight will per-
haps 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 Thorn, 7 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 8 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 main-
tains, 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 knowl-
edge for himself." And this is reinforced by the fact that
Mr. Thorn, though a scholar, was not conspicuous for learn-
ing, except in this his great pursuit. He was a paradoxer
on other points. He reconciled Calvinism and eternal repro-
bation with Universalism and final salvation ; showing these
two doctrines to be all one.
This gentleman must not be confounded with the Rev.
John Hamilton Thorn 9 (no relation), at or near the same
T The work was The Number and Names of the Apocalyptic
Beasts: with an explanation and application. Part I. London, 1848,
as mentioned below. Thorn also wrote The Assurance of Faith, or
Calvinism identified with Universalism (London, 1833), and various
other religious works.
8 See Vol. I, page 222, note 14.
'John Hamilton Thorn (1808-1894) was converted to Uni-
tarianism and was long a minister in that church, preaching in the
Renshaw Street Chapel from 1831 to 1866. De Morgan refers to
the Liverpool Unitarian controversy conducted by James Martineau
THE NUMBER OF THE BEAST. 227
time, and until recently, of Renshaw Street Chapel, Liver-
pool, who was one of the minority in the Liverpool contro-
versy when, nearly thirty years ago, three heretical Unitarian
schooners exchanged shotted sermons with thirteen Ortho-
dox 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 "J ews Turks, Infidels, and
Heretics." So much for the distinction, which both gentle-
men 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
Thorn'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 MDCLXVIof 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 Caesar Atheus (or Aug. 10 ) ; Diocles
Augustus ; Ludovicus ; Silvester Secundus ; Linus Secundus ;
and Henry Giles in response to a challenge by thirteen Anglican
clergy. In 1839 Thorn contributed four lectures and a letter to
this controversy. Among his religious works were a Life of Blanco
White (1845) and Hymns, Chants, and Anthems (1854).
10 The spelling of these names is occasionally changed to meet
the condition that the numerical value of the letters shall be 666,
"the number of the beast" of Revelations. The names include Julius
Caesar; Valerius Jovius Diocletianus (249-313), emperor from 287
to 305, persecutor of the Christians ; Louis, presumably Louis XIV ;
Gerbert (940-1003), who reigned as Pope Sylvester II from 999 to
1003, known to mathematicians for his abacus and his interest in
geometry, and accused by his opponents as being in league with the
devil; Linus, the second Bishop of Rome, the successor of Peter;
Camillo Borghese (1552-1621), who reigned as Pope Paul V from
1605 to 1621, and who excommunicated all Venice in 1606 for its
claim to try 'ecclesiastics before lay tribunals, thus taking a position
228 A BUDGET OF PARADOXES.
Vicarius Filii Dei ; Doctor et Rex Latinus ; Paulo V. Vice-
Deo; Vicarius Generalis Dei in Terris; Ipse Catholicae
Ecclesiae Visibile Caput ; Dux Cleri ; Una, Vera, Catholica,
Infallibilis Ecclesia ; Auctoritas politica ecclesiasticaque Pa-
palis (Latina will also do) ; Lutherus Ductor Gregis ; Cal-
vinus tristis fidei interpres ; Die Lux ; Ludvvic ; Will. Laud ;
Aaretvos J 11 *} Xarivr] /Sao-iActa ; CK/cA^ata iraAiKa ; cvavQas ; reirav ;
apvovfJif. J Aa/X7TTt5 J 6 viKrjTT/s | KaKOS oSr/yos ; a\r]0r]<: /?Aa/?epos ',
TraAai /Jatr/cavos ', d/w>s dSwcos ', avrefws ; yevo^/otKOs ; evivas ; Bcve~
SIKTOS ; B<w/?aw>s y. Tra-rra . rj. . e. a., meaning Bonif ace III.
Pope 68th, bishop of bishops the first! ovATrios; Sios et/tu ^
7;pas ; rj /AMTOU T; TramKr) ; \ov0pava ; aa^ovctos ; Bea dvrt^cos
(Beza) J 17 dAaoveta jStov ; Mao/Acrts ; Mao//,cry5 ^8- ; #cos etfit CTTI
yaiT/5 ; laTTcros ; TraTrctaKOs J StOKAaAatrtavos ', ^ctva ; fipacrKt ; lov
; KOV7TOK5 (cowpox, s being the vau; certainly the vac-
which he was forced to abandon; Luther, Calvin; Laud (see Vol. I,
page 145, note 7) ; Genseric (c. 406-477), king of the Vandals, who
sacked Rome in 455 and persecuted the orthodox Christians in Af-
rica; Boniface III, who was pope for nine months in 606; Beza
(see Vol. I, page 66, note 6) ; Mohammed; /3pcur/ci, who was Giovanni
Angelo Braschi (1717-1799), and who reigned as Pope Pius VI from
1775 to 1799, dying in captivity because he declined to resign his
temporal power to Napoleon ; Bonaparte ; and, under IOP Ilavvc, pos-
sibly Pope John XIV, who reigned in 983 and 984 during the absence
of Boniface VII in Constantinople.
"The Greek words and names are also occasionally misspelled
so as to fit them to the number 666. They are Aarcti/oj (Latin),
^ \arivi} /9o<Tt\cta (the Latin kingdom), e/c/c\?;<ria traXi/ca (the Italian
Church), cvavdas (blooming), retrav (Titan), apvovpc (renounce),
Xa/xTrerij (the lustrous), d pt/CTjrijs (conqueror), /ca/cos 6577705 (bad
guide), dX?70?75 /3Xa/3epoj (truthful harmful one), raXou paffKavos (a
slanderer of old), ^"os d5t/cos (unmanageable lamb), (We/jos (An-
temos), yevfftjpiKos (Genseric), euiyaj (with stout fibers) ; BcpeSiKros
(Benedict), BoytjSaftos 7. iraira f 77. e. e. a. (Boniface III, pope 68,
bishop of bishops I), OV\TTIOS (baneful), Sios efyu T) fyms (I, a god, am
the), "h fitffffa $ irawiKr) (the papal brief), \ov0epava (Lutheran),
(rofoj/ctos (Saxon), Beffa avnOfos (Beza antigod), ^ a\aoveia /9iou
(the illusion of life), Mao/uens (Mahomet) ; Mao/uer?;? /3. (Maho-
met II), 0ee>5 elm CTTI 701775 (I am lord over the earth), laireros (Is-
petos, father of Atlas), 7ra?rct<r/cos (Paspeisoks), 5toAcXaXa<rtayos (Dio-
cletian), xeiva (Cheina = Cain? China?), /Spaovct (Braschi, as ex-
plained in note 10), lov Tlawc (Paunian violet, but see note 10),
KOVTTOKS cowpox), 'BovvejrapTr} (Bonneparte), N. EovijirapTe (N. Bone-
parte), cinropta. (facility), irapado<ris (surrender), TO pcyaQripiov (the
megathereum, the beast).
THE NUMBER OF THE BEAST. 229
cinated have the mark of the Beast) ; BowirapTrj ; N.
Trapre ; cvTropta ', 7ra/oa8ocris ', TO fiya6rjptov-
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
nJ W Jesus 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 "J esus
Nazarene," but the Hebrew wants an article quite as much
as the English wants "the."
Mr. David Thorn's own solution hits hard at all sides:
he finds a 666 for both beasts ; rj <f>pr)v (the mind) for the
first, and eV/cAi/o-uu OU/OKUCCU (fleshly churches) for the second.
A solution which embodies all mental philosophy in one
beast and all dogmatic theology in the other, is very tempt-
ing: 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 Protes-
tant, are, in corruption of Christianity, six of one and half
a dozen of the other: the distinctions of units, tens, hun-
dreds, 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 Thorn found a young gentleman of the
name St. Claire busy at the Beast number: he forthwith
added the letters in or icAcupe 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 8 into
n, solemnly referred the difficulty to the Almighty : this was
poor earnest.
230 A BUDGET OF PARADOXES.
I am glad I did not notice, in time to insert it in the
Athenaum, a very remarkable paradoxer brought forward
by Mr. Thorn, his friend Mr. Wapshare 12 : it is a little too
strong for the general public. In the Athenaum 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, I H S. 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
"James Wapshare, whose Harmony of the Word of God in
Spirit and in Truth appeared in 1849.
THE NUMBER OF THE BEAST. 231
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. Thorn prints it as
convinced of its piety, and "pronounces no opinion." Mys-
tics 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 sen-
tence (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. Thorn, published Oct. 27: three notes had ar-
rived 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 K. 13
"So that 'Zaphnath Paaneah' may be after all the re-
vealer of the 'Northern Tau' <<n>epoa> To make manifest,
shew, or explain ; and this may satisfy the House of Joseph
in Amos 5 C . While Belteshazzar = 666 may be also satis-
factory to the House of David, and so we may have Zech.
10. 6 V . in operation when Ezekiel 37 C . 16 V . has been real-
ised ; but there, what is the use of writing, it is all Coptic
13 The literature relating to the Swastika is too extended to per-
mit of any adequate summary in these notes.
232 A BUDGET OF PARADOXES.
to a man who has not ffi, The Thau of the North, the
double Vahu ^. Look at Jeremiah 3 C . 8 V . and then to
Psalm 83 for 'hidden ones' njlj ^1DV_The Zephoni Jehovah,
and say whether they have any connection with the Zephon
Thau. The Hammer of Thor of Jeremiah 23 C . 29 V . 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
C= 20
i= 10
N= 50
666
There will be thousands of Morgans who will be among
the wise and prudent of Hosea 14 C . 9 V . when the Seventh
Angel sounds, let me number that One by Greek, Rev. 17 C . l v ;
THE NUMBER OF THE BEAST. 233
S = 200
E= 5
Xv= 6
E= s
N== 50
A= i
N= 50
XG= 6
= 5
L= 30
666
London, October 29, 1866.
"Dear Sir,
In re rtt versus >J.
However pretentious the X or ^ may be, and it is pecu-
liarly so just now in this land ; after all it is only made of
two Roman V's and so is only= I (10) and therefore is
not the perfect number 12 of Revel n , but is the mark of the
goddess Decimal 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
I^HENRY E. MANNING. 14
Shilling versus Franc.
Teutonic Long Hundred 120 versus 100 or the Decimal
question.
"Henry Edward Manning (1808-1892), at first an Anglican
clergyman, he became a Roman Catholic priest in 1851, and became
Cardinal in 1875. He succeeded Cardinal Wiseman as Archbishop
of Westminster in 1865. He wrote a number of religious works.
234 A BUDGET OF PARADOXES.
By English Key. H= 8
E= 5
N = 40 8
R=: 80 Z
EC
= A
D= 4
A= X
R= 80 -g u
D= 4 4^
M= 30 ^
A= 1 |"
N= 40 rt
N= 40 !,;
i= 9 ^g|?
N= 40 g ^^
G= 7 0||
' ffi== 12 ^o
666
Cutting from newspaper:
ITALY.
Rome (via Marseilles), October 24.
Mr. Gladstone has paid a visit to the Pope.
By Greek Power. G= 6
L= 30
A= 1
D= 4
o= 70
N= 50
E= 5
And what then ffi ? 666
THE NUMBER OF THE BEAST. 235
In other letters John Stuart Mill is 666 if the a be left
out ; Chasuble is perfect. John Brighte 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. Thorn and his 666 appeared on
October 27: and on the 29th I received from the editor a
copy of Mr. Thorn's sermons published in 1863 (he died
Feb. 27, 1862) with best wishes for my health and happi-
ness. 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 3 \ of my diameter if the signature, name
and writing both, were not that of my Q nm g friend Mr.
James Smith ! And so I have come in contact with him on
'666 as well as on TT! 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 armis-
tice? 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
"John Bright (1811-1889), Quaker, cotton manufacturer, and
statesman. He worked with Cobden for free trade, peace, and re-
form of the electorate.
236 A BUDGET OF PARADOXES.
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 Athen&um 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
Athenaum, 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. 16 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 char-
acter 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 Athen&um and forestall him.
When I saw myself thus quoted yes! quoted! double
commas, first person I felt as I suppose did Wm. Wilber-
force 17 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 18 of
M "The fallacy of many questions."
"William Wilberforce (1759-1833), best known for his long
light for the abolition of the slave trade.
"Richard Martin (1754-1834), high sheriff of County Galway
and owner of a large estate in Connemara. Curiously enough, he
was known both for his readiness in duelling and for his love for
animals. He was known as "Humanity Martin," and in 1822 secured
THE NUMBER OF THE BEAST. 237
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 &-istical attack on the wind-
mills. The principle is, Prove something in as roundabout
a way as possible, mention the circle once or twice irrele-
vantly 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, 6 = 5: let
c = 658, the number of the House: let d = 666, the number
of the Beast. Then of necessity d = a + b + c+l; so that 1 is
a harmonious and logical quantification of the number of
which we are to take care. Now, &, the middle of our
digital system, is, by mathematical and geometrical com-
bination, a mean between 5 + 1 and 2 + 2. Let 1 be re-
moved 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 & Mar-
shall 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 con-
the passage of an act "to prevent the cruel and improper treatment
of cattle." He was one of the founders (1824) of the Royal Society
for the Prevention of Cruelty to Animals. He is usually considered
the original of Godfrey O'Malley in Lever's novel, Charles O'Malley.
238 A BUDGET OF PARADOXES.
nection 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 agri 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, re-
sembles 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 Quadra-
ture 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 Faure 19 and Joseph Scaliger 20 come into my
head: my reader may look back for them.
"Three circlesquarers to the manner born,
Switzerland, France, and England did adorn,
De Faure 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\"
19 See Vol. I, page, 149, note 1, also text on same page.
"See Vol. I, page 44, note 9, also text, Vol. I, page 110.
THE NUMBER OF THE BEAST. 239
As to my locus pcenitentia 21 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 pose sur un coussinet." 22
Joanna Southcott 23 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 argu-
ment is in my jokes, and the best of the joke is in his argu-
ments." 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 U a
perdu le droit d'etre frappe de V evidence ; I might have
said pendu. 25 To which I now add, in plain Latin, Sapienti
pauca, indocto nihil. 26 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 indi-
vidual 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
"Penitential seat.
"Well placed upon the cushion."
See Vol. II, page 58, note 2.
"He has lost the right of being influenced by evidence."
"Hung up."
"A few things to the wise, nothing to the unlettered."
240 A BUDGET OF PARADOXES.
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 mas-
ter 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. Thorn's sermons,
after my account of his queer doings about 666. He is evi-
dently an honest and devout man, much wanting in dis-
crimination. 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 judg-
ment 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. 241
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: 1
Let *=1
Then x 2 = x
And x*-\ = x-\
Divide both sides by x - 1 ; then
^+1 = 1; but x-\, 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 3-J, because I think
Mr. James Smith better fitted to be the leader of an organ-
ized 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 coelum jusseris, ibit" 2
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
1 The fallacy results from dividing both members of an equation
by 0, x 1 being the same as 1 1, and calling the quotients finite.
1 "If you order him to the sky he will go."
242 A BUDGET OF PARADOXES.
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 op-
portunity 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 TT.
Mr. Smith is satisfied at last that what between argu-
ment 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 cyclom-
eters : 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 mathe-
matical answers, of which there were several. The follow-
ing 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
JAMES SMITH ONCE MORE. 243
he departs from truth the more easy it must be to refute
him, [this by no means always true] some of your cor-
respondents 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 'II' is wrong, in No. 23, where he de-
clares 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 re-
garded as the 'elements' of mathematical truth. Would it
not be better for 'n' 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 homoeopathic treatment of the 3J
quadrature remember, homoeopathic, similia similibus* 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 com-
mon as the description of the other side's remarks as "vul-
gar 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
8 Similia similibus curanter, "Like cures like," the homeopathic
motto.
244 A BUDGET OF PARADOXES.
unproducible salvo pudore* 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." 5 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 an-
tiquity, but makes it English. Our old translation 6 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 7 in the rear.
'"Without harm to the proprieties."
6 "What are you doing? I am standing here."
"Lors feist TAnglois tel signe. La main gausche toute ouverte
il leva hault en 1'aer, puis ferma au poing les quatres doigtz d'icelle
et le poulce estendu assit sus la pinne du nez. Soubdain apres leva
la dextre toute ouverte, et toute ouverte la baissa, joignant la poulce
au lieu que fermait le petit doigt de la gausche, et les quatre doigtz
d'icelle mouvoit lentement en 1'aer. Puis au rebours feit de la dextre
ce qu'il avoit faict de la gausche, et de la gausche ce que avoit faict
de la dextre. A. De M.
7 Suaviter in modo, fortiter in re, "Gentle in manners, firm in
action."
JAMES SMITH ONCE MORE. 245
My Budget was announced (March 23, 1867) for com-
pletion 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 Athenaum.
"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 tute-
lary. 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 contro-
vert my proofs. [I thought so too; and tried neither].
246 , A BUDGET OF PARADOXES.
"May 6. My dear Sir. Very sincerely yours. All to my-
self, and nothing to note.
"July 2. No more in this interval. All that precedes is
a desperate attempt to induce me to continue my descrip-
tions : notoriety at any price." v f
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 8 to
Mr. James Smith. The Master of Trinity was conspicuous as
a rough customer, an intellectual bully, an overbearing dispu-
tant : 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 dicta-
torial, and he was perfectly accessible to proposal of objec-
tions. He came in contact with me in his slashing way twice
in our after joint lives, and on both occasions he acknowl-
edged himself overcome, by that change of manner, and
apologetic mode of continuance, which I had seen him em-
ploy towards others under like circumstances.
I had expressed my wish to have a thermometer of prob-
ability, 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 and oo are of
number, and illustrated by an urn with 1 white and n black
8 See Vol. I, page 101, note 4.
JAMES SMITH ONCE MORE. 247
balls, w 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. Whe-
well, with "I think"... "Ugh! you think!" was the an-
swer. I repeated my phrase, and gave as a reason the
words which Lord Grey 9 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 dis-
cutient 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 skil-
fully 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 propo-
sition 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 oc-
curs, 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 be-
fore. Does not this satisfy you that you cannot have proved
a property of that special figure a circle?
See Vol. I, page 315, note 3.
248 A BUDGET OF PARADOXES.
"Or you may do this : calculate the side of a polygon of
24 sides inscribed in a circle. I think you are a Mathemati-
cian 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 propo-
sition 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. Glad-
stone asked how many members of the House could divide
1330/. 17s. 6d. by 21. 13s. Sd. 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 ab-
stract 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 sup-
press, 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 21. 16s. Sd.? (Laughter.) The question
might be asked, 'How many times 2s. will go into 11. ?' but
that was not dividing by money; it was simply dividing
20 by 2. He might be asked, 'How many times will 6s. Sd.
go into a pound?' but it was only required to divide 240
by 80. If the right hon. gentleman were to ask the hon.
AN M.P/S ARITHMETIC. 249
member for Brighton (Professor Fawcett), 1 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. 2 I shall be sure to have something to lawgh
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 40x40 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 mis-
fortune 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
1 Henry Fawcett (1833-1884) became totally blind in 1858, but in
spite of this handicap he became professor of political economy at
Cambridge and sat in parliament for a number of years. He cham-
pioned the cause of reform and in particular he was prominent in the
protection of the native interests of India. The establishing of the
parcels post (1882) took place while he was postmaster general
(1880-1884).
* Of course the whole thing depends upon what definition of divi-
sion is taken. We can multiply 2 ft. by 3 ft. if we define multi-
plication so as to allow it, or 2 ft. by 3 ft), getting foot-pounds,
as is done in physics.
250 A BUDGET OF PARADOXES.
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 SI.
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 5/. 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 3 (Richard, no doubt, but it cannot
be proved) who published Selden's 4 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 sub-
sidies 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
"Richard Milward (1609-1680), for so the name is usually given,
was rector of Great Braxted (Essex) and* canon of Windsor. He
was long the amanuensis of John Selden, and the Table Talk was
published nine years after Milward's death, from notes that he left.
Some doubt has been cast upon the authenticity of the work owing
to many of the opinions that it ascribes to Selden.
4 John Selden (1584-1654) was a jurist, legal antiquary, and
Oriental scholar. He sat in the Long Parliament, and while an ad-
vocate of reform he was not an extremist. He was sent to the Tower
for his support of the resolution against "tonnage and poundage," in
1629. His History of Tythes (1618) was suppressed at the demand
of the bishops. His De Diis Syriis (1617) is still esteemed a classic
on Semitic mythology.
ERRONEOUS ARITHMETICAL NOTIONS. 251
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 1 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 x 4 or 20 square inches,
people say that five inches multiplied by four inches is
twenty square inches: and, thinking that they have multi-
plied 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. Multiplica-
tion must be repetition : the repeating process must be indi-
cated by number of times. I once had difficulty in per-
suading another of my betters that if you repeat five shil-
lings as often as there are hairs in a horse's tail, you do not
multiply -five shillings by a horsetail. 2
I am very sorry to say that these wrong notions have
found support I think they do so no longer in the Uni-
versity 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
1 See Vol. I, page 42, note 4.
' See Vol. II, page 249, note 2.
252 A BUDGET OF PARADOXES.
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 col-
lege examination, to divide 22557 days, 20 hours, 20 min-
utes, 48 seconds, by 57 minutes, 12 seconds, and also to
explain the fraction
321. IBs. Sd.
621. 12s. 9rf."
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 Cam-
bridge, 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 re-
markable 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
ON LITERARY BARGAINS. 253
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 him-
self 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, 1 the improver of the mail coach system,
is smothered. He was to" have an office and a salary, and
2\ 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 spar-
ingly, and dismissed it speedily.
The government did not choose to remember what pri-
vate persons must remember, and are made to remember,
if needful. When Dr. Lardner 2 made his bargain with the
'John Palmer (1742-1818) was a theatrical manager. In 1782
he set forth a plan for forwarding the mails by stage coaches instead
of by postmen. Pitt adopted the plan in 1784. Palmer was made
comptroller-general of the post office in 1786 and was dismissed six
years later for arbitrarily suspending a deputy. He had been verbally
promised 2 l / 2 % on the increased revenue, but Pitt gave him only a
pension of 3000. In 1813 he was awarded 50,000 in addition to his
pension.
"Dionysius Lardner (1793-1859), professor of natural philosophy
in London University (now University College). His Cabinet Cyclo-
paedia (1829-1849) contained 133 volumes. De Morgan wrote on
probabilities, and Lardner on various branches of mathematics, and
there were many other well-known contributors. Lardner is said to
have made $200,000 on a lecture tour in America.
254 A BUDGET OF PARADOXES.
publishers for the Cabinet Cyclopedia 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 per-
centage, 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 Drought to book before a
sworn jury, are ruled only by public opinion. John Palmer's
day was also the day of Thomas Fyshe Palmer, 8 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 paradox-
ical 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 scien-
* Thomas Fysche Palmer (1747-1802) joined the Unitarians in
1783, and in 1785 took a charge in Dundee. He was arrested for
sedition because of an address that it was falsely alleged that he
gave before a society known as the "Friends of Liberty." As a
matter of fact the address was given by an uneducated weaver, and
Palmer was merely asked to revise it, declining to do even this.
Nevertheless he was sentenced to Botany Bay (1794) for seven
years. The trial aroused great indignation.
DECLARATION OF BELIEF. 255
tific truth are perverted by some in our own times into occa-
sion 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, 1 who in refusing to sign the writ sent to
him, administered a rebuke in the Athenaum, 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 z 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 re-
ligious doctrine or statement, however carefully or cau-
tiously 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 differ-
ences 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
1 See Vol. I, page 80, note 5.
1 See Vol. II, page 244, note 7.
256 A BUDGET OF PARADOXES.
feelings of thousands of estimable and well-intentioned men
with all the harshness of controversial hostility."
Other doses were administered by Sir J. Bowring, 8 Sir
W. Rowan Hamilton, 4 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 speci-
men 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 signa-
tures ; 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 decla-
ration of difference of opinion, not of blame for that differ-
ence. 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
See Vol. I, page 352, note 1.
*See Vol. I, page 332, note 4.
DECLARATION OF BELIEF. 257
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 per-
sons are, I understand, divided in opinion about the time
at which the next attempt shall be made upon men of scien-
tific 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
Athenaum, 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 Stu- WE, the undersigned Stu-
dents of the Natural Scien- dents of Theology and of
ces, desire to express our Nature, desire to express our
sincere regret, that re- sincere regret, that common
searches into scientific truth notions of religious truth are
are perverted by some in our perverted by some in our
own times into occasion for own times into occasion for
casting doubt upon the Truth casting reproach upon the
and Authenticity of the Holy advocates of demonstrated
Scriptures. or highly probable scientific
theories.
258
A BUDGET OF PARADOXES.
We conceive that it is im-
possible for the Word of
God, as written in the book
of nature, and God's Word
written in Holy Scripture,
to contradict one another,
however much they may ap-
pear to differ.
We are not forgetful that
Physical Science is not com-
plete, but is only in a con-
dition of progress, and that
at present our finite reason
enables us only to see as
through a glass darkly,
and we confidently believe,
that a time will come when
the two records will be seen
to agree in every particular.
We cannot but deplore that
Natural Science should be
looked upon with suspicion
by many who do not make
a study of it, merely on ac-
count of the unadvised man-
We conceive that it is im-
possible for the Word of
God, as correctly read in the
Book of Nature, and the
Word of God, as truly inter-
preted out of the Holy Scrip-
ture, to contradict one an-
other, however much they
may appear to differ.
We are not forgetful that
neither theological interpre-
tation nor physical knowl-
edge is yet complete, but
that both are in a condition
of progress ; and that at pres-
ent our finite reason enables
us only to see both one and
the other as through a glass
darkly [the writers of the
original declaration have dis-
tinctively applied to physical
science the phrase by which
St. Paul denotes the imper-
fections of theological vision,
which they tacitly assume to
be quite perfect],
and we confidently believe,
that a time will come when
the two records will be seen
to agree in every particular.
We cannot but deplore that
Religion should be looked
upon with suspicion by some
and Science by others, of the
students of either who do
not make a study of the
DECLARATION OF BELIEF.
259
ner in which some are pla-
cing it in opposition to Holy
Writ.
We believe that it is the duty
of every Scientific Student
to investigate nature simply
for the purpose of elucida-
ting truth,
and that if he finds that some
of his results appear to be in
contradiction to the Written
Word, or rather to his own
interpretations of it, which
may be erroneous, he should
not presumptuously affirm
that his own conclusions
must be right, and the state-
ments of Scripture wrong;
rather, leave the two side by
side till it shall please God
to allow us to see the manner
in which they may be recon-
ciled ;
and, instead of insisting upon
the seeming differences be-
tween Science and the Scrip-
other, merely on account of
the unadvised manner in
which some are placing Re-
ligion in opposition to Sci-
ence, and some are placing
Science in opposition to Re-
ligion.
We believe that it is the duty
of every theological student
to investigate the Scripture,
and of every scientific stu-
dent to investigate Nature,
simply for the purpose of
elucidating truth.
And if either should find
that some of his results ap-
pear to be in contradiction,
whether to Scripture or to
Nature, or rather to his own
interpretation of one or the
other, which may be errone-
ous, he should not affirm as
with certainty that his own
conclusion must be right,
and the other interpretation
wrong :
but should leave the two side
by side for further inquiry
into both, until it shall please
God to allow us to arrive at
the manner in which they
may be reconciled.
In the mean while, instead
of insisting, and least of all
with acrimony or injurious
260 A BUDGET OF PARADOXES.
tures, it would be as well to statements about others,upon
rest in faith upon the points the seeming differences be-
in which they agree. tween Science and the Scrip-
tures, 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 com-
posers, 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 interpre-
tation. 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 appli-
cation: 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 : ayopaioi ayovrai ey*a-
AeiTaxrav dAA^Aois. 5 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 6 that his appearance
was very like that of a corpse. The John Bull newspaper
"The lawyers are brought into court: let them accuse each
other."
"Samuel Rogers (1763-1855), the poet and art connoisseur. He
SCRIPTURE AND SCIENCE. 261
suppose we now say Theodore Hook 7 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 Hceretico Commiserando. 1
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 Scrip-
ture 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 in-
trusion 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.
declined the laureateship on the death of Wordsworth (1850). Byron,
his pretended friend, wrote a lampoon (1818) ridiculing his cadav-
erous appearance.
T Theodore Edward Hook (1788-1841), the well-known wit. He
is satirized as Mr. Wagg in Vanity Fair. The John Bull was founded
in 1820 and Hook was made editor.
1 "On pitying the heretic."
262 A BUDGET OF PARADOXES.
"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 falla-
cies before a writer on logic. Ah! my dear Sir John!
thought I, if you had shown yourself to be well up in
Barbara Celarent? and had ever and anon astonished the
natives with the distinction between simpliciter and secun-
dum quid, no autograph-hunters would have baited a trap
with non sequitur* 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 h&retico 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 f uisse ; tales cum sint reliquiae."*
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-f aggot :
a A term of medieval logic. Barbara: All M is P, all S is M,
hence all S is P. Celarent : No M is P, all S is M, hence no S is P.
8 "Simply," "According to which," "It does not follow."
"O sweet soul, what good shall I declare
That heretofore was thine, since such are thy remains !"
SCRIPTURE AND SCIENCE. 263
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 ab-
surdity 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
Jungel 5 and then they must fight. There is a gentleman
in the upper fifteen of the signers of the writ the hawk-
ing 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 my-
self; they can have no idea of the feeling with which I
'"Stupid fellow!"
264 A BUDGET OF PARADOXES.
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: J 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 para-
dox, 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 per-
son 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 1 Bible of 1599, I saw an
'Christopher Barker (c. 1529-1599), also called Barkar, was the
Queen's printer. He began to publish books in 1569, but did no
THE FLY-LEAF PARADOX. 265
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 unedu-
cated 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 observa-
tions may be silly or irrelevant, but you cannot tell what
use they may be of long after you are gone where Bud-
geteers cease from troubling.
I picked up the following book, printed by J. Franklin 2
at Boston, during the period in which his younger brother
Benjamin was his apprentice. And as Benjamin was ap-
prenticed 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 thir-
teen at the time. As this set of editions of Hodder* (by
actual printing until 1576. In 1575 the Geneva Bible was first printed
in England, the work being done for Barker. He published 38 partial
or complete editions of the Bible from 1575 to 1588, and 34 were
published by his deputies (1588-1599).
'James Franklin (1697-1735) was born in Boston, Mass., and
was sent to London to learn the printer's trade. He returned in
1717 and started a printing house. Benjamin, his brother, was ap-
prenticed to him but ran away (1723). James published the New
England Courant (1721-1727), and Benjamin is said to have begun
his literary career by writing for it.
'James Hodder was a writing master in Tokenhouse Yard,
Lothbury, in 1661, and later kept a boarding school in Bromley-by-
Bow. His famous arithmetic appeared at London in 1661 and went
266 A BUDGET OF PARADOXES.
Mose 4 ) 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. But-
tolph, 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 y e 14, 1796, att ten in y e forenoon
we sail d from Boston, came too twice, once in King Rode,
and once in y e Narrows. Sail d by y e lighthouse in y e evens."
through many editions. It was the basis of Cocker's work. (See
Vol. I, page 42, note 4.) It was long thought to have been the
first arithmetic published in America, and it was the first English
one. There was, however, an arithmetic published much earlier
than this, in Mexico, the Sumario compendioso . . .con algunas reglas
tocantes al Aritmetica, by "Juan Diaz Freyle," in 1556.
4 Henry Mose, Hodder's successor, kept a school in Sherborne
Lane, London.
PARADOXES OF ORTHOGRAPHY AND COMPUTATION. 267
No ordinary map would decide these points : so I had to
apply to my friend Sir Francis Beaufort, 5 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 Abbe Sabatier de Castres, 1 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 VHP and Galileo, references to the works of two
Englishmen, the Rev. Win Worewel and the Rev. Raden
Powen. [Wm. Whewell and Baden Powell]. 3
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 compu-
tation," anything as surprisingly small by the "utmost com-
putation" ; and these are the two great subdivisions of "mod-
erate computation." In this way we learn that 70,000 per-
sons were executed in one reign, and 150,000 persons
'Rear Admiral Sir Francis Beaufort (1774-1857), F.R.S., was
hydrographer to the Navy from 1829 to 1855. He prepared an atlas
that was printed by the Society for the Diffusion of Useful Knowl-
edge.
1 Antoine Sabatier (1742-1817), born at Castres, was known as
the Abbe but was really nothing more than a "clerc tonsure." He
lived at Court and was pensioned to write against the philosophers
of the Voltaire group. He posed as the defender of morality, a
commodity of which he seems to have possessed not the slightest
trace.
a Maffeo Barberini was pope, as Urban VIII, from 1623 to 1644.
It was during his ambitious reign that Galileo was summoned to
Rome to make his recantation (1633), the exact nature of which is
still a matter of dispute.
'This Baden Powell (1796-1860) was the Savilian professor of
geometry (1827-1860) at Oxford.
268 A BUDGET OF PARADOXES.
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 8,852,000/. But
6,400,000 people pay the clergy of the Anglo-Irish Establish-
ment 8,896,000/.; and 14,600,000 of other denominations
pay 1,024,000/. When I read moderate computations, I
always think of Voltaire and the "memoires du fameux
eveque de Chiapa, par lesquels il parait qu'il avait egorge,
ou brule, ou noye dix millions d'infideles en Amerique pour
les convertir. Je crus que cet eveque exaggerait; mais
quand on reduisait ces sacrifices a cinq millions de victimes,
cela serait encore admirable." 4
CENTRIFUGAL FORCE.
My Budget has been arranged by authors. This is the
only plan, for much of the remark is personal : the peculiar-
ities 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 in-
stance. But there are others which cannot be drawn out
so as to be conspicuous in a review of writers: as one in-
stance, 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
'"Memoirs of the famous bishop of Chiapa, by which it ap-
pears that he had butchered or burned or drowned ten million in-
fidels in America in order to convert them. I believe that this bishop
exaggerated; but if we should reduce these sacrifices to five million
victims, this would still be admirable."
CAMBRIDGE POETS. 269
was not to blame for more than fve 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 sys-
tem, 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, 1 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 herCj
for want of room.
I
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
Alfonso X (1221-1284), known as El Sabio (the Wise), was
interested in astronomy and caused the Alphonsine Tables to be pre-
pared. These table were used by astronomers for a long time. It is
said^that when the Ptolemaic system of the universe was explained
to him he remarked that if he had been present at the Creation he
could have shown how to arrange things in a much simpler fashion.
270 A BUDGET OF PARADOXES.
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 1 wakes a genuine poet's fires,
And modern Britons glory in their sires." 8
There is some account of the Rev. Geo. Richards, Fel-
low of Oriel and Vicar of Bampton, (M.A. in 1791) in the
Living Authors by Watkins 3 and Shoberl 4 (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, 3 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
George Richards (c. 1767-1837), fellow of Oriel (1790-1796),
Bampton lecturer (1800), Vicar of St. Martin's-in-the-Fields, West-
minster (1824), and a poet of no mean ability.
'The "Aboriginal Britons," an excellent poem, by Richards.
(Note by Byron.) A. De M.
'John Watkins (d. after 1831), a teacher and miscellaneous
writer.
* Frederic Shoberl (1775-1853), a miscellaneous writer.
6 He wrote, besides the Aboriginal Britons, Songs of the Ab-
original Bards (1792), Modern France: a Poem (1793), Odin, a
drama (1804), Emma, a drama on the model of the Greek theatre
(1804), Poems (2 volumes, 1804), and a Monody on the Death of
Lord Nelson (1806).
CAMBRIDGE POETS. 271
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 great-
ness 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 subse-
quent efforts.
To enhance the position in which the satirist placed
himself, two things should be remembered. First, the glow-
ing 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 6
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 speak-
ing 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 pas-
sage of the same poem:
'Henry Kirke White (1785-1806), published his first volume of
poems at the age of 18. Southey and William Wilberforce became
interested in him and procured for him a sizarship at St. John's
College, Cambridge. He at once showed great brilliancy, but he died
of tuberculosis at the age of 21.
272 A BUDGET OF PARADOXES.
"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 any-
thing, 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 candi-
dates 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 John-
son's biographers. Peter Pindar 1 may be excused, as per-
sonal satire was his object, for addressing Bos well and Mrs.
Piozzi 2 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:
'John Wolcot, known as Peter Pindar (1738-1819), was a Lon-
" See Vol. I, page 235, note 8.
don physician. He wrote numerous satirical poems. His Bossy and
Piozzi, or the British Biographers, appeared in 1786, and reached
the 9th edition in 1788.
BYRON AND WORDSWORTH. 273
"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 tor-
tured 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 suc-
cessors, 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 Bos-
well 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 protec-
tion, 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, sup-
pose that some poet were now to speak
274 A BUDGET OF PARADOXES.
"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, 1 in his Taste, trans-
lated part of Gray's Bard into Greek. Some of his lines
are
ia 8' 6 Tcyywi/ Sa/cpva o-TOva^ais
ovAov ficAos <f>o/3e.p(]i
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 :
8e Ttyywv SaKpva
Pindar's re'yywv 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
1 Richard Payne Knight (1750-1824) was a collector of bronzes,
gems, and coins, many of his pieces being now in the British Mu-
seum. He sat in parliament for twenty-six years (1780-1806), but
took no active part in legislation. He opposed the acquisition of the
Elgin Marbles, holding them to be of little importance. His Ana-
lytical Inquiry into the Principles of Taste appeared in 1808.
BYRON AND WORDSWORTH. 275
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 occa-
sion, 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 pos-
sibly 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, 2 and without scru-
ples 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 8 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 Edin-
burgh 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
'Mario Nizzoli (1498-1566), a well-known student of Cicero,
was for a time professor at the University of Parma. His Observa-
tiones in M. Tulliunt Ciceronem appeared at Pratalboino in 1535.
It was revised by his nephew under the title Thesaurus Ciceronianus
(Venice, 1570).
8 See Vol. I, page 314, note 4.
276 A BUDGET OF PARADOXES.
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 Words-
worth 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 be-
ginning of the visit to the end, and that was reverence. !' "
Lady Byron told my wjfe 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 Chry-
sippus or Guinea, an animal which multiplies itself by divi-
sion, 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 be-
fore the R 1 Society" ; and next year, 1743, a quarto re-
print 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 e '1 geometra che tutto s' affige
Per misurar lo cerchio, e non ritruova,
Pensando qual principio ond' egli indige." 4
"Like the geometer, who bends all his powers
To measure the circle, and does not succeed,
Thinking what principle he needs."
DE BECOURT. 277
And Quarles 5 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 for-
gotten. 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 com-
mon 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 Becourt 1 by A. Dalmas. It supports, but I suspect
not very accurately, the views of the old Hindu books.
"Francis Quarles (1592-1644), a religious poet. He wrote
paraphrases of the Bible and numerous elegies. In the early days
of the revolutionary struggle he sided with the Royalists. One of
his most popular works was the Emblems (1635), with illustrations
by William Marshall.
1 Regnault de Becourt wrote La Creation du monde, ou Systeme
d" organisation primitive suivi de V interpretation des principaux phe-
nomenes et accidents que se sont operes dans la nature depuis I'ori-
gine de univers jusqu'a nos jours (1816). This may be the work
translated by Dalmas.
278 A BUDGET OF PARADOXES.
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. Becourt's temperament
are brought by a fancy. He fully grants, as certain, four
millions of years as the duration of the Hindu race, and
1956 as that of the universe. It must be admitted he is not
wholly wrong in saying that our errors about the universe
proceed from our ignorance of its origin, antiquity, organi-
zation, laws, and final destination. Living in an age of light,
he "avails himself of that opportunity" to remove this veil
of darkness, etc. The system of the Brahmins is the only
true one: he adds that it has never before been attempted,
as it could not be obtained except by him. The author
requests us first, to lay aside prejudice; next, to read all
he says in the order in which he says it: we may then
pronounce judgment upon a work which begins by taking
the Brahmins for granted. All the paradoxers make the
same requests. They do not see that compliance would
bring thousands of systems before the world every year:
we have scores as it is. How is a poor candid inquirer
to choose. Fortunately, the mind has its grand jury as
well as its little one: and it will not put a book upon its
trial without a prima facie case in its favor. And with
most of those who really search for themselves, that case
is never made out without evidence of knowledge, standing
out clear and strong, in the book to be examined.
BEQUEST OF A QUADRATURE.
There is much private history which will never come to
light, caret quia vate sacro, 1 because no Budgeteer comes
across it. Many years ago a man of business, whose life
was passed in banking, amused his leisure with quadrature,
was successful of course, and bequeathed the result in a
sealed book, which the legatee was enjoined not to sell
1 "Because it lacks a holy prophet."
BEQUEST OF A QUADRATURE. 279
under a thousand pounds. The true ratio was 3 . 1416 :
I have the anecdote from the legatee's executor, who opened
the book. That a banker should square the circle is very
credible: but how could a City man come by the notion
that a thousand pounds could be got for it? A friend of
mine, one of the twins of my zodiac, will spend a thousand
pounds, if he have not done it already, in black and white
cyclometry: but I will answer for it that he, a man of
sound business notions, never entertained the idea of
recouping him, as they now say. I speak of individual suc-
cess: of course if a company were formed, especially if it
were of unlimited lie-ability, the shares would be taken.
No offence; there is nothing but what a pun will either
sanctify, justify, or nullify:
"It comes o'er the soul like the sweet South
That breathes upon a bank of vile hits."
The shares would be at a premium of 3% on the day after
issue. If they presented me with the number of shares I
deserve, for suggestion and advertisement, I should stand
up for the Archpriest of St. Vitus 2 and 3%, with a view
to a little more gold on the bridge.
I now insert a couple of reviews, one about Cyclopaedias,
one about epistolary collections. Should any reader wish
for explanation of this insertion, I ask him to reflect a
moment, and imagine me set to justify all the additions
now before him ! In truth these reviews are the repositories
of many odds and ends : they were not made to the books ;
the materials were in my notes, and the books came as to
a ready-made clothes shop, and found what would fit them.
Many remember Curll's 3 bequest of some very good titles
* Anghera. See Vol. II, page 60, note la.
'Edmund Curll (1675-1747), a well-known bookseller, publisher,
and pamphleteer. He was for a time at "The Peacock without
Temple Bar." and later at "The Dial and Bible against St. Dunstan's
Church." He was fined repeatedly for publishing immoral works,
and once stood in the pillory for it. He is ridiculed in the Dunciad
for having been tossed in a blanket by the boys of Westminster
School because of an oration that displeased them.
280 A BUDGET OF PARADOXES.
which only wanted treatises written to them. Well! here
were some tolerable reviews as times go which only
wanted books fitted to them. Accordingly, some tags were
made to join on the books; and then as the reader sees.
I should find it hard to explain why the insertion is
made in this place rather than another. But again, suppose
I were put to make such an explanation throughout the
volume. The improver who laid out grounds and always
studied what he called unexpectedness, was asked what
name he gave it for those who walked over his grounds
a second time. He was silenced; but I have an answer:
It is that which is given by the very procedure of taking
up my book a second time.
REVIEW OF CYCLOPEDIAS.
October 19, 1861. The English Cyclopedia. Conducted by
Charles Knight. 1 22 vols. : viz., Geography, 4 vols. ; Biography,
6 vols.; Natural History, 4 vols.; Arts and Sciences, 8 vols.
(Bradbury & Evans.)
The Encyclopedia Britannica: a Dictionary of Arts, Sciences,
and General Literature. Eighth Edition. 21 vols. and Index.
(Black.)
The two editions above described are completed at the
same time: and they stand at the head of the two great
branches into which pantological undertakings are divided,
as at once the largest and the best of their classes.
When the works are brought together, the first thing
that strikes the eye is the syllable of difference in the
names. The word Cyclopedia is a bit of modern purism.
Though eyKVK\oirai8fia 2 is not absolutely Greek of Greece,
we learn from both Pliny 3 and Quintilian 4 that the circle
1 See Vol. II, page 109, note 7.
1 Encyclopaedia.
8 Author of the Historia Naturalis '(77 A. D.)
4 Author of the De Institutione Oratoria Libri XII (c. 91 A. D.)
REVIEW OF CYCLOPAEDIAS. 281'
of the sciences was so called by the Greeks, and Vitruvius 5
has thence naturalized encyclium in Latin. Nevertheless
we admit that the initial en would have euphonized but
badly with the word Penny: and the English Cyclopedia
is the augmented, revised, and distributed edition of the
Penny Cyclopaedia. It has indeed been said that Cyclo-
paedia should mean the education of a circle, just as Cyro-
paedia is the education of Cyrus. But this is easily upset
by Aristotle's word Kv/cAo(/>opia, 6 motion in a circle, and by
many other cases, for which see the lexicon.
The earliest printed Encyclopaedia of this kind was per-
haps the famous "myrrour of the worlde," which Caxton 7
translated from the French and printed in 1480. The
original Latin is of the thirteenth century, or earlier. This
is a collection of very short treatises. In or shortly after
1496 appeared the Margarita Philosophica of Gregory
Reisch, 8 the same we must suppose, who was confessor
to the Emperor Maximilian. 9 This is again a collection of
treatises, of much more pretension: and the estimation
formed of it is proved by the number of editions it went
through. In 1531 appeared the little collection of works
of Ringelberg, 10 which is truly called an Encyclopaedia by
5 His De Architectures Libri X was not merely a work on archi-
tecture and building, but on the education of the architect
8 Cyclophoria.
T William Caxton (c. 1422 c.1492), sometime Governor of the
Company of Merchant Adventurers in Bruges (between 1449 and
1470). He learned the art of printing either at Bruges or Cologne,
and between 1471 and 1477 set up a press at Westminster. Tradition
says that the first book printed in England was his Game and Playe
of Chesse (1474). The Myrrour of the Worlde and th'ymage of
the same appeared in 1480. It contains a brief statement on arith-
metic, the first mathematics to appear in print in England.
* See Vol. I, page 45, note 6. De Morgan is wrong as to the
date of the Margarita Philosophica. The first edition appeared at
Freiburg in 1503.
'Reisch was confessor to Maximilian I (1459-1519), King of the
Romans (1486) and Emperor (1493-1519).
10 Joachim Sterck Ringelbergh (c. 1499-c. 1536), teacher of philos-
ophy and mathematics in various cities of France and Germany. His
Institutionum astronomicarum libri III appeared at Basel in 1528,
his Cosmographia at Paris in 1529, and his Opera at Leyden in 1531.
282 A BUDGET OF PARADOXES.
Morhof, though the thumbs and fingers of the two hands
will meet over the length of its one volume. There are
more small collections ; but we pass on to the first work
to which the name of Encyclopedia is given. This is a
ponderous Scientiarum Omnium Encyclopedia of Alsted, 11
in four folio volumes, commonly bound in two : published in
1629 and again in 1649 ; the true parent of all the Encyclo-
paedias, or collections of treatises, or works in which that
character predominates. The first great dictionary may
perhaps be taken to be Hofman's Lexicon Universale 12
(1677); but Chambers's 18 (so called) Dictionary (1728)
has a better claim. And we support our proposed nomen-
clature by observing that Alsted accidentally called his
work Encyclopaedia, and Chambers simply Cyclopaedia.
We shall make one little extract from the myrrour,
and one from Ringelberg. Caxton's author makes a singu-
lar remark for his time; and one well worthy of attention.
The grammar rules of a language, he says, must have been
invented by foreigners: "And whan any suche tonge was
perfytely had and usyd amonge any people, than other
people not used to the same tonge caused rulys to be made
wherby they myght lerne the same tonge .... and suche
rulys be called the gramer of that tonge." Ringelberg
says that if the right nostril bleed, the little finger of the
right hand should be crooked, and squeezed with great
force ; and the same for the left.
"Johannes Heinrich Alsted (1588-1638) was professor of phi-
losophy and theology at his birthplace, Herborn, in Nassau, and
later at Weissenberg. _ He published several works, including the
Elementale mathematicum (1611), Systema physicae harmonicae
(1612), Methodus admirandorum mathematicorum (1613), Encyclo-
pedia septem tomis distincta (1630), and the work mentioned above.
12 Johann Jakob Hoffmann (1635-1706), professor of Greek and
history at his birthplace, Basel. He also wrote the Epitome metrica
histories universalis civilis et sacra ab orbe condito (1686).
"Ephraim Chambers (c. 1680-1740), a crotchety, penurious, but
kind-hearted freethinker. His Cyclopedia, or an Universal Dic-
tionary was translated into French and is said to have suggested the
great Encyclopedic.
REVIEW OF CYCLOPAEDIAS. 283
We pass on to the Encyclopedic, 14 commenced in 1751 ;
the work which has, in many minds, connected the word
encyclopedist with that of infidel. Readers of our day
are surprised when they look into this work, and wonder
what has become of all the irreligion. The truth is, that
the work though denounced ab oz/o 15 on account of the
character of its supporters was neither adapted, nor in-
tended, to excite any particular remark on the subject: no
work of which D'Alembert 18 was co-editor would have
been started on any such plan. For, first, he was a real
sceptic : that is, doubtful, with a mind not made up. Next,
he valued his quiet more than anything ; and would as soon
have gone to sleep over an hornet's nest as have contem-
plated a systematic attack upon either religion or govern-
ment. As to Diderot 17 of whose varied career of thought
it is difficult to fix the character of any one moment, but
who is very frequently taken among us for a pure atheist
we will quote one sentence from the article "Encyclo-
pedic," which he wrote himself: "Dans le moral, il n'y
a que Dieu qui doit servir de modele a I'homme; dans les
art, que la nature." 18
A great many readers in our country have but a very
hazy idea of the difference between the political Encyclo-
paedia, as we may call it, and the Encyclopedie Methodique,^
which we always take to be meant whether rightly or not
we cannot tell when we hear of the "great French En-
cyclopaedia." This work, which takes much from its prede-
14 Encyclopedic, ou Dictionnaire raisonne des sciences, des arts
et des metiers, par un societe de gens de lettres. Mis en ordre et
public par M. Diderot, et quant a la partie mathematique. par M.
d'Alembert. Paris, 1751-1780, 35 volumes.
""From the egg" (state).
" See Vol. I, page 382, note 12.
17 See Vol. II, page 4, note 15.
1 "In morals nothing should serve man as a model but God ; in
the arts, nothing but nature."
19 Encyclopedie Methodique, ou par ordre de matieres. Paris,
1782-1832, 16654 volumes.
284 A BUDGET OF PARADOXES.
cessor, professing to correct it, was begun in 1792, and
finished in 1832. There are 166 volumes of text, and
6439 plates, which are sometimes incorporated with the
text, sometimes make about 40 more volumes. This is
still the monster production of the kind; though probably
the German Cyclopaedia of Ersch and Gruber, 20 which was
begun in 1818, and is still in progress, will beat it in size.
The great French work is a collection of dictionaries; it
consists of Cyclopaedias of all the separate branches of
knowledge. It is not a work, but a collection of works,
one or another department is to be bought from time to
time; but we never heard of a complete set for sale in one
lot. As ships grow longer and longer, the question arises
what limit there is to the length. One answer is, that it will
never do to try such a length that the stern will be rotten
before the prow is finished. This wholesome rule has not
been attended to in the matter before us ; the earlier parts
of the great French work were antiquated before the whole
were completed : something of the kind will happen to that
of Ersch and Gruber.
The production of a great dictionary of either of the
kinds is far from an easy task. There is one way of man-
aging the Encyclopaedia which has been largely resorted to ;
indeed, we may say that no such work has been free from
it. This plan is to throw all the attention upon the great
treatises, and to resort to paste and scissors, or some process
of equally easy character, for the smaller articles. However
it may be done, it has been the rule that the Encyclopaedia
of treatises should have its supplemental Dictionary of a
very incomplete character. It is true that the treatises
are intended to do a good deal ; and that the Index, if it
be good, knits the treatises and the dictionary into one
whole of reference. Still there are two stools, and between
them a great deal will fall to the ground. The dictionary
portion of the Britannica is not to be compared with its
580 See Vol. II, page 193, note 5.
REVIEW OF CYCLOPAEDIAS. 285
treatises ; the part called Miscellaneous and Lexicographical
in the Metropolitana 21 is a great failure. The defect is
incompleteness. The biographical portion, for example, of
the Britannica is very defective: of many names of note in
literature and science, which become known to the reader
from the treatises, there is no account whatever in the dic-
tionary. So that the reader who has learnt the results of
a life in astronomy, for example, must go to some other
work to know when that life began and ended. This defect
has run through all the editions ; it is in the casting of the
work. The reader must learn to take the results at their
true value, which is not small. He must accustom himself
to regard the Britannica as a splendid body of treatises on
all that can be called heads of knowledge, both greater
and smaller; with help from the accompanying dictionary,
but not of the most complete character. Practically, we
believe, this defect cannot be avoided: two plans of essen-
tially different structure cannot be associated on the con-
dition of each or either being allowed to abbreviate the
other.
The defect of all others which it is most difficult to avoid
is inequality of performance. Take any dictionary you
please, of any kind which requires the association of a num-
ber of contributors, and this defect must result. We do
not merely mean that some will do their work better than
others ; this of course : we mean that there will be structural
differences of execution, affecting the relative extent of the
different parts of the whole, as well as every other point
by which a work can be judged. A wise editor will not
attempt any strong measures of correction : he will remem-
ber that if some portions be below the rest, which is a dis-
advantage, it follows that some portions must be above the
rest, which is an advantage. The only practical level, if
n Encyclopedia Metropolitana; or, Universal Dictionary of
Knowledge. London, 1845, 29 volumes. A second edition came out
in 1848-1858 in 40 volumes.
286 A BUDGET OF PARADOXES.
level there must be, is that of mediocrity, if not of absolute
worthlessness : any attempt to secure equality of strength
will result in equality of weakness. Efficient development
may be cut down into meager brevity, and in this way
only can apparent equality of plan be secured throughout.
It is far preferable to count upon differences of execution,
and to proceed upon the acknowledged expectation that
the prominent merits of the work will be settled by the
accidental character of the contributors; it being held im-
possible that any editorial efforts can secure a uniform
standard of goodness. Wherever the greatest power is
, found, it should be suffered to produce its natural effect.
There are, indeed, critics who think that the merit of a
book, like the strength of a chain, is that of its weakest
part: but there are others who know that the parallel does
not hold, and who will remember that the union of many
writers must show exaggeration of the inequalities which
almost always exist in the production of one person. The
true plan is to foster all the good that can be got, and to
give development in the directions in which most resources
are found : a Cyclopaedia, like a plant, should grow towards
the light.
The Penny Cyclopedia had its share of this kind of
defect or excellence, according to the way in which the
measure is taken. The circumstance is not so much noticed
as might be expected, and this because many a person is
in the habit of using such a dictionary chiefly with relation
to one subject, his own; and more still want it for the
pure dictionary purpose, which does not go much beyond
the meaning of the word. But the person of full and
varied reference feels the differences ; and criticism makes
capital of them. The Useful Knowledge Society was al-
ways odious to the organs of religious bigotry ; and one
of them, adverting to the fact that geography was treated
with great ability, and most unusual fullness, in the Penny
Cyclopcedia, announced it by making it the sole merit of
REVIEW OF CYCLOPAEDIAS. 287
the work that, with sufficient addition, it would make a
tolerably good gazetteer.
Some of our readers may still have hanging about them
the feelings derived from this old repugnance of a class to
all that did not associate direct doctrinal teaching of re-
ligion with every attempt to communicate knowledge. I
will take one more instance, by way of pointing out the
extent to which stupidity can go. If there be an astro-
nomical fact of the telescopic character which, next after
Saturn's ring and Jupiter's satellites, was known to all
the world, it was the existence of multitudes of double
stars, treble stars, etc. A respectable quarterly of the theo-
logical cast, which in mercy we refrain from naming, was
ignorant of this common knowledge, imagined that the
mention of such systems was a blunder of one of the writers
in the Penny Cyclopedia, and lashed the presumed igno-
rance of the statement in the following words, delivered in
April, 1837:
"We have forgotten the name of that Sidrophel who
lately discovered that the fixed stars were not single stars,
but appear in the heavens like soles at Billingsgate, in pairs ;
while a second astronomer, under the influence of that
competition in trade which the political economists tell us
is so advantageous to the public, professes to show us,
through his superior telescope, that the apparently single
stars are really three. Before such wondrous mandarins
of science, how continually must homunculi like ourselves
keep in the background, lest we come between the wind and
their nobility."
Certainly these little men ought to have kept in the
background ; but they did not : and the growing reputation
of the work which they assailed has chronicled them in
literary history; grubs in amber.
This important matter of inequality, which has led us
so far, is one to which the Encyclopedia is as subject as
the Cyclopedia; but it is not so easily recognized as a fault.
288 A BUDGET OF PARADOXES.
We receive the first book as mainly a collection of treat*
ises: we know their authors, and we treat them as indi-
viduals. We see, for instance, the names of two leading
writers on Optics, Brewster 22 and Herschel. 23 It would not
at all surprise us if either of these writers should be found
criticising the other by name, even though the very view
opposed should be contained in the same Encyclopedia
with the criticism. And in like manner, we should hold it
no wonder if we found some third writer not comparable
to either of those we have named. It is not so in the
Cyclopedia: here we do not know the author, except by
inference from a list of which we never think while con-
sulting the work. We do not dissent from this or that
author: we blame the book.
The Encyclopedia Britannica is an old friend. Though
it holds a proud place in our present literature, yet the
time was when it stood by itself, more complete and more
clear than anything which was to be found elsewhere.
There must be studious men alive in plenty who remember
when they were studious boys, what a literary luxury it
was to pass a few days in the house of a friend who had
a copy of this work. The present edition is a worthy suc-
cessor of those which went before. The last three editions,
terminating in 1824, 1842, and 1861, seem to show that a
lunar cycle cannot pass without an amended and augmented
edition. Detailed criticism is out of the question ; but we
may notice the effective continuance of the plan of giving
general historical dissertations on the progress of knowl-
edge. Of some of these dissertations we have had to take
separate notice ; and all will be referred to in our ordinary
treatment of current literature. 2 *
The literary excellence of these two extensive under-
takings is of the same high character. To many this will
* See Vol. I, page 137, note 8.
33 See Vol. I, page 80, note 5.
**De Morgan should be alive to satirize some of the statements
On the history of mathematics in the eleventh edition.
REVIEW OF CYCLOPAEDIAS. 289
need justification : they will not easily concede to the cheap
and recent work a right to stand on the same shelf with the
old and tried magazine, newly replenished with the best of
everything. Those who are cognizant by use of the kind
of material which fills the Penny Cyclopedia will need no
further evidence: to others we shall quote a very remark-
able and certainly very complete testimony. The Cyclopedia
of the Physical Sciences, published by Dr. Nichol 25 in 1857
(noticed by us, April 4), is one of the most original of
our special dictionaries. The following is an extract from
the editor's preface:
"When I assented to Mr. Griffin's proposal that I should
edit such a Cyclopaedia, I had it in my mind that I might
make the scissors eminently effective. Alas! on narrowly
examining our best Cyclopaedias, I found that the scissors
had become blunted through too frequent and vigorous use.
One great exception exists: viz., the Penny Cyclopedia of
Charles Knight. 26 The cheapest and the least pretending,
it is really the most philosophical of our scientific diction-
aries. It is not made up of a series of treatises, some good
and many indifferent, but is a thorough Dictionary, well
proportioned and generally written by the best men of the
time. The more closely it is examined, the more deeply
will our obligation be felt to the intelligence and conscien-
tiousness of its projector and editor."
After Dr. Nichol's candid and amusing announcement
of his scissorial purpose, it is but fair to state that nothing
of the kind was ultimately carried into effect, even upon the
work in which he found so much to praise. I quote this
testimony because it is of a peculiar kind.
John Pringle Nichol (1804-1859), Regius professor of astron-
omy at Glasgow and a popular lecturer on the subject. He lectured
in the United States in 1848-1849. His Views of the Architecture of
the Heavens (1838) was a very popular work, and his Planetary
System (1848, 1850) contains the first suggestion for the study of
sun spots by the aid of photography.
* See Vol. II, page 109, note 7.
290 A BUDGET OF PARADOXES.
The success of the Penny Magazine led Mr. Charles
Knight in 1832 to propose to the Useful Knowledge So-
ciety a Cyclopaedia in weekly penny numbers. These two
works stamp the name of the projector on the literature
of our day in very legible characters. Eight volumes of
480 pages each were contemplated; and Mr. Long 27 and
Mr. Knight were to take the joint management. The plan
embraced a popular account of Art and Science, with very
brief biographical and geographical information. The early
numbers of the work had some of the Penny Magazine
character : no one can look at the pictures of the Abbot and
Abbess in their robes without seeing this. By the time the
second volume was completed, it was clearly seen that the
plan was working out its own extension: a great develop-
ment of design was submitted to, and Mr. Long became sole
editor. Contributors could not be found to make articles
of the requisite power in the assigned space. One of them
told us that when he heard of the eight volumes, happening
to want a shelf to be near at hand for containing the work
as it went on, he ordered it to be made to hold twenty-five
volumes easily. But the inexorable logic of facts beat him
after all: for the complete work contained twenty-six vol-
umes and two thick volumes of Supplement.
The penny issue was brought to an end by the state of
the law, which required, in 1833, that the first and last page
of everything sold separately should contain the name and
address of the printer. The penny numbers contained this
imprint on the fold of the outer leaf: and qui tarn 28 in-
formations were laid against the agents in various towns.
* George Long (1800-1879), a native of Poulton, in Lancashire,
was called to the University of Virginia when he was only twenty-
four years old as professor of ancient languages. He returned to
England in 1828 to become professor of Greek at London Univer-
sity. From 1833 to 1849 he edited the twenty-nine volumes of the
Penny Cyclopadia. He was an authority on Roman law.
88 A legal phrase, "Qui tarn pro domina regina, quam pro se ipso
sequitur," "Who sues as much on the Queen's account a* on his
own."
REVIEW OF CYCLOPAEDIAS. 291
It became necessary to call in the stock; and the penny
issue was abandoned. Monthly parts were substituted,
which varied in bulk, as the demands of the plan became
more urgent, and in price from one sixpence to three. The
second volume of Supplement appeared in 1846, and during
the fourteen years of issue no one monthly part was ever
behind its time. This result is mainly due to the peculiar
qualities of Mr. Long, who unites the talents of the scholar
and the editor in a degree which is altogether unusual. If
any one should imagine that a mixed mass of contributors
is a punctual piece of machinery, let him take to editing
upon that hypothesis, and he shall see what he shall see
and learn what he shall learn.
The English contains about ten per cent more matter
than the Penny Cyclopedia and its supplements ; including
the third supplementary volume of 1848, which we now men-
tion for the first time. The literary work of the two edi-
tions cost within 500/. and 50,000/. : that of the two editions
of the Britannica cost 41,000/. But then it is to be re-
membered that the Britannica had matter to begin upon,
which had been paid for in the former editions. Roughly
speaking, it is probable that the authorship of a page of
the same size would have cost nearly the same in one as in
the other.
The longest articles in the Penny Cyclopedia were
"Rome" in 98 columns and "Yorkshire" in 86 columns.
The only article which can be called a treatise is the Astron-
omer Royal's "Gravitation," founded on the method of
Newton in the eleventh section, but carried to a much
greater extent. In the English Cyclopedia, the longest
article of geography is "Asia," in 45 columns. In natural
history the antelopes demand 36 columns. In biography,
"Wellington" uses up 42 columns, and his great military
opponent 41 columns. In the division of Arts and Sciences,
which includes much of a social and commercial character,
the length of articles often depends upon the state of the
292 A BUDGET OF PARADOXES.
times with regard to the subject. Our readers would not
hit the longest article of this department in twenty guesses :
it is "Deaf and Dumb" in 60 columns. As other speci-
mens, we may cite Astronomy, 19 ; Banking, 36 ; Blind, 24 ;
British Museum, 35 ; Cotton, 27 ; Drama, 26 ; Gravitation,
50; Libraries, 50; Painting, 34; Railways, 18; Sculpture,
36; Steam, etc., 37; Table, 40; Telegraph, 30; Welsh lan-
guage and literature, 39; Wool, 21. These are the long
articles of special subdivisions: the words under which the
Encyclopaedia gives treatises are not so prominent. As in
Algebra, 10; Chemistry, 12; Geometry, 8; Logic, 14;
Mathematics, 5 ; Music, 9. But the difference between the
collection of treatises and the dictionary may be illustrated
thus : though "Mathematics" have only five columns, "Mathe-
matics, recent terminology of," has eight : and this article we
believe to be by Mr. Cayley, 29 who certainly ought to know
his subject, being himself a large manufacturer of the new
terms which he explains. Again, though "Music" ingenere,
as the schoolmen said, has only nine columns, "Tempera-
ment and Tuning," has eight, and "Chord" alone has two.
And so on.
In a dictionary of this kind it is difficult to make a
total clearance of personality: by which we mean that ex-
hibition of peculiar opinion which is offensive to taste
when it is shifted from the individual on the corporate
book. The treatise of the known author may, as we have
said, carry that author's controversies on its own shoulders :
and even his crotchets, if we may use such a word. But
"Arthur Cayley (1821-1895) was a fellow of Trinity College,
Cambridge (1842-1846) and was afterwards a lawyer (1849-1863).
During his fourteen years at the bar he published some two hundred
mathematical papers. In 1863 he became professor of mathematics
at Cambridge, and so remained until his death. His collected papers,
nine hundred in number, were published by the Cambridge Press in
13 volumes (1889-1898). He contributed extensively to the theory
of invariants and covariants. De Morgan's reference to his coining
of new names is justified, ^ although his contemporary, Professor
Sylvester, so far surpassed him in this respect as to have been dubbed
"the mathematical Adam."
REVIEW OF CYCLOPAEDIAS. 293
the dictionary should not put itself into antagonism with
general feeling, nor even with the feelings of classes. We
refer particularly to the ordinary and editorial teaching of
the article. If, indeed, the writer, being at issue with man-
kind, should confess the difference, and give abstract of
his full grounds, the case is altered: the editor then, as it
were, admits a correspondent to a statement of his own
individual views. The dictionary portion of the Britannica
is quite clear of any lapses on this point, so far as we know :
the treatises and dissertations rest upon their authors. The
Penny Cyclopaedia was all but clear: and great need was
there that it should have been so. The Useful Knowledge
Society, starting on the principle of perfect neutrality in
politics and religion, was obliged to keep strict watch
against the entrance of all attempt even to look over the
hedge. There were two we believe only two instances
of what we have called personality. The first was in the
article "Bunyan." It is worth while to extract all that is
said in an article of thirty lines about a writer who is
all but universally held to be the greatest master of allegory
that ever wrote:
"His works were collected in two volumes, folio, 1736-7 :
among them 'The Pilgrim's Progress' has attained the great-
est notoriety. If a judgment is to be formed of the merits
of a book by the number of times it has been reprinted, and
the many languages into which it has been translated, no
production in English literature is superior to this coarse
allegory. On a composition which has been extolled by Dr.
Johnson, and which in our own times has received a very
high critical opinion in its favor [probably Southey], it is
hazardous to venture a disapproval, and we, perhaps, speak
the opinion of a small minority when we confess that to us
it appears to be mean, jejune and wearisome."
If the unfortunate critic who thus individualized himself
had been a sedulous reader of Bunyan, his power over
294 A BUDGET OF PARADOXES.
English would not have been so jejune as to have needed
that fearful word. This little bit of criticism excited
much amusement at the time of its publication: but it was
so thoroughly exceptional and individual that it was seldom
or never charged on the book. The second instance oc-
curred in the article "Socinians." It had been arranged
that the head-words of Christian sects should be intrusted
to members of the sects themselves, on the understanding
that the articles should simply set forth the accounts which
the sects themselves give of their own doctrines. Thus
the article on the Roman Church was written by Dr. Wise-
man. 30 But the Unitarians were not allowed to come within
the rule: as in other quarters, they were treated as the
gypsies of Christianity. Under the head "Socinians" a
name repudiated by themselves an opponent was allowed
not merely to state their alleged doctrines in his own
way, but to apply strong terms, such as "audacious unfair-
ness," to some of their doings. The protests which were
made against this invasion of the understanding produced,
in due time, the article "Unitarians," written by one of that
persuasion. We need not say that these errors have been
amended in the English Cyclopaedia : and our chief purpose
in mentioning them is to remark, that this is all we can
find on the points in question against twenty-eight large
volumes produced by an editor whose task was monthly,
and whose issue was never delayed a single hour. How
much was arrested before publication none but himself can
say. We have not alluded to one or two remonstrances
on questions of absolute fact, which are beside the present
purpose.
Both kinds of encyclopaedic works have been fashioned
upon predecessors, from the very earliest which had a
predecessor to be founded upon ; and the undertakings be-
fore us will be themselves the ancestors of a line of suc-
cessors. Those who write in such collections should be
80 See Vol. II, page 26, note 12.
REVIEW OF CYCLOPAEDIAS. 295
careful what they say, for no one can tell how long a mis-
statement may live. On this point we will give the history
of a pair of epithets. When the historian De Thou 31 died,
and left the splendid library which was catalogued by
Bouillaud 32 and the brothers Dupuis 33 (Bullialdus and
Puteanus), there was a manuscript of De Thou's friend
Vieta, 34 the Harmonicon Cceleste, of which it is on record,
under Bouillaud's hand, that he himself lent it to Cosmo
de' Medici, 35 to which must be added that M. Libri 36 found
it in the Magliabecchi Library at Florence in our own day.
Bouillaud, it seems, entirely forgot what he had done.
Something, probably, that Peter Dupuis said to Bouillaud,
while they were at work on 1 the catalogue, remained on his
memory, and was published by him in 1645, long after;
to the effect that Dupuis lent the manuscript to Mersenne, 87
from whom it was procured by some intending plagiarist,
who would not give it back. This was repeated by Sher-
burne, 38 in 1675, who speaks of the work, which "being
communicated to Mersennus was, by some perfidious ac-
quaintance of that honest-minded person, surreptitiously
taken from him, and irrecoverably lost or suppressed, to the
unspeakable detriment of the lettered world." Now let the
"See Vol. I, page 111, note 3.
83 See Vol. I, page 87, note 6.
88 Pierre Dupuy (1582-1651) was a friend and relative of De
Thou. With the collaboration of his brother and Nicolas Rigault
he published the 1620 and 1626 editions of De Thou's History. He
also wrote on law and history. His younger brother, Jacques (died
in 1656), edited his works. The two had a valuable collection of
books and manuscripts which they bequeathed to the Royal Library
at Paris.
84 See Vol. I, page 51, note 3.
"It was Cosmo de' Medici (1590-1621) who was the patron of
Galileo.
38 See Vol. I, page 40, note 4.
87 See Vol. I, page 106, note 4.
88 Sir Edward Sherburne (1618-1702), a scholar of considerable
reputation. The reference by De Morgan is to The Sphere of
Marcus ManiUus, in the appendix to which is a Catalogue of As-
tronomers, ancient and modern.
296 A BUDGET OF PARADOXES.
reader look through the dictionaries of the last century
and the present, scientific or general, at the article, "Vieta,"
and he will be amused with the constant recurrence of
"honest-minded" Mersenne, and his "surreptitious" acquain-
tance. We cannot have seen less than thirty copies of these
epithets.
REVIEW OF MACCLESFIELD LETTERS.
October 18, 1862. Correspondence of Scientific Men of the Seven-
teenth Century, in the Collection of the Earl of Macclesfield. 1
2 vols. (Oxford, University Press.)
Though the title-page of this collection bears the date
1841, it is only just completed by the publication of its
Table of Contents and Index. Without these, a work of
the kind is useless for consultation, and cannot make its
way. The reason of the delay will appear: its effect is
well known to us. We have found inquirers into the history
of science singularly ignorant of things which this collection
might have taught them.
In the same year, 1841, the Historical Society of Science,
which had but a brief existence, published a collection of
letters, eighty-three in number, edited by Mr. Halliwell, 2 of
English men of science, which dovetails with the one before
us, and is for the most part of a prior date. The two should
be bound up together. The smaller collection runs from
1562 to 1682 ; the larger, from 1606 to past 1700. We shall
speak of the two as the Museum collection and the Maccles-
field collection. And near them should be placed, in every
scientific library, the valuable collection published, by Mr.
Edleston, 3 for Trinity College, in 1850.
George Parker, second Earl of Macclesfield (1697-1764). He
erected an observatory at Shirburn Castle, Oxfordshire, in 1739,
and fitted it out with the best equipment then available. He was
President of the Royal Society in 1752.
3 See Vol. II, page 148, note 4.
' See Vol. I, page 140, note 7.
REVIEW OF MACCLESFIELD LETTERS. 297
The history of these letters runs back to famous John
Collins, the attorney-general of the mathematics, as he has
been called, who wrote to everybody, heard from everybody,
and sent copies of everybody's letter to everybody else. He
was in England what Mersenne 4 was in France : as early as
1671, E. Bernard 5 addresses him as "the very Mersennus
and intelligence of this age." John Collins 8 was never more
than accountant to the Excise Office, to which he was pro-
moted from teaching writing and ciphering, at the Restora-
tion: he died in 1682. We have had a man of the same
office in our own day, the late Prof. Schumacher, 1 who
made the little Danish Observatory of Altona the junction
of all the lines by which astronomical information was con-
veyed from one country to another. When the collision
took place between Denmark and the Duchies, the English
Government, moved by the Astronomical Society, instructed
its diplomatic agents to represent strongly to the Danish
Government, when occasion should arise, the great impor-
tance of the Observatory of Altona to the astronomical
communications of the whole world. But Schumacher had
his own celebrated journal, the Astronontische Nachrichten,
by which to work out part of his plan ; private correspond-
ence was his supplementary assistant. Collins had only
correspondence to rely on. Nothing is better known than
that it was Collins's collection which furnished the materials
put forward by the Committee of the Royal Society in
1712, as a defence of Newton against the partisans of
Leibnitz. The noted Commercium Epistolicum is but the
abbreviation of a title which runs on with "D. Johannis
Collins et aliorum ..."
The whole of this collection passed into the hands of
4 See Vol. I, page 106, note 4.
"Edward Bernard (1638-1696), although Savilian professor of
astronomy at Oxford, was chiefly interested in archeology.
8 See Vol. I, page 107, note 1.
T See Vol. I, page 107, note 1.
298 A BUDGET OF PARADOXES.
William Jones, 8 the father of the Indian Judge of the same
name, who died in 1749. Jones was originally a teacher,
but was presented with a valuable sinecure by the interest
of George, second Earl of Macclesfield, the mover of the bill
for the change of style in Britain, who died President of
the Royal Society. This change of style may perhaps be
traced to the union of energies which were brought into
concert by the accident of a common teacher : Lord Maccles-
field and Lord Chesterfield, the mover and the seconder,
and Daval, 10 who drew the bill, were pupils of De Moivre. 11
Jones, who was a respectable mathematician though not an
inventor, collected the largest mathematical library of his
day, and became possessor of the papers of Collins, which
contained those of Oughtred 12 and others. Some of these
papers passed into the custody of the Royal Society : but the
bulk was either bequeathed to, or purchased by, Lord
Macclesfield; and thus they found their way to Shirburn
Castle, where they still remain.
A little before 1836, this collection attracted the atten-
tion of a searching inquirer into points of mathematical
history, the late Professor Rigaud, 13 who died in 1839.
He examined the whole collection of letters, obtained Lord
Macclesfield's consent to their publication, and induced the
Oxford Press to bear the expense. It must be particularly
remembered that there still remains at Shirburn Castle a
8 See Vol. I, page 135, note 3.
'Philip Dormer Stanhope, fourth Earl of Chesterfield (1694-
1773), well known for the letters written to his son which were
published posthumously (1774).
"Peter Daval (died in 1763), Vice-President of the Royal So-
ciety, and an astronomer of some ability.
11 See Vol. I, page 376, note 1.
"William Oughtred (c. 1573-1660), a fellow of King's College,
Cambridge, and afterwards vicar of Aldbury, Surrey, wrote the best-
known arithmetic and trigonometry of his time. His Arithmetic as
in Numero & Speciebus Institutio. .. .quasi Clavis Mathematics est
(1631) went through many editions and appeared in English as
The Key to the Mathematicks new forged and filed in 1647.
18 See Vol. I, page 140, note 5.
REVIEW OF MACCLESFIELD LETTERS. 299
valuable mass of non-epistolary manuscripts. So far as
we can see, the best chance of a further examination and
publication lies in public encouragement of the collection
now before us: the Oxford Press might be induced to ex-
tend its operations if it were found that the results were
really of interest to the literary and scientific world. Rigaud
died before the work was completed, and the publication
was actually made by one of his sons, S. Jordan Rigaud, 14
who died Bishop of Antigua. But this publication was
little noticed, for the reasons given. The completion now
published consists of a sufficient table of contents, of the
briefest kind, by Professor De Morgan, and an excellent
index by the Rev. John Rigaud. 15 The work is now fairly
started on its career.
If we were charged to write a volume with the title
"Small things in their connection with great," we could not
do better than choose the small part of this collection of
letters as our basis. The names, as well as the contents, are
both great and small: the great names, those which are
known to every mathematician who has any infusion of the
history of his pursuit, are Briggs, 16 Oughtred, Charles
Cavendish, 17 Gascoigne, 18 Seth Ward, 19 Wallis, 20 Hufy]-
14 Stephen Jordan Rigaud (1816-1859) was senior assistant master
of Westminster School (1846) and head master of Queen Elizabeth's
School at Ipswich (1850). He was made Bishop of Antigua in
1858 and died of yellow fever the following year.
15 He also wrote a memoir of his father, privately printed at
Oxford in 1883.
19 See Vol. I, page 69, note 3.
17 See Vol. I, page 106, note 4.
"William Gascoigne was born at Middleton before 1612 and
was killed in the battle of Marston Moor in 1644. He was an astron-
omer and invented the micrometer with movable threads (before
1639).
19 Seth Ward (1617-1689) was deprived of his fellowship at
Cambridge for refusing to sign the covenant. He became professor
of astronomy at Oxford (1649), Bishop of Exeter (1662), Bishop
of Salisbury (1667), and Chancellor of the Garter (1671). He is
best known for his solution of Kepler's problem to approximate a
planet's orbit, which appeared in his Astronomia geometrica in 1656.
"See Vol. I, page 110, note 2.
300 A BUDGET OF PARADOXES.
20
gens, 21 Collins, 22 William Petty, 28 Hooke, 24 Boyle, 25 Pell,
Oldenburg," Brancker, 28 Slusius, 29 Bertit, 80 Bernard, 81 Bo-
relli, 82 Mouton, 88 Pardies, 84 Fermat, 85 Towneley, 86 Auzout, 37
* See Vol. I, page 100, note 2.
" See Vol. I, page 107, note 1.
* See Vol. I page 114, note 6.
* See Vol. I, page 77, note 4.
* See Vol. I, page 125, note 3.
" See Vol. I, page 105, note 2.
w Heinrich Oldenburgh (1626-1678) was consul in England for
the City of Bremen, his birthplace, and afterwards became a private
teacher in London. He became secretary of the Royal Society and
contributed on physics and astronomy to the Philosophical Trans-
actions.
"Thomas Brancker, or Branker (1636-1676) wrote the Doctrines
sphcerica adumbratio et usus globorum artificialium (1662) and
translated the algebra of Rhonius with the help of Pell. The latter
work appeared under the title of An Introduction to Algebra (1668),
and is noteworthy as having brought before English mathematicians
the symbol -f- for division. The symbol never had any standing on
the Continent for this purpose, but thereafter became so popular in
England that it is still used in all the English-speaking world.
"See Vol. I, page 118, note 1.
"Pierre Bertius (1565-1629) was a native of Flanders and was
educated at London and Leyden. He became a professor at Leyden,
and later held the chair of mathematics at the College de France.
He wrote chiefly on geography.
" See Vol. II, page 297, note 5.
M Giovanni Alphonso Borelli (1608-1679) was professor of mathe-
matics at Messina (1646-1656) and at Pisa (1656-1657), after which
he taught in Rome at the Convent of St. Panteleon. He wrote
several works on geometry, astronomy, and physics.
* See Vol. I, page 172, note 2.
"Ignace Gaston Pardies (c. 1636-1673), a Jesuit, professor of
ancient languages and later of mathematics and physics at the College
of Pau, and afterwards professor of rhetoric at the College Louis-
le-Grand at Paris. He wrote on geometry, astronomy and physics.
" Pierre Fermat was born in 1608 (or possibly in 1595) near
Toulouse, and died in 1665. Although connected with the parlia-
ment of Toulouse, his significant work was in mathematics. He was
one of the world's geniuses in the theory of numbers, and was one
of the founders of the theory of probabilities and of analytic geom-
etry. After his death his son published his edition of Diophantus
(1670) and his Varia opera mathematica (1679).
"This may be Christopher Townley (1603-1674) the antiquary,
or his nephew, Richard, who improved the micrometer already in-
vented by Gascoigne.
"Adrien Auzout a native of Rouen, who died at Rome in 1691.
REVIEW OF MACCLESFIELD LETTERS. 301
D. Gregory, 38 Halley, 39 Machin, 40 Montmort, 41 Cotes, 42
Jones, 43 Saunderson, 44 Reyneau, 45 Brook Taylor, 46 Mauper-
tuis, 47 Bouguer, 48 La Condamine, 49 Folkes, 50 Macclesfield, 51
He invented a screw micrometer with movable threads (1666) and
made many improvements in astronomical instruments.
M See Vol. I, page 66, note 9.
M See Vol. I, page 124, note 7.
** John Machin (d. 1751) was professor of astronomy at Gresham
College (1713-1751) and secretary of the Royal Society. He trans-
lated Newton's Principia into English. His computation of *" to 100
places is given in William Jones's Synopsis palmariorum matheseos
(1706).
41 Pierre Remond de Montmort (1678-1719) was canon of Notre
Dame until his marriage. He was a gentleman of leisure and devoted
himself to the study of mathematics, especially of probabilities.
"Roger Cotes (1682-1716), first Plumian professor of astronomy
and physics at Cambridge, and editor of the second edition of New-
ton's Principia. His posthumous Harmonia Mensurarum (1722)
contains "Cotes's Theorem" on the binomial equation. Newton said
of him, "If Mr. Cotes had lived we had known something."
tt See Vol. I, page 135, note 3.
44 See Vol. I, page 377, note 4.
** Charles Rene Reyneau (1656-1728) was professor of mathe-
matics at Angers. His Analyse demontree, ou Maniere de resoudre
les problemes de mathematiques (1708) was a successful attempt to
popularize the theories of men like Descartes, Newton, Leibnitz, and
the Bernoullis.
"Brook Taylor (1685-1731), secretary of the Royal Society, and
student of mathematics and physics. His Methodus incretnentorum
directa et inversa (1715) was the first treatise on the calculus of
finite differences. It contained the well-known theorem that bears
his name.
"Pierre Louis Moreau de Maupertuis (1698-1759) was sent
with Clairaut (1735) to measure an arc of a meridian in Lapland. He
was head of the physics department in the Berlin Academy from
1745 until 1753. He wrote Sur la figure de la terre (1738) and on
geography and astronomy.
48 Pierre Bouguer (1698-1758) was professor of hydrography at
Paris, and was one of those sent by the Academy of Sciences to
measure an arc of a meridian in Peru (1735). The object of this
and the work of Maupertuis was to determine the shape of the
earth and see if Newton's theory was supported.
"Charles Marie de la Condamine (1701-1774) was a member
of the Paris Academy of Sciences and was sent with Bouguer to
Peru, for the purpose mentioned in the preceding note. He wrote on
the figure of the earth, but was not a scientist of high rank.
" See Vol. I, page 136, note 5.
81 See Vol. II, page 296, note 1.
302 A BUDGET OF PARADOXES.
Baker, 82 Barrow, 83 Flamsteed, 54 Lord Brounker, 85 J. Greg-
ory, 86 Newton 57 and Keill. 58 To these the Museum collec-
tion adds the names of Thomas Digges, 59 Dee, 60 Tycho
Brahe, 61 Harriot, 62 Lydyat, 63 Briggs, 64 Warner, 68 Tarpor-
ley, Pell, 66 Lilly, 67 Oldenburg, 68 Collins, 68 Morland. 70
"Thomas Baker (c. 1625-1689) gave a geometric solution of the
biquadratic in his Geometrical Key, or Gate of Equations unlocked
(1684).
" See Vol. I, page 160, note 5.
64 See Vol. I, page 87, note 4.
88 See Vol. I, page 132, note 2.
" See Vol. I, page 118, second note 1.
BT The name of Newton is so well known that no note seems ne-
cessary. He was born at Woolsthorpe, Lincolnshire, in 1642, and died
at Kensington in 1727.
M John Keill ( 1671-1721 ) , professor of astronomy at Oxford from
1710, is said to have been the first to teach the Newtonian physics
by direct experiment, the apparatus being invented by him for the
purpose. He wrote on astronomy and physics. His Epistola de
legibus virium centripetarum, in the Philosophical Transactions for
1708, accused Leibnitz of having obtained his ideas of the calculus
from Newton, thus starting the priority controversy.
e * Thomas Digges (d. in 1595) wrote An Arithmeticall Militare
Treatise, named Stratioticos (1579), and completed A geometrical
practise, named Pantometria (1571) that had been begun by his
father, Leonard Digges.
"John Dee (1527-1608), the most famous astrologer of his day,
and something of a mathematician, wrote a preface to Billingsley's
translation of Euclid into English (1570).
w See Vol. I, page 76, note 3.
** Thomas Harriot (1560-1621) was tutor in mathematics to Sir
Walter Raleigh, who sent him to survey Virginia (1585). He was
one of the best English algebraists of his time, but his Artis Ana-
lytics Praxis ad Aequationes Algebraicas resohendas (1631) did
not appear until ten years after his death.
"Thomas Lydiat (1572-1626), rector of Alkerton, devoted his
life chiefly to the study of chronology, writing upon the subject and
taking issue with Scaliger (1601).
* See Vol. I, page 69, note 3.
" Walter Warner edited Harriot's Artis Analyticae Praxis (1631).
Tarporley is not known in mathematics.
" See Vol. I, page 105, note 2.
w See Vol. I, page 115, note 3.
" See Vol. II, page 300, note 27.
" See Vol. I, page 107, note 1.
"Sir Samuel Morland (1625-1695) was a diplomat and inven-
tor. For some years he was assistant to John Pell, then ambassador
REVIEW OF MACCLESFIELD LETTERS. 303
The first who appears on the scene is the celebrated
Oughtred, who is related to have died of joy at the Restora-
tion : but it should be added, by way of excuse, that he was
eighty-six years old. He is an animal of extinct race, an
Eton mathematician. Few Eton men, even of the minority
which knows what a sliding rule is, are aware that the in-
ventor was of their own school and college: but they may
be excused, for Dr. Hutton, 71 so far as his Dictionary bears
witness, seems not to have known it any more than they.
A glance at one of his letters reminds us of a letter from
the Astronomer Royal on the discovery of Neptune, which
we printed March 20, 1847. Mr. Airy 72 there contends, and
proves it both by Leverrier 73 and by Adams, 74 that the
limited publication of a private letter is more efficient than
the more general publication of a printed memoir. The
same may be true of a dead letter, as opposed to a dead
book. Our eye was caught by a letter of Oughtred (1629),
containing systematic use of contractions for the words
sine, cosine, etc., prefixed to the symbol of the angle. This
is so very important a step, simple as it is, that Euler 75 is
justly held to have greatly advanced trigonometry by its
introduction. Nobody that we know of has noticed that
Oughtred was master of the improvement, and willing to
have taught it, if people would have learnt. After looking
at his dead letter, we naturally turned to his dead book
on trigonometry, and there we found the abbreviations s,
sco, t, tco, se, seco, regularly established as part of the
system of the work. But not one of those who have in-
vestigated the contending claims of Euler and Thomas
to Switzerland. He wrote on arithmetical instruments invented by
him (1673), on hydrostatics (1697) and on church history (1658).
n See Vol. I, page 153, note 4.
Ta See Vol. I, page 85, note 2.
78 See Vol. I, page 43, note 8.
14 See Vol. I, page 43, note 7.
78 See Vol. I, page 382, note 13. The history of the subject may
be followed in Braunmuhl's Geschichte der Trigonometric.
304 A BUDGET OF PARADOXES.
Simpson 76 has chanced to know of Oughtred's "Trigonom-
etric": and the present revival is due to his letter, not to
his book.
A casual reader, turning over the pages, would imagine
that almost all the letters had been printed, either in the
General Dictionary, or in Birch, 77 etc.: so often does the
supplementary remark begin with "this letter has been printed
in ." For ourselves we thought, until we counted,
that a large majority of the letters had been given, either
in whole or in part. But the positive strikes the mind more
forcibly than the negative: we find that all of which any
portion has been in type makes up very little more than a
quarter; the cases in which the whole letter is given being
a minority of this quarter. The person who has been best
ransacked is Flamsteed: of 36 letters from him, 34 had
been previously given in whole or in part. Of 59 letters
to and from Newton, only 17 have been culled.
The letters have been modernized in spelling, and, to
some extent, in algebraical notation ; it also seems that con-
jectural methods of introducing interpolations into the text
have been necessary. For all this we are sorry: the scien-
tific value of the collection is little altered, but its literary
value is somewhat lowered. But it could not be helped:
the printers could not work from the originals, and Pro-
fessor Rigaud had to copy everything himself. A fac-simile
must have been the work of more time than he had to
give: had he attempted it, his death would have cut short
the whole undertaking, instead of allowing him to prepare
everything but a preface, and to superintend the printing
of one of the volumes. We may also add, that we believe
we have notices of all the letters in the Macclesfield col-
lection. We judge this because several which are too
trivial to print are numbered and described; and those
would certainly not have been noticed if any omissions had
76 See Vol. I, page 377, note 3.
77 See Vol. I, page 108, note 2.
REVIEW OF MACCLESFIELD LETTERS. 305
been made. And we know that every letter was removed
from Shirburn Castle to Oxford.
Two persons emerge from oblivion in this series of
letters. The first is Michael Dary, 78 an obscure mathema-
tician, who was in correspondence with Newton and other
stars. He was a gauger at Bristol, by the interest of Col-
lins; afterwards a candidate for the mathematical school
at Christ's Hospital, with a certificate from Newton: he
was then a gunner in the Tower, and is lastly described by
Wallis as "Mr. Dary, the tobacco-cutter, a knowing man in
algebra." In 1674, Dary writes to Newton at Cambridge,
as follows: "Although I sent you three papers yesterday,
I cannot refrain from sending you this. I have had fresh
thoughts this morning." Two months afterwards poor
Newton writes to Collins, "Mr. Dary is very solicitous
about mathematics": but in spite of the persecution, he
subscribes himself to Dary "your loving friend." Dary's
problem is that of finding the rate of interest of an annuity
of which the value and term are given. Dary's theorem,
which he seems to have invented specially for the solution
of his problem, though it is of wide range, can be exhibited
to mathematical readers even in our columns. In modern
language, it is that the limit of $ n x, when n increases
without limit, is a solution of $x = x. We have men-
tioned the I. Newton to whom Dary looked up; we add a
word about the one on whom he looked down. Dr. John
Newton, 79 a sedulous publisher of logarithms, tables of
interest, etc., who began his career before Isaac Newton,
sometimes puzzles those who do not know him, when de-
scribed as I. Newton. The scientific world was of opinion
that all that was valuable in one of his works was taken
from Dary's private communications.
78 Michael Dary wrote Dary's Miscellanies (1669), Gauging epit-
omized (1669), and The general Doctrine of Equation (1664).
"John Newton (1622-1678), canon of Hereford (1673), educa-
tional reformer, and writer on elementary mathematics and astron-
omy.
306 A BUDGET OF PARADOXES.
The second character above alluded to is one who car-
ried mathematical researches a far greater length than New-
ton himself : the assistance which he rendered in this re-
spect, even to Newton, has never been acknowledged in
modern times: though the work before us shows that his
contemporaries were fully aware of it, and never thought
of concealing it. In his theory of gravitation, in which, so
far as he went, we have every reason to believe he was
prior to Newton, he did not extend his calculations to the
distance of the moon ; his views in this matter were purely
terrestrial, and led him to charge according to weight. He
was John Stiles, the London and Cambridge carrier: his
name is a household word in the Macclesfield Letters, and is
even enshrined in the depths of Birch's quartos. Dary in-
forms Newton let us do his memory this justice that he
had paid John Stiles for the carriage. At the time when
the railroad to Cambridge was opened, a correspondent
recommended the directors, in our columns, to call an engine
by the name of John Stiles, and never to let that name go
off the road. We do not know whether the advice was
followed: if not, we repeat it.
Little points of life and manners come out occasionally.
Baker, the author of a work on algebra much esteemed at
the time, wrote to Collins that their circumstances are alike,
"having a just and equal number of chargeable olive-
branches, and being in the same predicament and blessed
condemnation with you, not more preaching than unpaid,
and preaching the art of contentment to others, am forced
to practise it." But the last sentence of his letter runs as
follows : "I have sent by the bearer .... twenty shillings, as
a token to you; desiring you to accept of it, as a small
taste from Yours, Thos. Baker." In our day, men of a
station to pay parish taxes do not offer their friends hard
money to buy liquor. But Flamsteed 80 writes to Collins as
follows : "Last week he sent us down the counterpart, which
80 See Vol. I, page 87, note 4.
REVIEW OF MACCLESFIELD LETTERS. 307
my father has scaled, and I return up to you by the carrier,
with 5/. to be paid to Mr. Leneve for the writing. I have
added 2s. 6d. over, which will pay the expenses and serve
to drink, with him." This would seem as odd to us as it
would have seemed thirty years ago that half-a-crown
should pay carriage for a deed from Derby to London, and
leave margin for a bottle of wine: in our day, the Post-
office and the French treaty would just manage it between
them. But Flamsteed does not limit his friend to one
bottle ; he adds, "If you expend more than the half-crown,
I will make it good after Whitsuntide." Collins does not
remember exactly where he had met James Gregory, and
mentions two equally likely places thus: "Sir, it was once
my good hap to meet with you in an alehouse or in Sion
College." There is a little proof how universally the dinner-
hour was twelve o'clock. Astronomers well know the
method of finding time by equal altitudes of the sun before
and after noon : Huyghens calls it "le moyen de deux egales
hauteurs du soleil devant et apres diner"**
There is one mention of "Mr. Cocker, 82 our famous
English graver and writer, now a schoolmaster at North-
ampton." This is the true Cocker: his genuine works are
specimens of writing, such as engraved copy-books, in-
cluding some on arithmetic, with copper-plate questions and
space for the working; also a book of forms for law-
stationers, with specimens of legal handwriting. It is
recorded somewhere that Cocker and another, whose name
we forget, competed with the Italians in the beauty of their
flourishes. This was his real fame : and in these matters he
was great. The eighth edition of his book of law forms
(1675), published shortly after Cocker's death, has a preface
signed "J. H." This was John Hawkins, who became
possessed of Cocker's papers at least he said so and sub-
81 "The average of the two equal altitudes of the sun before and
after dinner."
M See Vol. I, page 42, note 4.
308 A BUDGET OF PARADOXES.
sequently forged the famous Arithmetic, 83 a second work
on Decimal Arithmetic, and an English dictionary, all at-
tributed to Cocker. The proofs of this are set out in De
Morgan's Arithmetical Books. Among many other cor-
roborative circumstances, the clumsy forger, after declaring
that Cocker to his dying day resisted strong solicitation to
publish his Arithmetic, makes him write in the preface Hie
ego qui quondam 8 * of this kind : "I have been instrumental
to the benefit of many, by virtue of those useful arts, writing
and engraving ; and do now, with the same wonted alacrity,
cast this my arithmetical mite into the public treasury."
The book itself is not comparable in merit to at least half-
a-dozen others. How then comes Cocker to be the imper-
sonation of Arithmetic? Unless some one can show proof,
which we have never found, that he was so before 1756,
the matter is to be accounted for thus.
Arthur Murphy, 85 the dramatist, was by taste a man of
letters, and ended by being the translator of Tacitus ; though
many do not know that the two are one. His friends had
tried to make him a man of business ; and no doubt he had
been well plied with commercial arithmetic. His first dra-
matic performance, the farce of "The Apprentice," pro-
duced in 1756, is about an idle young man who must needs
turn actor. Two of the best known books of the day in
arithmetic were those of Cocker and Wingate. 86 Murphy
chooses Wingate to be the name of an old merchant who
83 London, 1678. It went though many editions.
84 "This I who once "
85 Arthur Murphy (1727-1805) worked in a banking house until
1754. He then went on the stage and met with some success at
Covent Garden. His first comedy, The Apprentice (1756) was so
successful that he left the stage and took to play writing. His
translation of Tacitus appeared in 1793, in four volumes.
86 Edmund Wingate (1596-1656) went to Paris in 1624 as tutor
to Princess Henrietta Maria and remained there several years. He
wrote L'usage de la regie de proportion (Paris, 1624, with an _ English
translation in 1626), Arithmetique Logarithmetique (Paris, 1626,
with an English translation in 1635), and Of Natural and Artificial
Arithmetic^ (London, 1630, revised in 1650-1652), part I of which
was one of the most popular textbooks ever produced in England.
REVIEW OF MACCLESFIELD LETTERS. 309
delights in vulgar fractions, and Cocker to be his arith-
metical catchword "You read Shakespeare! get Cocker's
Arithmetic ! you may buy it for a shilling on any stall ; best
book that ever was wrote!" and so on. The farce became
very popular, and, as we believe, was the means of ele-
vating Cocker to his present pedestal, where Wingate would
have been, if his name had had the droller sound of the
two to English ears.
A notoriety of an older day turns up, Major-General
Lambert. 87 The common story is that he was banished to
Guernsey, where he passed thirty years in confinement,
rearing and painting flowers. But Baker, in 1678, repre-
sents him as a prisoner at Plymouth, sending equations for
solution as a challenge: probably his place of confinement
was varied, and his occupation also.
[General Lambert was removed to Plymouth, probably
about 1668. His daughter captured the son of the Gover-
nor of Guernsey, who therefore probably was reckoned an
unsafe custodier thenceforward; though he assured the
king that he had turned the young couple out of doors, and
had never given them a penny. Great importance was at-
tached to Lambert's safe detention: probably the remaining
republicans looked upon him as to be their next Cromwell,
if such a thing were to be. There were standing orders to
shoot him at once on the first appearance of any enemy
before the island. See Notes and Queries, 3d S. iv. 89.]
Collins informs James Gregory that "some of the Royal
Academy wrote over to Mr. Oldenburg, who was desired to
impart the same to the Council of the Royal Society, that
the French King was willing to allow pensions to one or
two learned Englishmen, but they never made any answer
87 John Lambert (1619-1694) was Major-General during the
Revolution and helped to draw up the request for Cromwell to
assume the protectorate. He was imprisoned in the Tower by the
Rump Parliament. He was confined in Guernsey until the clandestine
marriaee of his daughter Mary to Charles Hatton, son of the gover-
nor, after which he was removed (1667) to St. Nicholas in Plymouth
Sound.
310 A BUDGET OF PARADOXES.
to such a proposal." This was written in 1671, and the
thing probably happened several years before. Mr. De
Morgan communicated the account of the proposal to Lord
Macaulay, who replied that he did not think that any Eng-
lishman received a literary pension from Louis; but that
there is a curious letter, about 1664, from the French Am-
bassador, in which he says that he has, by his master's
orders, been making inquiries as to the state of learning in
England, and that he is sorry to find that the best writer
is the infamous Miltonus. On two such independent testi-
monies it may be held proved that the French King had
attempted to buy a little adherence from English literature
and science; and the silent contempt of the Royal Society
is an honorable fact in their history.
Another little bit of politics is as follows. Oughtred is
informed that "Mr. Foster, 88 our Lecturer on Astronomy at
Gresham College, is put out because he will not kneel down
at the communion-table. A Scotsman [Mungo Murray],
one that is verbi bis minister, 89 is now lecturer in Mr.
Foster's place." Ward in his work on the Gresham Pro-
fessors, 90 suppresses the reason, and the suppression lowers
the character of his book. Foster was expelled in 1636,
and re-elected on a vacancy in 1641, when Puritanism had
gained strength.
The correspondence of Newton would require deeper
sifting than could be given in such an article as the present.
The first of the letters (1669) is curious, as presenting the
** Samuel Foster (d. in 1652) was made professor of astronomy
at Gresham College in March, 1636, but resigned in November of
that year, being succeeded by Mungo Murray. Murray vacated his
chair by marriage in 1641 and Foster succeeded him. He wrote on
dialling and made a number of improvements in geometric instru-
ments.
89 "Twice of the word a minister," that is, twice a minister of the
Gospel.
80 This is The Lives of the Professors of Gresham College to
which is prefixed the Life of the Founder, Sir Thomas Gresham,
London, 1740. It was written by John Ward (c. 1679-1758), pro-
fessor of rhetoric (1720) at Gresham College and vice-president
(1752) of the Royal Society.
REVIEW OF MACCLESFIELD LETTERS. 311
appearance of forms belonging to the great calculus which,
in this paragraph, we ought to call that of fluxions. We
find, of the date February 18, 1669-70, what we believe is
the earliest manifestation of that morbid part of Newton's
temperament which has been so variously represented. He
had solved a problem being that which we have called
Dary's on which he writes as follows: "The solution of
the annuity problem, if it will be of any use, you have my
leave to insert into the Philosophical Transactions, so it be
without my name to it. For I see not what there is desi-
rable in public esteem, were I able to acquire and maintain
it. It would perhaps increase my acquaintance, the thing
which I chiefly study to decline."
Three letters touch upon "the experiment of glass rubbed
to cause various motions in bits of paper underneath" : they
are supplements to the account given by Newton to the
Royal Society, and printed by Birch. It was Newton, so
far as appears, who added glass to the substances known to
be electric. Soon afterwards we come to a little bit of the
history of the appointment to the Mint. It has appeared
from the researches of late years that Newton was long
an aspirant for public employment : the only coolness which
is known to have taken place between him and Charles
Montague 91 [Halifax] arose out of his imagining that his
friend was not in earnest about getting him into the public
service. March 14, 1696, Newton writes thus to Halley : "And
if the rumour of preferment for me in the Mint should
hereafter, upon the death of Mr. Hoar [the comptroller],
or any other occasion, be revived, I pray that you would
"Charles Montagu (1661-1715), first Earl of Halifax, was
Lord of the Treasury in 1692, and was created Baron Halifax in
1700 and Viscount Sunbury and Earl of Halifax in 1714. He intro-
duced the bill establishing the Bank of England, the bill becoming a
law in 1694. He had troubles of his own, without considering New-
ton, for he was impeached in 1701, and was the subject of a damag-
ing resolution of censure as auditor of the exchequer in 1703. Al-
though nothing came of either of these attacks, he was out of office
during much of Queen Anne's reign.
312 A BUDGET OF PARADOXES.
endeavour to obviate it by acquainting your friends that I
neither put in for any place in the Mint, nor would meddle
with Mr. Hoar's place, were it offered to me." This means
that Mr. Hoar's place had been suggested, which Newton
seems to have declined. Five days afterwards, Montague
writes to Newton that he is to have the Wardenship. It is
fair to Newton to say that in all probability this was not
or only in a smaller degree a question of personal dignity,
or of salary. It must by this time have been clear to him
that the minister, though long bound to make him an object
of patronage, was actually seeking him for the Mint, be-
cause he wanted both Newton's name and his talents for
business which he knew to be great in the weighty and
dangerous operation of restoring the coinage. It may have
been, and probably was, the case that Newton had a toler-
ably accurate notion of what he would have to do, and of
what degree of power would be necessary to enable him to
do it in his own way.
We have said that the non-epistolary manuscripts are
still unexamined. There is a chance that one of them may
answer a question of two centuries' standing, which is
worth answering, because it has been so often asked. About
1640, Warner, 92 afterwards assisted by Pell, 93 commenced
a table of antilogarithms, of the kind which Dodson 94 after-
wards constructed anew and published. In the Museum
collection there is inquiry after inquiry from Charles Caven-
dish, 95 first, as to when the Analogies, as he called them,
would be finished; next, when they would be printed. Pell
answers, in 1644, that Warner left his papers to a kinsman,
who had become bankrupt, and proceeds thus:
"I am not a little afraid that all Mr. Warner's papers,
99 See Vol. II, page 302, note 65.
98 See Vol. I, page 105, note 2.
"James Dodson (d. 1757) was master of the Royal Mathemat-
ical School, Christ's Hospital. He was De Morgan's great-grand-
father. The Anti-Logarithmic Canon was published in 1742.
98 See Vol. I, page 106, note 4,
REVIEW OF MACCLESFIELD LETTERS. 313
and no small share of my labours therein, are seazed upon,
and most unmathematically divided between the sequestra-
tors and creditors, who (not being able to ballance the
account where there appeare so many numbers, and much
troubled at the sight of so many crosses and circles in the
superstitious Algebra and that black art of Geometry) will,
no doubt, determine once in their lives to become figure-
casters, and so vote them all to be throwen into the fire, if
some good body doe not reprieve them for pye-bottoms, for
which purposes you know analogicall numbers are incom-
parably apt, if they be accurately calculated."
Pell afterwards told Wallis 96 that the papers had fallen
into the hands of Dr. Busby, 97 and Collins 98 writes that they
were left in the hands of Dr. Thorndike, 99 a prebendary of
Westminster; whence Rigaud 100 seems to say that Thorn-
dike had left them to Dr. Busby. Birch 101 says that he
procured for the Royal Society four boxes from Busby's
trustees, containing papers of Warner and Pell: but there
is no other tradition of such things in the Society. But in
the Birch manuscripts at the British Museum, there turns
up, as printed in what we call the Museum collection, a list
of Warner's papers, with Collins's receipt to Dr. Thorndike
at the bottom, and engagement to restore them on demand.
The date is December 14, 1667 ; Wallis's statement being in
1693. It is possible that Busby may be a mistake altogether:
he was very unlikely to have had charge of any mathemat-
ical papers: there may have been a confusion between the
Prebendary of Westminster and the Head Master of West-
minster School. If so, in all probability Thorndike handed
"See Vol. I, page 110, note 2.
97 Richard Busby (1606-1695), master of Westminster School
(1640) had among his pupils Dryden and Locke.
98 See Vol. I, page 107, note 1.
99 Herbert Thorndike (1598-1672), fellow of Trinity College, Cam-
bridge (1620-1646), and Prebend of Westminster (1661), was a well-
known theological writer of the time.
100 See Vol. I, page 140, note 5.
101 See Vol. I, page 108, note 2.
314 A BUDGET OF PARADOXES.
the cumbrous lot over to the notorious collector of mathe-
matical papers, blessing himself that he got rid of them in a
manner which would insure their return if he were called
upon by the owners to restore them. It is much against
this hypothesis that Dodson, who certainly recalculated, can
say nothing more about Warner than a repetition of Wallis's
story: though, had Collins kept the papers, they would
probably have been in Jones's possession at the very time
when Dodson, who was a friend of Jones and a user of
his library, was engaged on his own computations. But
even books, and still more manuscripts, are often singularly
overlooked; and it remains not very improbable that War-
ner's table is now at Shirburn Castle, among the unexam-
ined manuscripts.
CYCLOMETRY AND STEEL PENS.
Redit labor actus in orbem. 1 Among the matters which
have come to me since the Budget opened, there is a pam-
phlet of quadrature of two pages and a half from Professor
Recalcati, 2 already mentioned. It ends with "Quelque ob-
jection qu'on fasse touchant les raisonnements ci-dessus on
tombera toujours dans 1'absurde." 3 A civil engineer so
he says has made the quadrature "no longer a problem,
but an axiom." As follows : "Take the quadrant of a circle
whose circumference is given, square the quadrant which
gives the true square of the circle. Because 30-^4 = 7.5x
7. 5 = 56. 25 = the positive square of a circle whose circum-
ference is 30." Brevity, the soul of wit, is the "wings of
mighty-winds" to quadrature, and sends it "flying all abroad."
'A surbodhicary something like M.A. or LL.D., I under-
stand at Calcutta, published in 1863 the division of an
1 "Labor performed returns in a circle."
1 See Vol. II, page 208.
'"Whatever objections one may make to the above arguments,
one always falls into an absurdity."
CYCLOMETRY AND STEEL PENS. 315
angle into any odd number of parts, demonstration and
all in when the diagram is omitted one page, good-sized,
well-leaded type, small duodecimo. But in the Preface he
acknowledges "sheer inability" to execute his task. Mr.
William Dean, of Todmorden, in 1863, announced 3% 4 as
proved both practically and geometrically: he has been al-
ready mentioned anonymously. Next I have the tract of
Don Juan Larriva, published at Leiria in 1856, and dedi-
cated to Queen Victoria. Mr. W. Peters,* already men-
tioned, who has for some months been circulating diagrams
on a card, publishes (August, 1865) The Circle Squared.
He agrees with the Archpriest of St. Vitus. He hints that
a larger publication will depend partly on the support he
receives, and partly on the castigation, for which last, of
course, he looks to me. Cyclometers have their several
styles of wit; so have anticyclometers too, for that matter.
Mr. Peters will not allow me any extra- journal being: I am
essentially a quotation from the Athenaum; "A. De Mor-
gan" et praterea nihil. 5 If he had to pay for keeping me
set up, he would find out his mistake, and would be glad
to compound handsomely for a stereotype. Next comes
a magnificent sheet of pasteboard, printed on both sides.
Having glanced at it and detected quadrature, I began
methodically at the beginning "By Royal Command," with
the lion and unicorn, and all that comes between. Mercy
on us! thought I to myself: has Her Majesty referred the
question to the Judicial Committee of the Privy Council,
where all the great difficulties go now-a-days, and is this
proclamation the result? On reading further I was re-
lieved by finding that the first side is entirely an advertise-
ment of Joseph Gillott's 6 steel pens, with engraving of his
4 See Vol. II, page 11, note 1. The Circle Squared; and the solu-
tion of the problem adapted to explain the difference between square
and superficial measurement appeared at Brighton in 1865.
8 "And beyond that nothing."
Gillott (1799-1873) was the pioneer maker of steel pens by
machinery, reducing the price from Is. each to 4d. a gross. He was
a great collector of paintings and old violins.
316 A BUDGET OF PARADOXES.
premises, and notice of novel application of his unrivalled
machinery. The second side begins with "the circle recti-
fied" by W. E. Walker, 7 who finds TT = 3. 141594789624155...
This is an off-shoot from an accurate geometrical rectifica-
tion, on which is to be presumed Mr. Gillott's new machinery
is founded. I have no doubt that Mr. Walker's error, which
is only in the sixth place of decimals, will not hurt the pens,
unless it be by the slightest possible increase of the tendency
to open at the points. This arises from Mr. Walker having
rectified above proof by .000002136034362. . .
Lastly, I, even I myself, who have long felt that I was a
quadrature below par, have solved the problem by means
which, in the present state of the law of libel, I dare not
divulge. But the result is permitted; and it goes far to
explain all the discordances. The ratio of the circumference
to the diameter is not always the same ! Not that it varies
with the radius; the geometers are right enough on that
point: but it varies with the time, in a maner depending
upon the difference of the true longitudes of the Sun and
Moon. A friend of mine at least until he misbehaved
insisted on the mean right ascensions: but I served him as
Abraham served his guest in Franklin's parable. The true
formula is, A and a being the Sun's and Moon's longitudes,
Mr. James Smith obtained his quadrature at full moon ;
the Archpriest of St. Vitus and some others at new moon.
Until I can venture to publish the demonstration, I recom-
mend the reader to do as I do, which is to adopt 3.14159
---- , and to think of the matter only at the two points of
the lunar month at which it is correct. The Nautical Al-
manac will no doubt give these points in a short time: I
am in correspondence with the Admiralty, with nothing
'William Edward Walker wrote five works on circle squaring
(1853, 1854, 1857, 1862, 1864), mostly and perhaps all published at
Birmingham.
JACOB BEHMEN. 317
to get over except what I must call a perverse notion on
the part of the Superintendent of the Almanac, who sus-
pects one correction depending on the Moon's latitude ; and
the Astronomer Royal leans towards another depending on
the date of the Queen's accession. I have no patience with
these men : what can the Moon's node of the Queen's reign
possibly have to do with the ratio in question? But this
is the way with all the regular men of science; Newton is
to them etc. etc. etc. etc.
The following method of finding the circumference of
a circle (taken from a paper by Mr. S. Drach 8 in the Phil.
Mag., Jan. 1863, Suppl.) is as accurate as the use of
3.14159265. From three diameters deduct 8-thousandths
and 7-millionths of a diameter; to the result add five per
cent. We have then not quite enough ; but the shortcoming
is at the rate of about an inch and a sixtieth of an inch
in 14,000 miles.
JACOB BEHMEN.
Though I have met with nothing but a little tract from
the school of Jacob Behmen 1 (or Bohme; I keep to the old
English version of his name), yet there has been more, and
of a more recent date. I am told of an "Introduction to
Theosophy [Theo private, I suppose, as in theological] ; or,
the Science of the Mystery of Christ," published in 1854,
mostly from the writings of William Law 2 : and also of a
volume of 688 pages, of the same year, printed for private
circulation, containing notes for a biography of William
Law. The editor of the first work wishes to grow "a gen-
**j\ji
Epicvclic
chord (I
9 Solomon M. Drach wrote An easy Rule for formulising all
Heal Curves (London, 1849), On the Circle area and Heptagon-
(London, 1864), An easy general Rule for filling up all Magic
Squares (London, 1873), and Hebrew Almanack-Signs (London,
1877), besides numerous articles in journals.
1 See Vol. I, page 168, note 3.
"See Vol. I, page 254, note 2.
318 A BUDGET OF PARADOXES.
eration of perfect Christians" by founding a Theosophic
College, for which he requests the public to raise a hundred
thousand pounds. There is a good account of Jacob Behmen
in the Penny Cyclopedia. The author mentions inaccurate
accounts, one of which he quotes, as follows: "He derived
all his mystical and rapturous doctrine from Wood's 3 Athena
Oxonienses, Vol. I, p. 610, and Hist, et Antiq. Acad. Ox on.,
Vol. II, p. 308." On which the author remarks that Wood
was born after Behmen's death. There must have been a
few words which slipped out : what is meant is that Behmen
"derived his doctrine from Robert Fludd* for whom see
Wood's etc. etc." Even this is absurd enough : for Behmen
began to publish in 1610, and Fludd in 1616. Fludd was a
Rosicrucian, and a mystic of a different type from Behmen.
I have some of his works, and could produce out of them
paradoxes enough, according to our ways of thinking, to fit
out a host. But the Rosicrucian system was a recognized
school of its day, and Fludd, a man of great learning, had
abettors enough in all which he advanced, and predecessors
in most of it.
[A Correspondent has recently sent a short summary of
the claims of Jacob Behmen to rank higher than I have
placed him. I shall gladly insert this summary in the book
I contemplate, as a statement of what is said of Behmen
far less liable to suspicion of exaggeration than anything
I could write. I shall add a few extracts from Behmen
himself, in support of his right to be in my list.]
"Jacob Behmen. That Prof. De Morgan classes Jacob
Behmen among paradoxers can only be attributed to the
fact of his being avowedly unacquainted with the writings
* See Vol. I, page 98, note 6.
4 Robert Fludd or Flud (1574-1637) was a physician with a large
London practice. He denied the diurnal rotation of the earth, and
was attacked by Kepler and Mersenne, and accused of magic by
Gassendi. His Apologia Compendiania^ Fraternitatem de Rosea Cruce
suspicions . .. .maculis aspersam, veritatis quasi Fluctibus abluens
(Leyden, 1616) is one of a large number of works of the mystic
type.
JACOB BEHMEN. 319
of that author. Perhaps you may think a few words from
one who knows them well of sufficient interest to the
learned Professor, and your readers in general, to be worthy
of space in your columns. The metaphysical system of
Behmen the most perfect and only true one still awaits
a qualified commentator. Behmen's countryman, Dionysius
Andreas Freher, 5 who spent the greater part of his life in
this country, and whose exposition of Behmen exists only
in MS., filling many volumes, written in English, with the
exception of two, written in German, with numerous beauti-
ful, highly ingenious, and elaborate illustrations, copies of
some of which are in the British Museum, but all the
originals of which are in the possession of the gentleman
who is the editor of the two works alluded to by Professor
De Morgan, this Freher was the first to philosophically
expound Behmen's system, which was afterwards, with the
help of these MSS., as it were, popularized by William
Law ; but both Freher and Law confined themselves chiefly
to its theological aspect. In Behmen, however, is to be
found, not only the true ground of all theology, but also
that of all physical science. He demonstrated with a full-
ness, accuracy, completeness and certainty that leave noth-
ing to be desired, the innermost ground of Deity and
Nature ; and, confining myself to the latter, I can from my
own knowledge assert, that in Behmen's writings is to be
found the true and clear demonstration of every physical
fact that has been discovered since his day. Thus, the
science of electricity, which was not yet in existence when
he wrote, is there anticipated; and not only does Behmen
describe all the now known phenomena of that force, but
he even Drives us the origin, generation and birth of elec-
tricity itself. Again, positive evidence can be adduced that
Newton derived all his knowledge of gravitation and its
'Consult To the Christianity of the Age. Notes. . .comprising
an elucidation of the scofie and contents of the writings... of Dio-
nysius Andreas Freher (1854).
320 A BUDGET OF PARADOXES.
laws from Behmen, with whom gravitation or attraction is,
and very properly so, as he shows us, the first of the seven
properties of Nature. The theory defended by Mr. Grove, 6
at the Nottingham meeting of last year, that all the appar-
ently distinct causes of moral and physical phenomena are
but so many manifestations of one central force, and that
Continuity is the law of nature, is clearly laid down, and
its truth demonstrated, by Behmen, as well as the distinc-
tion between spirit and matter, and that the moral and
material world is pervaded by a sublime unity. And though
all this was not admitted in Behmen's days, because science
was not then sufficiently advanced to understand the deep
sense of our author, many of his passages, then unintelli-
gible, or apparently absurd, read by the light of the present
age, are found to contain the positive enunciation of prin-
ciples at whose discovery and establishment science has only
just arrived by wearisome and painful investigations. Every
new scientific discovery goes to prove his profound and in-
tuitive insight into the most secret workings of nature ; and
if scientific men, instead of sharing the prejudice arising
from ignorance of Behmen's system, would place themselves
on the vantage ground it affords, they would at once find
themselves on an eminence whence they could behold all
the arcana of nature. Behmen's system, in fact, shows us
the inside of things, while modern physical science is con-
tent with looking at the outside. Behmen traces back every
outward manifestation or development to its one central root,
to that one central energy which, as yet, is only suspected ;
every link in the chain of his demonstration is perfect, and
there is not one link wanting. He carries us from the out-
births of the circumference, along the radius to the center,
'Sir William Robert Grove (1811-1896), although called to the
bar (1835) and to the bench (1853), is best known for his work as
a physicist. He was professor of experimental philosophy (1840-
1847) at the London Institution, and invented a battery (1839)
known by his name. His Correlation of Physical Forces (1846) went
through six editions and was translated into French.
JACOB BEHMEN. 321
or point, and beyond that even to the zero, demonstrating
the constitution of the zero, or nothing, with mathematical
precision. C. W. H."
And so Behmen is no subject for the Budget! I waited
until I should chance to light on one of his volumes, know-
ing that any volume would do, and almost any page. My
first hap was on the second volume of the edition of 1664
(4to, published by M. Richardson) and opening near the be-
ginning, a turn or two brought me to page 13, where I saw
about sulphur and mercurius as follows:
"Thus SUL is the soul, in an herb it is the oil, and in
man also, according to the spirit of this world in the third
principle, which is continually generated out of the anguish
of the will in the mind, and the Brimstone-worm is the
Spirit, which hath the fire and burneth : PHUR is the sour
wheel in itself which causeth that.
"Mercurius comprehendeth all the four forms, even as the
life springeth up, and yet hath not its dark beginning in the
Center as the PHUR hath, but after the flash of fire, when
the sour dark form is terrified, where the hardness is
turned into pliant sharpness, and where the second will
(viz. the will of nature, which is called the Anguish) ariseth,
there Mercurius hath its original. For MER is the shiver-
ing wheel, very horrible, sharp, venomous, and hostile;
which assimulateth it thus in the sourness in the flash of
fire, where the sour wrathful life ariseth. The syllable CU
is the pressing out, of the Anxious will of the mind, from
Nature: which is climbing up, and willeth to be out aloft.
RI is the comprehension of the flash of fire, which in MER
giveth a clear sound and tune. For the flash maketh the
tune, and it is the Salt-Spirit which soundeth, and its form
(or quality) is gritty like sand, and herein arise noises,
sounds and voices, and thus CU comprehendeth the flash,
and so the pressure is as a wind which thrusteth, and giveth
a spirit to the flash, so that it liveth and burneth. Thus the
322 A BUDGET OF PARADOXES.
syllable US is called the burning fire, which with the spirit
continually driveth itself forth : and the syllable CU presseth
continually upon the flash."
Shades of Tauler 7 and Paracelsus, 8 how strangely you
do mix ! Well may Hallam call Germany the native soil of
Mysticism. Had Behmen been the least of a scholar, he
would not have divided sulph-ur and merc-ur-i-us as he has
done: and the inflexion us, that boy of all work, would
have been rejected. I think it will be held that a writer
from whom hundreds of pages like the above could be
brought together, is fit for the Budget. If Sampson Arnold
Mackay* had tied his etymologies to a mystical Christology,
instead of a mystical infidelity, he might have had a school
of followers. The nonsense about Newton borrowing gravi-
tation from Behmen passes only with those who know
neither what Newton did, not what was done before him.
The above reminds me of a class of paradoxers whom
I wonder that I forgot; they are without exception the
greatest bores of all, because they can put the small end of
their paradox into any literary conversation whatever. I
mean the people who have heard the local pronunciation of
celebrated names, and attempt not only to imitate it, but
to impose on others their broken German or Arabic, or
what not. They also learn the vernacular names of those
who are generally spoken of in their Latin forms ; at least,
they learn a few cases, and hawk them as evidences of eru-
dition. They are miserably mistaken : scholarship, as a rule,
T Johann Tauler (c. 1300-1361), a Dominican monk of Strass-
burg, a mystic, closely in touch with the Gottesfreunde of Basel.
His Sermons first appeared in print at Leipsic in 1498.
'Paracelsus (c. 1490-1541). His real name was Theophrastus
Bombast von Hohenheim, and he took the name by which he is
generally known because he held himself superior to Celsus. He was
a famous phvsician and pharmacist, but was also a mystic and neo-
Platonist. He lectured in German on medicine at Basel, but lost his
position through the opposition of the orthodox physicians and
apothecaries.
See Vol. I, page 256, note 2.
JACOB BEHMEN. 323
always accepts the vernacular form of a name which has
vernacular celebrity. Hallam writes Behmen: his index-
maker, rather superfluously, gives "Behmen or Boehm."
And he retains Melanchthon, 10 the name given by Reuch-
lin 11 to his little kinsman Schwartzerd, because the world
has adopted it : but he will none of Capnio, the name which
Reuchlin fitted on to himself, because the world has not
adopted it. He calls the old forms pedantry: but he sees
that the rejection of well-established results of pedantry
would be greater pedantry still. The paradoxers assume
the question that it is more correct to sound a man by lame
imitation of his own countrymen than as usual in the
country in which the sound is to be made. Against them
are, first, the world at large ; next, an overpowering majority
of those who know something about surnames and their his-
tory. Some thirty years ago a fact there appeared at the
police-office a complainant who found his own law. In
the course of his argument, he asked, "What does Kitty
say?" "Who's Kitty?" said the magistrate, "your wife,
or your nurse?" "Sir! I mean Kitty, the celebrated law-
yer." "Oh!" said the magistrate, "I suspect you mean
Mr. Chitty, 12 the author of the great work on pleading."
"I do sir! But Chitty is an Italian name, and ought to be
pronounced Kitty." This man was a full-blown flower:
but there is many a modest bud; and all ought either to
blush when seen or to waste their pronunciation on the
desert air.
10 Philip Schwarzerd (1497-1560) was professor of Greek at
Wittenberg. He helped Luther with his translation of the Bible.
11 Johann Reuchlin (1455-1522), the first great German humanist,
was very influential in establishing the study of Greek and Hebrew
in Germany. His lectures were mostly delivered privately in Heidel-
berg and Stuttgart. Unlike Melanchthon, he remained in the Catholic
Church.
"Joseph Chitty (1776-1841) published his Precedents of Plead-
ing in 1808 and his Reports of Cases on Practice and Pleading in
1820-23 (2 volumes).
324 A BUDGET OF PARADOXES.
A PLEA FOR KING CUSTOM.
I stand up for King Custom, or Usus, as Horace called
him, with whom is arbitrium the decision, and jus the right,
and norma the way of deciding, simply because he has
potestas the power. He may admit one and another principle
to advise: but Custom is not a constitutional king; he may
listen to his cabinet, but he decides for himself : and if the
ministry should resign, he blesses his stars and does without
them. We have a glorious liberty in England of owning
neither dictionary, grammar, nor spelling-book : as many as
choose write by either of the three, and decide all disputed
points their own way, those following them who please.
Throughout this book I have called people by the names
which denote them in their books, or by our vernacular
names. This is the intelligible way of proceeding. I might, for
instance (Vol. I, p. 44), have spoken of Charles deBovelles, 1
of Lefevre d'fitaples, 2 of Pelerin, 8 and of Etienne. 4 But I
prefer the old plan. Those who like another plan better,
are welcome to substitute with a pen, when they know what
to write ; when they do not, it is clear that they would not
have understood me if I had given modern names.
The principal advisers of King Custom are as follows.
First, there is Etymology, the chiffonnier, or general rag-
merchant, who has made such a fortune of late years in
his own business that he begins to be considered highly
respectable. He gives advice which is more thought of
than followed, partly on account of the fearful extremes
into which he runs. He lately asked some boys of sixteen,
at a matriculation examination in English, to what branch of
1 See Vol. I, page 44, note 1.
1 See Vol. I, page 44, note 4.
Jean Pelerin, also known as Viator, who wrote on perspective.
His work appeared in 1505, with editions in 1509 and 1521.
4 Henry Stephens. See Vol. I, page 44, note 3.
A PLEA FOR KING CUSTOM. 325
the Indo-Germanic family they felt inclined to refer the
Pushto language, and what changes in the force of the letters
took place in passing from Greek into Mceso-Gothic. Because
all syllables were once words, he is a little inclined to insist
that they shall be so still. He would gladly rule English
with a Saxon rod, which might be permitted with a certain
discretion which he has never attained: and when opposed,
he defends himself with analogies of the Aryan family until
those who hear him long for the discovery of an Athana-
syus. He will transport a word beyond seas he is recorder
of Rhematopolis on circumstantial evidence which looks
like mystery gone mad ; but, strange to say, something very
often comes to light after sentence is passed which proves
the soundness of the conviction.
The next adviser is Logic, a swearing old justice of
peace, quorum, and rotulorum, whose excesses brought on
such a fit of the gout that for many years he was unable
to move. He is now mending, and his friends say he has
sown his wild oats. He has some influence with the edu-
cated subjects of Custom, and will have more, if he can
learn the line at which interference ought to stop: with
them he has succeeded in making an affirmative of two
negatives ; but the vulgar won't never have nothing to say
to him. He has always railed at Milton for writing that
Eve was the fairest of her daughters ; but has never satis-
factorily shown what Milton ought to have said instead.
The third adviser has more influence with the mass of
the subjects of King Custom than the other two put to-
gether; his name is Fiddlef addle, the toy-shop keeper; and
the other two put him forward to do their worst work. In
return, he often uses their names without authority. He
took Etymology to witness that means to an end must be
plural: and he would have any one method to be a mean.
But Etymology proved him wrong, King Custom referred
him to his Catechism, in which is "a means whereby we
receive the same," and Analogy a subordinate of Etymol-
326 A BUDGET OF PARADOXES.
ogy asked whether he thought it a great new to hear that
he was wrong. It was either this Fiddlefaddle, or Lindley
Murray 5 his traveler, who persuaded the Miss Slipslops,
of the Ladies Seminary, to put "The Misses Slipslop" over
the gate. Sixty years ago, this bagman called at all the
girls' schools, and got many of the teachers to insist on
the pupils saying "Is it not" and "Can I not" for "Isn't it"
and "Can't I": of which it came that the poor girls were
dreadfully laughed at by their irreverent brothers when
they went home for the holidays. Had this bad adviser
not been severely checked, he might by this time have pro-
posed our saying "The Queen's of England son," declaring,
in the name of Logic, that the prince was the Queen's son,
not England's.
Lastly, there is Typography the metallurgist, an execu-
tive officer who is always at work in secret, and whose law-
less mode of advising is often done by carrying his notions
into effect without leave given. He it is who never ceases
suggesting that the same word is not to occur in a second
place within sight of the first. When the Authorized Ver-
sion was first printed, he began this trick at the passage,
"Let there be light, and there was light;" he drew a line
on the proof under the second light, and wrote "luminos-
ity ?" opposite. He is strongest in the punctuations and other
signs ; he has a pepper-box full of commas always by his
side. He puts everything under marks of quotation which
he has ever heard before. An earnest preacher, in a very
moving sermon, used the phrase Alas! and alack a day!
Typography stuck up the inverted commas because he had
read the old Anglo-Indian toast, "A lass and a lac a day!"
If any one should have the sense to leave out of his Greek
"The well-known grammarian (1745-1826). He was born at
Swatara, in Pennsylvania, and practised law in New York until 1784,
after which he resided in England. His grammar (1795) went
through 50 editions, and the abridgment (1818) through 120 editions.
Murray's ^ friend Dalton, the chemist, said that "of all the con-
trivances invented by human ingenuity for puzzling the brains of the
young, Lindley Murray's grammar was the worst."
TEST OF LANGUAGE. 327
the unmeaning scratches which they call accents, he goes
to a lexicon and puts them in. He is powerful in routine;
but when two routines interlace or overlap, he frequently
takes the wrong one.
Subject to bad advice, and sometimes misled for a sea-
son, King Custom goes on his quiet way and is sure to be
right at last.
"Treason does never prosper: what's the reason?
Why, when it prospers, none dare call it treason."
Language is in constant fermentation, and all that is thrown
in, so far as it is not fit to assimilate, is thrown off; and
this without any obvious struggle. In the meanwhile every
one who has read good authors, from Shakspeare down-
ward, knows what is and what is not English ; and knows,
also, that our language is not one and indivisible. Two
very different turns of phrase may both be equally good,
and as good as can be: we may be relieved of the conse-
quences of contempt of one court by habeas corpus issuing
out of another.
TEST OF LANGUAGE.
Hallam remarks that the Authorized Version of the
Bible is not in the language of the time of James the First :
that it is not the English of Raleigh or of Bacon. Here
arises the question whether Raleigh and Bacon are the true
expositors of the language of their time ; and whether they
were not rather the incipient promoters of a change which
was successfully resisted by among other things the
Authorized Version of the Testaments. I am not prepared
to concede that I should have given to the English which
would have been fashioned upon that of Bacon by imitators,
such as they usually are, the admiration which is forced
from me by Bacon's English from Bacon's pen. On this
point we have a notable parallel. Samuel Johnson com-
328 A BUDGET OF PARADOXES.
mands our admiration, at least in his matured style: but
we nauseate his followers. It is an opinion of mine that
the works of the leading writers of an age are seldom the
proper specimens of the language of their day, when that
language is in its state of progression. I judge of a lan-
guage by the colloquial idiom of educated men: that is, I
take this to be the best medium between the extreme cases
of one who is ignorant of grammar and one who is perched
upon a style. Dialogue is what I want to judge by, and
plain dialogue: so I choose Robert Recorde 1 and his pupil
in the Castle of Knowledge, written before 1556. When
Dr. Robert gets into his altitudes of instruction, he differs
from his own common phraseology as much as probably
did Bacon when he wrote morals and philosophy. But every
now and then I come to a little plain talk about a common
thing, of which I propose to show a specimen. Anything
can be made to look old by such changes as makes into
maketh, with a little old spelling. I shall invert these
changes, using the newer form of inflexion, and the modern
spelling: with no other variation whatever.
"Scholar. Yet the reason of that is easy enough to be
conceived, for when the day is at the longest the Sun must
needs shine the more time, and so must it needs shine the
less time when the day is at the shortest : this reason I have
heard many men declare.
Master. That may be called a crabbed reason, for it
1 Robert Recorde (c. 1510-1558) read and probably taught mathe-
matics and medicine at Cambridge up to 1545. After that he taught
mathematics at Oxford and practised medicine in London. His
Grounde of Artes, published about 1540, was the first arithmetic
published in English that had any influence. It went through many
editions. The Castle of Knowledge appeared in 1551. It was a text-
book on astronomy and the first to set forth the Copernican theory
in England. Like Recorde's other works it was written on the cate-
chism plan. His Whetstone of Witte . . . containying thextraction
of Rootes : The Cosike practise, with the rule of Equation : and the
woorkes of Surde Nombres appeared in 1557, and it is in this work
that the modern sign of equality first appears in print. The word
"Cosike" is an adjective that was used for a long time in Germany
as equivalent to algebraic, being derived from the Italian cosa, which
stood for the unknown quantity.
TEST OF LANGUAGE. 329
goes backward like a crab. The day makes not the Sun
to shine, but the Sun shining makes the day. And so the
length of the day makes not the Sun to shine long, neither
the shortness of the day causes not [sic] the Sun to shine
the lesser time, but contrariwise the long shining of the
Sun makes the long day, and the short shining of the Sun
makes the lesser day : else answer me what makes the days
long or short?
Scholar. I have heard wise men say that Summer
makes the long days, and Winter makes the long nights.
Master. They might have said more wisely, that long
days make summer and short days make winter.
Scholar. Why, all that seems one thing to me.
Master. Is it all one to say, God made the earth, and
the earth made God ? Covetousness overcomes all men, and
all men overcome covetousness ?
Scholar. No, not so ; for here the effect is turned to be
the cause, and the agent is made the patient.
Master. So is it to say Summer makes long days, when
you should say : Long days make summer.
Scholar. I perceive it now: but I was so blinded with
the vulgar error, that if you had demanded of me further
what did make the summer, I had been like to have an-
swered that green leaves do make summer; and the sooner
by remembrance of an old saying that a year should come
in which the summer should not be known but by the green
leaves.
Master. Yet this saying does not import that green
leaves do make summer, but that they betoken summer;
so are they the sign and not the cause of summer."
I have taken a whole page of our author, without omis-
sion, that the reader may see that I do not pick out sentences
convenient for my purpose. I have done nothing but alter
the third person of the verb and the spelling: but great is
the effect thereof. We say "the Sun shining makes the
day"; Recorde, "the Sonne shynynge maketh the daye."
330 . A BUDGET OF PARADOXES.
These points apart, we see a resemblance between our
English and that of three hundred years ago, in the com-
mon talk of educated persons, which will allow us to affirm
that the language of the authorized Bible must have been
very close to that of its time. For I cannot admit that
much change can have taken place in fifty years: and the
language of the version represents both our common Eng-
lish and that of Recorde with very close approximation.
Take sentences from Bacon and Raleigh, and it will be ap-
parent that these writers will be held to differ from all
three, Recorde, the version, and ourselves, by differences
of the same character. But we speak of Recorders conver-
sation, and of our own. We conclude that it is the plain
and almost colloquial character of the Authorized Version
which distinguishes it from the English of Bacon and Ra-
leigh, by approximating it to the common idiom of the time.
If any one will cast an eye upon the letters of instruction
written by Cecil 2 and the Bishop of London to the trans-
lators themselves, or to the general directions sent to them
in the King's name, he will find that these plain business
compositions differ from the English of Bacon and Raleigh
by the same sort of differences which distinguish the version
itself.
PRONUNCIATION.
The foreign word, or the word of a district, or class
of people, passes into the general vernacular ; but it is long
before the specially learned will acknowledge the right of
those with whom they come in contact to follow general
usage. 'The rule is simple: so long as a word is technical
or local, those who know its technical or local pronunciation
may reasonably employ it. But when the word has become
general, the specialist is not very wise if he refuse to follow
"Robert Cecil (c. 1563-1612), first Earl of Salisbury, Secretary of
State under Elizabeth (1596-1603) and under James I (1603-1612).
PRONUNCIATION. 331
the mass, and perfectly foolish if he insist on others follow-
ing him. There have been a few who demanded. that Euler
should be pronounced in the German fashion: 1 Euler has
long been the property of the world at large ; what does it
matter how his own countrymen pronounce the letters?
Shall we insist on the French pronouncing Newton without
that final tong which they never fail to give him? They
would be wise enough to laugh at us if we did. We re-
member that a pedant who was insisting on all the pronun-
ciations being retained, was met by a maxim in contradic-
tion, invented at the moment, and fathered upon Kaen-
foo-tzee, 2 an authority which he was challenged to dispute.
Whom did you speak of? said the bewildered man of
accuracy. Learn your own system, was the answer, before
you impose it on others ; Confucius says that too. 3
The old English has fote, fode, loke, coke, roke, etc., for
foot, etc. And above rhymes in Chaucer to remove. Sus-
pecting that the broader sounds are the older, we may
surmise that remove and food have retained their old
sounds, and that cook, once coke, would have rhymed to
our Luke, the vowel being brought a little nearer, perhaps,
to the o in our present coke, the fuel, probably so called
as used by cooks. If this be so, the Chief Justice Cook 41
of our lawyers, and the Coke (pronounced like the fuel)
of the greater part of the world, are equally wrong. The
lawyer has no right whatever to fasten his pronunciation
upon us: even leaving aside the general custom, he cannot
prove himself right, and is probably wrong. Those who
1 In America the German pronunciation is at present universal
among mathematicians, as in the case of most other German names.
This is due, no doubt, to the great influence that Germany has had
on American education in the last fifty years.
'The latest transliteration is substantially K'ung-fu-tzu.
'The tendency seems to be, however, to adopt the forms used of
individuals or places as rapidly as the mass of people comes to be
prepared for it. Thus the spelling Leipzig, instead of Leipsic, is
coming to be very common in America.
4 Sir Edward Coke (1552-1634), the celebrated jurist
332 A BUDGET OF PARADOXES.
know the village of Rokeby (pronounced Rookby) despise
the world for not knowing how to name Walter Scott's
poem: that same world never asked a question about the
matter, and the reception of the parody of Jokeby, which
soon appeared, was a sufficient indication of their notion.
Those who would fasten the hodiernal sound upon us may
be reminded that the question is, not what they call it now,
but what it was called in Cromwell's time. Throw away
general usage as a lawgiver, and this is the point which
emerges. Probably Ruke-by would be right, with a little
turning of the Italian u towards 6 of modern English.
[Some of the above is from an old review. I do not
always notice such insertions: I take nothing but my own
writings. A friend once said to me, "Ah ! you got that out
of the Athenaum\" "Excuse me/' said I. "the Athenceum
got that out of me!"]
APOLOGIES TO CLUVIER.
It is part of my function to do justice to any cyclometers
whose methods have been wrongly described by any ortho-
dox sneerers (myself included). In this character I must
notice Dethlevus Cluverius? as the Leipzig Acts call him
(probably Dethleu Cluvier), grandson of the celebrated
geographer, Philip Cluvier. The grandson was a Fellow of
the Royal Society, elected on the same day as Halley, 2
November 30, 1678: I suppose he lived in England. This
1 Dethlef Cluvier or Cliiver (d. 1708 at Hamburg) was a nephew,
not a grandson, of Philippe Cluvier, or Philipp Cluver (1580-c. 1623).
Dethlef traveled in France and Italy and then taught mathematics in
London. He wrote on astronomy and philosophy and also published
in the Ada Eruditorum (1686) his Schediasma geometricum de nova
infinitorum scientia. Quadratura circuit infinitis modis demonstrata,
and his Monitum ad geometras (1687). Philippe was geographer of
the Academy of Leyden. His introduction** in universatn geogra-
phiam torn veterem quant novam libri sex appeared at Leyden in
1624, about the time of his death.
8 See Vol. I, page 124, note 7.
APOLOGIES TO CLUVIER. 333
man is quizzed in the Leipzig Acts for 1686 ; and, if Mon-
tucla insinuate rightly, by Leibnitz, who is further suspected
of wanting to embroil Cluvier with his own opponent Nieu-
wentiit, 3 on the matter of infinitesimals. So far good: I
have nothing against Leibnitz, who though he was ironical,
told us what he laughed at. But Montucla has behaved
very unfairly: he represents Cluvier as placing the essence
of his method in the solution of the problem construere
mundum divina menti analogum, to construct a world cor-
responding to the divine mind. Nothing to begin with: no
way of proceeding. Now, it ought to have been ex data
linea construere* etc. : there is a given line, which is some-
thing to go on. Further, there is a way of proceeding: it
is to find the product of 1, 2, 3, 4, etc. for ever. Moreover,
Montucla charges Cluvier with unsquaring the parabola,
which Archimedes had squared as tight as a glove. But he
never mentions how very nearly Cluvier agrees with the
Greek: they only differ by 1 divided by 3n 2 , where n is
the infinite number of parts of which a parabola is com-
posed. This must have been the conceit that tickled Leib-
nitz, and made him wish that Cluvier and Nieuwentiit
should fight it out. Cluvier, was admitted, on terms of
irony, into the Leipzig Acts : he appeared on a more serious
footing in London. It is very rare for one cyclometer to
refute another: les corsair es ne se Patient pas. 6 The only
instance I recall is that of M. Cluvier, who (Phil. Trans.,
1686, No. 185) refuted M. Mallemont de Messange, 6 who
'Bernard Nieuwentijt (1654^718), a physician and burgomaster
at Purmerend. His Consider atipnes circa Analyseos ad quantitates
infinite parvas applicata Principia et Calculi Differentialis usum
(Amsterdam, 1694) was attacked by Leibnitz. He replied in his
Considerationes secunda (1694), and also wrote the Analysis Infini-
torum, seu Curvilineorum Proprietates ex Polygonorum Natura de-
ducta (1695). His most famous work was on the existence of God,
Het Regt Gebruik der Werelt Beschouwingen (1718).
4 "From a given line to construct" etc.
""Pirates do not fight one another."
'Claude Mallemens (Mallement) de Messanges (1653-1723) was
professor of philosophy at the College du Plessis, in Paris, for 34
334 A BUDGET OF PARADOXES.
published at Paris in 1686. He does it in a very serious
style, and shows himself a mathematician. And yet in the
year in which, in the Phil. Trans., he was a geometer, and
one who rebukes his squarer for quoting Matthew xi. 25,
in that very year he was the visionary who, in the Leipzig
Acts, professed to build a world resembling the divine mind
by multiplying together 1, 2, 3, 4, etc. up to infinity.
THE RAINBOW PARADOX.
There is a very pretty opening for a paradox which has
never found its paradoxer in print. The philosophers teach
that the rainbow is not material: it comes from rain-drops,
but those rain-drops do not take color. They only give it,
as lenses and mirrors; and each one drop gives all the
colors, but throws them in different directions. Accordingly,
the same drop which furnishes red light to one spectator
will furnish violet to another, properly placed. Enter the
paradoxer whom I have to invent. The philosopher has
gulled you nicely. Look into the water, and you will see
the reflected rainbow: take a looking-glass held sideways,
and you see another reflection. How could this be, if there
were nothing colored to reflect ? The paradoxer's facts are
true: and what are called the reflected rainbows are other
rainbows, caused by those other drops which are placed
so as to give the colors to the eye after reflection, at the
water or the looking-glass. A few years ago an artist ex-
hibited a picture with a rainbow and its apparent reflection :
he simply copied what he had seen. When his picture was
examined, some started the idea that there could be no re-
flection of a rainbow; they were right: they inferred that
the artist had made a mistake ; they were wrong. When it
was explained, some agreed and some dissented. Wanted,
years. The work to which De Morgan refers is probably the Fameux
Probltmt de la quadrature du cercle, resolu geometriquement par le
cercle tt a ligne droite that appeared in 1683.
TYCHO BRAKE REVIVED. 335
immediately, an able paradoxer: testimonials to be for-
warded to either end of the rainbow, No. 1. No circle-
squarer need apply, His Variegatedness having been pleased
to adopt 3.14159... from Noah downwards.
TYCHO BRAHE REVIVED.
The system of Tycho Brahe, 1 with some alteration and
addition, has been revived and 'contended for in our own
day by a Dane, W. Zytphen, 2 who has published The Motion
of the Sun in the Universe, (second edition) Copenhagen,
1865, 8vo, and Le Mouvement Sideral, 1865, 8vo. I make
an extract.
"How can one explain Copernically that the velocity of
the Moon must be added to the velocity of the Earth on
the one place in the Earth's orbit, to learn how far the
Moon has advanced from one fixed star to another; but
in another place in the orbit these velocities must be sub-
tracted (the movements taking place in opposite direc-
tions) to attain the same result? In the Copernican and
other systems, it is well known that the Moon, abstracting
from the insignificant excentricity of the orbit, always in
twenty-four hours performs an equally long distance. Why
has Copernicus never been denominated Fundamentus or
Fundator? Because he has never convinced anybody so
thoroughly that this otherwise so natural epithet has oc-
curred to the mind."
Really the second question is more effective against
Xewton than against Copernicus ; for it upsets gravity : the
first is of great depth.
1 On Tycho Brahe see Vol. I, page 76, note 3.
* Wilhelm Frederik von Zytphen also published the Tidens Strom,
a chronological table, in 1840. The work to which De Morgan refers,
the Solens Bevcegelse i Verdensrummet, appeared^ first in 1861. De
Morgan seems to have missed his Nogl Ord otn Cirkelens Quadratur
which appeared in 1865, at Copenhagen.
336 A BUDGET OF PARADOXES.
JAMES SMITH WILL NOT DOWN.
The Correspondent journal makes a little episode in the
history of my Budget (born May, 1865, died April, 1866).
It consisted entirely of letters written by correspondents.
In August, a correspondent who signed "Fair Play" and
who I was afterwards told was a lady thought it would
be a good joke to bring in the Cyclometers. Accordingly
a letter was written, complaining that though Mr. Syl-
vester's 1 demonstration of Newton's theorem then attract-
ing public attention was duly lauded, the possibly greater
discovery of the quadrature seemed to be blushing unseen,
and wasting etc. It went on as follows :
"Prof. De Morgan, who, from his position in the scien-
tific world, might fairly afford to look favourably on less
practised efforts than his own, seems to delight in ridiculing
the discoverer. Science is, of course, a very respectable
person when he comes out and makes himself useful in the
world [it must have been a lady ; each sex gives science to
the other] : but when, like a monk of the Middle Ages, he
shuts himself up [it must have been a lady; they always
snub the bachelors] in his cloistered cell, repeating his
mumpsimus from day to day, and despising the labourers
on the outside, we begin to think of Galileo, 2 Jenner, 3
Harvey,* and other glorious trios, who have been con-
temned..."
The writer then called upon Mr. James Smith 5 to come
1 James Joseph Sylvester (1814-1897), professor of natural phi-
losophy at University College, London (1837-1841), professor of
mathematics at the University of Virginia (1841-1845), actuary in
London (1845-1855), professor of mathematics at Woolwich (1877-
1884) and at Johns Hopkins University, Baltimore (1877-1884), and
Savilian professor of geometry at Oxford (1884-1894).
9 See Vol. I, page 76, note 3.
* See Vol. II, page 205, note 11.
* See Vol. I, page 76, note 3.
B See Vol. I, page 46, note 1.
JAMES SMITH WILL NOT DOWN. 337
forward. The irony was not seen; and that day fortnight
appeared the first of more than thirty letters from his pen.
Mr. Smith was followed by Mr. Reddie, 8 Zadkiel, 7 and
others, on their several subjects. To some of the letters
I have referred; to others I shall come. The Correspon-
dent was to become a first-class scientific journal; the time
had arrived at which truth had an organ: and I received
formal notice that I could not stifle it by silence, nor con-
vert it into falsehood by ridicule. When my reader sees my
extracts, he will readily believe my declaration that I should
have been the last to stifle a publication which was every
week what James Mill 8 would call a dose of capital for my
Budget. A few anti-paradoxers brought in common sense:
but to the mass of the readers of the journal it all seemed
to be the difference between Tweedledum and Tweedledee.
Some said that the influx of scientific paradoxes killed the
journal: but my belief is that they made it last longer than
it otherwise would have done. Twenty years ago I recom-
mended the paradoxers to combine and publish their views
in a common journal: with a catholic editor, who had no
pet theory, but a stern determination not to exclude any-
thing merely for absurdity. I suspect it would answer very
well. A strong title, or motto, would be wanted: not so
coarse as was roared out in a Cambridge mob when I was
an undergraduate "No King! No Church! No House of
Lords ! No nothing, blast me !" but something on that prin-
ciple.
At the end of 1867 I addressed the following letter to
the Athenaum:
PSEUDOMATH, PHILOMATH, AND GRAPHOMATH.
December 31, 1867
MANY thanks for the present of Mr. James Smith's letters
See Vol. II, page 183, note 2.
T See Vol. I, page 321, note 2.
8 James Mill, born 1773, died 1836.
338 A BUDGET OF PARADOXES.
of Sept. 28 and of Oct. 10 and 12. He asks where you will
be if you read and digest his letters: you probably will be
somewhere first. He afterwards asks what the WE of the
Athenceum will be if, finding it impossible to controvert, it
should refuse to print. I answer for you, that We- We of
the Athenceum, not being Wa-Wa the wild goose, so con-
spicuous in "Hiawatha," will leave what controverts itself
to print itself, if it please.
Philomath is a good old word, easier to write and speak
than mathematician. It wants the words between which I
have placed it. They are not well formed: pseudomathete
and graphomathete would be better: but they will do. I
give an instance of each.
The pseudomath is a person who handles mathematics
as the monkey handled the razor. The creature tried to
shave himself as he had seen his master do; but, not hav-
ing any notion of the angle at which the razor was to be
held, he cut his own throat. He never tried a second time,
poor animal! but the pseudomath keeps on at his work,
proclaims himself clean-shaved, and all the rest of the
world hairy. So great is the difference between moral and
physical phenomena ! Mr. James Smith is, beyond doubt,
the great pseudomath of our time. His 3J is the least of a
wonderful chain of discoveries. His books, like Whit-
bread's barrels, will one day reach from Simpkin & Mar-
shall's to Kew, placed upright, or to Windsor laid length-
ways. The Queen will run away on their near approach, as
Bishop Hatto did from the rats : but Mr. James Smith will
follow her were it to John o' Groats.
The philomath, for my present purpose, must be ex-
hibited as giving a lesson to presumption. The following
anecdote is found in Thiebault's 8 Souvenirs de vingt ans de
se jours a Berlin, published in 1804. The book itself got
a high character for truth. In 1807 Marshal Mollendorff 10
See Vol. II, page 3, note 11.
M See Vol. II, page 3, note 13.
JAMES SMITH WILL NOT DOWN. 339
answered an inquiry of the Due de Bassano, 11 by saying
that it was the most veracious of books, written by the
most honest of men. Thiebault does not claim personal
knowledge of the anecdote, but he vouches for its being
received as true all over the north of Europe. 12
Diderot 18 paid a visit to Russia at the invitation of
Catherine the Second. At that time he was an atheist, or
at least talked atheism: it would be easy to prove him
either one thing or the other from his writings. His lively
sallies on this subject much amused the Empress, and all
the younger part of her Court. But some of the older
courtiers suggested that it was hardly prudent to allow
such unreserved exhibitions. The Empress thought so too,
but did not like to muzzle her guest by an express prohi-
bition : so a plot was contrived. The scorner was informed
that an eminent mathematician had an algebraical proof
of the existence of God, which he would communicate be-
fore the whole Court, if agreeable. Diderot gladly con-
sented. The mathematician, who is not named, was Euler. 14
He came to Diderot with the gravest air, and in a tone of
perfect conviction said, "Monsieur!
n
done Dieu existe; repondes!" Diderot, to whom algebra
was Hebrew, though this is expressed in a very roundabout
way by Thiebault and whom we may suppose to have ex-
pected some verbal argument of alleged algebraical close-
ness, was disconcerted ; while peals of laughter sounded on
all sides. Next day he asked permission to return to
France, which was granted. An algebraist would have
n See Vol. II, page 3, note 14.
"This anecdote is printed at page 4 (Vol. II) ; but as it is used
in illustration here, and is given more in detail, I have not omitted
it S. E. De M.
u See Vol. II, page 4, note IS.
" See Vol. I, page 382, note 13.
""Monsieur, (o + b)/n = x, whence God exists; answer that!"
340 A BUDGET OF PARADOXES.
turned the tables completely, by saying, "Monsieur! vous
savez bien que votre raisonnement demande le developpe-
ment de x suivant les puissances entieres de w." 18 Gold-
smith could not have seen the anecdote, or he might have
been supposed to have drawn from it a hint as to the way
in which the Squire demolished poor Moses.
The graphomath is a person who, having no mathe-
matics, attempts to describe a mathematician. Novelists
perform in this way: even Walter Scott now and then
burns his fingers. His dreaming calculator, Davy Ram-
say, swears "by the bones of the immortal Napier." Scott
thought that the the philomaths worshiped relics : so they
do, in one sense. Look into Hutton's 17 Dictionary for
Napier's Bones, and you shall learn all about the little
knick-knacks by which he did multiplication and division.
But never a bone of his own did he contribute ; he preferred
elephants' tusks. The author of Headlong Hall 18 makes
a grand error, which is quite high science: he says that
Laplace proved the precession of the equinoxes to be a
periodical inequality. He should have said the variation
of the obliquity. But the finest instance is the following:
Mr. Warren, 19 in his well-wrought tale of the martyr-
philosopher, was incautious enough to invent the symbols
by which his savant satisfied himself Laplace 20 was right on
a doubtful point. And this is what he put together
v 2
- 3a 2 , IZZI 2 + 9 - n = 9, n X log e.
Now, to Diderot and the mass of mankind this might be
Laplace all over: and, in a forged note of Pascal, would
9 "Monsieur, you know very well that your argument requires
the development of x according to integral powers of n"
17 See Vol. I, page 153, note 4.
18 Thomas Love Peacock (1785-1866) an English novelist and poet.
"Perhaps Dr. Samuel Warren (1807-1877), the author of Ten
Thousand a Year (serially in Blackwood's in 1839; London, 1841).
" See Vol. I, page 255, note 6.
JAMES SMITH WILL NOT DOWN. 341
prove him quite up to gravitation. But I know of nothing
like it, except in the lately received story of the American
orator, who was called on for some Latin, and perorated
thus : "Committing the destiny of the country to your hands,
Gentlemeh, I may without fear declare, in the language of
the noble Roman poet,
E pluribus unum,
Multum in parvo,
Ultima Thule,
Sine qua non." 21
But the American got nearer to Horace than the martyr-
philosopher to Laplace. For all the words are in Horace, ex-
cept Thule, which might have been there. But I I is not a
symbol wanted by Laplace; nor can we see how it could
have been; in fact, it is not recognized in algebra. As to
the junctions, etc., Laplace and Horace are about equally
well imitated.
Further thanks for Mr. Smith's letters to you of Oct.
15, 18, 19, 28, and Nov. 4, 15. The last of these letters
has two curious discoveries. First, Mr. Smith declares that
he has seen the editor of theAthenaum: in several previous
letters he mentions a name. If he knew a little of journal-
ism he would be aware that editors are a peculiar race, ob-
tained by natural selection. They are never seen, even by
their officials ; only heard down a pipe. Secondly, "an
ellipse or oval" is composed of four arcs of circles. Mr.
Smith has got hold of the construction I was taught, when
a boy, for a pretty four-arc oval. But my teachers knew
better than to call it an ellipse: Mr. Smith does not; but
he produces from it such confirmation of 3J as would con-
vince any honest editor.
Surely the cyclometer is a Darwinite development of a
spider, who is always at circles, and always begins again
when his web is brushed away. He informs you that he
* "From many, one ; much in little ; Ultima Thule (the most re-
mote region) ; without which not."
342 A BUDGET OF PARADOXES.
has been privileged to discover truths unknown to the scien-
tific world. This we know ; but he proceeds to show that
he is equally fortunate in art. He goes on to say that he
will make use of you to bring those truths to light, "just
as an artist makes use of a dummy for the purpose of
arranging his drapery." The painter's lay-figure is for
flowing robes ; the hairdresser's dummy is for curly locks.
Mr. James Smith should read Sam Weller's pathetic story
of the "four wax dummies." As to his use of a dummy,
it is quite correct. When I was at University College, I
walked one day into a room in which my Latin colleague
was examining. One of the questions was, "Give the lives
and fates of Sp. Mselius, 22 and Sp. Cassius."" Umph! said
I, surely all know that Spurius Mselius was whipped for
adulterating flour, and that Spurius Cassius was hanged for
passing bad money. Now, a robe arranged on a dummy
would look just like the toga of Cassius on the gallows.
Accordingly, Mr. Smith is right in the drapery-hanger
which he has chosen : he has been detected in the attempt to
pass bad circles. He complains bitterly that his geometry,
instead of being read and understood by you, is handed over
to me to be treated after my scurrilous fashion. It is clear
enough that he would rather be handled in this way than
not handled at all, or why does he go on writing? He must
know by this time that it is a part of the institution that
his "untruthful and absurd trash" shall be distilled into
mine at the rate of about 3J pages of the first to one column
of the second. Your readers will never know how much they
gain by the process, until Mr. James Smith publishes it all
in a big book, or until they get hold of what he has already
published. I have six pounds avoirdupois of pamphlets
and letters; and there is more than half a pound of letters
* Spurius Mselius (fl. 440 B.C.), who distributed corn freely
among the poor in the famine of 440 B. C., and was assassinated by
the patricians.
83 Spurius Cassius Viscellinus, Roman consul in 502, 493, and
486 B. C. Put to death in 485.
JAMES SMITH WILL NOT DOWN. 343
written to you in the last two months. Your compositor
must feel aggrieved by the rejection of these clearly written
documents, without erasures, and on one side only. Your
correspondent has all the makings of a good contributor,
except the knowledge of his subject and the sense to get it.
He is, in fact, only a mask: of whom the fox
"0 quanta species, inquit, cerebrum non habet." 2 *
I do not despair of Mr. Smith on any question which does
not involve that unfortunate two-stick wicket at which he
persists in bowling. He has published many papers ; he has
forwarded them to mathematicians: and he cannot get an-
swers ; perhaps not even readers. Does he think that he
would get more notice if you were to print him in your
journal? Who would study his columns? Not the mathe-
matician, we know; and he knows. Would others? His
balls are aimed too wide to be blocked by any one who is
near the wicket. He has long ceased to be worth the an-
swer which a new invader may get. Rowan Hamilton, 25
years ago, completely knocked him over ; and he has never
attempted to point out any error in the short and easy
method by which that powerful investigator condescended
to show that, be right who may, he must be wrong. There
are some persons who feel inclined to think that Mr. Smith
should be argued with: let those persons understand that
he has been argued with, refuted, and has never attempted
to stick a pen into the refutation. He stated that it was a
remarkable paradox, easily explicable ; and that is all. After
this evasion, Mr. James Smith is below the necessity of
being told that he is unworthy of answer. His friends com-
plain that I do nothing but chaff him. Absurd ! I winnow
him; and if nothing but chaff results, whose fault is that?
I am usefully employed ; for he is the type of a class which
ought to be known, and which I have done much to make
known.
*"O what a fine bearing, he said, that has no brain."
* Sir William Rowan Hamilton. See Vol. I, page 332, note 4.
344 A BUDGET OF PARADOXES.
Nothing came of this until July 1869, when I received
a reprint of the above letter, with a comment, described as
Appendix D of a work in course of publication on the
geometry of the circle. The Athenczum journal received
the same: but the Editor, in his private capacity, received
the whole work, being The Geometry of the Circle and
Mathematics as applied to Geometry by Mathematicians,
shown to be a mockery, delusion, and a snare, Liverpool,
8vo, 1869. Mr. J. S. here appears in deep fight with Pro-
fessor Whitworth, 26 and Mr. Wilson, 27 the author of the
alleged amendment of Euclid. How these accomplished
mathematicians could be inveigled into continued discussion
is inexplicable. Mr. Whitworth began by complaining of
Mr. Smith's attacks upon mathematicians, continued to
correspond after he was convinced that J. S. proved an arc
and its chord to be equal, and only retreated when J. S.
charged him with believing in 3J, and refusing acknowledg-
ment. Mr. Wilson was introduced to J. S. by a volunteer
defense of his geometry from the assaults of the Athenaum.
This the editor would not publish ; so J. S. sent a copy to
Mr. Wilson himself. Some correspondence ensued, but Mr.
Wilson soon found out his man, and withdrew.
There is a little derision of the Athenceum and a merited
punishment for "that unscrupulous critic and contemptible
mathematical twaddler, De Morgan."
MR. REDDIE'S ASTRONOMY.
At p. 183 I mentioned Mr. Reddie, 1 the author of Vis
Inertia Victa and of Victoria tolo ccelo? which last is not
* William Allen Whitworth, the author of the well-known Choice
and Chance (Cambridge, 1867), and other works.
27 James Maurice Wilson, whose Elementary Geometry appeared
in 1868 and went through several editions.
1 See Vol. II, page 183, note 2.
""Force of inertia conquered," and "Victory in the whole
heavens."
345
an address to the whole heaven, either from a Roman
Goddess or a British Queen, whatever a scholar may sup-
pose. Between these Mr. Reddie has published The Me-
chanics of the Heavens, 8vo r 1862: this I never saw until
he sent it to me, with an invitation to notice it, he very
well knowing that it would catch. His speculations do
battle with common notions of mathematics and of mechan-
ics, which, to use a feminine idiom, he blasphemes so you
can't think! and I suspect that if you do not blaspheme
them too, you can't think. He appeals to the "truly scien-
tific," and would be glad to have readers who have read
what he controverts, i. e., Newton's Principia: I wish he
may get them; I mean I hope he may obtain them. To
none but these would an account of his speculations be in-
telligible: I accordingly disposed of him in a very short
paragraph of description. Now many paradoxers desire
notice, even though it be disparaging. I have letters from
more than one besides what have been sent to the Editor
of the Athenaum complaining that they are not laughed
at ; although they deserve it, they tell me, as much as some
whom I have inserted. Mr. Reddie informs me that I
have not said a single word against his books, though I
have given nearly a column to sixteen-string arithmetic, and
as much to animalcule universes. What need to say any-
thing to readers of Newton against a book from which I
quoted that revolution by gravitation is demonstrably im-
possible? It would be as useless as evidence against a man
who has pleaded guilty. Mr. Reddie derisively thanks me
for "small mercies" ; he wrote me private letters ; he pub-
lished them, and more, in the Correspondent. He gave me,
pro viribus suis? such a dressing you can't think, both for
my Budget non-notice, and for reviews which he assumed
me to have written. He outlawed himself by declaring
(Correspondent, Nov. 11, 1856) that I in a review had
made a quotation which was "garbled, evidently on purpose
"With all his might"
346 A BUDGET OF PARADOXES.
to make it appear that" he "was advocating solely a geo-
centric hypothesis, which is not true/' In fact, he did
his best to get larger "mercy." And he shall have it; and
at a length which shall content him, unless his mecometer
be an insatiable apparatus. But I fear that in other re-
spects I shall no more satisfy him than the Irish drummer
satisfied the poor culprit when, after several times changing
the direction of the stroke at earnest entreaty, he was at
last provoked to call out, "Bad cess to ye, ye spalpeen!
strike where one will, there's no plasing ye !"
Mr. Reddie attaches much force to Berkeley's 4 old argu-
ments against the doctrine of fluxions, and advances ob-
jections to Newton's second section, which he takes to be
new. To me they appear "such as have been often made,"
to copy a description given in a review: though I have no
doubt Mr. Reddie got them out of himself. But the whole
matter comes to this : Mr. Reddie challenged answer, espe-
cially from the British Association, and got none. He pre-
sumes that this is because he is right, and cannot be an-
swered: the Association is willing to risk itself upon the
counter-notion that he is wrong, and need not be answered ;
because so wrong that none who could understand an an-
swer would be likely to want one.
Mr. Reddie demands my attention to a point which had
already particularly struck me, as giving the means of
showing to all readers the kind of confusion into which
paradoxers are apt to fall, in spite of the clearest instruc-
tion. It is a very honest blunder, and requires notice: it
may otherwise mislead some, who may suppose that no one
able to read could be mistaken about so simple a matter,
'George Berkeley (1685-1753), Bishop of Cloyne, the idealistic
philosopher and author of the Principles of Human Knowledge
(1710), The Analyst, or a Discourse addressed to an Infidel Mathe-
matician (1734), and A Defense of Freethinking in Mathematics
(1735). He asserted that space involves the idea of movement with-
out the sensation of resistance. Space sensation less than the
"minima sensibilia" is, therefore, impossible. From this he argues
that infinitesimals are impossible concepts.
MR. REDDIE'S ASTRONOMY. 347
let him be ever so wrong about Newton. According to his
own mis-statement, in less than five months he made the
Astronomer Royal abandon the theory of the solar motion
in space. The announcement is made in August, 1865, as
follows: the italics are not mine:
"The third (Victoria...), although only published in
September, 1863, has already had its triumph. It is the
book that forced the Astronomer Royal of England, after
publicly teaching the contrary for years, to come to the
conclusion, "strange as it may appear," that "the whole
question of solar motion in space is at the present time in
doubt and abeyance." This admission is made in the Annual
Report of the Council of the Royal Astronomical Society,
published in the Society's Monthly Notices for February,
1864."
It is added that solar motion is "full of self-contradic-
tion, which "the astronomers" simply overlooked, but which
they dare not now deny after being once pointed out."
The following is another of his accounts of the matter,
given in the Correspondent, No. 18, 1865:
"... You ought, when you came to put me in the
'Budget/ to have been aware of the Report of the Council
of the Royal Astronomical Society, where it appears that
Professor Airy, 5 with a better appreciation of my demon-
strations, had admitted 'strange/ say the Council, 'as it
may appear/ that 'the whole question of solar motion in
space [and here Mr. Reddie omits some words] is now in
doubt and abeyance.' You were culpable as a public
teacher of no little pretensions, if you were 'unaware* of
this. If aware of it, you ought not to have suppressed
such an important testimony to my really having been 'very
successful' in drawing the teeth of the pegtops, though
you thought them so firmly fixed. And if you still suppress
1 See Vol. I, page 85, note 2.
348 A BUDGET OF PARADOXES.
it, in your Appendix, or when you reprint your 'Budget/
you will then be guilty of a suppressio veri, also of further
injury to me, who have never injured you. . ."
Mr. Reddie must have been very well satisfied in his own
mind before he ventured such a challenge, with an answer
from me looming in the distance. The following is the
passage of the Report of the Council, etc., from which he
quotes :
"And yet, strange to say, notwithstanding the near co-
incidence of all the results of the before-mentioned inde-
pendent methods of investigation, the inevitable logical in-
ference deduced by Mr. Airy is, that the whole question
of solar motion in space, so far at least as accounting for
the proper motion of the stars is concerned, [I have put
in italics the words omitted by Mr. Reddie] appears to
remain at this moment in doubt and abeyance."
Mr. Reddie has forked me, as he thinks, on a dilemma :
if unaware, culpable ignorance; if aware, suppressive in-
tention. But the thing is a trilemma, and the third horn,
on which I elect to be placed, is surmounted by a doubly-
stuffed seat. First, Mr. Airy has not changed his opinion
about the fact of solar motion in space, but only suspends
it as to the sufficiency of present means to give the amount
and direction of the motion. Secondly, all that is alluded
to in the Astronomical Report was said and printed before
the Victoria proclamation appeared. So that the author,
instead of drawing the tooth of the Astronomer Royal's
pegtop, has burnt his own doll's nose.
William Plerschel, 6 and after him about six other astron-
omers, had aimed at determining, by the proper motions
of the stars, the point of the heavens towards which the
solar system is moving: their results were tolerably ac-
cordant. Mr. Airy, in 1859, proposed an improved method,
and, applying it to stars of large proper motion, produced
8 See Vol. I, page 81, note 6.
MR. REDDIE'S ASTRONOMY. 349
much the same result as Herschel. Mr. E. Dunkin, 7 one
of Mr. Airy's staff at Greenwich, applied Mr. Airy's method
to a very large number of stars, and produced, again, nearly
the same result as before. This paper was read to the
Astronomical Society in March, 1863, was printed in ab-
stract in the Notice of that month, was printed in full in
the volume then current, and was referred to in the Annual
Report of the Council in February, 1864, under the name
of "the Astronomer Royal's elaborate investigation, as ex-
hibited by Mr. Dunkin." Both Mr. Airy and Mr. Dunkin
express grave doubts as to the sufficiency of the data : and,
regarding the coincidence of all the results as highly curious,
feel it necessary to wait for calculations made on better
data. The report of the Council states these doubts. Mr.
Reddie, who only published in September, 1863, happened
to see the Report of February, 1864, assumes that the doubts
were then first expressed, and declares that his book of
September had the triumph of forcing the Astronomer
Royal to abandon the fact of motion of the solar system
by the February following. Had Mr. Reddie, when he saw
that the Council were avowedly describing a memoir pre-
sented some time before, taken the precaution to find out
when that memoir was presented, he would perhaps have
seen that doubts of the results obtained, expressed by one
astronomer in March, 1863, and by another in 1859, could
not have been due to his publication of September, 1863.
And any one else would have learnt that neither astronomer
doubts the solar motion, though both doubt the sufficiency
of present means to determine its amount and direction.
This is implied in the omitted words, which Mr. Reddie
whose omission would have been dishonest if he had seen
their meaning no doubt took for pleonasm, superfluity,
overmuchness. The rashness which pushed him headlong
T Edwin Dunkin revised Lardner's Handbook of Astronomy
(1869) and Milner's The Heavens and the Earth (1873) and wrote
The Midnight Sky (1869).
350 A BUDGET OF PARADOXES.
into the quillet that his thunderbolt had stopped the chariot
of the Sun and knocked the Greenwich Phaeton off the box,
is the same which betrayed him into yet grander error
which deserves the full word, quidlibet about the Prin-
cipla of Newton. There has been no change of opinion
at all. When a person undertakes a long investigation, his
opinion is that, at a certain date, there is prima facie
ground for thinking a sound result may be obtained. Should
it happen that the investigation ends in doubt upon the
sufficiency of the grounds, the investigator is not put in the
wrong. He knew beforehand that there was an alternative :
and he takes the horn of the alternative indicated by his
calculations. The two sides of this case present an in-
structive contrast. Eight astronomers produce nearly the
same result, and yet the last two doubt the sufficiency of
their means: compare them withjjhe what's-his-name who
rushes in where thing-em-bobs fear to tread.
I was not aware, until I had written what precedes, that
Mr. Airy had given a sufficient answer on the point. Mr.
Reddie says (Correspondent, Jan. 20, 1866) :
"I claim to have forced Professor Airy to give up the
notion of 'solar motion in space' altogether, for he admits
it to be 'at present in doubt and abeyance.' I first made
that claim in a letter addressed to the Astronomer Royal
himself in June, 1864, and in replying, very courteously,
to other portions of my letter, he did not gainsay that part
of it."
Mr. Reddie is not ready at reading satire, or he never
would have so missed the meaning of the courteous reply
on one point, and the total silence upon another. Mr. Airy
must be one of those peculiar persons who, when they do
not think an assertion worth notice, let it alone, without
noticing it by a notification of non-notice. He would never
commit the bull of "Sir! I will not say a word on that
subject." He would put it thus, "Sir! I will only say ten
words on that subject," and, having thus said them, would
MR. REDDIE'S ASTRONOMY. 351
proceed to something else. He assumed, as a matter of
form, that Mr. Reddie would draw the proper inference
from his silence : and this because he did not care whether
or no the assumption was correct.
The Mechanics of the Heavens, which Mr. Reddie sends
to be noticed, shall be noticed, so far as an extract goes :
"My connection with this subject is, indeed, very simply
explained. In endeavoring to understand the laws of phys-
ical astronomy as generally taught, I happened to entertain
some doubt whether gravitating bodies could revolve, and
having afterwards imbibed some vague idea that the laws
of the universe were chemical and physical rather than
mechanical, and somehow connected with electricity and
magnetism as opposing correlative forces most probably
suggested to my mind, as to many others, by the transcen-
dent discoveries made in electro-magnetism by Professor
Faraday 8 my former doubts about gravitation were re-
vived, and I was led very naturally to try and discover
whether a gravitating body really could revolve; and I
became convinced it could not, before I had ever presumed
to look into the demonstrations of the Principia"
This is enough against the book, without a word from
me: I insert it only to show those who know the subject
what manner of writer Mr. Reddie is. It is clear that
"presumed" is a slip of the pen; it should have been con-
descended.
Mr. Reddie represents me as dreaming over paltry para-
doxes. He is right ; many of my paradoxes are paltry : he
is wrong ; I am wide awake to them. A single moth, beetle,
or butterfly, may be a paltry thing; but when a cabinet is
arranged by genus and species, we then begin to admire the
'Michael Faraday (1791-1867) the celebrated physicist and chem-
ist. He was an assistant to Sir Humphrey Davy (1813) and became
professor of chemistry at the Royal Institution, London, in 1827.
352 A BUDGET OF PARADOXES.
infinite variety of a system constructed on a wonderful
sameness of leading characteristics. And why should para-
doxes be denied that collective importance, paltry as many
of them may individually be, which is accorded to moths,
beetles, or butterflies ? Mr. Reddie himself sees that "there
is a method in" my "mode of dealing with paradoxes."
I hope I have atoned for the scantiness of my former
article, and put the demonstrated impossibility of gravita-
tion on that level with Hubongramillposanfy arithmetic
and inhabited atoms which the demonstrator not quite
without reason claims for it.
In the Introduction to a collected edition of the three
works, Mr. Reddie describes his Mechanism of the Heavens,
from which I have just quoted, as
"a public challenge offered to the British Association and
the mathematicians at Cambridge, in August, 1862, calling
upon them to point to a single demonstration in the Prin-
cipia or elsewhere, which even attempts to prove that Uni-
versal Gravitation is possible, or to show that a gravitating
body could possibly revolve about a center of attraction.
The challenge was not accepted, and never will be. No
such demonstration exists. And the public must judge for
themselves as to the character of a so-called "certain
science/' which thus shrinks from rigid examination, and
dares not defend itself when publicly attacked: also of the
character of its teachers, who can be content to remain
dumb under such circumstances."
ON PARADOXERS IN GENERAL.
The above is the commonplace talk of the class, of
which I proceed to speak without more application to this
paradoxer than to that. It reminds one of the funny young
rascals who used, in times not yet quite forgotten, to abuse
the passengers, as long as they could keep up with the
ON PARADOXERS IN GENERAL. 353
stage coach; dropping off at last with "Why don't you get
down and thrash us? You're afraid, you're afraid!" They
will allow the public to judge for themselves, but with
somewhat of the feeling of the worthy uncle in Tom Jones,
who, though he would let young people choose for them-
selves, would have them choose wisely. They try to be so
awfully moral and so ghastly satirical that they must be
answered: and they are best answered in their own divi-
sion. We have all heard of the way in which sailors cat's-
pawed the monkeys: they taunted the dwellers in the trees
with stones, and the monkeys taunted them with cocoa-nuts
in return. But these were silly dendrobats: had they be-
longed to the British Association they would have said
No! No! dear friends; it is not in the itinerary: if you
want nuts, you must climb, as we do. The public has referred
the question to Time: the procedure of this great king I
venture to describe, from precedents, by an adaptation of
some smart anapaestic tetrameters your anapaest is the foot
for satire to halt on, both in Greek and English which I
read about twenty years ago, and with the point of which
I was much tickled. Poetasters were laughed at ; but Mr.
Slum, whom I employed Mr. Charles Dickens obliged me
with his address converted the idea into that of a hit at
mathematicasters, as easily as he turned the Warren acrostic
into Jarley. As he observed, when I settled his little ac-
count, it is cheaper than any prose, though the broom was
not stolen quite ready made:
Forty stripes save one for the smaller Paradoxers.
Hark to the wisdom the sages preach
Who never have learnt what they try to teach.
We are the lights of the age, they say!
We are the men, and the thinkers we !
So we build up guess-work the livelong day,
In a topsy-turvy sort of way,
Some with and some wanting a plus b.
Let the British Association fuss;
What are theirs to the feats to be wrought by us?
354 A BUDGET OF PARADOXES.
Shall the earth stand still? Will the round come square?
Must Isaac's book be the nest of a mare?
Ought the moon to be taught by the laws of space
To turn half round without right-about-face?
Our whimsey crotchets will manage it all;
Deep ! Deep ! posterity will them call !
Though the world, for the present, lets them fall
Down ! Down ! to the twopenny box of the stall !
Thus they But the marplot Time stands by,
With a knowing wink in his funny old eye.
He grasps by the top an immense fool's cap,
Which he calls a philosophaster-trap :
And rightly enough, for while these little men
Croak loud as a concert of frogs in a fen,
He first singles out one, and then another,
Down goes the cap lo! a moment's pother,
A spirit like that which a rushlight utters
As just at the last it kicks and gutters:
When the cruel smotherer is raised again
Only snuff, and but little of that, will remain.
But though uno avulso thus comes every day
Non deficit alter is also in play:
For the vacant parts are, one and all,
Soon taken by puppets just as small;
Who chirp, chirp, chirp, with a grasshopper's glee,
We 're the lamps of the Universe, We ! We ! We !
But Time, whose speech is never long,
He hasn't time for it stops the song
And says Lilliput lamps ! leave the twopenny boxes,
And shine in the Budget of Paradoxes !
When a paradoxer parades capital letters and diagrams
which are as good as Newton's to all who know nothing
about it, some persons wonder why science does not rise
and triturate the whole thing. This is why: all who are
fit to read the refutation are satisfied already, and can, if
they please, detect the paradoxer for themselves. Those
who are not fit to do this would not know the difference
between the true answer and the new capitals and dia-
grams on which the delighted paradoxer would declare
ON PARADOXERS IN GENERAL. 355
that he had crumbled the philosophers, and not they him.
Trust him for having the last word: and what matters it
whether he crow the unanswerable sooner or later? There
are but two courses to take. One is to wait until he has
committed himself in something which all can understand,
as Mr. Reddie has done in his fancy about the Astronomer
Royal's change of opinion: he can then be put in his true
place. The other is to construct a Budget of Paradoxes,
that the world may see how the thing is always going on,
and that the picture I have concocted by cribbing and spoil-
ing a bit of poetry is drawn from life. He who wonders
at there being no answer has seen one or two : he does not
know that there are always fifty with equal claims, each
of whom regards his being ranked with the rest as forty-
nine distinct and several slanders upon himself, the great
Mully Ully Gue. And the fifty would soon be five hundred
if any notice were taken of them. They call mankind to
witness that science will not defend itself, though publicly
attacked in terms which might sting a pickpocket into stand-
ing up for his character : science, in return, allows mankind
to witness or not, at pleasure, that it does not defend itself,
and yet receives no injury from centuries of assault. Demon-
strative reason never raises the cry of Church in Danger \
and it cannot have any Dictionary of Heresies except a
Budget of Paradoxes. Mistaken claimants are left to Time
and his extinguisher, with the approbation of all thinking
non-claimants: there is no need of a succession of ex-
posures. Time gets through the job in his own workman-
like manner as already described.
On looking back more than twenty years, I find among
my cuttings the following passage, relating to a person who
had signalized himself by an effort to teach comets to the
conductor of the Nautical Almanac:
"Our brethren of the literary class have not the least
idea of the small amount of appearance of knowledge
356 A BUDGET OF PARADOXES.
which sets up the scientific charlatan. Their world is large,
and there are many who have that moderate knowledge, and
perception of what is knowledge, before which extreme
ignorance is detected in its first prank. There is a public of
moderate cultivation, for the most part sound in its judg-
ment, always ready in its decisions. Accordingly, all their
successful pretenders have some pretension. It is not so
in science. Those who have a right to judge are fewer and
farther between. The consequence is, that many scientific
pretenders have nothing but pretension."
This is nearly as applicable now as then. It is im-
possible to make those who have not studied for themselves
fully aware of the truth of what I have quoted. The best
chance is collection of cases; in fact, a Budget of Para-
doxes. Those who have no knowledge of the subject can
thus argue from the seen to the unseen. All can feel the
impracticability of the Hubongramillposanfy numeration,
and the absurdity of the equality of contour of a regular
pentagon and hexagon in one and the same circle. Many
may accordingly be satisfied, on the assurance of those who
have studied, that there is as much of impracticability, or
as much of absurdity, in things which are hidden under
"Sines, tangents, secants, radius, cosines
Subtangents, segments and all those signs;
Enough to prove that he who read 'em
Was just as mad as he who made 'em."
Not that I mean to be disrespectful to mathematical
terms: they are short and easily explained, and compete
favorably with those of most other subjects: for instance,
with
"Horse-pleas, traverses, demurrers,
Jeofails, imparlances, and errors,
Averments, bars, and protestandos,
And puis d'arreign continuandos."
ON PARADOXERS IN GENERAL. 357
From which it appears that, taking the selections made
by satirists for our samples, there are, one with another,
four letters more in a law term than in one of mathe-
matics. But pleading has been simplified of late years.
All paradoxers can publish ; and any one who likes may
read. But this is not enough; they find that they cannot
publish, or those who can find they are not read, and they
lay their plans athwart the noses of those who, they think,
ought to read. To recommend them to be content with
publication, like other authors, is an affront: of this I will
give the reader an amusing instance. My good nature, of
which I keep a stock, though I do not use it all up in this
Budget, prompts me to conceal the name.
I received the following letter, accompanied by a pros-
pectus of a work on metaphysics, physics, astronomy, etc.
The author is evidently one whom I should delight to honor :
"Sir, A friend of mine has mentioned your name in
terms of panigeric [sic], as being of high standing in
mathematics, and of greatly original thought. I send you
the enclosed without comment ; and, assuming that the bent
of your mind is in free inquiry, shall feel a pleasure in
showing you my portfolio, which, as a mathematician, you
will acknowledge to be deeply interesting, even in an educa-
tional point of view. The work is complete, and the system
so far perfected as to place it above criticism; and, so far
as regards astronomy, as will Ptolemy beyond rivalry [sic:
no doubt some words omitted]. Believe me to be, Sir, with
the profoundest respect, etc. The work is the result of
thirty-five years' travel and observation, labor, expense, and
self-abnegation."
I replied to the effect that my time was fully occupied,
and that I was obliged to decline discussion with many
persons who have views of their own ; that the proper way
is to publish, so that those who choose may read when they
can find leisure. I added that I should advise a precursor
in the shape of a small pamphlet, as two octavo volumes
358 A BUDGET OF PARADOXES.
would be too much for most persons. This was sound ad-
vice ; but it is not the first, second, or third time that it has
proved very unpalatable. I received the following answer,
to which I take the liberty of prefixing a bit of leonine wis-
dom:
"Si doceas stultum, laetum non dat tibi vultum;
Odit te multum; vellet te scire sepultum. 1 "
"Sir, I pray you pardon the error I unintentionally
have fallen into ; deceived by the F. R.S. [I am not F. R.S.]
I took you to be a man of science [omnis homo-est animal,
Sortes est homo, ergo Sortes est animal] 2 instead of the
mere mathematician, or human calculating-machine. Be-
lieve me, Sir, you also have mistaken your mission, as I
have mine. I wrote to you as I would to any other man
well up in mathematics, with the intent to call your atten-
tion to a singular fact of omission by Euclid, and other
great mathematicians: and, in selecting you, I did you an
honor which, from what I have just now heard, was en-
tirely out of place. I think, considering the nature of the
work set forth in the prospectus, you are guilty of both
folly and presumption, in assuming the character of a
patron ; for your own sense ought to have assured you that
was such my object I should not have sought him in a
De Morgan, who exists only by patronage of others. On
the other hand, I deem it to be an unpardonable piece of
presumption in offering your advice upon a subject the mag-
nitude, importance, and real utility of which you know
nothing about: by doing so you have offered me a direct
insult. The system is a manual of Philosophy, a one in-
separable whole of metaphysics and physic ; embracing
points the most interesting, laws the most important, doc-
lu lf you teach a fool he shows no joyous countenance; he cor-
dially hates you; he wishes you buried."
'"Every man is an animal, Sortes is a man, therefore Sortes is
an animal."
ON PARADOXERS IN GENERAL. 359
trines the most essential to advance man in accordance
with the spirit of the times. I may not live to see it in
print; for, at , life at best is uncertain: but, live or
die, be assured Sir, it is not my intention to debase the
work by seeking patronage, or pandering to the public
taste. Your advice was the less needed, seeing I am an
old-established . I remain, etc. P. S. You will oblige
me by returning the prospectus of my work."
My reader will, I am sure, not take this transition from
the "profoundest respect" to the loftiest insolence for an
apocraphical correspondence, to use a word I find in the
Prospectus: on my honor it is genuine. He will be better
employed in discovering whether I exist by patronizing
others, or by being patronized by them. I make any one
who can find it out a fair offer : I will give him my patron-
age if I turn out to be Bufo, on condition he gives me his,
if I turn out to be Bavius. 3 I need hardly say that I con-
sidered the last letter to be one of those to which no answer
is so good as no answer.
These letters remind me in one respect of the corre-
spondents of the newspapers. My other party wrote because
a friend had pointed me out : but he would not have written
if he had known what another friend told him just in time
for the second letter. The man who sends his complaint to
the newspaper very often says, in effect, "Don't imagine,
Sir, that I read your columns ; but a friend who sometimes
does has told me...." It is worded thus: "My attention
"May some choice patron bless each grey goose quill ;
May every Bavius have his Bufo still."
POPE, Prologue to the Satires.
Bavins has become proverbial as a bad poet from the lines in
Vergil's Eclogues (III, 90) :
"Qui Bavium non odit, amet tua carmina, Maevi,
Atque idem jungat vulpes, et mulgeat hircos."
"He who does not hate Bavius shall love thy verses, O Maevius ;
and the same shall yoke foxes and shall milk he-goats."
Bavius and Maevius were the worst of Latin poets, condemned
by Horace as well as Vergil.
360 A BUDGET OF PARADOXES.
has been directed to an article in your paper of .... " Many
thanks to my friend's friends for not mentioning the Budget :
had my friend's attention been directed to it I might have
lost a striking example of the paradoxer in search of a
patron. That my Friend was on this scent in the first
letter is revealed in the second. Language was given to
man to conceal his thoughts ; but it is not every one who
can do it.
Among the most valuable information which my readers
will get from me is comparison of the reactions of para-
doxers, when not admitted to argument, or when laughed
at. Of course, they are misrepresented; and at this they
are angry, or which is the same thing, take great pains to as-
sure the reader that they are not. So far natural, and so far
good; anything short of concession of a case which must
be seriously met by counter-reasons is sure to be misrepre-
sentation. My friend Mr. James Smith and my friend Mr.
Reddie are both terribly misrepresented: they resent it by
some insinuations in which it is not easy to detect whether
I am a conscious smotherer of truth, or only muddle-headed
and ignorant. [This was written before I received my last
communication from Mr. James Smith. He tells me that
I am wrong in saying that his work in which I stand in
the pillory is all reprint : I have no doubt I confounded some
of it with some of the manuscript or slips which I had
received from my much not-agreed-with correspondent. He
adds that my mistake was intentional, and that my reason
is obvious to the reader. This is information, as the sea-
serpent said when he read in the newspaper that he had a
mane and tusks.]
THE DOUBLE VAHU PROCESS.
My friend Dr. Thorn 1 sees deeper into my mystery. By
the way, he still sends an occasional touch at the old sub-
1 See Vol. II, page 158, note 1.
THE DOUBLE VAHU PROCESS. 361
ject; and he wants me particularly to tell my readers that
the Latin numeral letters, if M be left out, give 666. And
so they do : witness DCLXVI. A person who thinks of the
origin of symbols will soon see that 666 is our number be-
cause we have five fingers on each hand: had we had but
four, our mystic number would have been expressed by 555,
and would have stood for our present 365. Had n been
the number on each hand, the great number would have
been
(4n 2 +2n+l)
With no finger on each hand, the number would have
been 1 : with one finger less than none at all on each hand,
it would have been 0. But what does this mean? Here is
a question for an algebraical paradoxer! So soon as we
have found out how many fingers the inhabitants of any
one planet have on each hand, we have the means of know-
ing their number of the Beast, and thence all about them.
Very much struck with this hint of discovery, I turned
my attention to the means of developing it. The first point
was to clear my vision of all the old cataracts. I propose
the following experiment, subject of course to the con-
sent of parties. Let Dr. Thorn Double- Vahu Mr. James
Smith, and Thau Mr. Reddie: if either be deparadoxed by
the treatment, I will consent to undergo it myself. Pro-
vided always that the temperature required be not so high
as the Doctor hints at: if the Turkish Baths will do for
this world, I am content.
The three paradoxers last named and myself have a
pentasyllable convention, under which, though we go far
beyond civility, we keep within civilization. Though Mr.
James Smith pronounced that I must be dishonest if I did
not see his argument, which he knew I should not do [to
say nothing of recent accusation] ; though Dr. Thorn de-
clared me a competitor for fire and brimstone and my
wife, too, which doubles the joke: though Mr. Reddie
362 A BUDGET OF PARADOXES.
was certain I had garbled him, evidently on purpose to
make falsehood appear truth; yet all three profess respect
for me as to everything but power to see truth, or candor
to admit it. And on the other hand, though these were the
modes of opening communication with me, and though I
have no doubt that all three are proper persons of whom to
inquire whether I should go up-stairs or down-stairs, etc.,
yet I am satisfied they are thoroughly respectable men, as
to everything but reasoning. And I dare say our several
professions are far more true in extent than in many which
are made under more parliamentary form. We find ex-
cuses for each other: they make allowances for my being
hoodwinked by Aristotle, by Newton, by the Devil ; and I
permit them to feel, for I know they cannot get on without
it, that their reasons are such as none but a knave or a
sinner can resist. But they are content with cutting a slice
each out of my character: neither of them is more than
an uncle, a Bone-a-part; I now come to a dreadful nephew,
Bone-the-whole.
1 will not give the name of the poor fellow who has
fallen so far below both the honestum and the utile, to say
nothing of the decorum or the dulce. 2 He is the fourth
who has taken elaborate notice of me; and my advice to
him would be, Nee quarto, loqui persona laboret. 3 According
to him, I scorn humanity, scandalize learning, and disgrace
the press; it admits of no manner of doubt that my object
is to mislead the public and silence truth, at the expense
of the interests of science, the wealth of the nation, and
the lives of my fellow men. The only thing left to be set-
tled is, whether this is due to ignorance, natural distaste
for truth, personal malice, a wish to curry favor with the
Astronomer Royal, or mere toadyism. The only accusa-
tion which has truth in it is, that I have made myself a
"public scavenger of science": the assertion, which is the
2 "Honest," "useful," "handsome," "sweet."
8 "Let not the fourth man attempt to speak."
ORTHODOX PARADOXERS. 363
most false of all is, that the results of my broom and
spade are "shot right in between the columns of" the
Athenceum. I declare I never in my life inserted a word
between the columns of the Athenaum: I feel huffed and
miffed at the very supposition. I have made myself a public
scavenger; and why not? Is the mud never to be collected
into a heap? I look down upon the other scavengers, of
whom there have been a few mere historical drudges ;
Montucla, Hutton, etc. as not fit to compete with me. I
say of them what one crossing-sweeper said of the rest:
"They are well enough for the common thing ; but put them
to a bit of fancy-work, such as sweeping round a post, and
see what a mess they make of it!" Who can touch me at
sweeping round a paradoxer? If I complete my design of
publishing a separate work, an old copy will be fished up
from a stall two hundred years hence by the coming man,
and will be described in an article which will end by his
comparing our century with his own, and sighing out in the
best New Zealand pronunciation
"Dans ces terns-la
Cetait deja comme ga! 4
ORTHODOX PARADOXERS.
And pray, Sir! I have been asked by more than one
do your orthodox never fall into mistake, nor rise into ab-
surdity? They not only do both, but they admit it of
each other very freely; individually, they are convinced of
sin, but not of any particular sin. There is not a syndoxer
among them all but draws his line in such a way as to in-
clude among paradoxers a great many whom I should ex-
clude altogether from this work. My worst specimens are
but exaggerations of what may be found, occasionally, in
the thoughts of sagacious investigators. At the end of the
"In those old times, ah
Twas just like this, ah!"
364 A BUDGET OF PARADOXES.
glorious dream, we learn that there is a way to Hell from
the gates of Heaven, as well as from the City of Destruc-
tion: and that this is true of other things besides Christian
pilgrimage is affirmed at the end of the Budget of Para-
doxes. If D'Alembert 1 had produced enough of a quality
to match his celebrated mistake on the chance of throwing
head in two throws, he would have been in my list. If
Newton had produced enough to match his reception of
the story that Nausicaa, Homer's Phseacian princess, in-
vented the celestial sphere, followed by his serious surmise
that she got it from the Argonauts, then Newton himself
would have had an appearance entered for him, in spite of
the Principia. In illustration, I may cite a few words from
Tristram Shandy:
" 'A soldier,' cried my uncle Toby, interrupting the Cor-
poral, 'is no more exempt from saying a foolish thing, Trim,
than a man of letters.' 'But not so often, an' please your
honor,' replied the Corporal. My uncle Toby gave a nod."
I now proceed to die out. Some prefatory remarks will
follow in time. 2 I shall have occasion to insist that all is
not barren : I think I shall find, on casting up, that two out
of five of my paradoxers are not to be utterly contemned.
Among the better lot will be found all gradations of merit ;
at the same time, as was remarked on quite a different
subject, there may be little to choose between the last of
the saved and the first of the lost. The higher and better
class is worthy of blame; the lower and worse class is
worthy of praise. The higher men are to be reproved for
not taking up things in which they could do some good:
the lower men are to be commended for taking up things
in which they can do no great harm. The circle problem is
like Peter Peebles's lawsuit :
1 See Vol. I, page 382, note 12.
8 These remarks were never written. S. E. De M.
ORTHODOX PARADOXERS. 365
" 'But, Sir, I should really spoil any cause thrust on me
so hastily.' 'Ye cannot spoil it, Alan/ said my father, 'that
is the very cream of the business, man, . . . the case is
come to that pass that Stair or Arniston could not mend
it, and I don't think even you, Alan, can do it much harm/ "
I am strongly reminded of the monks in the darker
part of the Middle Ages. To a certain proportion of them,
perhaps two out of five, we are indebted for the preserva-
tion of literature, and their contemporaries for good teach-
ing and mitigation of socials evils. But the remaining three
were the fleas and flies and thistles and briars with whom
the satirist lumps them, about a century before the Refor-
mation :
"Flen, flyys, and freris, populum domini male caedunt ;
Thystlis and breris crescentia gramina laedunt.
Christe nolens guerras qui cuncta pace tueris,
Destrue per terras breris, flen, flyys, and freris.
Flen, flyys, and freris, foul falle hem thys fyften yeris,
For non that her is lovit flen, flyys ne freris." 3
I should not be quite so savage with my second class.
Taken together, they may be made to give useful warning
to those who are engaged in learning under better auspices :
aye, even useful hints ; for bad things are very often only
good things spoiled or misused. My plan is that of a pred-
ecessor in the time of Edward the Second:
"Meum est propositum genti imperitae
Artes frugi reddere melioris vitae. 4
To this end I have spoken with freedom of books as
books, of opinions as opinions, of ignorance as ignorance, of
1 "Fleas, flies, and friars, are masters who sadly the people abuse,
And thistles and briars are sure growing grains to abuse.
O Christ, who hatest strife and slayst all things in peace,
Destroy where'er are rife, briars, friars, flies and fleas.
Fleas, flies, and friars foul fall them these fifteen years
For none that there is loveth fleas, flies, nor freres."
4 "It is my plan to restore to an unskilled race the worthy arts
of a better life."
366 A BUDGET OF PARADOXES.
presumption as presumption ; and of writers as I judge may
be fairly inferred from what they have written. Some
to whom I am therefore under great obligation have per-
mitted me to enlarge my plan by assaults to which I have
alluded ; assaults which allow a privilege of retort, of which
I have often availed myself ; assaults which give my readers
a right of partnership in the amusement which I myself
have received.
For the present I cut and run: a Catiline, pursued by
a chorus of Ciceros, with Quousque tandem? Quamdiu nos?
Nihil ne te?* ending with, In te conferri pest em istam jam
pridem oportebat, quam tu in nos omnes jamdiu machinaris!
I carry with me the reflection that I have furnished to those
who need it such a magazine of warnings as they will not
find elsewhere; a signatis cavetote: 6 and I throw back at
my pursuers Valete, doctor es sine doctrina; facite ut pro-
ximo, congressu vos salvos corporibus et sanos mentibus
videamus. 7 Here ends the Budget of Paradoxes.
8 The first sentences of the first oration of Cicero against Cati-
line: "Quo usque tandem abutere, Catilina, patientia nostra?" (How
long, p Catiline, will you abuse our patience?) "Quamdiu etiam
furor iste tuus nos eludet?" (How long will this your madness
baffle us?) "Nihilne te nocturnum praesidium Palati,. . . .nihil horum
ora voltusque moverunt?" (Does the night watch of the Palatium,
do the faces and expressions of all these men fail to move you?)
"In te conferri...." (This plague should have been inflicted upon
you long ago, which you have plotted against us so long.)
'"Beware of the things that are marked."
T "Farewell, ye teachers without learning! See to it that at our
next meeting we may find you strong in body and sound in mind."
APPENDIX.
I think it right to give the proof that the ratio of the
circumference to the diameter is incommensurable. This
method of proof was given by Lambert, 1 in the Berlin
Memoirs for 1761, and has been also given in the notes to
Legendre's 2 Geometry, and to the English translation of
the same. Though not elementary algebra, it is within
the reach of a student of ordinary books. 3
Let a continued fraction, such as
b+c_
d+e_
/+etc.,
be abbreviated into ~ each fraction being
0+ a-\- f-\- etc.:
understood as falling down to the side of the preceding
sign -f In every such fraction we may suppose , d, /, etc.
1 See Vol. I, page 336, note 8.
* See Vol. I, page 229, note 2.
'This proof, although capable of improvement, is left as in the
original. Those who may be interested in the mathematics of the
question may consult F. Enriques, Fragen der Elementargeometrie
(German by Fleischer), Leipsic, 1907, Part II, p. 267; F. Rudio,
Archimedes, Huygens, Lambert, Legendre. Vier Abhandlungen uber
die Kreismessung, Leipsic, 1892 ; F. Klein, Famous Problems of Ele-
mentary Geometry (English by Beman and Smith), Boston, 1895;
J. W. A. Young, Monographs on Modern Mathematics, New York,
1911, Chap. IX (by the editor of the present edition of De Morgan.)
368 A BUDGET OF PARADOXES.
positive; a, c, e, &c. being as required: and all are supposed
integers. If this succession be continued ad infinitum, and
if 7", ^, T, etc. all lie between 1 and + 1, exclusive, the
limit of the fraction must be incommensurable with unity;
A
that is, cannot be , where A and B are integers.
Jt>
First, whatever this limit may be, it lies between 1
and + 1. This is obviously the case with any fraction
P i>
, where <> is between 1: for, , being < 1, and/ and
q integer, cannot be brought up to , by the value of <>
Hence, if we take any of the fractions
e
~ e
Cl C f* &* Q
sa y T, 3, 7, 7 we have, y being between 1, so is
b-\- a-\- /+ ft h
7, 7, so therefore is - T ,; and so therefore is
/+ h d-\- f-\- h o +
<L e _
d+ /+ h'
Now, if possible, let etc. be at the limit; A
0+ a-\- n
and B being integers. Let
*-A-? + 7+ etc " Q = P 7+ f+ etc - R =
P, Q, R, etc. being integer or fractional, as may be. It is
easily shown that all must be integer: for
+P
A'
APPENDIX. 369
p'
P /+R
Q'
or, R=<?P-/Q
etc., etc. Now, since a, B, b, A, are integers, so also is P;
A P O R
and thence Q; and thence R, etc. But since , , ^, ,
> A Jr (J
etc. are all between 1 and +1, it follows that the un-
limited succession of integers P, Q, R, are each less in
numerical value than the preceding. Now there can be
no such unlimited succession of descending integers: con-
sequently, it is impossible that - , , , etc. can have a
o+ a+
commensurable limit.
It easily follows that the continued fraction is incom-
mensurable if , , etc., being at first greater than unity,
become and continue less than unity after some one point.
Say that , , . . . are all less than unity. Then the fraction
K m
... is incommensurable, as proved: let it be K.
is incommensurable, say A.; e - is the same,
say M; also , say v, and - - , say p- But p is the frac-
tion 7 - . . . itself; which is therefore incommensurable.
o+ d+
Let <f>z represent
370 A BUDGET OF PARADOXES.
Let z be positive: this series is convergent for all values
of a, and approaches without limit to unity as z increases
without limit. Change z into ^+1, and form $z < (z+\)\
the following equation will result
or
$z being - ; of which observe that it diminishes
Z <P2
without limit as z increases without limit. Accordingly,
we have
And, $(z+n) diminishing without limit, we have
a <#>(^+l) a a a a
z-}-
; and let 4=-jc 2 . Then (*+l) is -
f Si
or cos .#: and the continued fraction is
1+ *+... r ~2 1+ 3+
APPENDIX. 371
x x 2 x 2
whence tan x =-
3+ 5+ 7
Or, as written in the usual way,
tan x=x^
l-x 2
5-x 2
7-...
This result may be proved in various ways: it may also
be verified by calculation. To do this, remember that if
03
= t>2 Pi P3 = fa Pz+as Pi, P 4 = 04 Ps+^4 P2, etc.
in the case before us we have
ai=x, az x? y 3= x 2 , 4= x 2 , as= x 2 , etc.
fo = l, 02 = 3, 03 = 5, 04 = 7, 05 = 9, etc.
Pi = x Qi = l
P 2 =3.*r Q 2 =3-^
-^ Q 3 =15-6^
Q 4 =105-45.* 2 +.* 4
Q5=945-420^ +15* 4
Q 6 = 10395 -4725^ +210^-^
We can use this algebraically, or arithmetically. If we
divide P n by Q n , we shall find a series agreeing with the
known series for tan x t as far as n terms. That series is
*3 2*5 17 * 7 62.K 9
3 .15 + +
372 A BUDGET OF PARADOXES.
Take PS, and divide it by Qs in the common way, and the
first five terms will be as here written. Now take x.\,
which means that the angle is to be one tenth of the actual
unit, or, in degrees 5. 729578. We find that when *=.!,
P 6 = 1038.24021, Q 6 =10347.770999; whence P 6 divided by Q 6
gives- 1003346711. Now 5.729578 is 5 43' 46i"; and from
the old tables of Rheticus 4 no modern tables carry the
tangents so far the tangent of this angle is -1003347670.
Now let #="; in which case tan x=I. If i^ be com-
mensurable with the unit, let it be , m and n being in-
tegers: we know that i^<l. We have then
- _m m z m z m rtfi m z m 2
n _ n z _ n z n 3n 5n 7 n ...
f^ 3~- 5^...
Now it is clear that , , =, etc. must at last become
o n on In
and continue severally less than unity. The continued
fraction is therefore incommensurable, and cannot be unity.
Consequently T 2 cannot be commensurable: that is, T is an
incommensurable quantity, and so also is T 2 .
I thought I should end with a grave bit of appendix,
deeply mathematical: but paradox follows me wherever I
go. The foregoing is in my own language from Dr.
(now Sir David) Brewster's 5 English edition of Legendre's
Geometry, (Edinburgh, 1824, 8vo.) translated by some one
who is not named. I picked up a notion, which others had
at Cambridge in 1825, that the translator was the late Mr.
Galbraith, 6 then known at Edinburgh as a writer and teacher.
* See Vol. I, page 69, note 2.
5 See Vol. I, page 137, note 8.
* Joseph Allen Galbraith who, with Samuel Haughton, wrote the
Galbraith and Haughton's Scientific Manuals. (Euclid, 1856; Alge-
bra, 1860; Trigonometry, 1854; Optics, 1854, and others.)
APPENDIX. 373
But it turns out that it was by a very different person, and
one destined to shine in quite another walk; it was a young
man named Thomas Carlyle. 7 He prefixed, from his own
pen, a thoughtful and ingenious essay on Proportion, as
good a substitute for the fifth Book of Euclid as could have
been given in the space; and quite enough to show that he
would have been a distinguished teacher and thinker on
first principles. But he left the field immediately.
(The following is the passage referred to at Vol. II,
page 54.)
Michael Stifelius 8 edited, in 1554, a second edition of
the Algebra (Die Coss.), of Christopher Rudolff. 9 This is
one of the earliest works in which -f- and are used.
Stifelius was a queer man . He has introduced into this
very work of Rudolff his own interpretation of the number
of the Beast. He determined to fix the character of Pope
Leo: so he picked the numeral letters from LEODECIMVS,
and by taking in X from LEO X. and striking out M as
standing for mysterium y he hit the number exactly. This
discovery completed his conversion to Luther, and his de-
termination to throw off his monastic vows. Luther dealt
with him as straight-forwardly as with Melanchthon about
his astrology: he accepted the conclusions, but told him to
clear his mind of all the premises about the Beast. Stifelius
7 This note on Carlyle (1795-1881) is interesting. The transla-
tion of Legendre appeared in the same year (1824) as his translation
of Goethe's Wilhelm Meister.
'Michael Stifel (1487-1567), also known as Stiefel, Styfel, and
Stifelius, was an Augustine monk but became a convert to Lutheran-
ism. He was professor of mathematics at Jena (1559-1567). His
edition of the Coss appeared at Konigsberg in 1553, the first edition
having been published in 1525. The + and signs first appeared
in print in Widman's arithmetic of 1489, but for purposes of algebra
this book was one of the first to make them known.
"Christoff Rudolff was born about 1500 and died between 1540
and 1552. Die Coss appeared in 1525 and his arithmetic in 1526.
374 A BUDGET OF PARADOXES.
did not take the advice, and proceeded to settle the end of
the world out of the prophet Daniel: he fixed on October,
1533. The parishioners of some cure which he held, having
full faith, began to spend their savings in all kinds of good
eating and drinking; we may charitably hope this was not
the way of preparing for the event which their pastor
pointed out. They succeeded in making themselves as fit
for Heaven as Lazarus, so far as beggary went: but when
the time came, and the world lasted on, they wanted to kill
their deceiver, and would have done so but for the inter-
ference of Luther.
INDEX.
Pages denoted by numerals of this kind (.287) refer to biographical notes,
chiefly by the editor. Numerals like 426 refer to books discussed by De Mor-
gan, or to leading topics in the text. Numerals like 126 indicate minor refer-
ences.
Abbott, Justice, I, 181.
Abernethy, J. f II, 219.
Aboriginal Britons, a poem, II, 270.
Academy of Sciences, French, I, 163.
Adair, J., I, 223.
Adam, M., I, 65.
Adams, J. C, I, 43, 82, 385, 388; II,
131, 135, 140, 303.
Ady, Joseph, II, 42, 42.
Agnew, H. C., I, 328.
Agricola, J., I, 394.
Agricultural Laborer's letter, II, 16.
Agrippa, H. C., I, 48, 48.
Ainsworth, W. H., II, 132.
Airy, I, 85, 88, 152, 242; II, 85, 140,
150, 303, 347.
Alchemy, I, 125.
Alfonso X (El Sabio), II, 269.
Alford, H., II, 221.
Alfred, King, Ballad of, II, 22.
Algebra, I, 121.
Algebraic symbols, I, 121.
Almanac, I, 300; II, 147, 148, 207.
{See Easter.)
Aloysius Lilius, I, 362.
Alsted, J. H., II, 282.
Ameen Bey, II, 15.
Amicable Society, I, 347.
Ampere, I, 86.
Amphisbaena serpent, I, 31.
Anagrams, De Morgan, I, 138.
Anaxagoras, II, 59.
Anghera, II, 60, 60, 61, 279.
Annuities, Fallacies of, I, 157.
Antichrist, I, 130.
Antimony, I, 125.
Antinewtonism, I, 162.
Antinomians, I, 394.
Antiphon, II, 59.
Antonie, F., I, 126, 126.
Apollonius, I, 41, 107.
Apparitions, II, 47.
Arago, I, 243, 390.
Aratus, II, 167.
Arbuthnot, I, 133, 134.
Archer, H., II, 90.
Archimedes, I, 5, 11, 42, 83, 107.
Archytas, I, 53.
Argoli, I, 104.
Aristocrat, as a scientist, I, 131.
Aristotle, I, 5, 331.
Arnobius, II, 73.
Arson, P. J., II, 207.
Ashton, R., II, 99.
Astrology, I, 118, 127, 128, 350; II,
43.
Astronomer's Drinking Song, I, 380.
Astronomical Aphorisms, I, 398.
Paradox, I, 394.
Police Report, I, 390.
Society. (See Royal Astronom-
ical Society.)
Astronomy, Bailly's exaggerated view
of, I, 166.
Astunica, Didacas, I, 90.
Athanasian Creed, I, 371.
Atheists, Philosophical, I, 1.
Atoms, II, 191.
376
A BUDGET OF PARADOXES.
Attraction, I, 136, 151, 155.
Augustine, St., II, 23.
Aurora borealis, I, 134.
Austen, Jane, I, 191.
Auzout, A., II, 300.
Aviation, Early ideas of, II, 8.
Babbage, C., I, 207, 290, 291; II, 181.
Bachet, de Meziriac, I, 161.
Bacon, F., I, 5, 75, 75, 76, 79, 89,
145, 331.
Bacon, R., I, 5, 126, 126, 360; II, 94.
Baconian controversy, I, 141.
Baden Powell, II, 267.
Bailly, J. S., I, 166, 166, 308.
Baily, F., I, 308, 309; II, 16, 143, 188.
Baily, R., II, 16.
Baker, T., II, 302.
Bakewell, F. C., II, 156, 156.
Banks, J., I, 28.
Barberini, M., II, 267.
Barker, C., II, 262.
Baronius, I, 33, 35; II, 62.
Barreme, I, 42.
Barrett, G., II, 188.
Barrow, I., I, 160; II, 302.
Baruel, de, I, 165.
Bassano, Due de, II, 3, 339.
Baxter, T., I, 146.
Bayle, P., II, 73.
Beaufort, F., II, 267.
Beaugrand, I, 119, 121.
Beaulieu, I, 119, 119, 121.
Beaune, de, II, 59.
Becourt, R., II, 277.
Bedford, Duke of, (6th), I, 182.
Behmen, I, 168, 254; II, 317.
Bellenden, W., 1,175.
Bentley, I, 110.
Berkeley, G., II, 346.
Bernard, E., II, 297, 300.
Bernardus Trevisanus, I, 126, 126.
Bernoullis, I, 130, 150, 335, 336.
Bertius, P., II, 300.
Bese, I, 66.
Bessel, I, 384; II, 2.
Bethune, I, 99, 279, 291.
Bettesworth, I, 19.
Beza. (See Bese.)
Bickersteth, E. H., I, 238.
Bidder, I, 86.
Biden, J., II, 158, 160.
Bidle, (Biddle), I, 239.
Biot, I, 85.
Birch, T., I, 108; II, 304, 313.
Birks, T. R., II, 158, 158.
Bishop, G., I, 386.
Bishops as Paradoxers, I, 226.
Boccaccio, I, 38.
Boethius, I, 42, 45.
Bohme. (.See Behmen.)
Boncompagni, I, 298.
Boniface, St., I, 32.
Bonnycastle, J., II, 16.
Booker, I, 115.
Boole, G., I, 261, 332; II, 75, 79.
A tribute to, II, 79.
Borelli, G. A., II, 300.
Borello, I, 69.
Boreman, I, 113.
Borron, Mrs., II, 7.
Boscovich, I, 156, 164.
Bouguer, II, 301.
Bouillaud, I,. 87; II, 295.
Bouvard, A., I, 327.
Bovillus, I, 44; II, 324. Epitome of,
I, 44.
Bowdler, H. M., I, 194.
Bowring, J., I, 352; II, 256.
Boyle, R., I, 24, 125; II, 300.
Bradley, I, 24.
Bradwardine, I, 227, 228, 229.
Brahe. (See Tycho B.)
Brancker, I, 107; II, 300.
Brenan, J., I, 330, 330.
Brewster, D., I, 39, 137, 140; II,
214, 288, 372.
Briggs, I, 69; II, 299, 302.
Bright, J., II, 235.
Brinkley, J., I, 311.
Britannicus, D., II, 8.
British Museum library, I, 151.
Brothers, R., I, 315; II, 97.
Brougham, Henry, Lord, I, 191.
Brouncker (Brounker), I, 132; II,
302.
Brown, W., II, 168.
Browne, T., I, 31.
Brucker, I, 61.
Brunet, I, 402.
Brunnow, I, 386.
Bruno, I, 59, 59.
Bryson, II, 59.
Burgi, I, 52.
Buffon, I, 282.
Bulstrode, II, 84.
Bungus, I, 55, 55, 57.
Buoncompagno, U., I, 362.
INDEX.
377
Burgon, J. W., II, 30.
Buridan, I, 37. Questiones morales,
I, 37.
Buridan's Ass, I, 37.
Burke, E., I, 173.
Burlesque, Frend's, I, 208.
Burnet, G., I, 107.
Burney, Frances, I, 190.
Burton, Frances B., I, 374.
Busby, R., II, 313.
Buteo, I, 51.
Butler, G., I, 199.
Butler, S., II, 21S.
Buxton, J., I, 86.
Byrgius. (See Burgi.)
Byrne, O., I, 329; II, 186, 190.
Byron, I, 186; II, 270, 273.
Cabbala, I, 272.
Calculating Boys, I, 86.
Calculus, I, 129.
Calendar. (See Easter.)
Cambridge Poets, II, 269.
Campanus, I, 42, 43.
Canning, Geo., II, 145.
Carcavi, I, 106.
Cardanus, II, 59.
Carlile, R., I, 271.
Carlyle, T., II, 373.
Carnot, I, 107.
Caroline tables, I, 124.
Casaubon, I, 111.
Case, J., I, 128, 128.
Cassini, J., I, 172.
Castel, I, 148, 148.
Castiglioni, I, 139.
Castlereagh, I, 185, 186.
Cataldi, I, 69, 69.
Catcott, A., I, 237.
Causans, de, I, 298.
Cavalieri, I, 106.
Cavendish, C., I, 106; II, 299, 312.
Cavendish, W., I, 290.
Caxton, W., II, 281.
Cayley, A., II, 292.
Cecil, R. (1st Earl of Salisbury), II,
330.
Centrifugal force, II, 268.
Ceulen. (See Van Ceulen.)
Challis, J., I, 390; II, 141.
Chalmers, I, 102; II, 219.
Chambers, E., II, 252.
Chambers, R., I, 344, 344.
Charles IX, II, 94.
Charles X, II, 1.
Chasles, I, 39, 229.
Chesterfield, Earl of (4th), II, 298.
Chiffinch, W., II, 50.
Ch'in Chiu-shang, II, 66.
Chitty, J., II, 323.
Chiu-chang, Suan-shu, II, 67.
Christian Evidence Society, I, 270.
Christie, I, 27.
Christmann, I, 272, 272.
Church question, I, 62.
Church, The word, II, 30.
Circle squarers. (See Squaring the
Circle.)
Circulating media of mathematics, I,
107.
Ciruelo. (See Sanchez.)
Clairaut, I, 219, 382.
Clarence, Duke of, I, 179.
Clarke, R., I, 255.
Clavius, I, 11, 69, 111, 112, 355, 362,
363, 372; II, 59.
Clayton., Geo., II, 98.
Cluvier, D., II, 332, 332.
Cobb, Mary, II, 117.
Cobbett, W., I, 177, 200, 399.
Cobden, R., II, 217.
Cocker, I, 42; II, 64, 173, 251, 307.
Cody, P., II, 208.
Coke, E., II, 331.
Colburn, Z., I, 86.
Colenso, I, 63, 247; II, 191.
Collins, J., I, 107; II, 297, 300, 302,
313.
Colvill, W. H., II, 68.
Cometic astrology, I, 128.
Comets, I, 128; II, 68, 83.
Cominale, C, I, 162, 162.
Compton, S. J. A., II, 19.
Computation, Paradoxes of, II, 251,
267.
Condamine, C. M. de la, II, 301.
Conduitt, John, I, 397.
Conduitt, Mrs., I, 136.
Congregation of the Index, I, 90.
Converse propositions, I, 295.
Convocation at Oxford, I, 96.
Cooke, Margaret, I, 310.
Cooper, A. A. (Shaftsbury), II, 181.
Copernicus, I, 5, 6, 76, 90, 121, 172,
380; II, 165, 335.
Copley, J. S., I, 198.
Cormouls, I, 225.
Cosmology, I, 172.
378
A BUDGET OF PARADOXES.
Cotes, R., II, 301.
Cottle, Mrs., II, 97, 97, 161.
Craig, J., I, 129, 129.
Creed, Mathematics of a, I, 329.
Cribb, T., I, 314.
Crotus, J., I, 318.
Cruickshank, G., I, 186.
Cube, Duplication of, I, 349.
Cumyns, Eliza, I, 299.
Cunningham, 1, 172, 172.
Curabelle, I, 221.
Curious Calculations, II, 66.
Curll, E., II, 279.
Cusa, I, 44, 47, 360.
Custom, II, 324.
Cyclometry, II, 208. (See Squaring
of the Circle.)
Cyclopaedias, Review of, II, 280.
D'Alembert, I, 382', II, 283, 364.
Dalgarno, I, 116, 117.
Dalton, J., I, 255.
D'Arblay, Mme., I, 190.
Darwin, E., II, 8.
Darwinism, Primitive, I, 344.
Dary, M., II, 305.
Daval, P., II, 298.
Davies, T. S., II, 151, 151, 188.
Day, A., I, 295, 295.
DeBaruel, I, 165.
De Beaune. (See Beaune.)
De Becourt, II, 277, 277.
Debenham, J., 1, 393.
De Causans. (See Causans.)
Dechales. (See de Challes.)
De Challes, I, 45.
Decimal coinage, II, 80, 168, 169.
Decimals run riot, II, 80.
Dee, J., II, 302.
De Faure, I, 149.
DC la Leu, I, 297.
Delambre, I, 160, 167, 354; II, 165.
Democritus, II, 34.
De Moivre, I, 24, 376; II, 298.
De Molieres, I, 220.
De Molina, I, 297.
Demonville, I, 291, 293.
De Morgan, A., I, 191, 383; II, 194.
Refusal of LL. D., I, 191.
DC Morgan, G. C., I, 383.
De Morgan, Mrs., I, 196; II, 194.
Denison, J., I, 348, 353.
Desaguliers, I, 153, 156, 157.
Desargues, I, 119, 221.
Descartes, I, 5, 59, 105, 132, 165,
204, 220; II, 94.
De Serres, II, 60.
De Sluse. (See Sluse.)
De Thou, I, 51, 111, 113; II, 295.
De Vausenville, I, 12.
Devonshire, Duke of (7th), I, 290.
Diamandi, I, 86.
Didacus Astunica, I, 90.
Diderot, II, 4, 283, 339.
Digby, K., I, 108.
Digges, T., and L., II, 302.
Dionysius Exiguus, I, 360.
Dircks, H., II, 138, 138.
Discoverers and discoveries, II, 206.
Discovery, Basis of, I, 85.
D'Israeli, L, I, 115, 118, 136, 188, 227.
Ditton, I, 133, 133.
Division, Nature of, II, 248.
Dobson, J., I, 234, 234.
Dodson, J., II, 312.
Dodt, I, 52.
Doggerel verse, I, 341.
Dolland, I, 577.
Double Vahu Process, II, 360.
Douglas, G., I, 232.
Drach, S. M., II, 317.
Drayson, G. A. W., II, 132, 132.
Dryden, II, 71.
Dual arithmetic, II, 186.
Duchesne, I, 52.
Dumortier, I, 313.
Duncan, A., I, 179.
Dunkin, E., II, 349.
Duodecimal scale, II, 68.
Duplication Problem, I, 349.
Dupuy, J. and P., II, 295.
Dutens, L., II, 90.
Dyer, G., I, 178.
Earth, Figure of, II, 54.
Easter, I, 359.
Easter Day Paradoxes, I, 353.
Ebrington, Thos., I, 247.
Edgeworth, Maria, I, 191.
Editorial System, I, 15. .
Edleston, I, 140; II, 296.
Edwards, J., I, 144.
Edwards, T., I, 112.
Eirenaeus Philalethes, I, .725, 125, 126.
Eldon, Lord (1st), II, 197.
Elephant story, I, 58.
Elizabeth, Queen, I, 128.
Ellenborough, Baron, I, 181.
INDEX.
379
Ellicot, I, 24.
Ellis, I, 76, 82.
Engel, I, 230.
English language, Origin of, I, 215.
Enriques, F., II, 367.
Epps, J., I, 153; II, 143.
Equation of fifth degree, I, 250, 373.
Erasmus, I, 110.
Erastus, I, 65.
Erichsen, I, 163.
Ersch, II, 193, 282.
Erskine, T., II, 127.
Esperanto, Forerunner of, I, 116.
Euclid, I, 5, 43; II, 118, 151. With-
out Axioms, I, 287.
Eudoxus, II, 164.
Euler, I, 221, 382; II, 3, 4, 303, 331,
339.
Eusebius, II, 220.
Eustace, J. C, II, 46.
Eutocius, I, 41; II, 60.
Evelyn, J., I, 108.
Everett, J., I, 346.
Evidence, I, 57, 58.
Faber. (See Stapulensis.)
Fairfax, Mary, I, 242.
Falco, I, 53.
Faraday, M., II, 351.
Faure, de, I, 149; II, 238.
Fawcett, H., II, 249.
Ferguson, J., II, 20.
Fermat, I, 122, 221; II, 300.
Ferrari, S., II, 68.
Fiction, New era in, I, 189.
Fienus, I, 74, 74.
Filopanti, Q. B., II, 93.
Finaeus, I, 50, 50, 113.
Finleyson, J., I, 314, 314.
Flamsteed, I, 87, 309; II, 45, 143,
302, 306.
Fletcher, I, 378.
Fludd, II, 318.
Fly-leaf Paradox, II, 264.
Folkes, M., I, 136; II, 301.
Fontenelle, I, 103.
Forbes, D., I, 237.
Forman, W., I, 296, 296, 306.
Forster, T. I. M., I, 320, 320.
Foscarini, I, 90.
Foster, S., II, 310.
Fourier, II, 66.
Fox, G., I, 397.
Francis, P., II, 96.
Francoeur, I, 365.
Frankland, W. B., I, 230, 287.
Franklin, J., II, 265.
Freedom of opinion, Growth of, I,
265.
Freher, A., II, 319.
French academy on circle squaring,
I, 163.
Frend, W., I, 196, 196, 206, 208, 252.
Fresnel, II, 48.
Fromondus, I, 74, 74, 99.
Frost, I. and J., I, 394.
Fry, Elizabeth, I, 224.
Fuller, T., I, 86.
Fulton, R., I, 148.
Gadbury, J., I, US, 115.
Galbraith, J. A., II, 372.
Galileo, I, 5, 6, 32, 76, 82, 83, 96,
122, 381.
Galle, J. G., I, 386; II, 7.
Galloway, I, 56, 57; II, 143.
Gamblers, I, 280.
Garrick, I, 21.
Gascoigne, W., II, 299.
Gassendi, I, 107.
Gauss, I, 86, 107, 310.
Gemistus, G., I, 188.
Gentleman's Monthly, Miscellany, I
208.
Gephryander. {See Salicetus.)
Gergonne, I, 336.
Ghetaldi, I, 83; II, 59.
Ghost paradox, II, 47.
Giddy (Gilbert), II, 174.
Gilbert, Davies, II, 66, 174.
Gilbert, William, I, 6, 68, 68, 76.
Gillot, II, 315.
Glazier (Glazion), II, 7.
Godwin, F., I, 103.
Godwin, W., I, 174.
Golius, I, 106.
Gompertz, B., I, 378.
Goulburn, I, 288.
Goulden, S., II, 88.
Graham, I, 24.
Grandamicus, I, 104, 104.
Granger, J., I, 156.
Grant, A. R., II, 131.
Grant, R., I, 392; II, 131.
Grassi, O., I, 262.
Grassini, I, 231.
Graunt, J., I, 113, 114, 154.
Gravity, I, 151, 244, 348, 353.
380
A BUDGET OF PARADOXES.
Gravity. Newton's apple, I, 136.
Greek numerals, II, 77.
Greene, R., I, 135, 135.
Greenhill, Sir G., I, 136.
Greenwich observatory, I, ' 87.
Gregg, T. D., II, 75, 75.
Gregorian Calendar, I, 363.
Gregory, D., I, 66; II, 301.
Gregory, J., I, 118, 118, 207; II, 302.
Gregory O., II, 71.
Gregory, Pope, I, 362.
Grevil, I, 202.
Grey, C, (2d Earl), I, 315; II, 247.
Grosart, I, 141. 141, 145.
Grove, W. R., II, 320.
Gruber, II, 193, 282.
Gruenberger, I, 70.
Grynaeus, I, 66.
Guaricus, I, 43.
Guillim, J., II, 28.
Guldin, I, 83
Gumpach, Von, II, 137, 137.
Gunning, H, I, 198.
Gurney. (See Fry, E.)
Guthrie, W., 1, 595.
Hailes, J. D., II, 135, 135.
Hailesean system of astronomy, II,
135.
Hale, M., I, 123, 123.
Hales, S., I, 123.
Hall, B., II, 181.
Hallam, I, 159.
Halley, I, 24, 124, 311; II, 301, 332.
Halliwell-Phillips, II, 148, 296.
Hamilton, W., I, 112, 117, 331, 335,
339, 341, 342; II, 52, 53, 111.
Hamilton, W. Rowan, I, 332; II, 104,
256, 343.
Hanover, King of, I, 201.
Hardy, C., I, 298.
Hardy, T., I, 178.
Harriot, T., II, 302.
Harvey, I, 76, 78; II, 201.
Hauff, I, 230.
Haughton, S., II, 372.
Hauksbee, F., I, 156.
Hayes, C., I, 132, 132.
Heath, D. D., I, 76.
Heinfetter, H., II, 94, 94.
Helmont, J. B. van, I, 125.
Henson, II, 8.
Heraclitus, II, 34.
Herbart, J. F., I, 253, 25 3; II, 78.
Herigone, II, 59.
Herschel, J., I, 80, 299, 326, 383,
386; II, 88, 95, 181, 255, 261, 262.
Herschel, W., I, 81, 151, 192, 225, 233,
299; II, 288, 348.
Heywood, F., II, 49.
Hicks, J. P., II, 67.
Higgins, G., I, 257, 274.
Hilarius, Pope, I, 359.
Hill, J., I, 21, 22, 23, 24.
Hill, Rev. R., I, 192.
Hill, Sir R., I, 165, 232.
Hind, J. R., I, 384.
Hippocrates, II, 59.
Hoax, An interesting, I, 163. Lunar
Caustic, I, 288 Moon (Herschel),
I, 326; II, 131.
Hobbes, I, 105, 109, 143, 144; II, 80.
Hobhouse, J. C, II, 126.
Hodder, J., II, 265.
Hodge, C. B., I, 114.
Hodges, W., I, 237.
Hoffmann, J. J., II, 282.
Hoffmann, J. J. I. von, I, 230.
Holloway, B., I, 237.
Holmes, O. W., I, 109.
Holyoake, G. J., I, 399, 399.
Hone, W., I, 124, 180, 184, 185.
Hook, T. E., II, 261.
Hooke, I, 77; II, 300.
Hooker, R., II, 201.
Hopkins, J., II, 41.
Horace, I, 40.
Home, G., I, 152, 152, 154, 155, 236.
Home, J., I, 178.
Horner, L., I, 176.
Horner, W. G., II, 66, 151, 187.
Houlston, W., II, 156, 156.
Howard, E., I, 131.
Howison, W., I, 256, 256".
Howitt, W., II, 193, 193.
Howley, I, 63.
Hulls, I, 147, 147; II, 8.
Hume, J., I, 352; II, 174.
Husain Rifki, II, 16.
Hussein Effendi, II, 15.
Hutchinson, J., I, 154, 154.
Hutton, C, I, 153, 161; II, 303, 340.
Huyghens, I, 100, 133; II, 300.
Imaginary numbers, II, 186.
Impalement by request, II, 133.
Inaudi, I, 86.
Index Expurgatorius, I, 90.
INDEX.
381
Infant prodigies, I, 86.
Inglis, J. B., II, 52.
Inglis, R. H., I, 352.
Ingliz Selim Effendi, II, 15.
Innocent I., I, 559.
Irving, E., II, 54.
Ivory, J., II, 142, 142.
Jabir ben Aflah, II, 59.
Jack, R., I, 149.
Jacotot, J., I, 278, 278.
Jameson, Mrs., II, 63.
Jeffreys, G., I, 183.
Jenner, E., II, 205.
Jesuit contributions, I, 164.
Johnson, H. C., I, 350.
Johnson, S., I, 20, 190, 259; II, 117.
Johnston, W. H., II, 67.
Jombert, I, 161.
Jonchere, I, 146, 146.
Jones, W., I, 135; II, 298, 301.
Jones, Rev. W., I, 257.
Jonson, B., I, 13.
Journals, Three classes of, II, 144.
Kantesian Jeweler, I, 258.
Karsten, I, 230.
Kastner, I, 43, 110, 112.
Kater, I, 11.
Keckermann, I, 3.
Keill, J., II, 302.
Kepler, I, 52, 76, 82, 381; II, 166.
Kerigan, T., I, 308, 353.
Keroualle, De, II, 50.
Kersey, I, 107.
King, Wm., I, 246.
Kircher, Adolphe, I, 229.
Kircher, Athanasius, I, 103.
Kirkringius, T., I, 125, 125.
Kittle, I, 236.
Klein, F., II, 367.
Knight, C., II, 109, 280, 289.
Knight, G., I, 151, 151.
Knight, R. P., II, 274.
Knight, Wm., I, 97.
Koenig, S., I, 150.
Lacomme, I, 46.
La Condamine, II, 301.
Lacroix, I, 41, 159, 207.
Lactantius, I, 33, 96.
Lagrange, I, 221, 288, 313, 382; II,
86.
Laing, F. H., II, 186, 186.
Lalande, I, 159.
Lamb, C., I, 178; II, 270.
Lambert, J. H., I, 556; II, 214, 367.
Lambert, John, II, 309.
Language, Test of, II, 327.
Lansbergius, I, 70, 70.
Laplace, I, 24, 255, 382; II, 1, 340.
Lardner, D., II, 255.
Lardner, N., I, 14; II, 221.
Laud, I, 145.
Lauder, W., I, 297.
Laurent, P., I, 309, 309.
Laurie, J., II, 4.
Laurie, P., II, 42.
Laurus, I, 381.
Law, Edmund, I, 181.
Law, Edward, I, 181.
Law, W., I, 168, 254; II, 317.
Le Coq, I, 86.
Lee, R., I, 66.
Lee, S., I, 131.
Lee, W., I, 157.
Legate, I, 59.
Legendre, I, 229; II, 215, 367.
Legh, P., II, 68, 83.
Leibnitz, I, 5, 7; II, 46.
Leo, St., I, 559.
Leverrier, I, 43, 82, 383, 386, 388,
390; II, 7, 135, 140, 303.
Lewis, G. C., II, 162, 162.
Libri, I, 40, 62; II, 295.
Lilius, Aloysius, I, 362.
Lilly, I, 115; II, 302.
Lipen, M., I, 29*.
Little, J., I, 206.
Livingston, R., I, 148.
Locke, J., I, 142, 142, 144; and So-
cinianism, I, 142.
Locke, R., I, 146.
Locke, R. A., I, 526; II, 86, 131.
Logan, W. E., I, 557.
Logic, Formal, I, 158; II, 75. Has
no paradoxes, 1,330.
London Mathematical Society, I, 383.
London, University of, I, 259; 11,71.
Long, G., II, 290.
Long, J. St. J., II, 38, 205.
Longitude problems, I, 132, 146, 249.
Longley, C. T., I, 525.
Longomontanus, I, 105, 105.
Lottery, I, 281.
Lovett, R., I, 165, 166.
Lowe, R., II, 169.
Lowndes, W. T., I, 402.
Lubbock, J., I, 279; II, 148.
382
A BUDGET OF PARADOXES.
Lucas, F., II, 28.
Lucian, I, 102.
Lunar Caustic Joke, I, 288.
Lunn, J. R., II, 66.
Lydiat, T., II, 302.
Lyndhurst, I, 198.
Macclesfield, Earls of, I, 7; II, 296,
301.
Macclesfield, Letters, II, 296.
Mac-Elshender, II, 87.
Machin, J., II, 301.
Mackey, John, I, 349.
Mackey, S. A., I, 256.
Maclear, T., II, 181.
Macleod, H. D., II, 184, 184.
Magic, I, 118.
Magna Charta, I, 25.
Magnus, I, 42.
Maitland, S., I, 63, 163.
Malacarne, I, 119.
Maiden, H., II, 162.
Malius, II, 342.
Mallemens, II, 333.
Mankind gullible, I, 115.
Manning, H. E., (Card.), II, 233.
Mansel, H. L., II, 162.
Marcelis, J., I, 129, 129.
Maret, II, 3.
Margarita Philosophica. (See Reisch.)
Marryat, Capt., II, 87.
Marsh, H., I, 199, 271.
Martin, B., I, 152, 153.
Martin, R., II, 236.
Maseres, F., I, 197, 203.
Mason, M., II, 132.
Mathematical Illustrations of Doc-
trine, II, 70; Psychology, 1,253;
Society, I, 374, 376,382; Theology,
I, 149.
Mathematics, Condensed history of,
II, 58.
Matter to Spirit, II, 194.
Maty, I, 23.
Maupertuis, II, 301.
Maurice, F. D., II, 101.
Maurolycus, I, 121.
Maxwell, A., I, 102.
Meadley, G. W., I, 223.
Mechanics Magazine, II, 141, 145.
Medici, Cosmo de, II, 295.
Medicine, Status of, I, 266.
Melanchthon, II, 323.
Menestrier, I, 127, 127.
Mercator, G., II, 92.
Mercator's projection, I, 84.
Mersenne, I, 106, 107; II, 295, 297.
Meslier, J., II, 195.
Meteorologist, An early, I, 320.
Meteorology, I, 327.
Metius, A. and P., I, 52, 99, 99.
Meton, II, 167.
Metric System, Forerunner of, I, 171.
Meziriac, I, 161.
Milbanke, A. I., I, 225.
Mill, Jas., I, 260.
Miller, Joe, I, 182.
Miller, S., I, 167.
Mills, Elizabeth, W., II, 7.
Milne, J., I, 286.
Milner, I., I, 251, 251.
Milner, J., II, 23.
Milner's lamp, I, 252.
Milward, II, 250.
Miracles vs. Nature, II, 6.
Mitchell, J., I, 242.
Moliere, I, 232.
Molina, A. C. de, I, 297.
Mollendorff, von, II, 3, 338.
Mondeux, I, 86.
Montague, C., II, 311.
Montmort, P. R. de, II, 301.
Montucla, I, 40, 45, 54, 65, 117, 120,
159, 163; II, 60.
Moon Hoax, I, 326; II, 131.
Moon, Nature of, II, 84; Rotation
of, II, 4, 19, 84, 87.
More, Hannah, I, 189, 192.
More, Henry, I, 123.
Moore, Dr. John, I, 190.
Moore, Sir John, I, 190.
Morgan, S., I, 6.
Morgan, T., I, 191.
Morgan, W., I, 223, 224.
Morhof, I, 61.
Morin, I, 99, 99.
Morinus, J. B., I, 149.
Morland, S., II, 302.
Mormonism, II, 69.
Morrison, R. J., I, 321; II, 43.
Mose, H., II, 266.
Mottelay, I, 68.
Motti, II, 60.
Mouton, I, 172; II, 300.
Muggleton, I, 394, 395.
Multiplication, Nature of, II, 251.
Murchison, R. I., I, 384.
Murhard, I, 43, 298.
INDEX.
383
Murphy, A., II, 308.
Murphy, J. L., II, 54, 54.
Murphy, P., I, 327, 398.
Murphy, R., I, 349, 349.
Murray, J., I, 186; II, 145.
Murray, L., II, 326.
Murray, Mungo, II, 310.
Musgrave, T., I, 324.
Mydorge, I, 298.
Mystrom, J. W., II, 182.
Mythological paradoxes, I, 256.
Names of Religious Bodies, II, 22.
Napier, J., I, 5, 66, 67, 82.
Napoleon, Doubts as to, I, 246.
Nautical Almanac, I, 300; II, 147.
Neal, I, 98.
Negative numbers, I, 196, 203.
Neile, W., II, 190.
Neptune, Discovery of, I, 387; II,
140. (See Adams, Lererrier.)
Nesse, C, I, 128, 128.
Newcomb, S., I, 162.
Newcomen, T., I, 147.
Newton, Sir Isaac, I, 5, 6, 8, 24, 39,
84, 88, 130, 136, 139, 144, 145, 148,
152, 154, 155, 162, 165, 167, 197,
225, 237, 242, 257, 282, 296, 297,
309, 311, 382, 394, 395, 396, 397;
II, 2, 70, 184, 297, 302, 305.
Newton, John, II, 305.
Nicene Creed, I, 371.
Nichol, J. P., II, 289.
Nicholas. (See Cusa.)
Nichols, J., I, 175.
Nicolas, N. H., I, 354.
Nicollet, I, 326; II, 131.
Nicolson, W., I, 201.
Nieuwentijt, II, 333.
Nizzoli, M., II, 275.
Non-Euclidean geometry, II, 83.
Northampton, Marquis of (2d), II,
19.
Novum Organum Moralium, II, 74.
Number, Mystery of, I, 55, 56, 169.
Number of the Beast (666), I, 55,
130, 272, 298, 352; II, 77, 159, 217,
218, 361, 373.
Numeral system, II, 68.
Nursery rhymes, II, 150.
Occam, Wm. of, II, 40.
Odgers, N., II, 191, 191.
Oinopides of Chios, II, 59.
Oldenburgh, H., II, 300, 302.
Orthodox Paradoxes, II, 363.
Orthography, Paradoxes of, II, 267.
Ortwinus, I, 319.
Oughtred, W., II, 298, 303.
Owenson, I, 191.
Ozanam, I, 161, 312.
Pagi, I, 32.
Paine, T., I, 173, 173, 271.
Paley, W., I, 222; II, 226.
Palmer, C., I, 225.
Palmer, H., I, 141, 141, 145.
Palmer, J., II, 253.
Palmer, T. F., II, 254.
Palmer, W., II, 37.
Palmerston, Viscount (3d), I, 290,
352.
Palmezeaux, I, 167.
Panizzi, A., I, 151.
Papist, II, 26.
Paracelsus, II, 322.
Paradox defined, I, 2, 31.
Paradox, religious, I, 236.
Paradoxers in general, II, 352.
Parallels, Theory of, I, 229, 344.
Pardies, I. G., II, 300.
Park, Mungo, II, 91, 132.
Parker, F., II, 94.
Parker, G. (Earl of Macclesfield), II,
296.
Parr, S., I, 173, 173, 175, 176, 184.
Parsey, I, 293, 293.
Partridge, J., I, 305.
Pasbergius, I, 381.
Pascal, I, 39, 119, 122, 220, 221; II,
73.
Pascal's Hexagram, I, 221.
Passot, I, 279, 279.
Passover, I, 358, 372.
Patriotic paradox, I, 231.
Paucton, I, 172.
Paulian, I, 165, 165.
Peacock, Geo., I, 196, 350.
Peacock, T. L., I, 190, 340.
Pearce, A. J., II, 43.
Pearne, T., I, 239.
Peel, Sir R., I, 290, 352.
Peel, W. Y., I, 290.
Pelerin, J., II, 324.
Pell, J., I, 105, 105, 107; II, 300, 302,
312.
Pepys, I, 113, 114.
Perigal H., II, 19, 20.
384
A BUDGET OF PARADOXES.
Perpetual motion, I, 118, 348; II, 55,
138.
Perspective, New theory of, I, 293.
Peters, W., II, 11, 315.
Petitioning Comet, I, 127.
Petrie, W. M. F., I, 328.
Petty, I, 114; II, 300.
Philalethes, Eirenaeus, I, 125, 125,
126.
Philalethes, Eugenius, I, 255.
Phillips, R., I, 242, 242, 245.
Philo of Gadara, I, 40, 40.
Philosopher's stone, I, 118, 125.
Philosophical atheists, II, 1.
Philosophy and Religion, II, 37.
Phonetic spelling, II, 81.
TT, values of, I, 11, 43, 45, 46, 52,
69, 100, 110, 129, 135, 146, 245,
283, 284, 294, 347, 348, 349, 350;
II, 60, 63, 105, 110, 118, 135, 156,
209, 279, 315, 316.
Pighius, I, 372.
Pike, S., I, 236, 236.
Pindar, P., II, 272.
Piozzi, Mrs., I, 235; II, 272.
Piscator, B., II, 25.
Pitman, F., II, 81, 81.
Place, F., I, 199.
Planets inhabitable, I, 100, 102.
Plato, I, 5.
Platt, H., I, 126, 126.
Playfair, J., I, 233.
Pletho, G., I, 188.
Pliny, II, 280.
Ploucquet, I, 336, 337.
Poe, E. A., II, 132.
Poincare, I, 136.
Poisson, I, 2P2; II, 2.
Pollock, J. F., II, 174.
Pons, II, 45.
Pope, Wm., I, 277, 277.
Porta, I, 68, 68, 83.
Porteus, B., I, 193, 203.
Porteus, H. F. A., II, 157, 157.
Porus, I, 44.
Powell, Baden, II, 267.
Powell, W. S., I, 222.
Pratt, H. F. A., II, 157, 157.
Pratt, O., II, 69.
Predaval, Count de, I, 348.
Prescot, B., I, 270, 270, 278.
Prester John, I, 70, 71, 152.
Price, R., I, 223.
Probability, Discourse on, I, 279.
Proclus, I, 188, 188.
Prodigies, Youthful, I, 219, 332.
Pronunciation, II, 330.
Protestant and Papal Christendom, II,
33.
Protimalethes, II, 6.
Ptolemy, I, 5, 33, 380.
Pullicino, II, 61, 61.
Pusey, I, 64.
Pyramids, The, I, 328; II, 95, 136.
Pythagoras, II, 59.
Quadrature problem. (.See Squaring
the circle.)
Quarles, F., II, 277. .
Quintilian, II, 280.
Quotem, C., I, 399.
Rabelais, I, 102.
Rainbow Paradox, II, 334.
Ramachandra, Y., I, 374.
Ramchundra, I, 374.
Ramus, I, 5.
Recalcati, II, 208, 314.
Recorde, R., II, 328.
Reddie, Jas., II, 183, 183, 344, 360.
Reeve, J., I, 395.
Regiomontanus, I, 48, 360.
Reisch, I, 45; II, 281.
Religion and Philosophy, II, 37.
Religious bodies, Names of, II, 22;
customs, Attacks on, I, 177; In-
surance, I, 345; Paradox, I, 236;
Tract society, I, 192.
Remigius, I, 50.
Reuchlin, J., II, 323.
Revelations, Napier on, I, 66.
Revilo, (O. Byrne), I, 241, 329,329.
Reyneau, C. R., II, 301.
Rheticus, I, 69; II, 372.
Rhonius, II, 300.
Ribadeneira, P. de, II, 62.
Riccioli, I, 96.
Richards, G., II, 270.
Rigaud, J., II, 299.
Rigaud, S. J., II, 299.
Rigaud, S. P., I, 140; II, 298, 313.
Ringelbergh, J. S., II, 281.
Ripley, G., I, 126, 126.
Ritchie, W., I, 295, 295.
Ritterhusius, I, 60.
Rive, J.-J., I, 160.
Robertson, Jas., I, 237.
Roberval, I, 105, 122.
INDEX.
385
Robinson, B., I, 148, 148.
Robinson, H. C, I, 314; II, 52, 275.
Robinson, R., I, 177.
Robinson, T. R., II, 181.
Roblin, J., II, 136
Rogers, S., II, 260.
Roget, P. M., I, 398.
Roomen, A. van, I, 110.
Ross, J. C., I, 303.
Rosse, I, 26.
Rossi, G., I, 231, 231.
Rotation of the Moon, II, 4, 19.
Rough, W. f I, 198.
Kowning, J., I, 155.
Royal Astronomical Society, I, 27;
Forerunner of, I, 374.
Royal Society, I, 21, 22, 24-30, 56,
57, 136, 153, 163, 164, 165.
Rudio, I, 159; II, 367.
Rudolff, C., II, 373.
Russell, Earl (1st), I, 296.
Rutherford, W., II, 109.
Sabatier, A., II, 267.
Sabellius, I, 241.
Sacrobosco, I, 360.
Sadler, T., I, 238, 241.
Saint-Martin, I, 167, 168, 206.
St.-Mesmin, M. de., I, 280.
St. Vincent, G. de., 110, 117.
St. Vitus, Patron of Cyclometers, II,
60.
Sales, de, I, 167.
Salicetus, I, 64.
Salisbury, Earl of (1st), II, 330.
Salmasius, Claudius, II, 168.
Salusbury, Hester, I, 235.
Sanchez, Petro, I, 229, 229.
Sanders, W., I, 207.
Sanderson, R., I, 135.
Sara, R., I, 297. ^
Saunderson, N., I, 377; II, 301.
Scaliger, I, 44, 110, 111, 112, 113; II,
238.
Scevole de St. Marthe, I, 113.
Schooten, Van, II, 59.
Schopp, I, 60.
Schott, I, 64; II, 64.
Schumacher, H. C., I, 107; II, 297.
Schwab, I, 230.
Scientific paradoxes, I, 232.
Scott, Michael, I, 38.
Scott's Devils, I, 38.
Scott, W., I, 20, 27, 38, 39, 155, 191.
Scripture and Science, II, 261.
Search, John, I, 247.
Selden, J., II, 250.
Senarmont, II, 48.
Serres, De, II, 60.
Shaftesbury, Earl of, II, 181.
Shakespeare, I, 13.
Shanks, II, 63, 65, 109.
Shaw, P., I, 142.
Sheepshanks, J., I, 147.
Sheepshanks, R., I, 290.
Shelley, I, 174.
Shepherd, S., I, 124.
Sherburne, E., II, 295.
Sheridan, R. B., I, 175.
Sheridan, T., I, 775.
Shoberl, R, II, 270.
Shrewsbury, I, 108.
Siddons, Mrs., I, 189.
Simms, W., I, 152.
Simplicius, II, 164.
Simpson, T., I, 377; II, 304.
Simson, R., I, 197, 202, 233.
Sinclair, G., I, 207.
Slander Paradoxes, II, 138.
Sloane, I, 24.
Sluse, R. de, I, 118, 118; II, 300.
Smith, Adam, II, 112.
Smith, Jas., I, 46; II, 103, 103, 154,
236, 237, 238, 241, 336, 360.
Smith, Jas., II, 217.
Smith, Jas. (Shepherd), II, 55, 193.
Smith, Joseph, II, 69.
Smith, Richarda, I, 242.
Smith, Thomas, I, 346, 346.
Smith, Wm., II, .752.
Smyth, C. P., I, 328; II, 65.
Snell, I, 75, 75.
Socinianism, I, 142, 143.
Socinus, I, 3, 143.
Socrates Scholasticus, I, 35*.
Sohncke, L. A., II, 131.
Somerville, Mrs., I, 242.
South, J., II, 181.
Southcott, Joanna, II, 58, 97, 239.
Spearman, R., I, 237.
Speculative thought in England, I
374.
Spedding, I, 76, 82, 142.
Speed, J., I, 201.
Speke, I, 70.
Spelling, phonetic, II, 81.
Spence, W., I, 231, 231.
Spencer, Earl (3d), II, 9.
386
A BUDGET OF PARADOXES.
Spinoza, I, 3, 37.
Spiritualism, II, 47, 55, 207.
Spurius Cassius Viscellinus, II, 342.
Spurius Maelius, II, 342.
Squaring the circle, I, 8, 42, 44, 46,
47, 50, 52, 53, 69, 70, 75, 109, 117,
119, 129, 135, 146, 149, 159, 163,
164, 347, 348, 374; II, 10, 11, 60,
105, 154, 156, 208, 278, 314.
Stackel, I, 230.
Stanhope, P. D., (Earl of Chester-
field), II, 298.
Stapulensis, I, 44; II, 324.
Star polygons, I, 229.
Starkie, G., I, 126, 126.
Statter, D., II, 80.
Steamship suggested, I, 147.
Steel, Jas., II, 68.
Stenography, II, 81.
Stephens, I, 44; II, 324.
Stephenson, G., II, 138.
Stephenson, R., II, 138.
Stevin, I, 83, 313; II, 59.
Stewart, D., II, 55.
Stewart, R., I, 186.
Stifel, M., II, 373.
Strafford, Earl of, I, 240.
Stratford, W. S., I, 300.
Street, T., I, 124.
Stukely, W., I, 236.
Suffield, G., II, 66.
Suidas, II, 29.
Sumner, C. R., I, 324.
Sumner, J. B., I, 324.
Sun as an electric space, II, 41.
Supernatural, The, II, 193.
Suvaroff, II, 85.
Swastika, II, 231.
Swedenborg, E., I, 255.
Swift, I, 19, 133.
Sylvester, J. J., II, 336.
Symington, W., I, 148.
Symons, II, 4, 5, 20, 84, 85.
Sympathetic powder, I, 108.
Synesius, I, 125.
Talbot, G., I, 22, 108.
Talbot's powder, I, 108.
Tartaglia, II, 59.
Tasse, I, 106.
Tate, J., I, 199.
Tauler, J., II, 322.
Taylor, Brook, II, 301.
Taylor, John, I, 352; II, 95.
Taylor, Robt., I, 270.
Taylor, T., I, 188, 188.
Teissier, I, 113.
Temple, H. J., I, 290.
Tenterden, Chief Justice, I, 181.
Thales, II, 59, 83.
Theism independent of Revelation, I,
399.
Thelwall, J., I, 178.
Theodoretus, I, 358.
Theological Paradoxes, I, 316.
Theology, Mathematical, I, 129, 149.
Theophrastus, II, 167.
Thiebault, II, 3, 338.
Thorn, D., II, 226, 240.
Thorn, J. H., II, 226.
Thompson, P., I, 7.
Thompson, T. P., I, 252, 287, 344;
II, 83, 185.
Thomson, Dr. I, 21.
Thomson, W., I, 325.
Thorn, W.,. II, 158, 158, 360.
Thorndike, H., II, 313.
Thrale, Mrs., I, 235.
Thurlow, Baron, I, 222.
Thyrxus, I, 50.
Tides, New theory of, I, 393.
Tombstones of mathematicians, I, 106.
Tonal System, II, 182.
Tooke, H., I, 178.
Torriano, E., I, 250.
Towneley, II, 300.
Townley, C., II, 300.
Trisection problem, I, 118; II, 10, 12,
13, 15.
Troughton, I, 152.
Turner, E., I, 137.
Tycho Brahe, I, 5, 76, 381; II, 302,
335.
Upton, W., II, 12, 12, 15.
Ursus, I, 52.
Valentine, B., I, 125, 125.
Van Ceulen, I, 52, 70, 100.
Van de Weyer, I, 313.
Van Etten, I, 161.
Van Helmont, I, 125, 125.
Van Roomen, I, 110.
Van Schooten, II, 59.
Vaughan, T., I, 255.
Victorinus, I, 359.
Viete, I, 51; II, 210, 295.
Virgil, St., I, 32, 33, 34, 99.
INDEX.
387
Virginia, University of, I, 233.
Viscellinus, II, 342.
Vitruvius, II, 281.
Vivian, T., I, 172, 172.
Vogel, A. F., I, 373.
Voltaire, I, 103, 165, 166, 167, 168,
248; II, 268.
Von Gumpach, II, 137, 137.
Von Hutten, I, 318.
Von Wolzogen. (.See Wolsogen.)
Vyse, R. W. H., I, 328.
Walker, W. E., II, 316.
Walkingame, F., II, 173.
Wallich, N., II, 14.
Wallis, J., I, 107, 109, 110; II, 299,
313.
Walpole, I, 23, 131.
Walsh, John, I, 260, 260; II, 157.
Wapshare, J., II, 230.
Warburton, H., I, 349.
Warburton, Wm., I, 55, 112; II, 174.
Ward, S., II, 299.
Waring, E., I, 203, 222.
Warner, W., II, 302, 312.
Warren, S., II, 340.
Watkins, J., II, 270.
Watson, Bp., I, 223.
Watt, R., I, 102, 402.
Watts, I., II, 18.
Weddle, T., II, 187.
Wentworth, Thos., I, 240.
W barton, I, 115.
Whately, R., I, 246, 246, 324.
Whately's Paradox, I, 246.
Whewell, I, 101, 101, 273, 314, 380;
II, 104, 246, 247.
Whigs, II, 22.
Whiston, J., I, 147.
Whiston, W., I, 133, 133, 146, 156,
311.
White, H. K., II, 271.
White, J. B., I, 248.
White, R., I, 11.
Whitford, I, 105.
Whitworth, W. A., II, 344.
Whizgig, On the, I, 254^
Wightman, I, 59.
Wilberforce, W., II, 236.
Wilkins, J., I, 96, 100, 116, 226.
Williams, J. B., I, 378.
Williams, T., I, 17U7J.
Wilson, Sir J., I, 221.
Wilson, J. M., II, 344.
Wilson, R., II, 7, 7.
Wilson's Theorem, I, 222.
Wingate, E, II, 308.
Winter, I, 46.
Wirgman, T., I, 258, 258.
Wiseman, N. P. S., II, 26, 61, 294.
Wolcot, J. (Peter Pindar), II, 272.
Wollstonecraft, I, 173, 173.
Wolzogen, I, 106.
Wood, A., I, 98.
Wood, John, I, 233.
Wood, Wm., I, 246, 246.
Woodley, W., I, 307, 307.
Wordsworth, II, 273.
Wright, E., I, 84.
Wright, T., I, 151, 151, 152, 153.
Wright, W., II, 9.
Wronski, I, 249, 250.
Wrottesley, J. (Baron), II, 181.
Young, B., II, 69.
Young, J. W. A., II, 367.
Young, T., I, 24, 30, 250.
Youthful Prodigies, I, 219.
Yvon, I, 297.
Zach, von, II, 45, 196.
Zachary, Pope, I, 32, 34.
Zadkiel, I, 321; II, 43.
Zetetic Astronomy, II, 88.
Zodiac, II, 136.
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