A Budget of Paradoxes, Volume II (of II)
by Augustus de Morgan
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Transcriber's note:

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

In mathematical formulae the carat (^) and underscore (_) introduce superscripts or subscripts respectively, of one character or a group enclosed in curly braces ({xyz}). Elsewhere underscores delimit italics in the text, and braces enclose the original page numbers thus {123}.








Volume II


* * * * *

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

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

* * * * *





With the general run of the philosophical atheists of the last century the notion of a God was an hypothesis. There was left an admitted possibility that the vague somewhat which went by more names than one, might be personal, intelligent, and superintendent. In the works of Laplace,[1] who is sometimes called an atheist from his writings, there is nothing from which such an inference can be drawn: unless indeed a Reverend Fellow of the Royal Society may be held to be the fool who said in his heart, etc., etc., if his contributions to the Philosophical Transactions go no higher than nature. The following anecdote is well known in Paris, but has never been printed entire. Laplace once went in form to present some edition of his "Systeme du Monde" to the First Consul, or Emperor. Napoleon, whom some wags had told that this book contained no mention of the name of God, and who was fond of putting embarrassing questions, received it with—"M. Laplace, they tell me you have written this large book on the system of the universe, and have never even mentioned its Creator." Laplace, who, though the most supple of politicians, was as stiff as a martyr on every point of his philosophy or religion (e. g., even under Charles X he never concealed his dislike of the priests), drew himself up and answered {2} bluntly, "Je n'avais pas besoin de cette hypothese-la."[2] Napoleon, greatly amused, told this reply to Lagrange, who exclaimed, "Ah! c'est une belle hypothese; ca explique beaucoup de choses."[3]

It is commonly said that the last words of Laplace were, "Ce que nous connaissons est peu de chose; ce que nous ignorons est immense."[4] This looks like a parody on Newton's pebbles:[5] the following is the true account; it comes to me through one remove from Poisson.[6] After the publication (in 1825) of the fifth volume of the Mecanique Celeste, Laplace became gradually weaker, and with it musing and abstracted. He thought much on the great problems of existence, and often muttered to himself, Qu'est ce que c'est que tout cela![7] After many alternations, he appeared at last so permanently prostrated that his family applied to his favorite pupil, M. Poisson, to try to get a word from him. Poisson paid a visit, and after a few words of salutation, said, "J'ai une bonne nouvelle a vous annoncer: on a recu au Bureau des Longitudes une lettre d'Allemagne annoncant que M. Bessel a verifie par l'observation vos decouvertes theoriques sur les satellites de Jupiter."[8] Laplace opened his eyes and answered with deep {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 illustrates what I have said: a supreme and guiding intelligence—apart from a blind rule called nature of things—was an hypothesis. The absolute denial of such a ruling power was not in the plan of the higher philosophers: it was left for the smaller fry. A round assertion of the non-existence of anything which stands in the way is the refuge of a certain class of minds: but it succeeds only with things subjective; the objective offers resistance. A philosopher of the appropriative class tried it upon the constable who appropriated him: I deny your existence, said he; Come along all the same, said the unpsychological policeman.

Euler[10] was a believer in God, downright and straightforward. The following story is told by Thiebault,[11] in his Souvenirs de vingt ans de sejour a Berlin,[12] published in his old age, about 1804. This volume was fully received as trustworthy; and Marshall Mollendorff[13] told the Duc de Bassano[14] in 1807 that it was the most veracious of books written by the most honest of men. Thiebault says that he has no personal knowledge of the truth of the story, but {4} 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, donc Dieu existe; repondez![16] Diderot, to whom algebra was Hebrew, was embarrassed and disconcerted; while peals of laughter rose on all sides. He asked permission to return to France at once, which was granted.


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

A systematic attack of the character afterwards made with less skill and more notice by Mr. Jellinger Symons.

July 1866, J. L. appears as Mr. James Laurie, with a new pamphlet "The Astronomical doctrines of the Moon's rotation ..." Edinburgh. Of all the works I have seen on the question, this is the most confident, and the sorest. {5} A writer on astronomy said of Mr. Jellinger Symons,[18] "Of course he convinced no one who knew anything of the subject." This "ungenerous slur" on the speculator's memory appears to have been keenly felt; but its truth is admitted. Those who knew anything of the subject are "the so-called men of science," whose three P's were assailed; prestige, pride, and prejudice: this the author tries to effect for himself with three Q's; quibble, quirk, and quiddity. He explains that the Scribes and Pharisees would not hear Jesus, and that the lordly bishop of Rome will not cast his tiara and keys at the feet of the "humble presbyter" who now plays the part of pope in Scotland. I do not know whom he means: but perhaps the friends of the presbyter-pope may consider this an ungenerous slur. The best proof of the astronomer is just such "as might have been expected from the merest of blockheads"; but as the giver is of course not a blockhead, this circumstance shows how deeply blinded by prejudice he must be.

Of course the paradoxers do not persuade any persons who know their subjects: and so these Scribes and Pharisees reject the Messiah. We must suppose that the makers of this comparison are Christians: for if they thought the Messiah an enthusiast or an impostor, they would be absurd in comparing those who reject what they take for truth with others who once rejected what they take for falsehood. And if Christians, they are both irreverent and blind to all analogy. The Messiah, with His Divine mission proved by miracles which all might see who chose to look, is degraded into a prototype of James Laurie, ingeniously astronomizing upon ignorant geometry and false logic, and comparing to blockheads those who expose his nonsense. Their comparison is as foolish as—supposing {6} them Christians—it is profane: but, like errors in general, its other end points to truth. There were Pseudochrists and Antichrists; and a Concordance would find the real forerunners of all the paradoxers. But they are not so clever as the old false prophets: there are none of whom we should be inclined to say that, if it were possible, they would deceive the very educated. Not an Egyptian among them all can make uproar enough to collect four thousand men that are murderers—of common sense—to lead out into the wilderness. Nothing, says the motto of this work, is so difficult to destroy as the errors and false facts propagated by illustrious men whose words have authority. I deny it altogether. There are things much more difficult to destroy: it is much more difficult to destroy the truths and real facts supported by such men. And again, it is much more difficult to prevent men of no authority from setting up false pretensions; and it is much more difficult to destroy assertions of fancy speculation. Many an error of thought and learning has fallen before a gradual growth of thoughtful and learned opposition. But such things as the quadrature of the circle, etc., are never put down. And why? Because thought can influence thought, but thought cannot influence self-conceit: learning can annihilate learning: but learning cannot annihilate ignorance. A sword may cut through an iron bar; and the severed ends will not reunite: let it go through the air, and the yielding substance is whole again in a moment.

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

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


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

Against the moon's rotation on her axis.

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

1847. In the United Service Magazine for September, 1847, Mrs. Borron,[21] of Shrewsbury, published some remarks tending to impeach the fact that Neptune, the planet found by Galle,[22] really was the planet which Le Verrier and Adams[23] had a right to claim. This was followed (September 14) by two pages, separately circulated, of "Further Observations upon the Planets Neptune and Uranus, with a Theory of Perturbations"; and (October 19, 1848) by three pages of "A Review of M. Leverrier's Exposition." Several persons, when the remarkable discovery was made, contended that the planet actually discovered was an intruder; and the future histories of the discovery must contain some account of this little afterpiece. Tim Linkinwater's theory that there is no place like London for coincidences, would have been utterly overthrown in favor of what they used to call the celestial spaces, if there had been a planet which by chance was put {8} near the place assigned to Neptune at the time when the discovery was made.


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

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

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

Darwin's contemporaries, no doubt, smiled pity on the poor man. It is worth note that the two true prophecies have been fulfilled in a sense different from that of the predictions. Darwin was thinking of the suggestion of Jonathan Hulls,[26] when he spoke of dragging the slow barge: it is only very recently that the steam-tug has been employed on the canals. The car was to be driven, not drawn, and on the common roads. Perhaps, the flying chariot will {9} be something of a character which we cannot imagine, even with the two prophecies and their fulfilments to help us.[27]


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

Light is the sustainer of motion both in the earth and in the blood. The natural standard, the pulse of a person in health, four beats to one respiration, gives the natural second, which is the measure of the earth's progress in its daily revolution. The Greek fable of the Titans is an elaborate exposition of the atomic theory: but any attempt to convince learned classics would only meet their derision; so much does long-fostered prejudice stand in the way of truth. The author complains bitterly that men of science will not attend to him and others like him: he observes, that "in the time occupied in declining, a man of science might test the merits." This is, alas! too true; so well do applicants of this kind know how to stick on. But every rule has its exception: I have heard of one. The late Lord Spencer[28]—the Lord Althorp of the House of Commons—told me that a speculator once got access to him at the Home Office, and was proceeding to unfold his way of serving the public. "I do not understand these things," said Lord Althorp, "but I happen to have —— (naming an eminent engineer) upstairs; suppose you talk to him on the subject." The discoverer went up, and in half-an-hour returned, and said, "I am very much obliged to your Lordship for introducing me to Mr. ——; he has convinced me {10} 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.


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 {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).[29]

Suggestions as to the necessity for a revolution in philosophy; and prospectus for the establishment of a new quarterly, to be called the Physical Philosopher and Heterodox Review. By Q. E. D. 8vo. 1848.

These works are by one author, who also published, as appears by advertisement,

"Newton rescued from the precipitancy of his followers through a century and a half,"[30] and "Dangers along a coast by correcting (as it is called) a ship's reckoning by bearings of the land at night fall, or in a fog, nearly out of print. Subscriptions are requested for a new edition."

The area of a circle is made four-fifths of the circumscribed square: proved on an assumption which it is purposed to explain in a longer essay.[31] The author, as Q. E. D., was in controversy with the Athenaeum journal, and criticised a correspondent, D., who wrote against a certain class of discoverers. He believed the common theories of hydrostatics to be wrong, and one of his questions was:

"Have you ever taken into account anent gravity and gravitation the fact that a five grain cube of cork will of itself half sink in the water, whilst it will take 20 grains of brass, which will sink of itself, to pull under the other half? Fit this if you can, friend D., to your notions of gravity and specific gravity, as applied to the construction of a universal law of gravitation."

This the Athenaeum published—but without some Italics, for which the editor was sharply reproved, as a sufficient {12} specimen of the quod erat D. monstrandum: on which the author remarks—"D,—Wherefore the e caret? is it D apostrophe? D', D'M, D'Mo, D'Monstrandum; we cannot find the wit of it." This I conjecture to contain an illusion to the name of the supposed author; but whether De Mocritus, De Mosthenes, or De Moivre was intended, I am not willing to decide.

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

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

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

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

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

One of Mr. Upton's trisections, if true, would prove the truth of the following equation:

3 cos ([theta] / 3) = 1 + [root](4 - sin^2[theta])

which is certainly false.[34]


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

sin 3[theta] . cos(5[theta]/2) + sin^2 [theta] sin (5[theta]/2)

divided by the square root of

sin^2 3[theta] . cos^2 (5[theta]/2) + sin^4 [theta] + sin 3[theta] . sin 5[theta] . sin^2 [theta].

This is from my rough notes, and I believe it is correct.[36] It is so nearly true, unless the angle be very obtuse, that common drawing, applied to the construction, will not detect the error. There are many formulae of this kind: and I have several times found a speculator who has discovered the corresponding construction, has seen the approximate success of his drawing—often as great as absolute truth could give in graphical practice,—and has then set about his demonstration, in which he always succeeds to his own content.

There is a trisection of which I have lost both cutting and reference: I think it is in the United Service Journal. I could not detect any error in it, though certain there must {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 0 deg. or 180 deg..

Aug. 22, 1866. Mr. Upton sticks to his subject. He has just published "The Uptonian Trisection. Respectfully dedicated to the schoolmasters of the United Kingdom." It seems to be a new attempt. He takes no notice of the sentence I have put in italics: nor does he mention my notice of him, unless he means to include me among those by whom he has been "ridiculed and sneered at" or "branded as a brainless heretic." I did neither one nor the other: I thought Mr. Upton a paradoxer to whom it was likely to be worth while to propound the definite assertion now in italics; and Mr. Upton does not find it convenient to take issue on the point. He prefers general assertions about algebra. So long as he cannot meet algebra on the above question, he may issue as many "respectful challenges" to the mathematicians as he can find paper to write: he will meet with no attention.

There is one trisection which is of more importance than that of the angle. It is easy to get half the paper on which you write for margin; or a quarter; but very troublesome to get a third. Show us how, easily and certainly, to fold the paper into three, and you will be a real benefactor to society.

Early in the century there was a Turkish trisector of the angle, Hussein Effendi, who published two methods. He was the father of Ameen Bey, who was well known in England thirty years ago as a most amiable and cultivated gentleman and an excellent mathematician. He was then a student at Cambridge; and he died, years ago, in command of the army in Syria. Hussein Effendi was instructed in mathematics by Ingliz Selim Effendi, who translated a work {16} of Bonnycastle[37] into Turkish.[38] This Englishman was Richard Baily, brother of Francis Baily[39] the astronomer, who emigrated to Turkey in his youth, and adopted the manners of the Turks, but whether their religion also I never heard, though I should suppose he did.

I now give the letters from the agricultural laborer and his friend, described on page 12, Vol. I. They are curiosities; and the history of the quadrature can never be well written without some specimens of this kind:

"Doctor Morgan, Sir. Permit me to address you

"Brute Creation may perhaps enjoy the faculty of beholding visible things with a more penitrating eye than ourselves. But Spiritual objects are as far out of their reach as though they had no being

"Nearest therefore to the brute Creation are those men who Suppose themselves to be so far governed by external objects as to believe nothing but what they See and feel And Can accomedate to their Shallow understanding and Imaginations

"My Dear Sir Let us all Consult ourselves by the wise proverb.

"I believe that evry man^s merit & ability aught to be appreciated and valued In proportion to its worth & utility

"In whatever State or Circumstances they may fortunately or unfortunately be placed

"And happy it is for evry man to know his worth and place

"When a Gentleman of your Standing in Society Clad with those honors Can not understand or Solve a problem That is explicitly explained by words and Letters and {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 knowledge of the unfair way that I am treated In my own nati County

"I am told and have reasons to believe that it is the Clergy that treat me so unjust.

"I am not Desirous of heaping Disonors upon my own nation. But if I have to Leave this kingdom without my Just dues. The world Shall know how I am and have been treated.

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

"1849 July 3."

"July 7th, 1849.

"Sir, I have been given to understand that a friend of mine one whom I shall never be ashamed to acknowledge as {18} such tho' lowly his origine; nay not only not ashamed but proud of doing so for I am one of those who esteem and respect a man according to his ability and probity, deeming with Dr. Watts 'that the mind is the standard of the man,'[40] has laid before you and asked your opinion of his extraordinary performance, viz. the quadrature of the circle, he did this with the firmest belief that you would not only treat the matter in a straightforward manner but with the conviction that from your known or supposed knowledge of mathematicks would have given an upright and honorable decision upon the subject; but the question is have you done so? Could I say yes I would with the greatest of pleasure and have congratulated you upon your decision whatever it might have been but I am sorry to say that I cannot your letter is a paltry evasion, you say 'that it is a great pity that you (Mr. ——) should have attempted this (the quadrature of the circle) for your mathematical knowledge is not sufficient to make you know in what the problem consists,' you don't say in what it does consist according to your ideas, oh! no nothing of the sort, you enter into no disquisition upon the subject in order to show where you think Mr. —— is wrong and why you have not is simply—because you cannot—you know that he has done it and what is if I am not wrongly informed you have been heard to say so. He has done what you nor any other mathematician as those who call themselves such have done. And what is the reason that you will not candidly acknowledge to him as you have to others that he has squared the circle shall I tell you? it is because he has performed the feat to obtain the glory of which mathematicians have battled from time immemorial that they might encircle their brows with a wreath of laurels far more glorious than ever conqueror won it is simply this that it is a poor man a {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 I gave it unhesitatingly in the affirmative and I am backed in my opinion not only by Mr. —— a mathematician and watchmaker residing in the boro of Southwark but by no less an authority than the Professor of mathematics of —— College —— —— United States Mr. —— and I presume that he at least is your equal as an authority and Mr. —— says that the government of the U.S. will recompense M. D. for the discovery he has made if so what a reflection upon Old england the boasted land of freedom the nursery of arts and sciences that her sons are obliged to go to a foreign country to obtain that recompense to which they are justly entitled

"In conclusion I had to contradict an assertion you made to the effect that 'there is not nor ever was any reward offered by the government of this country for the discovery of the quadrature of the circle.' I beg to inform you that there was but that it having been deemed an impossibility the government has withdrawn it. I do this upon no less an authority than the Marquis of Northampton.[41]

"I am, sir, yours ——"

"Dr. Morgan."


Notes on the Kinematic Effects of Revolution and Rotation, with reference to the Motions of the Moon and of the earth. By Henry Perigal, Jun. Esq. London, 1846-1849, 8vo.

On the misuse of technical terms. Ambiguity of the terms Rotation and Revolution, owing to the double meaning improperly {20} attributed to each of the words. (No date nor place, but by Mr. Perigal,[42] I have no doubt, and containing letters of 1849 and 1850.)

The moon controversy. Facts v. Definitions. By H. P., Jun. London, 1856, 8vo. (pp. 4.)

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


A poet appears in the field (July 19, 1863) who calls himself Cyclops, and writes four octavo pages. He makes a distinction between rotation and revolution; and his doctrines and phrases are so like those of Mr. Perigal that he is a follower at least. One of his arguments has so often been used that it is worth while to cite it:

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

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

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

The absurdity of the verses is in the argument. The writer was not so ignorant or so dishonest as to affirm that nothing had been offered by the other side as proof; accordingly, his syllogism amounts to this: If your proposition were true, you could have given proof satisfactory to me; but this you have not done, therefore, your proposition is not true.

The echoes of the moon-controversy reached Benares in 1857, in which year was there published a pamphlet "Does the Moon Rotate?" in Sanskrit and English. The {22} arguments are much the same as those of the discussion at home.


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

The word Christian (Vol. I, p. 248[46]) is an instance. When words begin, they carry their meanings. The Jews, who had their Messiah to come, and the followers of Jesus of Nazareth, who took Him for their Messiah, were both Christians (which means Messianites): the Jews would never have invented the term to signify Jesuans, nor would the disciples have invented such an ambiguous term for themselves; had they done so, the Jews would have disputed it, as they would have done in later times if they had had fair play. The Jews of our day, I see by their newspapers, speak of Jesus Christ as the Rabbi Joshua. But the {23} heathens, who knew little or nothing about the Jewish hope, would naturally apply the term Christians to the only followers of a Messiah of whom they had heard. For the Jesuans invaded them in a missionary way; while the Jews did not attempt, at least openly, to make proselytes.

All such words as Catholic, etc., are well enough as mere nomenclature; and the world falls for the most part, into any names which parties choose to give themselves. Silly people found inferences on this concession; and, as usually happens, they can cite some of their betters. St. Augustine,[47] a freakish arguer, or, to put it in the way of an old writer, lectorem ne multiloquii taedio fastidiat, Punicis quibusdam argutiis recreare solet,[48] asks, with triumph, to what chapel a stranger would be directed, if he inquired the way to the Catholic assembly. But the best exhibition of this kind in our own century is that made by the excellent Dr. John Milner,[49] in a work (first published in 1801 or 1802) which I suppose still circulates, "The End of Religious Controversy": a startling title which, so far as its truth is concerned, might as well have been "The floor of the bottomless pit." This writer, whom every one of his readers will swear to have been a worthy soul, though many, even of his own sect, will not admire some of his logic, speaks as follows:

"Letter xxv. On the true Church being Catholic. In treating of this third mark of the true Church, as expressed in our common creed, I feel my spirits sink within me, and I am almost tempted to throw away my pen in despair. For what chance is there of opening the eyes of candid Protestants to the other marks of the Church, if they are capable of keeping them shut to this? Every time they address the {24} God of Truth, either in solemn worship or in private devotion [stretch of rhetoric], they are forced, each of them, to repeat: I believe in THE CATHOLIC Church, and yet if I ask any of them the question: Are you a CATHOLIC? he is sure to answer me, No, I am a PROTESTANT! Was there ever a more glaring instance of inconsistency and self-condemnation among rational beings!"

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

He shortened his clause; and for a reason. If he had used the whole epithet which he knew so well, any one might have given his argument a half-turn. Had he written, as he ought, "the Holy Catholic Church" and then argued as above, some sly Protestant would have parodied him with "and yet if I ask any of them the question: Are you HOLY? he is sure to answer me No, I am a SINNER." To take the adjective from the Church, and apply it to the individual partisan, is recognized slipslop, but not ground of argument. If Dr. M. had asked his Protestant whether he belonged to the Catholic Church, the answer would have been Yes, but not to the Roman branch. When he put his question as he did, he was rightly answered and in his own division. This leaving out words is a common practice, especially when the omitter is in authority, and cannot be exposed. A year or two ago a bishop wrote a snubbing letter to a poor parson, who had complained that he was obliged, in burial, to send the worst of sinners to everlasting happiness. The bishop sternly said, "hope[50] is not assurance." {25} Could the clergyman have dared to answer, he would have said, "No, my Lord! but 'sure and certain hope' is as like assurance as a minikin man is like a dwarf." Sad to say, a theologian must be illogical: I feel sure that if you took the clearest headed writer on logic that ever lived, and made a bishop of him, he would be shamed by his own books in a twelvemonth.

Milner's sophism is glaring: but why should Dr. Milner be wiser than St. Augustine, one of his teachers? I am tempted to let out the true derivation of the word Catholic, as exclusively applied to the Church of Rome. All can find it who have access to the Rituale of Bonaventura Piscator[51] (lib. i. c. 12, de nomine Sacrae Ecclesiae, p. 87 of the Venice {26} folio of 1537). I am told that there is a Rituale in the Index Expurgatorius, but I have not thought it worth while to examine whether this be the one: I am rather inclined to think, as I have heard elsewhere, that the book was held too dangerous for the faithful to know of it, even by a prohibition: it would not surprise me at all if Roman Christians should deny its existence.[52]

It amuses me to give, at a great distance of time, a small Rowland for a small Oliver,[53] which I received, de par l'Eglise,[54] so far as lay in the Oliver-carrier more than twenty years ago. The following contribution of mine to Notes and Queries (3d Ser. vi. p. 175, Aug. 27, 1864) will explain what I say. There had been a complaint that a contributor had used the term Papist, which a very excellent dignitary of the Papal system pronounced an offensive term:


The term papist should be stripped of all except its etymological meaning, and applied to those who give the higher and final authority to the declaration ex cathedra[55] of the Pope. See Dr. Wiseman's[56] 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 {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 records of Johnson that he always used the words "dissenting teacher," refusing minister and clergyman to all but the recipients of episcopal ordination.

This distinctive phrase has been widely adopted: it occurs in the Index of 3d S. iv. [Notes and Queries]. Here we find "Platts (Rev. John), Unitarian teacher, 412;" the article indexed has "Unitarian minister."

This, of course is habit: an intentional refusal of the word minister would never occur in an index. I remember that, when I first read about Sam Johnson's little bit of exclusiveness, I said to myself: "Teacher? Teacher? surely I remember One who is often called teacher, but never minister or clergyman: have not the dissenters got the best of it?"

When I said that the Roman Church concedes the epithet Christians to Protestants, I did not mean that all its adherents do the same. There is, or was, a Roman newspaper, the Tablet, which, seven or eight years ago, was one of the most virulent of the party journals. In it I read, referring to some complaint of grievance about mixed marriages, that if Christians would marry Protestants they must take the consequences. My memory notes this well; because I recollected, when I saw it, that there was in the stable a horse fit to run in the curricle with this one. About seventeen years ago an Oxford M. A., who hated {28} mathematics like a genuine Oxonian of the last century, was writing on education, and was compelled to give some countenance to the nasty subject. He got out cleverly; for he gave as his reason for the permission, that man is an arithmetical, geometrical, and mechanical animal, as well as a rational soul.

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


The mention of Dr. Wiseman reminds me of another word, appropriated by Christians to themselves: fides;[59] the Roman faith is fides, and nothing else; and the adherents are fideles.[60] Hereby hangs a retort. When Dr. Wiseman was first in England, he gave a course of lectures in defence of his creed, which were thought very convincing by those who were already convinced. They determined to give him a medal, and there was a very serious discussion about the legend. Dr. Wiseman told me himself that he had answered to his subscribers that he would not have the medal at all unless—(naming some Italian authority, whom I forget) approved of the legend. At last pro fide vindicata[61] was chosen: this may be read either in a Popish or heretical sense. The feminine substantive fides means confidence, trust, (it is made to mean belief), but fidis, with the same ablative, fide, and also feminine, is a fiddle-string.[62] If a Latin writer had had to make a legend signifying "For the defence of the fiddle-string," he could not have done it otherwise, in the terseness of a legend, than by writing pro fide vindicata. Accordingly, when a Roman Christian talks to you of the faith, as a thing which is his and not yours, you may say fiddle. I have searched Bonaventura Piscator in vain for notice of this ambiguity. But the Greeks said fiddle; according to Suidas,[63] [Greek: skindapsos][64]—a word meaning a four stringed instrument played with a quill—was an exclamation of contemptuous dissent. How the wits of different races jump!


I am reminded of a case of fides vindicata, which, being in a public letter, responding to a public invitation, was not meant to be confidential. Some of the pupils of University College, in which all subdivisions of religion are (1866; were, 1867) on a level, have of course changed their views in after life, and become adherents of various high churches. On the occasion of a dinner of old students of the College, convened by circular, one of these students, whether then Roman or Tractarian Christian I do not remember, not content with simply giving negative answer, or none at all, concocted a jorum of theological rebuke, and sent it to the Dinner Committee. Heyday! said one of them, this man got out of bed backwards! How is that? said the rest. Why, read his name backwards, and you will see. As thus read it was—No grub![65]


To return to Notes and Queries. The substitution in the (editorial) index of "Unitarian teacher," for the contributor's "Unitarian minister," struck me very much. I have seldom found such things unmeaning. But as the journal had always been free from editorial sectarianisms,—and very apt to check the contributorial,—I could not be sure in this case. True it was, that the editor and publisher had been changed more than a year before; but this was not of much force. Though one swallow does not make a summer, I have generally found it show that summer is coming. However, thought I to myself, if this be Little Shibboleth, we shall have Big Shibboleth by-and-bye. At last it came. About a twelvemonth afterwards, (3d S. vii. p. 36) the following was the editorial answer to the question when the establishment was first called the "Church of England and Ireland":


"That unmeaning clause, 'The United Church of England and Ireland,' which occurs on the title-page of The Book of Common Prayer, was first used at the commencement of the present century. The authority for this phrase is the fifth article of the Union of 1800: 'That the Churches of England and Ireland be united into one Protestant (!) episcopal Church, to be called "The United Church of England and Ireland."' Of course, churchmen are not responsible for the theology of Acts of Parliament, especially those passed during the dark ages of the Georgian era."

That is to say, the journal gives its adhesion to the party which—under the assumed title of the Church of England—claims for the endowed corporation for the support of religion rights which Parliament cannot control, and makes it, in fact, a power above the State. The State has given an inch: it calls this corporation by the name of the "United Church of England and Ireland," as if neither England nor Ireland had any other Church. The corporation, accordingly aspires to an ell. But this the nation will only give with the aspiration prefixed. To illustrate my allusion in a delicate way to polite ears, I will relate what happened in a Johnian lecture-room at Cambridge, some fifty years ago, my informant being present. A youth of undue aspirations was giving a proposition, and at last said, "Let E F be produced to 'L':" "Not quite so far, Mr. ——," said the lecturer, quietly, to the great amusement of the class, and the utter astonishment of the aspirant, who knew no more than a Tractarian the tendency of his construction.

This word Church is made to have a very mystical meaning. The following dialogue between Ecclesiastes and Haereticus, which I cannot vouch for, has often taken place in spirit, if not in letter: E. The word Church ([Greek: ekklesia])[66] is never used in the New Testament except generally or locally for that holy and mystical body to which the sacraments and the ordinances of Christianity are entrusted. {32} H. Indeed! E. It is beyond a doubt (here he quoted half a dozen texts in support). H. Do you mean that any doctrine or ordinance which was solemnly practised by the [Greek: ekklesia] 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 [Greek: ekklesia] (Acts xix. 32, 41), at Ephesus; which any one might take to be true Church, by the more part not knowing wherefore they were come together, and which was dismissed, after one of the most sensible sermons ever preached, by the Recorder. E. I see your meaning: it is true, there is that one exception! H. Why, the Recorder's sermon itself contains another, the [Greek: ennomos ekklesia],[67] legislative assembly. E. Ah! the New Testament can only be interpreted by the Church! H. I see! the Church interprets itself into existence out of the New Testament, and then interprets the New Testament out of existence into itself!

I look upon all the Churches as fair game which declare of me that absque dubio in aeternum peribo;[68] not for their presumption towards God, but for their personal insolence towards myself. I find that their sectaries stare when I say this. Why! they do not speak of you in particular! These poor reasoners seem to think that there could be no meaning, as against me, unless it should be propounded that "without doubt he shall perish everlastingly, especially A. De Morgan." But I hold, with the schoolmen, that "Omnis homo est animal" in conjunction with "Sortes est homo" amounts to "Sortes est animal."[69] But they do not mean it personally! Every universal proposition is {33} personal to every instance of the subject. If this be not conceded, then I retort, in their own sense and manner, "Whosoever would serve God, before all things he must not pronounce God's decision upon his neighbor. Which decision, except every one leave to God himself, without doubt he is a bigoted noodle."

The reasoning habit of the educated community, in four cases out of five, permits universal propositions to be stated at one time, and denied, pro re nata,[70] at another. "Before we proceed to consider any question involving physical principles, we should set out with clear ideas of the naturally possible and impossible." The eminent man who said this, when wanting it for his views of mental education (!) never meant it for more than what was in hand, never assumed it in the researches which will give him to posterity! I have heard half-a-dozen defences of his having said this, not one of which affirmed the truth of what was said. A worthy clergyman wrote that if A. B. had said a certain thing the point in question would have been established. It was shown to him that A. B. had said it, to which the reply was a refusal to admit the point because A. B. said it in a second pamphlet and in answer to objections. And I might give fifty such instances with very little search. Always assume more than you want; because you cannot tell how much you may want: put what is over into the didn't-mean-that basket, or the extreme case what-not.


Something near forty years of examination of the theologies on and off—more years very much on than quite off—have given me a good title—to myself, I ask no one else for leave—to make the following remarks: A conclusion has premises, facts or doctrines from proof or authority, and mode of inference. There may be invention or {34} falsehood of premise, with good logic; and there may be tenable premise, followed by bad logic; and there may be both false premise and bad logic. The Roman system has such a powerful manufactory of premises, that bad logic is little wanted; there is comparatively little of it. The doctrine-forge of the Roman Church is one glorious compound of everything that could make Heraclitus[71] sob and Democritus[72] snigger. But not the only one. The Protestants, in tearing away from the Church of Rome, took with them a fair quantity of the results of the Roman forge, which they could not bring themselves to give up. They had more in them of Martin than of Jack. But they would have no premises, except from the New Testament; though some eked out with a few general Councils. The consequence is that they have been obliged to find such a logic as would bring the conclusions they require out of the canonical books. And a queer logic it is; nothing but the Roman forge can be compared with the Protestant loom. The picking, the patching, the piecing, which goes to the Protestant termini ad quem,[73] would be as remarkable to the general eye, as the Roman manufacture of termini a quo,[74] if it were not that the world at large seizes the character of an asserted fact better than that of a mode of inference. A grand step towards the deification of a lady, made by alleged revelation 1800 years after her death, is of glaring evidence: two or three additional shiffle-shuffles towards defence of saying the Athanasian curse in church and unsaying it out of church, are hardly noticed. Swift has bungled his satire where he makes Peter a party to finding out what he wants, totidem syllabis and totidem literis, {35} when he cannot find it totidem verbis[75] This is Protestant method: the Roman plan is viam faciam; the Protestant plan is viam inveniam.[76] The public at large begins to be conversant with the ways of wriggling out, as shown in the interpretations of the damnatory parts of the Athanasian Creed, the phrases of the Burial Service, etc. The time will come when the same public will begin to see the ways of wriggling in. But one thing at a time: neither Papal Rome nor Protestant Rome was built—nor will be pulled down—in a day.

The distinction above drawn between the two great antitheses of Christendom may be illustrated as follows. Two sets of little general dealers lived opposite to one another: all sold milk. Each vaunted its own produce: one set said that the stuff on the other side the way was only chalk and water; the other said that the opposites sold all sorts of filth, of which calves' brain was the least nasty. Now the fact was that both sets sold milk, and from the same dairy: but adulterated with different sorts of dirty water: and both honestly believed that the mixture was what they were meant to sell and ought to sell. The great difference between them, about which the apprentices fought each other like Trojans, was that the calves' brain men poured milk into the water, and the chalk men poured water into the milk. The Greek and Roman sects on one side, the Protestant sects on the other, must all have churches: the Greek and Roman sects pour the New Testament into their churches; the Protestant sects pour their churches into the New Testament. The Greek and Roman insist upon the New Testament being no more than part and parcel of their churches: the Protestant insist upon their churches being as much part and parcel of the New Testament. All dwell vehemently upon the doctrine that there must be milk {36} somewhere; and each says—I have it. The doctrine is true: and can be verified by any one who can and will go to the dairy for himself. Him will the several traders declare to have no milk at all. They will bring their own wares, and challenge a trial: they want nothing but to name the judges. To vary the metaphor, those who have looked at Christianity in open day, know that all who see it through painted windows shut out much of the light of heaven and color the rest; it matters nothing that the stains are shaped into what are meant for saints and angels.

But there is another side to the question. To decompose any substance, it must be placed between the poles of the battery. Now theology is but one pole; philosophy is the other. No one can make out the combinations of our day unless he read the writings both of the priest and the philosopher: and if any one should hold the first word offensive, I tell him that I mean both words to be significant. In reading these writings, he will need to bring both wires together to find out what it is all about. Time was when most priests were very explicit about the fate of philosophers, and most philosophers were very candid about their opinion of priests. But though some extremes of the old sorts still remain, there is now, in the middle, such a fusion of the two pursuits that a plain man is wofully puzzled. The theologian writes a philosophy which seems to tell us that the New Testament is a system of psychology; and the philosopher writes a Christianity which is utterly unintelligible as to the question whether the Resurrection be a fact or a transcendental allegory. What between the theologian who assents to the Athanasian denunciation in what seems the sense of no denunciation, and the philosopher who parades a Christianity which looks like no revelation, there is a maze which threatens to have the only possible clue in the theory that everything is something else, and nothing is anything at all. But this is a paradox far beyond my handling: it is a Budget of itself. {37}


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

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

If Religion and Philosophy be the two poles of a battery, whose is the battery Religion and Philosophy have been made the poles of? Is the change in the relation of the wires any presumption of a removal of the managers? We know pretty well who handled the instrument: has he resigned or been[77] turned out? Has he been put under {38} restriction? A fool may ask more questions than twenty sages can answer: but there is hope; for twenty sages cannot ask more questions than one reviewer can answer. I should like to see the opposite sides employed upon the question, What are the commoda, and what the pericula,[78] of the current approximation of Religion and Philosophy?

All this is very profane and irreverent! It has always been so held by those whose position demands such holding. To describe the Church as it is passes for assailing the Church as it ought to be with all who cannot do without it. In Bedlam[79] a poor creature who fancied he was St. Paul, was told by another patient that he was an impostor; the first maniac lodged a complaint against the second for calling St. Paul an impostor, which, he argued, with much appearance of sanity, ought not to be permitted in a well regulated madhouse. Nothing could persuade him that he had missed the question, which was whether he was St. Paul. The same thing takes place in the world at large. And especially must be noted the refusal to permit to the profane the millionth part of the licence assumed by the sacred. I give a sound churchman the epitaph of St. John Long; the usual pronunciation of whose name must be noted—

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

How shameful to pronounce this of the poor man! What, Mr. Orthodox! may I not do in joke to one pretender what {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 ancient men are brought to help the general cause. Only distant hints are given that by possibility it may end in the formation of all living organisms from a very few, if not from one. The better heads above mentioned know that their theory, if true, does not bear upon morals. The formation of solar systems from a nebular hypothesis, followed by organizations gradually emerging from some curious play of particles, nay, the very evolution of mind and thought from such an apparatus, are all as consistent with a Personal creative power to whom homage and obedience are due, and who has declared himself, as with a blind Nature of Things. A pure materialist, as to all things visible, may be even a bigotted Christian: this is not frequent, but it is possible. There is a proverb which says, A pig may fly, but it isn't a likely bird. But when the psychological speculator comes in, he often undertakes to draw inferences from the physical conclusions, by joining on his tremendous apparatus of a priori knowledge. He deduces that he can do without a God: he can deduce all things {40} without any such necessity. With Occam[81] and Newton he will have no more causes than are necessary to explain phenomena to him: and if by pure head-work combined with results of physical observation he can construct his universe, he must be a very unphilosophical man who would encumber himself with a useless Creator! There is something tangible about my method, says he; yours is vague. He requires it to be granted that his system is positive and that yours is impositive. So reasoned the stage coachman when the railroads began to depose him—"If you're upset in a stage-coach, why, there you are! but if you're upset on the railroad, where are you?" The answer lies in another question, Which is most positive knowledge, God deduced from man and his history, or the postulates of the few who think they can reason a priori on the tacit assumption of unlimited command of data?

We are not yet come to the existence of a school of philosophers who explicitly deny a Creator: but we are on the way, though common sense may interpose. There are always straws which show the direction of the wind. I have before me the printed letter of a medical man—to whose professional ability I have good testimony—who finds the vital principle in highly rarefied oxygen. With the usual logic of such thinkers, he dismisses the "eternal personal identity" because "If soul, spirit, mind, which are merely modes of sensation, be the attribute or function of nerve-tissue, it cannot possibly have any existence apart from its material organism!" How does he know this impossibility? If all the mind we know be from nerve-tissue, how does it appear that mind in other planets may not be another thing? Nay, when we come to possibilities, does not his own system give a queer one? If highly rarefied oxygen be vital power, more highly rarefied oxygen {41} may be more vital and more powerful. Where is this to stop? Is it impossible that a finite quantity, rarefied ad infinitum, may be an Omnipotent? Perhaps the true Genesis, when written, will open with "In the beginning was an imperial quart of oxygen at 60 deg. of Fahrenheit, and the pressure of the atmosphere; and this oxygen was infinitely rarefied; and this oxygen became God." For myself, my aspirations as to this system are Manichaean. The quart of oxygen is the Ormuzd, or good principle: another quart, of hydrogen, is the Ahriman, or evil principle! My author says that his system explains Freewill and Immortality so obviously that it is difficult to read previous speculations with becoming gravity. My deduction explains the conflict of good and evil with such clearness that no one can henceforward read the New Testament with becoming reverence. The surgeon whom I have described is an early bud which will probably be nipped by the frost and wither on the ground: but there is a good crop coming. Material pneuma is destined to high functions; and man is to read by gas-light.


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

The author says:

"I am satisfied that I have given the true laws constituting the Sun to be space; and I call upon those disposed to maintain the contrary, to give true laws showing him to be a body: until such can be satisfactorily established, I have an undoubted claim to the credit of my theory,—That the Sun is an Electric Space, fed and governed by the {42} planets, which have the property of attracting heat from it; and the means of supplying the necessary pabulum by their degenerated air driven off towards the central space—the wonderful alembic in which it becomes transmuted to the revivifying necessities of continuous action; and the central space or Sun being perfectly electric, has the counter property of repulsing the bodies that attract it. How wonderful a conception! How beautiful, how magnificent an arrangement!

"O Centre! O Space! O Electric Space!"


1849. Joseph Ady[83] is entitled to a place in this list of discoverers: his great fault, like that of some others, lay in pushing his method too far. He began by detecting unclaimed dividends, and disclosing them to their right owners, exacting his fee before he made his communication. He then generalized into trying to get fees from all of the name belonging to a dividend; and he gave mysterious hints of danger impending. For instance, he would write to a clergyman that a legal penalty was hanging over him; and when the alarmed divine forwarded the sum required for disclosure, he was favored with an extract from some old statute or canon, never repealed, forbidding a clergyman to be a member of a corporation, and was reminded that he had insured his life in the —— Office, which had a royal charter. He was facetious, was Joseph: he described himself in his circulars as "personally known to Sir Peter Laurie[84] and all other aldermen"; which was nearly true, {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 displeased him by a decision, his circulars of 1849 contain the following:

"Should you have cause to complain of any party, Sir J. Duke has contrived a new law of evidence, viz., write to him, he will consider your letter sufficient proof, and make the parties complained of pay without judge or jury, and will frank you from every expense."

I strongly suspect that Joseph Ady believed in himself.

He sometimes issued a second warning, of a Sibylline character:

"Should you find cause to complain of anybody, my voluntary referee, the Rt. Hon. Sir Peter Laurie, Kt., perpetual Deputy Lord Mayor, will see justice done you without any charge whatever: he and his toady, — —— ——. The accursed of Moses can hang any man: thus, by catching him alone and swearing Naboth spake evil against God and the King. Therefore (!) I admit no strangers to a personal conference without a prepayment of 20s. each. Had you attended to my former notice you would have received twice as much: neglect this and you will lose all."


Zadkiel's Almanac for 1849. Nineteenth number.

Raphael's Prophetic Almanac for 1849. Twenty-ninth number.

Reasons for belief in judicial astrology, and remarks on the dangerous character of popish priestcraft. London, 1849, 12mo.

Astronomy in a nutshell: or the leading problems of the solar system solved by simple proportion only, on the theory of magnetic attraction. By Lieut. Morrison,[85] N. N. London (s. a.) 12mo.


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

1850. A letter in the handwriting of an educated man, dated from a street in which it must be taken that educated persons live, is addressed to the Secretary of the {45} Astronomical Society about a matter on which the writer says "his professional pursuit will enable him to give a satisfactory reply." In a question before a court of law it is sworn on one side that the moon was shining at a certain hour of a certain night on a certain spot in London; on the other side it is affirmed that she was clouded. The Secretary is requested to decide. This is curious, as the question is not astrological. Persons still send to Greenwich, now and then, to have their fortunes told. In one case, not very many years ago, a young gentleman begged to know who his wife was to be, and what fee he was to remit.

Sometimes the astronomer turns conjurer for fun, and his prophesies are fulfilled. It is related of Flamsteed[87] that an old woman came to know the whereabouts of a bundle of linen which had strayed. Flamsteed drew a circle, put a square into it, and gravely pointed out a ditch, near her cottage, in which he said it would be found. He meant to have given the woman a little good advice when she came back: but she came back in great delight, with the bundle in her hand, found in the very place. The late Baron Zach[88] received a letter from Pons,[89] a successful finder of comets, complaining that for a certain period he had found no comets, though he had searched diligently. Zach, a man of much sly humor, told him that no spots had been seen on the sun for about the same time—which was true,—and assured him that when the spots came back, the comets would come with them. Some time after he got a letter {46} from Pons, who informed him with great satisfaction that he was quite right, that very large spots had appeared on the sun, and that he had found a fine comet shortly after. I do not vouch for the first story, but I have the second in Zach's handwriting. It would mend the joke exceedingly if some day a real relation should be established between comets and solar spots: of late years good reason has been shown for advancing a connection between these spots and the earth's magnetism.[90] If the two things had been put to Zach, he would probably have chosen the comets. Here is a hint for a paradox: the solar spots are the dead comets, which have parted with their light and heat to feed the sun, as was once suggested. I should not wonder if I were too late, and the thing had been actually maintained. My list does not contain the twentieth part of the possible whole.

The mention of coincidences suggests an everlasting source of explanations, applicable to all that is extraordinary. The great paradox of coincidence is that of Leibnitz, known as the pre-established harmony, or law of coincidences, by which, separately and independently, the body receives impressions, and the mind proceeds as if it had perceived them from without. Every sensation, and the consequent state of the soul, are independent things coincident in time by the pre-established law. The philosopher could not otherwise account for the connection of mind and matter; and he never goes by so vulgar a rule as Whatever is, is; to him that which is not clear as to how, is not at all. Philosophers in general, who tolerate each other's theories much better than Christians do each other's failings, seldom revive Leibnitz's fantasy: they seem to act upon the maxim quoted by Father Eustace[91] from the {47} Decretals, Facinora ostendi dum puniuntur, flagitia autem abscondi debent.[92]

The great ghost-paradox, and its theory of coincidences, will rise to the surface in the mind of every one. But the use of the word coincidence is here at variance with its common meaning. When A is constantly happening, and also B, the occurrence of A and B at the same moment is the mere coincidence which may be casualty. But the case before us is that A is constantly happening, while B, when it does happen, almost always happens with A, and very rarely without it. That is to say, such is the phenomenon asserted: and all who rationally refer it to casualty, affirm that B is happening very often as well as A, but that it is not thought worthy of being recorded except when A is simultaneous. Of course A is here a death, and B the spectral appearance of the person who dies. In talking of this subject it is necessary to put out of the question all who play fast and loose with their secret convictions: these had better give us a reason, when they feel internal pressure for explanation, that there is no weathercock at Kilve; this would do for all cases. But persons of real inquiry will see that first, experience does not bear out the asserted frequency of the spectre, without the alleged coincidence of death: and secondly, that if the crowd of purely casual spectres were so great that it is no wonder that, now and then the person should have died at or near the moment, we ought to expect a much larger proportion of cases in which the spectre should come at the moment of the death of one or another of all the cluster who are closely connected with the original of the spectre. But this, we know, is almost without example. It remains then, for all, who speculate at all, to look upon the asserted phenomenon, think what they may of it, the thing which is to be explained, as a connection in time of the death, and the {48} simultaneous appearance of the dead. Any person the least used to the theory of probabilities will see that purely casual coincidence, the wrong spectre being comparatively so rare that it may be said never to occur, is not within the rational field of possibility.

The purely casual coincidence, from which there is no escape except the actual doctrine of special providences, carried down to a very low point of special intention, requires a junction of the things the like of each of which is always happening. I will give three instances which have occurred to myself within the last few years: I solemnly vouch for the literal truth of every part of all three:

In August 1861, M. Senarmont,[93] of the French Institute, wrote to me to the effect that Fresnel[94] had sent to England, in or shortly after 1824, a paper for translation and insertion in the European Review, which shortly afterwards expired. The question was what had become of that paper. I examined the Review at the Museum, found no trace of the paper, and wrote back to that effect at the Museum, adding that everything now depended on ascertaining the name of the editor, and tracing his papers: of this I thought there was no chance. I posted this letter on my way home, at a Post Office in the Hampstead Road at the junction with Edward Street, on the opposite side of which is a bookstall. Lounging for a moment over the exposed books, sicut meus est mos,[95] I saw, within a few minutes of the posting of the letter, a little catch-penny book of anecdotes of Macaulay, which I bought, and ran over for a minute. My eye was soon caught by this sentence: "One of the young fellows immediately wrote to the editor (Mr. Walker) {49} of the European Review." I thus got the clue by which I ascertained that there was no chance of recovering Fresnel's paper. Of the mention of current reviews, not one in a thousand names the editor.

In the summer of 1865 I made my first acquaintance with the tales of Nathaniel Hawthorne, and the first I read was about the siege of Boston in the War of Independence. I could not make it out: everybody seemed to have got into somebody else's place. I was beginning the second tale, when a parcel arrived: it was a lot of old pamphlets and other rubbish, as he called it, sent by a friend who had lately sold his books, had not thought it worth while to send these things for sale, but thought I might like to look at them and possibly keep some. The first thing I looked at was a sheet which, being opened, displayed "A plan of Boston and its environs, shewing the true situation of his Majesty's army and also that of the rebels, drawn by an engineer, at Boston Oct. 1775." Such detailed plans of current sieges being then uncommon, it is explained that "The principal part of this plan was surveyed by Richard Williams, Lieutenant at Boston; and sent over by the son of a nobleman to his father in town, by whose permission it was published." I immediately saw that my confusion arose from my supposing that the king's troops were besieging the rebels, when it was just the other way.

April 1, 1853, while engaged in making some notes on a logical point, an idea occurred which was perfectly new to me, on the mode of conciliating the notions omnipresence and indivisibility into parts. What it was is no matter here: suffice it that, since it was published elsewhere (in a paper on Infinity, Camb. Phil. Trans. vol. xi. p. 1) I have not had it produced to me. I had just finished a paragraph on the subject, when a parcel came in from a bookseller containing Heywood's[96] Analysis of Kant's Critick, 1844.

{50} On turning over the leaves I found (p. 109) the identical thought which up to this day, I only know as in my own paper, or in Kant. I feel sure I had not seen it before, for it is in Kant's first edition, which was never translated to my knowledge; and it does not appear in the later editions. Mr. Heywood gives some account of the first edition.

In the broadsheet which gave account of the dying scene of Charles II, it is said that the Roman Catholic priest was introduced by P. M. A. C. F. The chain was this: the Duchess of Portsmouth[97] applied to the Duke of York, who may have consulted his Cordelier confessor, Mansuete, about procuring a priest, and the priest was smuggled into the king's room by the Duchess and Chiffinch.[98] Now the letters are a verbal acrostic of Pere Mansuete a Cordelier Friar, and a syllabic acrostic of PortsMouth and ChifFinch. This is a singular coincidence. Macaulay adopted the first interpretation, preferring it to the second, which I brought before him as the conjecture of a near relative of my own. But Mansuete is not mentioned in his narrative: it may well be doubted whether the writer of a broadside for English readers would use 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 {51} survivors, at the taking of Pondicherry, Captain John Fletcher, Captain De Morgan, and Lieutenant Bosanquet, each distinctly foretold his own death on the morning of his fate." I have no doubt of all three; and I knew it of my grandfather long before I read the above passage. He saw that the battery he commanded was unduly exposed: I think by the sap running through the fort when produced. He represented this to the engineer officers, and to the commander-in-chief; the engineers denied the truth of the statement, the commander believed them, my grandfather quietly observed that he must make his will, and the French fulfilled his prediction. His will bore date the day of his death; and I always thought it more remarkable than the fulfilment of the prophecy that a soldier should not consider any danger short of one like the above, sufficient reason to make his will. I suppose the other officers were similarly posted. I am told that military men very often defer making their wills until just before an action: but to face the ordinary risks intestate, and to wait until speedy death must be the all but certain consequence of a stupid mistake, is carrying the principle very far. In the matter of coincidences there are, as in other cases, two wonderful extremes with every intermediate degree. At one end we have the confident people who can attribute anything to casual coincidence; who allow Zadok Imposture and Nathan Coincidence to anoint Solomon Selfconceit king. At the other end we have those who see something very curious in any coincidence you please, and whose minds yearn for a deep reason. A speculator of this class happened to find that Matthew viii. 28-33 and Luke viii. 26-33 contain the same account, that of the demons entering into the swine. Very odd! chapters tallying, and verses so nearly: is the versification rightly managed? Examination is sure to show that there are monstrous inconsistencies in the mode of division, which being corrected, the verses tally as well as the chapters. And then how comes it? I cannot go on, {52} for I have no gift at torturing a coincidence, but I would lay twopence, if I could make a bet—which I never did in all my life—that some one or more of my readers will try it. Some people say that the study of chances tends to awaken a spirit of gambling: I suspect the contrary. At any rate, I myself, the writer of a mathematical book and a comparatively popular book, have never laid a bet nor played for a stake, however small: not one single time.

It is useful to record such instances as I have given, with precision and on the solemn word of the recorder. When such a story as that of Flamsteed is told, a priori assures us that it could not have been: the story may have been a ben trovato,[99] but not the bundle. It is also useful to establish some of the good jokes which all take for inventions. My friend Mr. J. Bellingham Inglis,[100] before 1800, saw the tobacconist's carriage with a sample of tobacco in a shield, and the motto Quid rides[101] (N. & Q., 3d S. i. 245). His father was able to tell him all about it. The tobacconist was Jacob Brandon, well known to the elder Mr. Inglis, and the person who started the motto, the instant he was asked for such a thing, was Harry Calender of Lloyd's, a scholar and a wit. My friend Mr. H. Crabb Robinson[102] remembers the King's Counsel (Samuel Marryat) who took the motto Causes produce effects, when his success enabled him to start a carriage.

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