REPRINTED WITH THE AUTHOR'S ADDITIONS FROM THE ATHENAEUM

SECOND EDITION EDITED BY DAVID EUGENE SMITH

WITH A NEW INTRODUCTION BY ERNEST NAGEL

PROFESSOR OF PHILOSOPHY, COLUMBIA UNIVERSITY

UNABRIDGED EDITION—TWO VOLUMES BOUND AS ONE

DOVER PUBLICATIONS, INC., NEW YORK

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

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

[1]

ON SOME PHILOSOPHICAL ATHEISTS.

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

It is commonly said that the last words of Laplace were, "Ce que nous connaissons est peu de chose; ce que nous ignorons est immense."^[4] This looks like a parody on Newton's pebbles:^[5] the following is the true account; it comes to me through one remove from Poisson.^[6] After the publication (in 1825) of the fifth volume of the Mécanique Céleste, Laplace became gradually weaker, and with it musing and abstracted. He thought much on the great problems of existence, and often muttered to himself, Qu'est ce que c'est que tout cela!^[7] After many alternations, he appeared at last so permanently prostrated that his family applied to his favorite pupil, M. Poisson, to try to get a word from him. Poisson paid a visit, and after a few words of salutation, said, "J'ai une bonne nouvelle à vous annoncer: on a reçu au Bureau des Longitudes une lettre d'Allemagne annonçant que M. Bessel a vérifié par l'observation vos découvertes théoriques sur les satellites de Jupiter."^[8] Laplace opened his eyes and answered with deep [3]gravity, "L'homme ne poursuit que des chimères."^[9] He never spoke again. His death took place March 5, 1827.

The language used by the two great geometers illustrates what I have said: a supreme and guiding intelligence—apart from a blind rule called nature of things—was an hypothesis. The absolute denial of such a ruling power was not in the plan of the higher philosophers: it was left for the smaller fry. A round assertion of the non-existence of anything which stands in the way is the refuge of a certain class of minds: but it succeeds only with things subjective; the objective offers resistance. A philosopher of the appropriative class tried it upon the constable who appropriated him: I deny your existence, said he; Come along all the same, said the unpsychological policeman.

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

ROTATION OF THE MOON.

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.

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

[7]

Against the moon's rotation on her axis.

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.

EARLY IDEAS OF AVIATION.

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:

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]

THE SECRET OF THE UNIVERSE DIVULGED.

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.

THE TRISECTION AND QUADRATURE AGAIN.

"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.

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

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

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

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

This the Athenæum published—but without some Italics, for which the editor was sharply reproved, as a sufficient [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.

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.

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:

which is certainly false.^[34]

[14]

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

divided by the square root of

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° or 180°.

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

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

Early in the century there was a Turkish trisector of the angle, Hussein Effendi, who published two methods. He was the father of Ameen Bey, who was well known in England thirty years ago as a most amiable and cultivated gentleman and an excellent mathematician. He was then a student at Cambridge; and he died, years ago, in command of the army in Syria. Hussein Effendi was instructed in mathematics by Ingliz Selim Effendi, who translated a work [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

"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.

"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]

"Dr. Morgan."

THE MOON'S ROTATION.

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

[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 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:

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:

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.

ON THE NAMES OF RELIGIOUS BODIES.

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

The word Christian (Vol. I, p. 248^[46]) is an instance. When words begin, they carry their meanings. The Jews, who had their Messiah to come, and the followers of Jesus of Nazareth, who took Him for their Messiah, were both Christians (which means Messianites): the Jews would never have invented the term to signify Jesuans, nor would the disciples have invented such an ambiguous term for themselves; had they done so, the Jews would have disputed it, as they would have done in later times if they had had fair play. The Jews of our day, I see by their newspapers, speak of Jesus Christ as the Rabbi Joshua. But the [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 tædio fastidiat, Punicis quibusdam argutiis recreare solet,^[48] asks, with triumph, to what chapel a stranger would be directed, if he inquired the way to the Catholic assembly. But the best exhibition of this kind in our own century is that made by the excellent Dr. John Milner,^[49] in a work (first published in 1801 or 1802) which I suppose still circulates, "The End of Religious Controversy": a startling title which, so far as its truth is concerned, might as well have been "The floor of the bottomless pit." This writer, whom every one of his readers will swear to have been a worthy soul, though many, even of his own sect, will not admire some of his logic, speaks as follows:

"Letter xxv. On the true Church being Catholic. In treating of this third mark of the true Church, as expressed in our common creed, I feel my spirits sink within me, and I am almost tempted to throw away my pen in despair. For what chance is there of opening the eyes of candid Protestants to the other marks of the Church, if they are capable of keeping them shut to this? Every time they address the [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!"

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 Sacræ Ecclesiæ, 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:

PAPIST.

The term papist should be stripped of all except its etymological meaning, and applied to those who give the higher and final authority to the declaration ex cathedrâ^[55] of the Pope. See Dr. Wiseman's^[56] article, Catholic Church, in the Penny Cyclopædia.

What is one to do about these names? First, it is clear that offence should, when possible, be avoided: secondly, no one must be required to give a name which favors any assumption made by those to whom it is given, and not [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.

[29]

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

[30]

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

THE WORD CHURCH.

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

[31]

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

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

This word Church is made to have a very mystical meaning. The following dialogue between Ecclesiastes and Hæreticus, which I cannot vouch for, has often taken place in spirit, if not in letter: E. The word Church (ἐκκλησια)^[66] is never used in the New Testament except generally or locally for that holy and mystical body to which the sacraments and the ordinances of Christianity are entrusted. [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 ἐκκλησια is binding upon you and me? E. Certainly, unless we should be cut off from the congregation of the faithful. H. Have you a couple of hours to spare? E. What for? H. If you have, I propose we spend them in crying, Great is Diana of the Ephesians! E. What do you mean? H. You ought to know the solemn service of the ἐκκλησια (Acts xix. 32, 41), at Ephesus; which any one might take to be true Church, by the more part not knowing wherefore they were come together, and which was dismissed, after one of the most sensible sermons ever preached, by the Recorder. E. I see your meaning: it is true, there is that one exception! H. Why, the Recorder's sermon itself contains another, the ἐννομος ἐκκλησια,^[67] legislative assembly. E. Ah! the New Testament can only be interpreted by the Church! H. I see! the Church interprets itself into existence out of the New Testament, and then interprets the New Testament out of existence into itself!

I look upon all the Churches as fair game which declare of me that absque dubio in æternum peribo;^[68] not for their presumption towards God, but for their personal insolence towards myself. I find that their sectaries stare when I say this. Why! they do not speak of you in particular! These poor reasoners seem to think that there could be no meaning, as against me, unless it should be propounded that "without doubt he shall perish everlastingly, especially A. De Morgan." But I hold, with the schoolmen, that "Omnis homo est animal" in conjunction with "Sortes est homo" amounts to "Sortes est animal."^[69] But they do not mean it personally! Every universal proposition is [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.

PROTESTANT AND PAPAL CHRISTENDOM.

Something near forty years of examination of the theologies on and off—more years very much on than quite off—have given me a good title—to myself, I ask no one else for leave—to make the following remarks: A conclusion has premises, facts or doctrines from proof or authority, and mode of inference. There may be invention or [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.

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 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—

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° of Fahrenheit, and the pressure of the atmosphere; and this oxygen was infinitely rarefied; and this oxygen became God." For myself, my aspirations as to this system are Manichæan. The quart of oxygen is the Ormuzd, or good principle: another quart, of hydrogen, is the Ahriman, or evil principle! My author says that his system explains Freewill and Immortality so obviously that it is difficult to read previous speculations with becoming gravity. My deduction explains the conflict of good and evil with such clearness that no one can henceforward read the New Testament with becoming reverence. The surgeon whom I have described is an early bud which will probably be nipped by the frost and wither on the ground: but there is a good crop coming. Material pneuma is destined to high functions; and man is to read by gas-light.

THE SUN AN ELECTRIC SPACE.

The 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!"

JOSEPH ADY.

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

ON MODERN ASTROLOGY.

[44]

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 Père Mansuete a Cordelier Friar, and a syllabic acrostic of PortsMouth and ChifFinch. This is a singular coincidence. Macaulay adopted the first interpretation, preferring it to the second, which I brought before him as the conjecture of a near relative of my own. But Mansuete is not mentioned in his narrative: it may well be doubted whether the writer of a broadside for English readers would use Père instead of Father. And the person who really "reminded" the Duke of "the duty he owed to his brother," was the Duchess and not Mansuete. But my affair is only with the coincidence.

But there are coincidences which are really connected without the connection being known to those who find in them matter of astonishment. Presentiments furnish marked cases: sometimes there is no mystery to those who have the clue. In the Gentleman's Magazine (vol. 80, part 2, p. 33) we read, the subject being presentiment of death, as follows: "In 1778, to come nearer the recollection of [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.

The coincidences of errata are sometimes very remarkable: it may be that the misprint has a sting. The death of Sir W. Hamilton^[103] of Edinburgh was known in London on a Thursday, and the editor of the Athenæum wrote to [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 reasons for believing in my entire innocence. Of course I could not see a proof: and two errata occurred. The words "addition to Stewart"^[104] require "for addition to read edition of." This represents what had been insisted on by the Edinburgh publisher, who, frightened by the edition of Reid,^[105] had stipulated for a simple reprint without notes. Again "principles of logic and mathematics" required "for mathematics read metaphysics." No four words could be put together which would have so good a title to be Hamilton's motto.

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

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 [54]pass for Irving's^[106] preaching—though a person to whom it was presented as such would say that most likely the head and tail would make something more like head and tail of it—we are astounded by a declaration from the Holy Spirit, speaking of himself, that he is "not ashamed of the Gospel of Christ." It would be long before we should find in educated rhapsody—of which there are specimens enough—such a thing as a person of the Trinity taking merit for moral courage enough to stand where St. Peter fell. The following declaration comes next—"I will judge between cattle and cattle, that use their tongues."

THE FIGURE OF THE EARTH.

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?

PERPETUAL MOTION.

1851. The following letter was written by one of a class of persons whom, after much experience of them, I [55]do not pronounce insane. But in this case the second sentence gives a suspicion of actual delusion of the senses; the third looks like that eye for the main chance which passes for sanity on the Stock Exchange and elsewhere:

15th Sept. 1851.

"Gentlemen,—I pray you take steps to make known that yesterday I completed my invention which will give motion to every country on the Earth;—to move Machinery!—the long sought in vain 'Perpetual Motion'!!—I was supported at the time by the Queen and H.R.H. Prince Albert. If, Gentlemen, you can advise me how to proceed to claim the reward, if any is offered by the Government, or how to secure the Patent for the machine, or in any way assist me by advice in this great work, I shall most graciously acknowledge your consideration.

These are my convictions that my SEVERAL discoveries will be realized: and this great one can be at once acted upon: although at this moment it only exists in my mind, from my knowledge of certain fixed principles in nature:—the Machine I have not made, as I only completed the discovery YESTERDAY, Sunday!

ON SPIRITUALISM.

I have several books on that great paradox of our day, Spiritualism, but I shall exclude all but three. The bibliography of this subject is now very large. The question is one both of evidence and speculation;—Are the facts [56]true? Are they caused by spirits? These I shall not enter upon: I shall merely recommend this work as that of a spiritualist who does not enter on the subject, which he takes for granted, but applies his derived views to the history of mankind with learning and thought. Mr. Smith was a man of a very peculiar turn of thinking. He was, when alive, the editor, or an editor, of the Family Herald: I say when alive, to speak according to knowledge; for, if his own views be true, he may have a hand in it still. The answers to correspondents, in his time, were piquant and original above any I ever saw. I think a very readable book might be made out of them, resembling "Guesses at Truth:" the turn given to an inquiry about morals, religion, or socials, is often of the highest degree of unexpectedness; the poor querist would find himself right in a most unpalatable way.

Answers to correspondents, in newspapers, are very often the fag ends of literature. I shall never forget the following. A person was invited to name a rule without exception, if he could: he answered "A man must be present when he is shaved." A lady—what right have ladies to decide questions about shaving?—said this was not properly a rule; and the oracle was consulted. The editor agreed with the lady; he said that "a man must be present when he is shaved" is not a rule, but a fact.

[Among my anonymous communicants is one who states that I have done injustice to the Rev. James Smith in "referring to him as a spiritualist," and placing his "Divine Drama" among paradoxes: "it is no paradox, nor do spiritualistic views mar or weaken the execution of the design." Quite true: for the design is to produce and enforce "spiritualistic views"; and leather does not mar nor weaken a shoemaker's plan. I knew Mr. Smith well, and have often talked to him on the subject: but more testimony from me is unnecessary; his book will speak for itself. [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 England, it is evident that no country in the world is better prepared for the great Battle of Opinion. Where else can the battle be fought but where the armies are arrayed? And here they all are, Greek, Roman, Anglican, Scotch, Lutheran, Calvinist, Established and Territorial, with Baronial Bishops, and Nonestablished of every grade—churches with living prophets and apostles, and churches with dead prophets and apostles, and apostolical churches without apostles, and philosophies without either prophets or apostles, and only wanting one more, 'the Christian Church,' like Aaron's rod, to swallow up and digest them all, and then bud and flourish. As if to prepare our minds for this desirable and inevitable consummation, different parties have been favored with a revival of that very spirit of revelation by which the Church itself was originally founded. There is a complete series of spiritual revelations in England and the United States, besides mesmeric phenomena that bear a resemblance to revelation, and thus gradually open the mind of the philosophical and infidel classes, as well as the professed believers of that old revelation which they never witnessed in living action, to a better understanding of that Law of Nature (for it is a Law of Nature) in which all revelation originates and by which its spiritual communications are regulated."

Mr. Smith proceeds to say that there are only thirty-five incorporated churches in England, all formed from the New Testament except five, to each of which five he concedes a revelation of its own. The five are the Quakers, the Swedenborgians, the Southcottians, the Irvingites, and the Mormonites. Of Joanna Southcott he speaks as follows: [58]

(P. 592.) "Joanna Southcott^[109] is not very gallantly treated by the gentlemen of the Press, who, we believe, without knowing anything about her, merely pick up their idea of her character from the rabble. We once entertained the same rabble idea of her; but having read her works—for we really have read them—we now regard her with great respect. However, there is a great abundance of chaff and straw to her grain; but the grain is good, and as we do not eat either the chaff or straw if we can avoid it, nor even the raw grain, but thrash it and winnow it, and grind it and bake it, we find it, after undergoing this process, not only very palatable, but a special dainty of its kind. But the husk is an insurmountable obstacle to those learned and educated gentlemen who judge of books entirely by the style and the grammar, or those who eat grain as it grows, like the cattle. Such men would reject all prological revelation; for there never was and probably never will be a revelation by voice and vision communicated in classical manner. It would be an invasion of the rights and prerogatives of Humanity, and as contrary to the Divine and Established order of mundane government, as a field of quartern loaves or hot French rolls."

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

A CONDENSED HISTORY OF MATHEMATICS.

I cut the following from a Sunday paper in 1849:

"X. Y.—The Chaldeans began the mathematics, in which the Egyptians excelled. Then crossing the sea, by means [59]of Thales,^[110] the Milesian, they came into Greece, where they were improved very much by Pythagoras,^[111] Anaxagoras,^[112] and Anopides^[113] of Chios. These were followed by Briso,^[114] Antipho, [two circle-squarers; where is Euclid?] and Hippocrates,^[115] but the excellence of the algebraic art was begun by Geber,^[116] an Arabian astronomer, and was carried on by Cardanus,^[117] Tartaglia,^[118] Clavius,^[119], Stevinus,^[120] Ghetaldus,^[121] Herigenius,^[122] Fran. Van Schooten [meaning Francis Van Schooten^[123]], Florida de Beaume,^[124] etc."

Bryso was a mistaken man. Antipho had the disadvantage of being in advance of his age. He had the notion of which the modern geometry has made so much, that of [60]a circle being the polygon of an infinitely great number of sides. He could make no use of it, but the notion itself made him a sophist in the eyes of Aristotle, Eutocius,^[125] etc. Geber, an Arab astronomer, and a reputed conjurer in Europe, seems to have given his name to unintelligible language in the word gibberish. At one time algebra was traced to him; but very absurdly, though I have heard it suggested that algebra and gibberish must have had one inventor.

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

ST. VITUS, PATRON OF CYCLOMETERS.

I have looked for St. Vitus in catalogues of saints, but never found his legend, though he figures as a day-mark in the oldest almanacs. He must be properly accredited, since he was an archpriest. And I pronounce and ordain, by right accruing from the trouble I have taken in this subject, that he, St. Vitus, who leads his votaries a never-ending and unmeaning dance, shall henceforth be held and taken to be the patron saint of the circle-squarer. His day is the 15th of June, which is also that of St. Modestus,^[129] with whom the said circle-squarer often has nothing to do. And he must not put himself under the first saint with a slantendicular reference to the other, as is much to be feared was done by the Cardinal who came to govern England with a title containing St. Pudentiana,^[130] who shares a day with St. Dunstan. The Archpriest of St. Vitus will have it that the square inscribed in a semicircle is half of the semicircle, or the circumference 3-1/5 diameters. He is active and able, with [62]nothing wrong about him except his paradoxes. In the second tract named he has given the testimonials of crowned heads and ministers, etc. as follows. Louis-Napoleon gives thanks. The minister at Turin refers it to the Academy of Sciences, and hopes so much labor will be judged degna di pregio.^[131] The Vice-Chancellor of Oxford—a blunt Englishman—begs to say that the University has never proposed the problem, as some affirm. The Prince Regent of Baden has received the work with lively interest. The Academy of Vienna is not in a position to enter into the question. The Academy of Turin offers the most distinct thanks. The Academy della Crusca attends only to literature, but gives thanks. The Queen of Spain has received the work with the highest appreciation. The University of Salamanca gives infinite thanks, and feels true satisfaction in having the book. Lord Palmerston gives thanks, by the hand of "William San." The Viceroy of Egypt, not being yet up in Italian, will spend his first moments of leisure in studying the book, when it shall have been translated into French: in the mean time he congratulates the author upon his victory over a problem so long held insoluble. All this is seriously published as a rate in aid of demonstration. If these royal compliments cannot make the circumference of a circle about 2 per cent. larger than geometry will have it —which is all that is wanted—no wonder that thrones are shaky.

I am informed that the legend of St. Vitus is given by Ribadeneira^[132] in his lives of Saints, and that Baronius,^[133] in [63]his Martyrologium Romanum, refers to several authors who have written concerning him. There is an account in Mrs. Jameson's^[134] History of Sacred and Legendary Art (ed. of 1863, p. 544). But it seems that St. Vitus is the patron saint of all dances; so that I was not so far wrong in making him the protector of the cyclometers. Why he is represented with a cock is a disputed point, which is now made clear: next after gallus gallinaceus^[135] himself, there is no crower like the circle-squarer.

CELEBRATED APPROXIMATIONS OF π.

The following is an extract from the English Cyclopædia, Art. Tables:

"1853. William Shanks,^[136] Contributions to Mathematics, comprising chiefly the Rectification of the Circle to 607 Places of Tables, London, 1853. (Quadrature of the Circle.) Here is a table, because it tabulates the results of the subordinate steps of this enormous calculation as far as 527 decimals: the remainder being added as results only during the printing. For instance, one step is the calculation of the reciprocal of 601.5⁶⁰¹; and the result is given. The number of pages required to describe these results is 87. Mr. Shanks has also thrown off, as chips or splinters, the values of the base of Napier's logarithms, and of its logarithms of 2, 3, 5, 10, to 137 decimals; and the value of the modulus .4342 ... to 136 decimals: with the 13th, 25th, 37th ... up to the 721st powers of 2. These tremendous stretches of calculation—at least we so call them in our day—are useful in several respects; they prove more than [64]the capacity of this or that computer for labor and accuracy; they show that there is in the community an increase of skill and courage. We say in the community: we fully believe that the unequalled turnip which every now and then appears in the newspapers is a sufficient presumption that the average turnip is growing bigger, and the whole crop heavier. All who know the history of the quadrature are aware that the several increases of numbers of decimals to which π has been carried have been indications of a general increase in the power to calculate, and in courage to face the labor. Here is a comparison of two different times. In the day of Cocker,^[137] the pupil was directed to perform a common subtraction with a voice-accompaniment of this kind: '7 from 4 I cannot, but add 10, 7 from 14 remains 7, set down 7 and carry 1; 8 and 1 which I carry is 9, 9 from 2 I cannot, etc.' We have before us the announcement of the following table, undated, as open to inspection at the Crystal Palace, Sydenham, in two diagrams of 7 ft. 2 in, by 6 ft. 6 in.: 'The figure 9 involved into the 912th power, and antecedent powers or involutions, containing upwards of 73,000 figures. Also, the proofs of the above, containing upwards of 146,000 figures. By Samuel Fancourt, of Mincing Lane, London, and completed by him in the year 1837, at the age of sixteen. N.B. The whole operation performed by simple arithmetic.' The young operator calculated by successive squaring the 2d, 4th, 8th, etc., powers up to the 512th, with proof by division. But 511 multiplications by 9, in the short (or 10-1) way, would have been much easier. The 2d, 32d, 64th, 128th, 256th, and 512th powers are given at the back of the announcement. The powers of 2 have been calculated for many purposes. In Vol. II of his Magia Universalis Naturæ et Artis, Herbipoli, 1658, 4to, the Jesuit Gaspar Schott^[138] having discovered, on some grounds of theological [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 π which attracts attention, perhaps without deserving it. It might be expected that, in so many figures, the nine digits and the cipher would occur each about the same number of times; that is, each about 61 times. But the fact stands thus: 3 occurs 68 times; 9 and 2 occur 67 times each; 4 occurs 64 times; 1 and 6 occur 62 times each; 0 occurs 60 times; 8 occurs 58 times; 5 occurs 56 times; and 7 occurs only 44 times. Now, if all the digits were equally likely, and 608 drawings were made, it is 45 to 1 against the number of sevens being as distant from the probable average (say 61) as 44 on one side or 78 on the other. There must be some reason why the number 7 is thus deprived of its fair share in the structure. Here is a field of speculation in which two branches of inquirers might unite. There is but one number which is treated with an unfairness which is incredible as an accident; and that number is the mystic number seven! If the cyclometers and the apocalyptics would lay their heads together until they come to a unanimous verdict on this phenomenon, and would publish nothing until they are of one mind, they would earn the gratitude of their race.—I was wrong: it is the Pyramid-speculator who should have been appealed to. A correspondent of my friend Prof. Piazzi Smyth^[139] notices that 3 is the number of most frequency, and that 3-1/7 is the nearest approximation to it in simple digits. Professor Smyth himself, whose word on Egypt is paradox of a very high order, backed by a great quantity of useful labor, the results which will be made available by those who do not receive [66]the paradoxes, is inclined to see confirmation for some of his theory in these phenomena.

CURIOUS CALCULATIONS.

These paradoxes of calculation sometimes appear as illustrations of the value of a new method. In 1863, Mr. G. Suffield,^[140] M.A., and Mr. J. R. Lunn,^[141] M.A., of Clare College and of St. John's College, Cambridge, published the whole quotient of 10000 ... divided by 7699, throughout the whole of one of the recurring periods, having 7698 digits. This was done in illustration of Mr. Suffield's method of Synthetic division.

Another instance of computation carried to paradoxical length, in order to illustrate a method, is the solution of x³ - 2x = 5, the example given of Newton's method, on which all improvements have been tested. In 1831, Fourier's^[142] posthumous work on equations showed 33 figures of solution, got with enormous labor. Thinking this a good opportunity to illustrate the superiority of the method of W. G. Horner,^[143] not yet known in France, and not much known in [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,^[144] of Dundalk, and of the Excise Office, went to 101 decimal places. To test the accuracy of this, I requested Mr. Johnston to undertake another equation, connected with the former one in a way which I did not explain. His solution verified the former one, but he was unable to see the connection, even when his result was obtained. My reader may be as much at a loss: the two solutions are:

The results are published in the Mathematician, Vol. III, p. 290. In 1851, another pupil of mine, Mr. J. Power Hicks,^[145] carried the result to 152 decimal places, without knowing what Mr. Johnston had done. The result is in the English Cyclopædia, article Involution and Evolution.

I remark that when I write the initial of a Christian name, the most usual name of that initial is understood. I never saw the name of W. G. Horner written at length, until I applied to a relative of his, who told me that he was, as I supposed, Wm. George, but that he was named after a relative of that surname.

The square root of 2, to 110 decimal places, was given [68]me in 1852 by my pupil, Mr. William Henry Colvill, now (1867) Civil Surgeon at Baghdad. It was

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

as the square.

This is a serious proposal to alter our numeral system and to count by twelves. Thus 10 would be twelve, 11 thirteen, etc., two new symbols being invented for ten and eleven. The names of numbers must of course be changed. There are persons who think such changes practicable. I thought this proposal absurd when I first saw it, and I think so still:^[147] but the one I shall presently describe beats it so completely in that point, that I have not a smile left for this one.

ON COMETS.

The author is the late Mr. Peter Legh,^[148] of Norbury Booths Hall, Knutsford, who published for eight or ten [69]years the Ombrological Almanac, a work of asserted discovery in meteorology. The theory of comets is that the joint attraction of the new moon and several planets in the direction of the sun, draws off the gases from the earth, and forms these cometic meteors. But how these meteors come to describe orbits round the sun, and to become capable of having their returns predicted, is not explained.

A NEW PHASE OF MORMONISM.

A newspaper headed by a grand picture of starred and striped banners, beehive, and eagle surmounting it. A scroll on each side: on the left, "Mormon creed. Mind your own business. Brigham Young;"^[149] on the right, "Given by inspiration of God. Joseph Smith."^[150] A leading article on the discoveries of Prof. Orson Pratt^[151] says, "Mormonism has long taken the lead in religion: it will soon be in the van both in science and politics." At the beginning of the paper is Professor Pratt's "Law of Planetary Rotation." The cube roots of the densities of the planets are as the square roots of their periods of rotation. The squares of the cube roots of the masses divided by the squares of the diameters are as the periods of rotation. Arithmetical verification attempted, and the whole very modestly stated [70]and commented on. Dated G. S. L. City, Utah Ter., Aug. 1, 1855. If the creed, as above, be correctly given, no wonder the Mormonites are in such bad odor.

MATHEMATICAL ILLUSTRATIONS OF DOCTRINE.

The author has published mathematical works with his name. The present tract is intended to illustrate mathematically a point which may be guessed from the title. But the symbols do very little in the way of illustration: thus, x being the present value of the future estate (eternal happiness), and a of all that this world can give, the author impresses it on the mathematician that, x being infinitely greater than a, x + a = x, so that a need not be considered. This will not act much more powerfully on a mathematician by virtue of the symbols than if those same symbols had been dispensed with: even though, as the author adds, "It was this method of neglecting infinitely small quantities that Sir Isaac Newton was indebted to for his greatest discoveries."

There has been a moderate quantity of well-meant attempt to enforce, sometimes motive, sometimes doctrine, by arguments drawn from mathematics, the proponents being persons unskilled in that science for the most part. The ground is very dangerous: for the illustration often turns the other way with greater power, in a manner which requires only a little more knowledge to see. I have, in my life, heard from the pulpit or read, at least a dozen times, that all sin is infinitely great, proved as follows. The greater the being, the greater the sin of any offence against him: therefore the offence committed against an infinite being is infinitely great. Now the mathematician, of which the proposers of this argument are not aware, is perfectly familiar with quantities which increase together, and never cease increasing, but so that one of them remains finite when [71]the other becomes infinite. In fact, the argument is a perfect non sequitur.^[152] Those who propose it have in their minds, though in a cloudy and indefinite form, the idea of the increase of guilt being proportionate to the increase of greatness in the being offended. But this it would never do to state: for by such statement not only would the argument lose all that it has of the picturesque, but the asserted premise would have no strong air of exact truth. How could any one undertake to appeal to conscience to declare that an offence against a being 4-7/10 times as great as another is exactly, no more and no less, 4-7/10 times as great an offence against the other?

The infinite character of the offence against an infinite being is laid down in Dryden's Religio Laici,^[153] and is, no doubt, an old argument:

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

My old friend, the late Dr. Olinthus Gregory,^[154] who was a sound and learned mathematician, adopted this dangerous kind of illustration in his Letters on the Christian Religion. [72]He argued, by parallel, from what he supposed to be the necessarily mysterious nature of the impossible quantity of algebra to the necessarily mysterious nature of certain doctrines of his system of Christianity. But all the difficulty and mystery of the impossible quantity is now cleared away by the advance of algebraical thought: and yet Dr. Gregory's book continues to be sold, and no doubt the illustration is still accepted as appropriate.

The mode of argument used by the author of the tract above named has a striking defect. He talks of reducing this world and the next to "present value," as an actuary does with successive lives or next presentations. Does value make interest? and if not, why? And if it do, then the present value of an eternity is not infinitely great. Who is ignorant that a perpetual annuity at five per cent is worth only twenty years' purchase? This point ought to be discussed by a person who treats heaven as a deferred perpetual annuity. I do not ask him to do so, and would rather he did not; but if he will do it, he must either deal with the question of discount, or be asked the reason why.

When a very young man, I was frequently exhorted to one or another view of religion by pastors and others who thought that a mathematical argument would be irresistible. And I heard the following more than once, and have since seen it in print, I forget where. Since eternal happiness belonged to the particular views in question, a benefit infinitely great, then, even if the probability of their arguments were small, or even infinitely small, yet the product of the chance and benefit, according to the usual rule, might give a result which no one ought in prudence to pass over. They did not see that this applied to all systems as well as their own. I take this argument to be the most perverse of all the perversions I have heard or read on the subject: there is some high authority for it, whom I forget.

The moral of all this is, that such things as the preceding should be kept out of the way of those who are not [73]mathematicians, because they do not understand the argument; and of those who are, because they do.

[The high authority referred to above is Pascal, an early cultivator of mathematical probability, and obviously too much enamoured of his new pursuit. But he conceives himself bound to wager on one side or the other. To the argument (Pensées, ch. 7)^[155] that "le juste est de ne point parier," he answers, "Oui: mais il faut parier: vous êtes embarqué; et ne parier point que Dieu est, c'est parier qu'il n'est pas."^[156] Leaving Pascal's argument to make its way with a person who, being a sceptic, is yet positive that the issue is salvation or perdition, if a God there be,—for the case as put by Pascal requires this,—I shall merely observe that a person who elects to believe in God, as the best chance of gain, is not one who, according to Pascal's creed, or any other worth naming, will really secure that gain. I wonder whether Pascal's curious imagination ever presented to him in sleep his convert, in the future state, shaken out of a red-hot dice-box upon a red-hot hazard-table, as perhaps he might have been, if Dante had been the later of the two. The original idea is due to the elder Arnobius,^[157] who, as cited by Bayle,^[158] speaks thus:

"Sed et ipse [Christus] quæ pollicetur, non probat. Ita est. Nulla enim, ut dixi, futurorum potest existere comprobatio. Cum ergo hæc sit conditio futurorum, ut teneri et comprehendi nullius possint anticipationis attactu; nonne [74]purior ratio est, ex duobus incertis, et in ambigua expectatione pendentibus, id potius credere, quod aliquas spes ferat, quam omnino quod nullas? In illo enim periculi nihil est, si quod dicitur imminere, cassum fiat et vacuum: in hoc damnum est maximum, id est salutis amissio, si cum tempus advenerit aperiatur non fuisse mendacium."^[159]

Really Arnobius seems to have got as much out of the notion, in the third century, as if he had been fourteen centuries later, with the arithmetic of chances to help him.]

NOVUM ORGANUM MORALIUM.

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

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

For myself, and for my old friend Mr. Boole, who I am sure would join me, I disclaim both priority, simultaneity, and posteriority, and request that nothing may be trumpeted from the mountain top except our abjuration of all community of thought or operation with this Novum Organum.

To such community we can make no more claim than Americus could make to being the forerunner of Columbus who popularized his discoveries. We do not wish for any ευρηκασι and not even for εὑρηκασι. For self and Boole, I point out what would have convinced either of us that this house is divided against itself.

Α being an apostolic element, δ the doctrinal element, and Χ the body of the faithful, the church is Α δ Χ, we are told. Also, that if Α become negative, or the Apostolicity become Diabolicity [my words]; or if δ become negative, and doctrine become heresy; or if Χ become negative, that is, if the faithful become unfaithful; the church becomes negative, "the very opposite to what it ought to be." For self and Boole, I admit this. But—which is not noticed—if Α and δ should both become negative, diabolical origin [77]and heretical doctrine, then the church, Α δ Χ, is still positive, what it ought to be, unless Χ be also negative, or the people unfaithful to it, in which case it is a bad church. Now, self and Boole—though I admit I have not asked my partner—are of opinion that a diabolical church with false doctrine does harm when the people are faithful, and can do good only when the people are unfaithful. We may be wrong, but this is what we do think. Accordingly, we have caught nothing, and can therefore roast nothing of our own: I content myself with roasting a joint of Mr. Gregg's larder.

These mathematical vagaries have uses which will justify a large amount of quotation: and in a score of years this may perhaps be the only attainable record. I therefore proceed.

After observing that by this calculus juries (heaven help them! say I) can calculate damages "almost to a nicety," and further that it is made abundantly evident that c e x is "the general expression for an individual," it is noted that the number of the Beast is not given in the Revelation in words at length, but as χξϜ'.^[163] On this the following remark is made:

"Can it be possible that we have in this case a specimen given to us of the arithmetic of heaven, and an expression revealed, which indicates by its function of addibility, the name of the church in question, and of each member of it; and by its function of multiplicability the doctrine, the mission, and the members of the great Synagogue of Apostacy? We merely propound these questions;—we do not pretend to solve them."

After a translation in blank verse—a very pretty one—of the 18th Psalm, the author proceeds as follows, to render it into differential calculus:

[78]

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

which, in the terms of ordinary language, just means, the increase of David's educational excellence or qualities—his piety, his prayerfulness, his humility, obedience, etc.—was so great, that when multiplied by his original talent and position, it produced a product so great as to be equal in its amount to royalty, honor, wealth, and power, etc.: in short, to all the attributes of majesty."^[165]

The "solution of the family problem" is of high interest. It is to determine the effect on the family in general from a change [of conduct] in one of them. The person chosen is one of the maid-servants.

"Let c e x be the father; c₁e₁x₁ the mother, etc. The family then consists of the maid's master, her mistress, her young master, her young mistress, and fellow servant. Now the master's calling (or c) is to exercise his share of control over this servant, and mind the rest of his business: call this remainder a, and let his calling generally, or all his affairs, be to his maid-servant as m : y, i.e., y = (mz/c); ... [79]and this expression will represent his relation to the servant. Consequently,

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

I have no objection to repeat so far; but I will not give the formula for the maid's relation to her young master; for I am not quite sure that all young masters are to be trusted with it. Suffice it that the son will be affected directly as his influence over her, and inversely as his vocational power: if then he should have some influence and no vocational power, the effect on him would be infinite. This is dismal to think of. Further, the formula brings out that if one servant improve, the other must deteriorate, and vice versa. This is not the experience of most families: and the author remarks as follows:

"That is, we should venture to say, a very beautiful result, and we may say it yielded us no little astonishment. What our calculation might lead to we never dreamt of; that it should educe a conclusion so recondite that our unassisted power never could have attained to, and which, if we could have conjectured it, would have been at best the most distant probability, that conclusion being itself, as it would appear, the quintessence of truth, afforded us a measure of satisfaction that was not slight."

That the writings of Mr. Boole and myself "go to the full justification of" this "principle," is only true in the sense in which the Scotch use, or did use, the word justification.

A TRIBUTE TO BOOLE.

[The last number of this Budget had stood in type for months, waiting until there should be a little cessation of correspondence more connected with the things of the day. [80]I had quite forgotten what it was to contain; and little thought, when I read the proof, that my allusions to my friend Mr. Boole, then in life and health, would not be printed till many weeks after his death. Had I remembered what my last number contained, I should have added my expression of regret and admiration to the numerous obituary testimonials, which this great loss to science has called forth.

The system of logic alluded to in the last number of this series is but one of many proofs of genius and patience combined. I might legitimately have entered it among my paradoxes, or things counter to general opinion: but it is a paradox which, like that of Copernicus, excited admiration from its first appearance. That the symbolic processes of algebra, invented as tools of numerical calculation, should be competent to express every act of thought, and to furnish the grammar and dictionary of an all-containing system of logic, would not have been believed until it was proved. When Hobbes,^[166] in the time of the Commonwealth, published his Computation or Logique, he had a remote glimpse of some of the points which are placed in the light of day by Mr. Boole. The unity of the forms of thought in all the applications of reason, however remotely separated, will one day be matter of notoriety and common wonder: and Boole's name will be remembered in connection with one of the most important steps towards the attainment of this knowledge.]

DECIMALS RUN RIOT.

[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 apostles! Even rejecting Judas, there is a whole apostle of difficulty. These points the author does not touch.

ON PHONETIC SPELLING.

I write the titles of a couple out of several tracts which I have by me. But the number of publications issued by the promoters of this spirited attempt is very large indeed.^[169] The attempt itself has had no success with the mass of the public. This I do not regret. Had the world found that the change was useful, I should have gone contentedly with the stream; but not without regretting our old language. I admit the difficulties which our unpronounceable spelling puts in the way of learning to read: and I have no doubt that, as affirmed, it is easier to teach children phonetically, and afterwards to introduce them to our common system, than to proceed in the usual way. But by the usual way I mean proceeding by letters from the very beginning. If, which I am sure is a better plan, children be taught at the commencement very much by complete words, as if they were learning Chinese, and be gradually accustomed to [82]resolve the known words into letters, a fraction, perhaps a considerable one, of the advantage of the phonetic system is destroyed. It must be remembered that a phonetic system can only be an approximation. The differences of pronunciation existing among educated persons are so great, that, on the phonetic system, different persons ought to spell differently.

But the phonetic party have produced something which will immortalize their plan: I mean their shorthand, which has had a fraction of the success it deserves. All who know anything of shorthand must see that nothing but a phonetic system can be worthy of the name: and the system promulgated is skilfully done. Were I a young man I should apply myself to it systematically. I believe this is the only system in which books were ever published. I wish some one would contribute to a public journal a brief account of the dates and circumstances of the phonetic movement, not forgetting a list of the books published in shorthand.

A child beginning to read by himself may owe terrible dreams and waking images of horror to our spelling, as I did when six years old. In one of the common poetry-books there is an admonition against confining little birds in cages, and the child is asked what if a great giant, amazingly strong, were to take you away, shut you up,

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. [83]

A HANDFUL OF LITTLE PARADOXERS.

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

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

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

1856. A stranger applied to me to know what the ideas of a friend of his were worth upon the magnitude of the earth. The matter being one involving points of antiquity, I mentioned various persons whose speculations he seemed to have ignored; among others, Thales. The reply was, "I am instructed by the author to inform you that he is perfectly acquainted with the works of Thales, Euclid, Archimedes, ..." I had some thought of asking whether he had used the Elzevir edition of Thales,^[172] which is known to be very incomplete, or that of Professor Niemand with the lections, Nirgend, 1824, 2 vols. folio; just to see whether the [84]last would not have been the very edition he had read. But I refrained, in mercy.

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

LUNAR MOTION AGAIN.

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

[85]

The Astronomer Royal endeavored to disentangle Mr. J. C. Symons, but failed. Mr. Airy^[175] can correct the error of a ship's compasses, because he can put her head which way he pleases: but this he cannot do with a speculator.

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

Would it not be a good thing to exercise boys, in pairs, in the following dialogue:—Sir, you are quite wrong!—Sir, [86]I am sure you honestly think so! This was suggested by what used to take place at Cambridge in my day. By statute, every B.A. was obliged to perform a certain number of disputations, and the father of the college had to affirm that it had been done. Some were performed in earnest: the rest were huddled over as follows. Two candidates occupied the places of the respondent and the opponent: Recte statuit Newtonus, said the respondent: Recte non statuit Newtonus,^[177] said the opponent. This was repeated the requisite number of times, and counted for as many acts and opponencies. The parties then changed places, and each unsaid what he had said on the other side of the house: I remember thinking that it was capital drill for the House of Commons, if any of us should ever get there. The process was repeated with every pair of candidates.

The real disputations were very severe exercises. I was badgered for two hours with arguments given and answered in Latin,—or what we called Latin—against Newton's first section, Lagrange's^[178] derived functions, and Locke^[179] on innate principles. And though I took off everything, and was pronounced by the moderator to have disputed magno honore,^[180] I never had such a strain of thought in my life. For the inferior opponents were made as sharp as their betters by their tutors, who kept lists of queer objections, drawn from all quarters. The opponents used to meet the day before to compare their arguments, that the same might not come twice over. But, after I left Cambridge, it became the fashion to invite the respondent to be present, who therefore learnt all that was to be brought against him. This made the whole thing a farce: and the disputations were abolished.

[87]

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

But suppose the general body were to combine, in opposition to those who have studied. Of course all my list must be admitted to their trial; and then arises the question whether both sides are to be heard. If so, the general body of the intelligent must hear all the established side have to say: that is, they must become just as much of students as the inculpated orthodox themselves. And will they not then get into professional rule, pique, pride, and prejudice, as the others did? But if, which I suspect, they are intended to judge as they are, they will be in a rare difficulty. All the paradoxers are of like pretensions: they cannot, as a class, be right, for each one contradicts a great many of the rest. There will be the puzzle which silenced the crew of the cutter in Marryat's novel of the Dog Fiend.^[182] "A tog is a tog," said Jansen.—"Yes," replied another, "we all know a dog is a dog; but the question is—Is this dog [88]a dog?" And this question would arise upon every dog of them all.

ZETETIC ASTRONOMY.

Though only a traveling lecturer's advertisement, there are so many arguments and quotations that it is a little pamphlet. The lecturer gained great praise from provincial newspapers for his ingenuity in proving that the earth is a flat, surrounded by ice. Some of the journals rather incline to the view: but the Leicester Advertiser thinks that the statements "would seem very seriously to invalidate some of the most important conclusions of modern astronomy," while the Norfolk Herald is clear that "there must be a great error on one side or the other." This broadsheet is printed at Aylesbury in 1857, and the lecturer calls himself Parallax: but at Trowbridge, in 1849, he was S. Goulden.^[183] In this last advertisement is the following announcement: "A paper on the above subjects was read before the Council and Members of the Royal Astronomical Society, Somerset House, Strand, London (Sir John F. W. Herschel,^[184] President), Friday, Dec. 8, 1848." No account of such a paper appears in the Notice for that month: I suspect that the above is Mr. S. Goulden's way of representing the following occurrence: Dec. 8, 1848, the Secretary of the Astronomical Society (De Morgan by name) said, at the close of the proceedings,—"Now, gentlemen, if you will promise not to tell the Council, I will read something for your amusement": and he then read a few of the arguments which had been transmitted by the lecturer. The fact is worth noting that from 1849 to 1857, arguments on the roundness or flatness of the earth did itinerate. I have [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 explain why the large hull of a ship disappeared before the sails. The persons present and waiting for the second lecture assuaged their disappointment by concluding that the lecturer had slipped off the icy edge of his flat disk, and that he would not be seen again till he peeped up on the opposite side.

But, strange as it may appear, the opposer of the earth's roundness has more of a case—or less of a want of case—than the arithmetical squarer of the circle. The evidence that the earth is round is but cumulative and circumstantial: scores of phenomena ask, separately and independently, what other explanation can be imagined except the sphericity of the earth. The evidence for the earth's figure is tremendously powerful of its kind; but the proof that the circumference is 3.14159265... times the diameter is of a higher kind, being absolute mathematical demonstration.

The Zetetic system still lives in lectures and books; as it ought to do, for there is no way of teaching a truth comparable to opposition. The last I heard of it was in lectures at Plymouth, in October, 1864. Since this time a prospectus has been issued of a work entitled "The Earth not a Globe"; but whether it has been published I do not know. The contents are as follows:

"The Earth a Plane—How circumnavigated.—How time is lost or gained.—Why a ship's hull disappears (when outward bound) before the mast head.—Why the Polar Star sets when we proceed Southward, etc.—Why a pendulum vibrates with less velocity at the Equator than [90]at the Pole.—The allowance for rotundity supposed to be made by surveyors, not made in practice.—Measurement of Arcs of the Meridian unsatisfactory.—Degrees of Longitude North and South of the Equator considered.—Eclipses and Earth's form considered.—The Earth no motion on axis or in orbit.—How the Sun moves above the Earth's surface concentric with the North Pole.—Cause of Day and Night, Winter and Summer; the long alternation of light and darkness at the Pole.—Cause of the Sun rising and setting.—Distance of the Sun from London, 4,028 miles—How measured.—Challenge to Mathematicians.—Cause of Tides.—Moon self-luminous, NOT a reflector.—Cause of Solar and Lunar eclipses.—Stars not worlds; their distance.—Earth, the only material world; its true position in the universe; its condition and ultimate destruction by fire (2 Peter iii.), etc."

I wish there were geoplatylogical lectures in every town; in England (platylogical, in composition, need not mean babbling). The late Mr. Henry Archer^[185] would, if alive, be very much obliged to me for recording his vehement denial of the roundness of the earth: he was excited if he heard any one call it a globe. I cannot produce his proof from the Pyramids, and from some caves in Arabia. He had other curious notions, of course: I should no more believe that a flat earth was a man's only paradox, than I should that Dutens,^[186] the editor of Leibnitz, was eccentric only in supplying a tooth which he had lost by one which he found in an Italian tomb, and fully believed that it had once belonged to Scipio Africanus, whose family vault was discovered, it is supposed, in 1780. Mr. Archer is of note as [91]the suggester of the perforated border of the postage-stamps, and, I think, of the way of doing it; for this he got 4000l. reward. He was a civil engineer.

(August 28, 1865.) The Zetetic Astronomy has come into my hands. When, in 1851, I went to see the Great Exhibition, I heard an organ played by a performer who seemed very desirous to exhibit one particular stop. "What do you think of that stop?" I was asked.—"That depends on the name of it," said I.—"Oh! what can the name have to do with the sound? 'that which we call a rose,' etc."—"The name has everything to do with it: if it be a flute-stop, I think it very harsh; but if it be a railway-whistle-stop, I think it very sweet." So as to this book: if it be childish, it is clever; if it be mannish, it is unusually foolish. The flat earth, floating tremulously on the sea; the sun moving always over the flat, giving day when near enough, and night when too far off; the self-luminous moon, with a semi-transparent invisible moon, created to give her an eclipse now and then; the new law of perspective, by which the vanishing of the hull before the masts, usually thought to prove the earth globular, really proves it flat;—all these and other things are well fitted to form exercises for a person who is learning the elements of astronomy. The manner in which the sun dips into the sea, especially in tropical climates, upsets the whole. Mungo Park,^[187] I think, gives an African hypothesis which explains phenomena better than this. The sun dips into the western ocean, and the people there cut him in pieces, fry him in a pan, and then join him together again, take him round the underway, and set him up in the east. I hope this book will be read, and that many will be puzzled by it: for there are many whose notions of astronomy deserve no better fate. There is no subject on which there is so little [92]accurate conception as that of the motions of the heavenly bodies. The author, though confident in the extreme, neither impeaches the honesty of those whose opinions he assails, nor allots them any future inconvenience: in these points he is worthy to live on a globe, and to revolve in twenty-four hours.

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

To which I answer:

The great wish of persons who expose themselves as above, is to be argued with, and to be treated as reputable [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 argument will turn wrong into right. These two things balance; and we are just where we were: but you should answer our arguments, for whom, I ask? Would reason convince this kind of reasoner? The issue is a short and a clear one. If these parties be what I contend they are, then ridicule is made for them: if not, for what or for whom? If they be right, they are only passing through the appointed trial of all good things. Appeal is made to the future: and my Budget is intended to show samples of the long line of heroes who have fallen without victory, each of whom had his day of confidence and his prophecy of success. Let the future decide: they say roundly that the earth is flat; I say flatly that it is round.

The paradoxers all want reason, and not ridicule: they are all accessible, and would yield to conviction. Well then, let them reason with one another! They divide into squads, each with a subject, and as many different opinions as persons in each squad. If they be really what they say they are, the true man of each set can put down all the rest, and can come crowned with glory and girdled with scalps, to the attack on the orthodox misbelievers. But they know, to a man, that the rest are not fit to be reasoned with: they pay the regulars the compliment of believing that the only chance lies with them. They think in their hearts, each one for himself, that ridicule is of fit appliance to the rest.

The name of the author is Filopanti.^[189] He announces himself as the 49th and last Emanuel: his immediate [94]predecessors were Emanuel Washington, Emanuel Newton, and Emanuel Galileo. He is to collect nations into one family. He knows the transmigrations of the whole human race. Thus Descartes became William III of England: Roger Bacon became Boccaccio. But Charles IX,^[190] in retribution for the massacre of St. Bartholomew, was hanged in London under the name of Barthélemy for the murder of Collard: and many of the Protestants whom he killed as King of France were shouting at his death before the Old Bailey.

THE SABBATH—THE GREAT PYRAMID

This gentleman is well known to the readers of the Athenæum, in which, for nearly twenty years, he has inserted, as advertisements, long arguments in favor of Christians keeping the Jewish Sabbath, beginning on Friday Evening. The present letter maintains that, by the force of the definite article, the days of creation may not be consecutive, but may have any time—millions of years—between them. This ingenious way of reconciling the author of Genesis and the indications of geology is worthy to be added to the list, already pretty numerous. Mr. Heinfetter has taken such pains to make himself a public agitator, that [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.

This work is very learned, and may be referred to for the history of previous speculations. It professes to connect the dimensions of the Pyramid with a system of metrology which is supposed to have left strong traces in the systems of modern times; showing the Egyptians to have had good approximate knowledge of the dimensions of the earth, and of the quadrature of the circle. These are points on which coincidence is hard to distinguish from intention. Sir John Herschel^[193] noticed this work, and gave several coincidences, in the Athenæum, Nos. 1696 and 1697, April 28 and May 5, 1860: and there are some remarks by Mr. Taylor in No. 1701, June 2, 1860.

Mr. Taylor's most recent publication is—

This is intended as an appendix to the work on the Pyramid. Mr. Taylor distinctly attributes the original system to revelation, of which he says the Great Pyramid is the record. We are advancing, he remarks, towards the end of the Christian dispensation, and he adds that it is satisfactory to see that we retain the standards which were given by unwritten revelation 700 years before Moses. This is lighting the candle at both ends; for myself, I shall not undertake to deny or affirm either what is said about the dark past or what is hinted about the dark future.

[96]

My old friend Mr. Taylor is well known as the author of the argument which has convinced many, even most, that Sir Philip Francis^[194] was Junius: pamphlet, 1813; supplement, 1817; second edition "The Identity of Junius with a distinguished living character established," London, 1818, 8vo. He told me that Sir Philip Francis, in a short conversation with him, made only this remark, "You may depend upon it you are quite mistaken:" the phrase appears to me remarkable; it has an air of criticism on the book, free from all personal denial. He also mentioned that a hearer told him that Sir Philip said, speaking of writers on the question,—"Those fellows, for half-a-crown, would prove that Jesus Christ was Junius."

Mr. Taylor implies, I think, that he is the first who started the suggestion that Sir Philip Francis was Junius, which I have no means either of confirming or refuting. If it be so [and I now know that Mr. Taylor himself never heard of any predecessor], the circumstance is very remarkable: it is seldom indeed that the first proposer of any solution of a great and vexed question is the person who so nearly establishes his point in general opinion as Mr. Taylor has done.

As to the Junius question in general, there is a little bit of the philosophy of horse-racing which may be usefully applied. A man who is so confident of his horse that he places him far above any other, may nevertheless, and does, refuse to give odds against all in the field: for many small adverse chances united make a big chance for one or other of the opponents. I suspect Mr. Taylor has made it at least 20 to 1 for Francis against any one competitor who has been named: but what the odds may be against the [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 temperament, he had a curious turn for vexed questions. But he reflected very long and very patiently before he published: and all his works are valuable for their accurate learning, whichever side the reader may take.)

MRS. ELIZABETH COTTLE.

1859. The Cottle Church.—For more than twenty years printed papers have been sent about in the name of Elizabeth Cottle.^[195] It is not so remarkable that such papers should be concocted as that they should circulate for such a length of time without attracting public attention. Eighty years ago Mrs. Cottle might have rivalled Lieut. Brothers or Joanna Southcott.^[196] Long hence, when the now current volumes of our journals are well-ransacked works of reference, those who look into them will be glad to see this [98]feature of our time: I therefore make a few extracts, faithfully copied as to type. The Italic is from the New Testament; the Roman is the requisite interpretation:

"Robert Cottle 'was numbered (5196) with the transgressors' at the back of the Church in Norwood Cemetery, May 12, 1858—Isa. liii. 12. The Rev. J. G. Collinson, Minister of St. James's Church, Chapham, the then district church, before All Saints was built, read the funeral service over the Sepulchre wherein never before man was laid.

"Hewn on the stone, 'at the mouth of the Sepulchre,' is his name,—Robert Cottle, born at Bristol, June 2, 1774; died at Kirkstall Lodge, Clapham Park, May 6, 1858. And that day (May 12, 1858) was the preparation (day and year for 'the PREPARED place for you'—Cottleites—-by the widowed mother of the Father's house, at Kirkstall Lodge—John xiv. 2, 3). And the Sabbath (Christmas Day, Dec. 25, 1859) drew on (for the resurrection of the Christian body on 'the third [Protestant Sun]-day'—1 Cor. xv. 35). Why seek ye the living (God of the New Jerusalem—Heb. xii. 22; Rev. iii. 12) among the dead (men): he (the God of Jesus) is not here (in the grave), but is risen (in the person of the Holy Ghost, from the supper of 'the dead in the second death' of Paganism). Remember how he spake unto you (in the church of the Rev. George Clayton,^[197] April 14, 1839). I will not drink henceforth (at this last Cottle supper) of the fruit of this (Trinity) vine, until that day (Christmas Day, 1859), when I (Elizabeth Cottle) drink it new with you (Cottleites) in my Father's kingdom—John xv. If this (Trinitarian) cup may not pass away from me (Elizabeth Cottle, April 14, 1839), except I drink it ('new with you Cottleites, in my Father's Kingdom'), thy will be done—Matt. xxvi. 29, 42, 64. 'Our Father which art (God) in Heaven,' hallowed be thy name, thy (Cottle) kingdom [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 Elizabeth) a kingdom (of God,) which cannot be moved (by Satan) let us have grace (in his Grace of Canterbury) whereby we may serve God acceptably (with the acceptable sacrifice of Elizabeth's body and blood of the communion of the Holy Ghost) with reverence (for truth) and godly fear (of the unpardonable sin of blasphemy against the Holy Ghost) for our God (the Holy Ghost) is a consuming fire (to the nation that will not serve him in the Cottle Church). We cannot defend ourselves against the Almighty, and if He is our defence, no nation can invade us.

"In verse 4 the Church of St. Peter is in prison between four quaternions of soldiers—the Holy Alliance of 1815. Rev. vii. i. Elizabeth, the Angel of the Lord Jesus appears to the Jewish and Christian body with the vision of prophecy to the Rev. Geo. Clayton and his clerical brethren, April 8th, 1839. Rhoda was the name of her maid at Putney Terrace who used to open the door to her Peter, the Rev. Robert Ashton,^[198] the Pastor of 'the little flock' 'of 120 names together, assembled in an upper (school) room' at Putney Chapel, to which little flock she gave the revelation (Acts. i. 13, 15) of Jesus the same King of the Jews yesterday at the prayer meeting, Dec. 31, 1841, and to-day, [100]Jan. 1, 1842, and for ever. See book of Life, page 24. Matt. xviii. 19, xxi. 13-16. In verse 6 the Italian body of St. Peter is sleeping 'in the second death' between the two Imperial soldiers of France and Austria. The Emperor of France from Jan. 1, to July 11, 1859, causes the Italian chains of St. Peter to fall off from his Imperial hands.

"I say unto thee, Robert Ashton, thou art Peter, a stone, and upon this rock, of truth, will I Elizabeth, the angel of Jesus, build my Cottle Church, and the gates of hell, the doors of St. Peter, at Rome, shall not prevail against it—Matt. xvi. 18. Rev. iii. 7-12."

This will be enough for the purpose. When any one who pleases can circulate new revelations of this kind, uninterrupted and unattended to, new revelations will cease to be a good investment of excentricity. I take it for granted that the gentlemen whose names are mentioned have nothing to do with the circulars or their doctrines. Any lady who may happen to be intrusted with a revelation may nominate her own pastor, or any other clergyman, one of her apostles; and it is difficult to say to what court the nominees can appeal to get the commission abrogated.

March 16, 1865. During the last two years the circulars have continued. It is hinted that funds are low: and two gentlemen who are represented as gone "to Bethlehem asylum in despair" say that Mrs. Cottle "will spend all that she hath, while Her Majesty's Ministers are flourishing on the wages of sin." The following is perhaps one of the most remarkable passages in the whole:

"Extol and magnify Him (Jehovah, the Everlasting God, see the Magnificat and Luke i. 45, 46—68—73—79), that rideth (by rail and steam over land and sea, from his holy habitation at Kirkstall Lodge, Psa. lxxvii. 19, 20), upon the (Cottle) heavens, as it were (Sept. 9, 1864, see pages 21, 170), upon an (exercising, Psa. cxxxi. 1), horse-(chair, bought of Mr. John Ward, Leicester-square)." [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 following. A printed letter to the Western Times, by Mr. Robert Cottle, was accompanied by a manuscript letter from Mrs. Cottle, apparently a circular. The date was Nov^r. 1853, and the subject was the procedure against Mr. Maurice^[199] at King's College for doubting that God would punish human sins by an existence of torture lasting through years numbered by millions of millions of millions of millions (repeat the word millions without end,) etc. The memory of Mr. Cottle has, I think, a right to the quotation: he seems to have been no participator in the notions of his wife:

"The clergy of the Established Church, taken at the round number of 20,000, may, in their first estate, be likened to 20,000 gold blanks, destined to become sovereigns, in succession,—they are placed between the matrix of the Mint, when, by the pressure of the screw, they receive the impress that fits them to become part of the current coin of the realm. In a way somewhat analogous this great body of the clergy have each passed through the crucibles of Oxford and Cambridge,—have been assayed by the Bishop's chaplain, touching the health of their souls, and the validity of their call by the Divine Spirit, and then the gentle pressure of a prelate's hand upon their heads; and the words—'Receive the Holy Ghost,' have, in a brief space of time, wrought a [102]change in them, much akin to the miracle of transubstantiation—the priests are completed, and they become the current ecclesiastical coin of our country. The whole body of clergy, here spoken of, have undergone the preliminary induction of baptism and confirmation; and all have been duly ordained, professing to hold one faith, and to believe in the selfsame doctrines! In short, to be as identical as the 20,000 sovereigns, if compared one with the other. But mind is not malleable and ductile, like gold; and all the preparations of tests, creeds, and catechisms will not insure uniformity of belief. No stamp of orthodoxy will produce the same impress on the minds of different men. Variety is manifest, and patent, upon everything mental and material. The Almighty has not created, nor man fashioned, two things alike! How futile, then, is the attempt to shape and mould man's apprehension of divine truth by one fallible standard of man's invention! If proof of this be required, an appeal might be made to history and the experience of eighteen hundred years."

This is an argument of force against the reasonableness of expecting tens of thousands of educated readers of the New Testament to find the doctrine above described in it. The lady's argument against the doctrine itself is very striking. Speaking of an outcry on this matter among the Dissenters against one of their body, who was the son of "the White Stone (Rev. ii. 17), or the Roman cement-maker," she says—

"If the doctrine for which they so wickedly fight were true, what would become of the black gentlemen for whose redemption I have been sacrificed from April 8 1839."

There are certainly very curious points about this revelation. There have been many surmises about the final restoration of the infernal spirits, from the earliest ages of Christianity until our own day: a collection of them would be worth making. On reading this in proof, I see a possibility that by "black gentlemen" may be meant the clergy: [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.

When my work appeared in numbers, I had not anything like an adequate idea of Mr. James Smith's superiority to the rest of the world in the points in which he is superior. He is beyond a doubt the ablest head at unreasoning, and the greatest hand at writing it, of all who have tried in our day to attach their names to an error. Common cyclometers sink into puny orthodoxy by his side.

The behavior of this singular character induces me to pay him the compliment which Achilles paid Hector, to drag him round the walls again and again. He was treated with unusual notice and in the most gentle manner. The unnamed mathematician, E. M. bestowed a volume of mild correspondence upon him; Rowan Hamilton^[201] quietly proved him wrong in a way accessible to an ordinary schoolboy; Whewell,^[202] as we shall see, gave him the means of seeing himself wrong, even more easily than by Hamilton's method. Nothing would do; it was small kick and silly fling at all; and he exposed his conceit by alleging that he, James Smith, had placed Whewell in the stocks. He will therefore be universally pronounced a proper object of the severest literary punishment: but the opinion of all who can put two propositions together will be that of the many strokes I have given, the hardest and most telling are my republications of his own attempts to reason.

He will come out of my hands in the position he ought [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 Athenæum of May 11, 1861. Mr. Smith says I wrote it: this I neither affirm nor deny; to do either would be a sin against the editorial system elsewhere described. Many persons tell me they know me by my style; let them form a guess: I can only say that many have declared as above while fastening on me something which I had never seen nor heard of.

"A few weeks ago we were in perpetual motion. We did not then suppose that anything would tempt us on a circle-squaring expedition: but the circumstances of the book above named have a peculiarity which induces us to give it a few words.

"Mr. James Smith, a gentleman residing near Liverpool, was some years ago seized with the morbus cyclometricus.^[203] The symptoms soon took a defined form: his circumference shrank into exactly 3-1/8 times his diameter, instead of close to 3-16/113, which the mathematician knows to be so near to truth that the error is hardly at the rate of a foot in 2,000 miles. This shrinking of the circumference remained until it became absolutely necessary that it should be examined by the British Association. This body, which as Mr. James Smith found to his sorrow, has some interest in 'jealously guarding the mysteries of their profession,' refused at first to entertain the question. On this Mr. Smith changed his 'tactics' and the name of his paper, and smuggled in the subject under the form of 'The Relations of a Circle inscribed in a Square'! The paper was thus forced upon the Association, for Mr. Smith informs us that he [106]'gave the Section to understand that he was not the man that would permit even the British Association to trifle with him.' In other words, the Association bore with and were bored with the paper, as the shortest way out of the matter. Mr. Smith also circulated a pamphlet. Some kind-hearted man, who did not know the disorder as well as we do, and who appears in Mr. Smith's handsome octavo as E. M.—the initials of 'eminent mathematician'—wrote to him and offered to show him in a page that he was all wrong. Mr. Smith thereupon opened a correspondence, which is the bulk of the volume. When the correspondence was far advanced, Mr. Smith announced his intention to publish. His benevolent instructor—we mean in intention—protested against the publication, saying 'I do not wish to be gibbeted to the world as having been foolish enough to enter upon what I feel now to have been a ridiculous enterprise.'

"For this Mr. Smith cared nothing: he persisted in the publication, and the book is before us. Mr. Smith has had so much grace as to conceal his kind adviser's name under E. M., that is to say, he has divided the wrong among all who may be suspected of having attempted so hopeless a task as that of putting a little sense into his head. He has violated the decencies of private life. Against the will of the kind-hearted man who undertook his case, he has published letters which were intended for no other purpose than to clear his poor head of a hopeless delusion. He deserves the severest castigation; and he will get it: his abuse of confidence will stick by him all his days. Not that he has done his benefactor—in intention, again—any harm. The patience with which E. M. put the blunders into intelligible form, and the perseverance with which he tried to find a cranny-hole for common reasoning to get in at, are more than respectable: they are admirable. It is, we can assure E. M., a good thing that the nature of the circle-squarer should be so completely exposed as in this volume. The benefit which he intended Mr. James Smith may be [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 3-1/8 times the diameter by making it the supposition to set out with that there was such a circle; and then finding certain consequences which, so it happened, were not inconsistent with the supposition on which they were made. Error is sometimes self-consistent. However, E. M., to be quite sure of his ground, wrote a short letter, stating what he took to be Mr. Smith's hypothesis, containing the following: 'On AC as diameter, describe the circle D, which by hypothesis shall be equal to three and one-eighth times the length of AC.... I beg, before proceeding further, to ask whether I have rightly stated your argument.' To which Mr. Smith replied: 'You have stated my argument with perfect accuracy.' Still E. M. went on, and we could not help, after the above, taking these letters as the initials of Everlasting Mercy. At last, however, when Mr. Smith flatly denied that the area of the circle lies between those of the inscribed and circumscribed polygons, E. M. was fairly beaten, and gave up the task. Mr. Smith was left to write his preface, to talk about the certain victory of truth—which, oddly enough, is the consolation of all hopelessly mistaken men; to compare himself with Galileo; and to expose to the world the perverse behavior of the Astronomer Royal, on whom he wanted to fasten a conversation, and who replied, 'It would be a waste of time, Sir, to listen to anything you could have to say on such a subject.'

"Having thus disposed of Mr. James Smith, we proceed to a few remarks on the subject: it is one which a journal would never originate, but which is rendered necessary from time to time by the attempts of the autopseustic to become [108]heteropseustic. To the mathematician we have nothing to say: the question is, what kind of assurance can be given to the world at large that the wicked mathematicians are not acting in concert to keep down their superior, Mr. James Smith, the current Galileo of the quadrature of the circle.

"Let us first observe that this question does not stand alone: independently of the millions of similar problems which exist in higher mathematics, the finding of the diagonal of a square has just the same difficulty, namely, the entrance of a pair of lines of which one cannot be definitely expressed by means of the other. We will show the reader who is up to the multiplication-table how he may go on, on, on, ever nearer, never there, in finding the diagonal of a square from the side.

"Write down the following rows of figures, and more, if you like, in the way described:

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

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 [109]question, while that of the second was not demonstrated, completely, until the last century.

"The mathematicians have many methods, totally different from each other, of arriving at one and the same result, their celebrated approximation to the circumference of the circle. An intrepid calculator has, in our own time, carried his approximation to what they call 607 decimal places: this has been done by Mr. Shanks,^[204] of Houghton-le-Spring, and Dr. Rutherford^[205] has verified 441 of these places. But though 607 looks large, the general public will form but a hazy notion of the extent of accuracy acquired. We have seen, in Charles Knight's^[206] English Cyclopædia, an account of the matter which may illustrate the unimaginable, though rationally conceivable, extent of accuracy obtained.

"Say that the blood-globule of one of our animalcules is a millionth of an inch in diameter. Fashion in thought a globe like our own, but so much larger that our globe is but a blood-globule in one of its animalcules: never mind the microscope which shows the creature being rather a bulky instrument. Call this the first globe above us. Let the first globe above us be but a blood-globule, as to size, in the animalcule of a still larger globe, which call the second globe above us. Go on in this way to the twentieth globe above us. Now go down just as far on the other side. Let the blood-globule with which we started be a globe peopled with animals like ours, but rather smaller: [110]and call this the first globe below us. Take a blood-globule out of this globe, people it, and call it the second globe below us: and so on to the twentieth globe below us. This is a fine stretch of progression both ways. Now give the giant of the twentieth globe above us the 607 decimal places, and, when he has measured the diameter of his globe with accuracy worthy of his size, let him calculate the circumference of his equator from the 607 places. Bring the little philosopher from the twentieth globe below us with his very best microscope, and set him to see the small error which the giant must make. He will not succeed, unless his microscopes be much better for his size than ours are for ours.

"Now it must be remembered by any one who would laugh at the closeness of the approximation, that the mathematician generally goes nearer; in fact his theorems have usually no error at all. The very person who is bewildered by the preceding description may easily forget that if there were no error at all, the Lilliputian of the millionth globe below us could not find a flaw in the Brobdingnagian of the millionth globe above. The three angles of a triangle, of perfect accuracy of form, are absolutely equal to two right angles; no stretch of progression will detect any error.

"Now think of Mr. Lacomme's mathematical adviser (ante, Vol. I, p. 46) making a difficulty of advising a stonemason about the quantity of pavement in a circular floor!

"We will now, for our non-calculating reader, put the matter in another way. We see that a circle-squarer can advance, with the utmost confidence, the assertion that when the diameter is 1,000, the circumference is accurately 3,125: the mathematician declaring that it is a trifle more than 3,141½. If the squarer be right, the mathematician has erred by about a 200th part of the whole: or has not kept his accounts right by about 10s. in every 100l. Of course, if he set out with such an error he will accumulate blunder upon blunder. Now, if there be a process in which [111]close knowledge of the circle is requisite, it is in the prediction of the moon's place—say, as to the time of passing the meridian at Greenwich—on a given day. We cannot give the least idea of the complication of details: but common sense will tell us that if a mathematician cannot find his way round the circle without a relative error four times as big as a stockbroker's commission, he must needs be dreadfully out in his attempt to predict the time of passage of the moon. Now, what is the fact? His error is less than a second of time, and the moon takes 27 days odd to revolve. That is to say, setting out with 10s. in 100l. of error in his circumference, he gets within the fifth part of a farthing in 100l. in predicting the moon's transit. Now we cannot think that the respect in which mathematical science is held is great enough—though we find it not small—to make this go down. That respect is founded upon a notion that right ends are got by right means: it will hardly be credited that the truth can be got to farthings out of data which are wrong by shillings. Even the celebrated Hamilton^[207] of Edinburgh, who held that in mathematics there was no way of going wrong, was fully impressed with the belief that this was because error was avoided from the beginning. He never went so far as to say that a mathematician who begins wrong must end right somehow.

"There is always a difficulty about the mode in which the thinking man of common life is to deal with subjects he has not studied to a professional extent. He must form opinions on matters theological, political, legal, medical, and social. If he can make up his mind to choose a guide, there is, of course, no perplexity: but on all the subjects mentioned the direction-posts point different ways. Now why should he not form his opinion upon an abstract mathematical question? Why not conclude that, as to the circle, it is possible Mr. James Smith may be the man, just [112]as Adam Smith^[208] was the man of things then to come, or Luther, or Galileo? It is true that there is an unanimity among mathematicians which prevails in no other class: but this makes the chance of their all being wrong only different in degree. And more than this, is it not generally thought among us that priests and physicians were never so much wrong as when there was most appearance of unanimity among them? To the preceding questions we see no answer except this, that the individual inquirer may as rationally decide a mathematical question for himself as a theological or a medical question, so soon as he can put himself into a position in mathematics, level with that in which he stands in theology or medicine. The every-day thought and reading of common life have a certain resemblance to the thought and reading demanded by the learned faculties. The research, the balance of evidence, the estimation of probabilities, which are used in a question of medicine, are closely akin in character, however different the matter of application, to those which serve a merchant to draw his conclusions about the markets. But the mathematicians have methods of their own, to which nothing in common life bears close analogy, as to the nature of the results or the character of the conclusions. The logic of mathematics is certainly that of common life: but the data are of a different species; they do not admit of doubt. An expert arithmetician, such as is Mr. J. Smith, may fancy that calculation, merely as such, is mathematics: but the value of his book, and in this point of view it is not small, is the full manner in which it shows that a practised arithmetician, venturing into the field of mathematical demonstration, may show himself utterly destitute of all that distinguishes the reasoning geometrical investigator from the calculator.

[113]

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

I will insert now at length, from the Athenæum of June 8, 1861, the easy refutation given by my deceased friend, with the remarks which precede.

"Mr. James Smith, of whose performance in the way of squaring the circle we spoke some weeks ago in terms short of entire acquiescence, has advertised himself in our columns, as our readers will have seen. He has also forwarded his letter to the Liverpool Albion, with an additional statement, which he did not make in our journal. He denies that he has violated the decencies of private life, since his correspondent revised the proofs of his own letters, and his 'protest had respect only to making his name public.' This statement Mr. James Smith precedes by saying that we have treated as true what we well knew to be false: and he follows by saying that we have not read his work, or we should have known the above facts to be true. Mr. Smith's pretext is as follows. His correspondent E. M. says, 'My letters were not intended for publication, and I protest against their being published,' and he subjoins 'Therefore I must desire that my name may not be used.' The obvious meaning is that E. M. protested against the publication altogether, but, judging that Mr. Smith was [114]determined to publish, desired that his name should not be used. That he afterwards corrected the proofs merely means that he thought it wiser to let them pass under his own eyes than to leave them entirely to Mr. Smith.

"We have received from Sir W. Rowan Hamilton^[209] a proof that the circumference is more than 3⅛ diameters, requiring nothing but a knowledge of four books of Euclid. We give it in brief as an exercise for our juvenile readers to fill up. It reminds us of the old days when real geometers used to think it worth while seriously to demolish pretenders. Mr. Smith's fame is now assured: Sir W. R. Hamilton's brief and easy exposure will procure him notice in connection with this celebrated problem.

"It is to be shown that the perimeter of a regular polygon of 20 sides is greater than 3⅛ diameters of the circle, and still more, of course, is the circumference of the circle greater than 3⅛ diameters.

"1. It follows from the 4th Book of Euclid, that the rectangle under the side of a regular decagon inscribed in a circle, and that side increased by the radius, is equal to the square of the radius. But the product 791 (791 + 1280) is less than 1280 × 1280; if then the radius be 1280 the side of the decagon is greater than 791.

"2. When a diameter bisects a chord, the square of the chord is equal to the rectangle under the doubles of the segments of the diameter. But the product 125 (4 × 1280 - 125) is less than 791 × 791. If then the bisected chord be a side of the decagon, and if the radius be still 1280, the double of the lesser segment exceeds 125.

"3. The rectangle under this doubled segment and the radius is equal to the square of the side of an inscribed regular polygon of 20 sides. But the product 125 × 1280 is equal to 400 × 400; therefore, the side of the last-mentioned polygon is greater than 400, if the radius be still 1280. In other words, if the radius be represented by the new [115]member 16, and therefore the diameter by 32, this side is greater than 5, and the perimeter exceeds 100. So that, finally, if the diameter be 8, the perimeter of the inscribed regular polygon of 20 sides, and still more the circumference of the circle, is greater than 25: that is, the circumference is more than 3⅛ diameters."

The last work in the list was thus noticed in the Athenæum, May 27, 1865.

"Mr. James Smith appears to be tired of waiting for his place in the Budget of Paradoxes, and accordingly publishes a long letter to Professor De Morgan, with various prefaces and postscripts. The letter opens by a hint that the Budget appears at very long intervals, and 'apparently without any sufficient reason for it.' As Mr. Smith hints that he should like to see Mr. De Morgan, whom he calls an 'elephant of mathematics,' 'pumping his brains' 'behind the scenes'—an odd thing for an elephant to do, and an odd place to do it in—to get an answer, we think he may mean to hint that the Budget is delayed until the pump has worked successfully. Mr. Smith is informed that we have had the whole manuscript of the Budget, excepting only a final summing-up, in our hands since October, 1863. [This does not refer to the Supplement.] There has been no delay: we knew from the beginning that a series of historical articles would be frequently interrupted by the things of the day. Mr. James Smith lets out that he has never been able to get a private line from Mr. De Morgan in answer to his communications: we should have guessed it. He says, 'The Professor is an old bird and not to be easily caught, and by no efforts of mine have I been able, up to the present moment, either to induce or twit him into a discussion....' Mr. Smith curtails the proverb: old birds are not to be caught with chaff, nor with twit, which seems to be Mr. Smith's word for his own chaff, and, so long as the first letter is sounded, a very proper word. Why does he not try a little grain of sense? Mr. Smith evidently [116]thinks that, in his character as an elephant, the Professor has not pumped up brain enough to furnish forth a bird. In serious earnest, Mr. Smith needs no answer. In one thing he excites our curiosity: what is meant by demonstrating 'geometrically and mathematically?'"

I now proceed to my original treatment of the case.

Mr. James Smith will, I have no doubt, be the most uneclipsed circle-squarer of our day. He will not owe this distinction to his being an influential and respected member of the commercial world of Liverpool, even though the power of publishing which his means give him should induce him to issue a whole library upon one paradox. Neither will he owe it to the pains taken with him by a mathematician who corresponded with him until the joint letters filled an octavo volume. Neither will he owe it to the notice taken of him by Sir William Hamilton, of Dublin, who refuted him in a manner intelligible to an ordinary student of Euclid, which refutation he calls a remarkable paradox easily explainable, but without explaining it. What he will owe it to I proceed to show.

Until the publication of the Nut to Crack Mr. James Smith stood among circle-squarers in general. I might have treated him with ridicule, as I have done others: and he says that he does not doubt he shall come in for his share at the tail end of my Budget. But I can make a better job of him than so, as Locke would have phrased it: he is such a very striking example of something I have said on the use of logic that I prefer to make an example of his writings. On one point indeed he well deserves the scutica,^[210] if not the horribile flagellum.^[211] He tells me that he will bring his solution to me in such a form as shall compel me to admit it as un fait accompli [une faute accomplie?]^[212] [117]or leave myself open to the humiliating charge of mathematical ignorance and folly. He has also honored me with some private letters. In the first of these he gives me a "piece of information," after which he cannot imagine that I, "as an honest mathematician," can possibly have the slightest hesitation in admitting his solution. There is a tolerable reservoir of modest assurance in a man who writes to a perfect stranger with what he takes for an argument, and gives an oblique threat of imputation of dishonesty in case the argument be not admitted without hesitation; not to speak of the minor charges of ignorance and folly. All this is blind self-confidence, without mixture of malicious meaning; and I rather like it: it makes me understand how Sam Johnson came to say of his old friend Mrs. Cobb,^[213]—"I love Moll Cobb for her impudence." I have now done with my friend's suaviter in modo,^[214] and proceed to his fortiter in re^[215]: I shall show that he has convicted himself of ignorance and folly, with an honesty and candor worthy of a better value of π.

Mr. Smith's method of proving that every circle is 3⅛ diameters is to assume that it is so,—"if you dislike the term datum, then, by hypothesis, let 8 circumferences be exactly equal to 25 diameters,"—and then to show that every other supposition is thereby made absurd. The right to this assumption is enforced in the "Nut" by the following analogy:

"I think you (!) will not dare (!) to dispute my right to this hypothesis, when I can prove by means of it that every other value of π will lead to the grossest absurdities; unless indeed, you are prepared to dispute the right of Euclid to adopt a false line hypothetically for the purpose [118]of a 'reductio ad absurdum'^[216] demonstration, in pure geometry."

Euclid assumes what he wants to disprove, and shows that his assumption leads to absurdity, and so upsets itself. Mr. Smith assumes what he wants to prove, and shows that his assumption makes other propositions lead to absurdity. This is enough for all who can reason. Mr. James Smith cannot be argued with; he has the whip-hand of all the thinkers in the world. Montucla would have said of Mr. Smith what he said of the gentleman who squared his circle by giving 50 and 49 the same square root, Il a perdu le droit d'être frappé de l'évidence.^[217]

It is Mr. Smith's habit, when he finds a conclusion agreeing with its own assumption, to regard that agreement as proof of the assumption. The following is the "piece of information" which will settle me, if I be honest. Assuming π to be 3⅛, he finds out by working instance after instance that the mean proportional between one-fifth of the area and one-fifth of eight is the radius. That is,

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—

We naturally ask what sort of glimmer can Mr. Smith have of the subject which he professes to treat? On this point he has given satisfactory information. I had mentioned the old problem of finding two mean proportionals, [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^[218] for the sign of the square root, which embarrasses small type:

"This establishes the following infallible rule, for finding two mean proportionals OF EQUAL VALUE, and is more than a preliminary, to the famous old problem of 'Squaring the circle.' Let any finite number, say 20, and its fourth part = ¼(20) = 5, be given numbers. Then rq(20 × 5) = rq 100 = 10, is their mean proportional. Let this be a given mean proportional TO FIND ANOTHER MEAN PROPORTIONAL OF EQUAL VALUE. Then

will be the first number; as

will be the second number; therefore rq(15.625 × 6.4) = rq 100 = 10, is the required mean proportional.... Now, my good Sir, however competent you may be to prove every man a fool [not every man, Mr. Smith! only some; pray learn logical quantification] who now thinks, or in times gone by has thought, the 'Squaring of the Circle' a possibility; I doubt, and, on the evidence afforded by your Budget, I cannot help doubting, whether you were ever before competent to find two mean proportionals by my unique method."—(Nut, pp. 47, 48.) [That I never was, I solemnly declare!]

All readers can be made to see the following exposure. When 5 and 20 are given, x is a mean proportional when in 5, x, 20, 5 is to x as x to 20. And x must be 10. But x and y are two mean proportionals when in 5, x, y, 20, x [120]is a mean proportional between 5 and y, and y is a mean proportional between x and 20. And these means are x = 5 ³√4, y = 5 ³√16. But Mr. Smith finds one mean, finds it again in a roundabout way, and produces 10 and 10 as the two (equal!) means, in solution of the "famous old problem." This is enough: if more were wanted, there is more where this came from. Let it not be forgotten that Mr. Smith has found a translator abroad, two, perhaps three, followers at home, and—most surprising of all—a real mathematician to try to set him right. And this mathematician did not discover the character of the subsoil of the land he was trying to cultivate until a goodly octavo volume of letters had passed and repassed. I have noticed, in more quarters than one, an apparent want of perception of the full amount of Mr. Smith's ignorance: persons who have not been in contact with the non-geometrical circle-squarers have a kind of doubt as to whether anybody can carry things so far. But I am an "old bird" as Mr. Smith himself calls me; a Simorg, an "all-knowing Bird of Ages" in matters of cyclometry.

The curious phenomena of thought here exhibited illustrate, as above said, a remark I have long ago made on the effect of proper study of logic. Most persons reason well enough on matter to which they are accustomed, and in terms with which they are familiar. But in unaccustomed matter, and with use of strange terms, few except those who are practised in the abstractions of pure logic can be tolerably sure to keep their feet. And one of the reasons is easily stated: terms which are not quite familiar partake of the vagueness of the X and Y on which the student of logic learns to see the formal force of a proposition independently of its material elements.

I make the following quotation from my fourth paper on logic in the Cambridge Transactions:

"The uncultivated reason proceeds by a process almost entirely material. Though the necessary law of thought [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 increases, the laws of thought which are of most usual application are applied to familiar matter with tolerable safety. But difficulty and risk of error make a new appearance with a new subject; and this, in most cases, until new subjects are familiar things, unusual matter common, untried nomenclature habitual; that is, until it is a habit to be occupied upon a novelty. It is observed that many persons reason well in some things and badly in others; and this is attributed to the consequence of employing the mind too much upon one or another subject. But those who know the truth of the preceding remarks will not have far to seek for what is often, perhaps most often, the true reason.... I maintain that logic tends to make the power of reason over the unusual and unfamiliar more nearly equal to the power over the usual and familiar than it would otherwise be. The second is increased; but the first is almost created."

Mr. James Smith, by bringing ignorance, folly, dishonesty into contact with my name, in the way of conditional insinuation, has done me a good turn: he has given me right to a freedom of personal remark which I might have declined to take in the case of a person who is useful and respected in matters which he understands.

Tit for tat is logic all the world over. By the way, what has become of the rest of the maxim: we never hear it [122]now. When I was a boy, in some parts of the country at least, it ran thus:

He is a glaring instance of the truth of the observations quoted above. I will answer for it that, at the Mersey Dock Board, he never dreams of proving that the balance at the banker's is larger than that in the book by assuming that the larger sum is there, and then proving that the other supposition—the smaller balance—is upon that assumption, an absurdity. He never says to another director, How can you dare to refuse me a right to assume the larger balance, when you yourself, the other day, said,—Suppose, for argument's sake, we had 80,000l. at the banker's, though you knew the book only showed 30,000l.? This is the way in which he has supported his geometrical paradox by Euclid's example: and this is not the way he reasons at the board; I know it by the character of him as a man of business which has reached my ears from several quarters. But in geometry and rational arithmetic he is a smatterer, though expert at computation; at the board he is a trained man of business. The language of geometry is so new to him that he does not know what is meant by "two mean proportionals:" but all the phrases of commerce are rooted in his mind. He is most unerasably booked in the history of the squaring of the circle, as the speculator who took a right to assume a proposition for the destruction of other propositions, on the express ground that Euclid assumes a proposition to show that it destroys itself: which is as if the curate should demand permission to throttle the squire because St. Patrick drove the vermin to suicide to save themselves from slaughter. He is conspicuous as a speculator who, more visibly than almost any other known to history, reasoned in a circle by way of reasoning on a circle. But [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 disciplines. To this end I should desire him to continue his efforts, to amplify and develop his great principle, that of proving a proposition by assuming it and taking as confirmation every consequence that does not contradict the assumption.

Since my Budget commenced, Mr. Smith has written me notes: the portion which I have preserved—I suppose several have been mislaid—makes a hundred and seven pages of note-paper, closely written. To all this I have not answered one word: but I think I cannot have read fewer than forty pages. In the last letter the writer informs me that he will not write at greater length until I have given him an answer, according to the "rules of good society." Did I not know that for every inch I wrote back he would return an ell? Surely in vain the net is spread in the eyes of anything that hath a wing. There were several good excuses for not writing to Mr. J. Smith: I will mention five. First, I distinctly announced at the beginning of this Budget that I would not communicate with squarers of the circle. Secondly, any answer I might choose to give might with perfect propriety be reserved for this article; had the imputation of incivility been made after the first note, I should immediately have replied to this effect: but I presumed it was quite understood. Thirdly, Mr. Smith, by his publication of E. M.'s letters against the wish of the writer, had put himself out of the pale of correspondence. Fourthly, he had also gone beyond the rules of good society in sending [124]letter after letter to a person who had shown by his silence an intention to avoid correspondence. Fifthly, these same rules of good society are contrived to be flexible or frangible in extreme cases: otherwise there would be no living under them; and good society would be bad. Father Aldrovand has laid down the necessary distinction—"I tell thee, thou foolish Fleming, the text speaketh but of promises made unto Christians, and there is in the rubric a special exemption of such as are made to Welchmen." There is also a rubric to the rules of good society; and squarers of the circle are among those whom there is special permission not to answer: they are the wild Welchmen of geometry, who are always assailing, but never taking, the Garde Douloureuse^[219] of the circle. "At this commentary," proceeds the story, "the Fleming grinned so broadly as to show his whole case of broad strong white teeth." I know not whether the Welchman would have done the like, but I hope Mr. James Smith will: and I hope he has as good a case to show as Wilkin Flammock. For I wish him long life and long health, and should be very glad to see so much energy employed in a productive way. I hope he wishes me the same: if not, I will give him what all his judicious friends will think a good reason for doing so. His pamphlets and letters are all tied up together, and will form a curious lot when death or cessation of power to forage among book-shelves shall bring my little library to the hammer. And this time may not be far off: for I was X years old in A.D. X²; not 4 in A.D. 16, nor 5 in A.D. 25, but still in one case under that law. And now I have made my own age a problem of quadrature, and Mr. J. Smith may solve it. But I protest against his method of assuming a result, and making itself prove itself: he might in this way, as sure as eggs is eggs (a corruption of X is X), make me 1,864 years old, which is a great deal too much.

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

But he promises to give the public his nut-cracker if I do not, before the Budget is concluded, "unravel" the paradox, which is the mathematico-geometrical nut he has given me to crack. Mr. Smith is a crack man: he will crack his own nut; he will crack my shell; in the mean time he cracks himself up. Heaven send he do not crack himself into lateral contiguity with himself.

On June 27 I received a letter, in the handwriting of Mr. James Smith, signed Nauticus. I have ascertained [126]that one of the letters to the Athenæum signed Nauticus is in the same handwriting. I make a few extracts:

"... The important question at issue has been treated by a brace of mathematical birds with too much levity. It may be said, however, that sarcasm and ridicule sometimes succeed, where reason fails.... Such a course is not well suited to a discussion.... For this reason I shall for the future [this implies there has been a past, so that Nauticus is not before me for the first time] endeavor to confine myself to dry reasoning from incontrovertible premises.

... It appears to me that so far as his theory is concerned he comes off unscathed. You might have found "a hole in Smith's circle" (have you seen a pamphlet bearing this title? [I never heard of it until now]), but after all it is quite possible the hole may have been left by design, for the purpose of entrapping the unwary."

[On the publication of the above, the author of the pamphlet obligingly forwarded a copy to me of A Hole in Smith's Circle—by a Cantab: Longman and Co., 1859, (pp. 15). "It is pity to lose any fun we can get out of the affair," says my almamaternal brother: to which I add that in such a case warning without joke is worse than none at all, as giving a false idea of the nature of the danger. The Cantab takes some absurdities on which I have not dwelt: but there are enough to afford a Cantab from every college his own separate hunting ground.]

Does this hint that his mode of proof, namely, assuming the thing to be proved, was a design to entrap the unwary? if so, it bangs Banagher. Was his confounding two mean proportionals with one mean proportional found twice over a trick of the same intent? if so, it beats cockfighting. That Nauticus is Mr. Smith appears from other internal evidence. In 1819, Mr. J. C. Hobhouse^[222] was sent to Newgate for a [127]libel on the House of Commons which was only intended for a libel on Lord Erskine.^[223] The ex-Chancellor had taken Mr. Hobhouse to be thinking of him in a certain sentence; this Mr. Hobhouse denied, adding, "There is but one man in the country who is always thinking of Lord Erskine." I say that there is but one man of our day who would couple me and Mr. James Smith as a "brace of mathematical birds."

Mr. Smith's "theory" is unscathed by me. Not a doubt about it: but how does he himself come off? I should never think of refuting a theory proved by assumption of itself. I left Mr. Smith's π untouched: or, if I put in my thumb and pulled out a plum, it was to give a notion of the cook, not of the dish. The "important question at issue" was not the circle: it was, wholly and solely, whether the abbreviation of James might be spelled Jimm.^[224] This is personal to the verge of scurrility: but in literary controversy the challenger names the weapons, and Mr. Smith begins with charge of ignorance, folly, and dishonesty, by conditional implication. So that the question is, not the personality of a word, but its applicability to the person designated: it is enough if, as the Latin grammar has it, Verbum personale concordat cum nominativo.^[225]

I may plead precedent for taking a liberty with the orthography of Jem. An instructor of youth was scandalized at the abrupt and irregular—but very effective—opening of Wordsworth's little piece:

[128]

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

The brother, we infer from sound, was to be James, and the blank must therefore be filled up with Jimb.

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

Mr. Smith invites me to say which is wrong, the quadrature, or the tables: I leave him to guess. He says his assertions "arise naturally and necessarily out of the arguments of a circle-squarer:" he might just as well lay down that all the pigs went to market because it is recorded that "This pig went to market." I must say for circle-squarers that very few bring their pigs to so poor a market. I answer the above argument because it is, of all which Mr. James Smith has produced, the only one which rises to the level of a schoolboy: to meet him halfway I descend to that level.

Mr. Smith asks me to solve a problem in the Athenæum: [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 xy? secondly, what is the angle of which xy represents the circular measure?"

If x represent 15° and y be ¼, xy represents 3° 45', whether x - y be xy or no. But, y being ¼, x - y is not xy unless x be ⅓, that is, unless 12x or π be 4, which Mr. Smith would not admit. How could a person who had just received such a lesson as I had given immediately pray for further exposure, furnishing the stuff so liberally as this? Is it possible that Mr. Smith, because he signs himself Nauticus, means to deny his own very regular, legible, and peculiar hand? It is enough to make the other members of the Liverpool Dock Board cry, Mersey on the man!

Mr. Smith says that for the future he will give up what he calls sarcasm, and confine himself, "as far as possible," to what he calls dry reasoning from incontrovertible premises. If I have fairly taught him that his sarcasm will not succeed, I hope he will find that his wit's end is his logic's beginning.

I now reply to a question I have been asked again and again since my last Budget appeared: Why do you take so much trouble to expose such a reasoner as Mr. Smith? I answer as a deceased friend of mine used to answer on like occasions—A man's capacity is no measure of his power to do mischief. Mr. Smith has untiring energy, which does something; self-evident honesty of conviction, which does more; and a long purse, which does most of all. He has made at least ten publications, full of figures which few readers can criticize. A great many people are staggered to this extent, that they imagine there must be [130]the indefinite something in the mysterious all this. They are brought to the point of suspicion that the mathematicians ought not to treat "all this" with such undisguised contempt, at least. Now I have no fear for π: but I do think it possible that general opinion might in time demand that the crowd of circle-squarers, etc. should be admitted to the honors of opposition; and this would be a time-tax of five per cent., one man with another, upon those who are better employed. Mr. James Smith may be made useful, in hands which understand how to do it, towards preventing such opinion from growing. A speculator who expressly assumes what he wants to prove, and argues that all which contradicts it is absurd, because it cannot stand side by side with his assumption, is a case which can be exposed to all. And the best person to expose it is one who has lived in the past as well as the present, who takes misthinking from points of view which none but a student of history can occupy, and who has something of a turn for the business.

Whether I have any motive but public good must be referred to those who can decide whether a missionary chooses his pursuit solely to convert the heathen. I shall certainly be thought to have a little of the spirit of Col. Quagg, who delighted in strapping the Grace-walking Brethren. I must quote this myself: if I do not, some one else will, and then where am I? The Colonel's principle is described as follows:

"I licks ye because I kin, and because I like, and because ye'se critters that licks is good for. Skins ye have on, and skins I'll have off; hard or soft, wet or dry, spring or fall. Walk in grace if ye like till pumpkins is peaches; but licked ye must be till your toe-nails drop off and your noses bleed blue ink. And—licked—they—were—accordingly."

I am reminded of this by the excessive confidence with which Mr. James Smith predicted that he would treat me as Zephaniah Stockdolloger (Sam Slick calls it slockdollager) treated Goliah Quagg. He has announced his [131]intention of bringing me, with a contrite heart, and clean shaved,—4159265... razored down to 25,—to a camp-meeting of circle-squarers. But there is this difference: Zephaniah only wanted to pass the Colonel's smithy in peace; Mr. James Smith sought a fight with me. As soon as this Budget began to appear, he oiled his own strap, and attempted to treat me as the terrible Colonel would have treated the inoffensive brother.

He is at liberty to try again.

THE MOON HOAX.

This is a reprint of the hoax already mentioned. I suppose R. A. Locke is the name assumed by M. Nicollet.^[227] The publisher informs us that when the hoax first appeared day by day in a morning paper, the circulation increased fivefold, and the paper obtained a permanent footing. Besides this, an edition of 60,000 was sold off in less than one month.

The discovery was also published under the name of A. R. Grant.^[228] Sohncke's^[229] Bibliotheca Mathematica confounds this Grant with Prof. R. Grant^[230] of Glasgow, the author of the History of Physical Astronomy, who is accordingly made to guarantee the discoveries in the moon. I hope Adams Locke will not merge in J. C. Adams,^[231] the co-discoverer of Neptune. Sohncke gives the titles of [132]three French translations of the Moon hoax at Paris, of one at Bordeaux, and of Italian translations at Parma, Palermo, and Milan.

A Correspondent, who is evidently fully master of details, which he has given at length, informs me that the Moon hoax appeared first in the New York Sun, of which R. A. Locke was editor. It so much resembled a story then recently published by Edgar A. Poe, in a Southern paper, "Adventures of Hans Pfaal," that some New York journals published the two side by side. Mr. Locke, when he left the New York Sun, started another paper, and discovered the manuscript of Mungo Park;^[232] but this did not deceive. The Sun, however, continued its career, and had a great success in an account of a balloon voyage from England to America, in seventy-five hours, by Mr. Monck Mason,^[233] Mr. Harrison Ainsworth,^[234] and others. I have no doubt that M. Nicollet was the author of the Moon hoax,^[235] written in a way which marks the practised observatory astronomer beyond all doubt, and by evidence seen in the most minute details. Nicollet had an eye to Europe. I suspect that he took Poe's story, and made it a basis for his own. Mr. Locke, it would seem, when he attempted a fabrication for himself, did not succeed.

The earth 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 [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.

Athenæum, August, 19, 1865. Notice to Correspondents.

"R. W.—If you will consult the opening chapter of the Budget of Paradoxes, you will see that the author presents only works in his own library at a given date; and this for a purpose explained. For ourselves we have carefully avoided allowing any writers to present themselves in our columns on the ground that the Budget has passed them over. We gather that Mr. De Morgan contemplates additions at a future time, perhaps in a separate and augmented work; if so, those who complain that others of no greater claims than themselves have been ridiculed may find themselves where they wish to be. We have done what we can for you by forwarding your letter to Mr. De Morgan."

The author of "An Essay on the Constitution of the Earth," published in 1844, demanded of the Athenæum, as an act of fairness, that a letter from him should be published, proving that he had as much right to be "impaled" as Capt. Drayson. He holds, on speculative grounds, what the other claims to have proved by measurement, namely, that the earth is growing; and he believes that in time—a good long time, not our time—the earth and other planets may grow into suns, with systems of their own.

This gentleman sent me a copy of his work, after the commencement of my Budget; but I have no recollection of having received it, and I cannot find it on the (nursery? [134]quarantine?) shelves on which I keep my unestablished discoveries. Had I known of this work in time, (see the Introduction) I should of course, have impaled it (heraldically) with the other work; but the two are very different. Capt. Drayson professes to prove his point by results of observation; and I think he does not succeed. The author before me only speculates; and a speculator can get any conclusion into his premises, if he will only build or hire them of shape and size to suit. It reminds me of a statement I heard years ago, that a score of persons, or near it, were to dine inside the skull of one of the aboriginal animals, dear little creatures! Whereat I wondered vastly, nothing doubting; facts being stubborn and not easy drove, as Mrs. Gamp said. But I soon learned that the skull was not a real one, but artificially constructed by the methods—methods which have had striking verifications, too—which enable zoologists to go the whole hog by help of a toe or a bit of tail. This took off the edge of the wonder: a hundred people can dine inside an inference, if you draw it large enough. The method might happen to fail for once: for instance, the toe-bone might have been abnormalized by therian or saurian malady; and the possibility of such failure, even when of small probability, is of great alleviation. The author before me is, apparently, the sole fabricator of his own premises. With vital force in the earth and continual creation on the part of the original Creator, he expands our bit of a residence as desired. But, as the Newtoness of Cookery observed, First catch your hare. When this is done, when you have a growing earth, you shall dress it with all manner of proximate causes, and serve it up with a growing Moon for sauce, a growing Sun, if it please you, at the other end, and growing planets for side-dishes. Hoping this amount of impalement will be satisfactory, I go on to something else. [135]

THE HAILESEAN SYSTEM OF ASTRONOMY.

He offers to take 100,000l. to 1,000l. that he shows the sun to be less than seven millions of miles from the earth. The earth in the center, revolving eastward, the sun revolving westward, so that they "meet at half the circle distance in the 24 hours." The diameter of the circle being 9839458303, the circumference is 30911569920.

The following written challenge was forwarded to the Council of the Astronomical Society: it will show the "general reader"—and help him towards earning his name—what sort of things come every now and then to our scientific bodies. I have added punctuation:

Mr. Hailes still issues his flying sheets. The last I have met with (October 7, 1863) informs us that the latitude of [136]England is slowly increasing, which is the true cause of the alteration in the variation of the magnet.

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

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

A CHANCE FOR INVENTORS.

[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 Esné, offered, at five francs a head, to tell the shareholders the exact amount of gold and diamonds which each would get, and to make up the amount predicted to those who got less. There are moods of the market in England in which this company could have been formed: so we must not laugh at our neighbors.

JOHANNES VON GUMPACH.

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 [138]recognized law of optics to the astronomical theory, showing the true orbits of the heavenly bodies to be perfectly circular, and their orbital motions to be perfectly uniform." all irregularities being, I suppose, optical delusions. Mr. Von Gumpach is a learned man; what else, time must show.

SLANDER PARADOXES.

A useful collection on the history of the attempts at perpetual motion, that is, at obtaining the consequences of power without any power to produce them. September 7, 1863, a correspondent of the Times gave an anecdote of George Stephenson,^[244] which he obtained from Robert Stephenson.^[245] A perpetual motionist wanted to explain his method; to which George replied—"Sir! I shall believe it when I see you take yourself up by the waistband, and carry yourself about the room." Never was the problem better stated.

There is a paradox of which I ought to give a specimen, I mean the slander-paradox; the case of a person who takes it into his head, upon evidence furnished entirely by the workings of his own thoughts, that some other person has committed a foul act of which the world at large would no more suppose him guilty than they would suppose that the earth is a flat bordered by ice. If I were to determine on giving cases in which the self-deluded person imagines [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.^[246]

1862. On new year's day, 1862, when the nation was in the full tide of sympathy with the Queen, and regret for its own loss, a paper called the Free Press published a number devoted to the consideration of the causes of the death of the Prince Consort. It is so rambling and inconsecutive that it takes more than one reading to understand it. It is against the Times newspaper. First, the following insinuation:

"To the legal mind, the part of [the part taken by] the Times will present a prima facie case of the gravest nature, in the evident fore-knowledge of the event, and the preparation to turn it to account when it should have occurred. The article printed on Saturday must have been written on Friday. That article could not have appeared had the Prince been intended to live."

Next, it is affirmed that the Times intended to convey the idea that the Prince had been poisoned.

"Up to this point we are merely dealing with words which the Times publishes, and these can leave not a shadow of doubt that there is an intention to promulgate the idea that Prince Albert had been poisoned."

The article then goes on with a strange olio of [140]insinuations to the effect that the Prince was the obstacle to Russian intrigue, and that if he should have been poisoned,—which the writer strongly hints may have been the case,—some Minister under the influence of Russia must have done it. Enough for this record. Un sot trouve toujours un plus sot qui l'admire:^[247] who can he be in this case?

THE NEPTUNE CONTROVERSY.

1846. At the end of this year arose the celebrated controversy relative to the discovery of Neptune. Those who know it are well aware that Mr. Adams's^[248] now undoubted right to rank with Le Verrier^[249] was made sure at the very outset by the manner in which Mr. Airy,^[250] the Astronomer Royal, came forward to state what had taken place between himself and Mr. Adams. Those who know all the story about Mr. Airy being arrested in his progress by the neglect of Mr. Adams to answer a letter, with all the imputations which might have been thrown upon himself for laxity in the matter, know also that Mr. Airy's conduct exhibited moral courage, honest feeling, and willingness to sacrifice himself, if need were, to the attainment of the ends of private justice, and the establishment of a national claim. A writer in a magazine, in a long and elaborate article, argued the supposition—put in every way except downright assertion, after the fashion of such things—that Mr. Airy had communicated Mr. Adams's results to M. Le Verrier, with intention that they should be used. His presumption as to motive is that, had Mr. Adams been recognized, "then the discovery must have been indisputably an Englishman's, and that Englishman not the Astronomer Royal." Mr. Adams's conclusions were "retouched in France, and sent [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 Challis's^[251] valuable testimony as to their probable accuracy, and did not bring the French astronomer acquainted with them, especially as he was aware that his friend was engaged in matters bearing directly upon these results?"

The whole argument the author styles "evidence which I consider it difficult to refute." He ends by calling upon certain persons, of whom I am one, to "see ample justice done." This is the duty of every one, according to his opportunities. So when the reputed author—the article being anonymous—was, in 1849, proposed as a Fellow of the Astronomical Society, I joined—if I remember right, I originated—an opposition to his election, until either the authorship should be denied, or a proper retraction made. The friends of the author neither denied the first, nor produced the second: and they judged it prudent to withdraw the proposal. Had I heard of any subsequent repentance, I would have taken some other instance, instead of this: should I yet hear of such a thing, I will take care to notice it in the continuation of this list, which I confidently expect, life and health permitting, to be able to make in a few years. This much may be said, that the author, in a lecture on the subject, given in 1849, and published with his name, did not repeat the charge.

[The libel was published in the Mechanics' Magazine,^[252] (vol. for 1846, pp. 604-615): and the editor supported it as follows, (vol. for 1847, p. 476). In answer to Mr. Sheepshanks's charitable hope that he had been hoaxed, [142]he says: "Mr. Sheepshanks cannot certainly have read the article referred to.... Severe and inculpatory it is—unjust some may deem it (though we ourselves are out of the number.)... A 'hoax' forsooth! May we be often the dupes of such hoaxes!" He then goes on to describe the article as directed against the Astronomer Royal's alleged neglect to give Mr. Adams that "encouragement and protection" which was his due, and does not hint one word about the article containing the charge of having secretly and fraudulently transmitted news of Mr. Adams's researches to France, that an Englishman might not have the honor of the discovery. Mr. Sheepshanks having called this a "deliberate calumny," without a particle of proof or probability to support it, the editor says "what the reverend gentleman means by this, we are at a loss to understand." He then proceeds not to remember. I repeat here, what I have said elsewhere, that the management of the journal has changed hands; but from 1846 to 1856, it had the collar of S.S. (scientific slander). The prayer for more such things was answered (See p. 349).]

JAMES IVORY.^[253]

I have said that those who are possessed with the idea of conspiracy against themselves are apt to imagine both conspirators and their bad motives and actions. A person who should take up the idea of combination against himself without feeling ill-will and originating accusations would be indeed a paradox. But such a paradox has existed. It is very well known, both in and beyond the scientific world, that the late James Ivory was subject to the [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, especially from my friend the late Thomas Galloway^[254]—who came after him at Sandhurst—one of the few persons with whom he was intimate:—I have decided, after full deliberation, to forestall the future biographies.

That Ivory was haunted by the fear of which I have spoken, to the fullest extent, came to my own public and official knowledge, as Secretary of the Astronomical Society. It was the duty of Mr. Epps,^[255] the Assistant Secretary, at the time when Francis Baily^[256] first announced his discovery of the Flamsteed Papers, to report to me that Mr. Ivory had called at the Society's apartments to inquire into the contents of those papers, and to express his hope that Mr. Baily was not attacking living persons under the names of Newton and Flamsteed.^[257] Mr. Galloway, to whom I communicated this, immediately went to Mr. Ivory, and succeeded, after some explanation, in setting him right. This is but one of many instances in which a man of thoroughly sound judgment in every other respect seemed to be under a complete chain of delusions about the conduct of [144]others to himself. But the paradox is this:—I never could learn that Ivory, passing his life under the impression that secret and unprovoked enemies were at work upon his character, ever originated a charge, imputed a bad motive, or allowed himself an uncourteous expression. Some letters of his, now in my possession, referring to a private matter, are, except in the main impression on which they proceed, unobjectionable in every point: they might have been written by a cautious friend, whose object was, if possible, to prevent a difference from becoming a duel without compromising his principal's rights or character. Knowing that in some quarters the knowledge of Ivory's peculiarity is more or less connected with a notion that the usual consequences followed, I think the preceding statement due to his memory.

THREE CLASSES OF JOURNALS.

In such a record as the present, which mixes up the grossest speculative absurdities with every degree of what is better, an instance of another kind may find an appropriate place. The faults of journalism, when merely exposed by other journalism pass by and are no more regarded. A distinct account of an undeniable meanness, recorded in a work of amusement and reference both, may have its use: such a thing may act as a warning. An editor who is going to indulge his private grudge may be prevented from counting upon oblivion as a matter of certainty.

There are three kinds of journals, with reference to the mode of entrance of contributors. First, as a thing which has been, but which now hardly exists, there is the journal in which the editor receives a fixed sum to find the matter. In such a journal, every article which the editor can get a friend to give him is so much in his own pocket, which has a great tendency to lower the character of the articles; but I am not concerned with this point. Secondly, there is the journal which is supported by voluntary contributions of [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^[258] declined a cheque forwarded for an article in the Quarterly, John Murray^[259] sent it back with a blunt threat that if he did not take his money he could never be admitted again. The great publisher told him that if men like himself in position worked for nothing, all the men like himself in talent who could not afford it would not work for the Quarterly. If the above did not happen between Canning and Murray, it must have happened between some other two. Now journals of the second class—and of the first, if such there be—have a fault to which they alone are very liable, to say nothing of the editorial function (see the paper at the beginning, p. 11 et seq.), being very much cramped, a sort of gratitude towards effective contributors leads the journal to help their personal likes and dislikes, and to sympathize with them. Moreover, this sort of journal is more accessible than others to articles conveying personal imputation: and when these provoke discussion, the journal is apt to take the part of the assailant to whom it lent itself in the first instance.

THE MECHANICS' MAGAZINE.

Among the journals which went all lengths with contributors whom they valued, was the Mechanics' Magazine^[260] in the period 1846-56. I cannot say that matters have not mended in the last ten years: and I draw some [146]presumption that they have mended from my not having heard, since 1856, of anything resembling former proceedings. And on actual inquiry, made since the last sentence was written, I find that the property has changed hands, the editor is no longer the same, and the management is of a different stamp. This journal is chiefly supported by voluntary articles: and it is the journal in which, as above noted, the ridiculous charge against the Astronomer Royal was made in 1849. The following instance of attempt at revenge is so amusing that I select it as the instance of the defect which I intend to illustrate; for its puerility brings out in better relief the points which are not so easily seen in more adult attempts.

The Mechanics' Magazine, which by its connection with engineering, etc., had always taken somewhat of a mathematical character, began, a little before 1846, to have more to do with abstract science. Observing this, I began to send short communications, which were always thankfully received, inserted, and well spoken of. Any one who looks for my name in that journal in 1846-49, will see nothing but the most respectful and even laudatory mention. In May 1849 occurred the affair at the Astronomical Society, and my share in forcing the withdrawal of the name of the alleged contributor to the journal. In February 1850 occurred the opportunity of payment. The Companion to the Almanac^[261] had to be noticed, in which, as then usual, was an article signed with my name. I shall give the review of this article entire, as a sample of a certain style, as well as an illustration of my point. The reader will observe that my name is not mentioned. This would not have done; the readers of the Magazine would have stared to see a name of not infrequent occurrence in previous years all of a sudden fallen from the heaven of respect into the pit of contempt, like Lucifer, son of the morning. But before [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 forward to shield his champion. This gave deadly offence, as appear from the following passage, (February 16, 1850):

"It was our intention to enter into a comparison of the contents of our Nautical Almanack with those of its rival, the Connaissance des Temps; but we shall defer it for the present. The Nautical Almanack for 1851 will contain Mr. Adams's paper 'On the Perturbation of Uranus'; and when it comes, in due course, before the public, we are quite sure that that gentleman will expect that we shall again enter upon the subject with peculiar delight. Whilst we have a thorough loathing for mean, cowardly, crawlers—we have an especial pleasure in maintaining the claims of men who are truly grateful as well as highly talented: Mr. Adams, therefore, will find that he cannot be disappointed—and the occasion will afford us an opportunity for making the comparison to which we have adverted."

This passage illustrates what I have said on the editorial function (Vol. I, p. 15). What precedes and follows has some criticism on the Government, the Astronomer Royal, etc., but reserved in allusion, oblique in sarcasm, and not fiercely uncourteous. The coarseness of the passage I have quoted shows editorial insertion, which is also shown by its blunder. The inserter is waiting for the Almanac of 1851 that he may review Mr. Adams's paper, which is to be contained in it. His own contributor, only two sentences before the insertion, had said, "The Nautical Almanac, we believe, is published three or four years in advance." In fact, the Almanac for 1851—with Mr. Adams's paper at the end—was published at the end of 1847 or very beginning of 1848; it had therefore been more than two years before the public when the passage quoted was written. And probably every person in the country who was fit to review Mr. Adams's [148]paper—and most of those who were fit to read it—knew that it had been widely circulated, in revise, at the end of 1846: my copy has written on it, "2d revise, December 27, 1846, at noon," in the handwriting of the Superintendent of the Almanac; and I know that there was an extensive issue of these revises, brought out by the Le-Verrier-and-Adams discussion. I now give the review of myself, (February 23, 1850):

"The British Almanack and Companion.

"The Companion to this Almanack, for some years after its first publication, annually contained scientific articles by Sir J. Lubbock^[262] and others of a high order and great interest; we have now, however, closed the publication as a scientific one in remembrance of what it was, and not in consequence of what it is. Its list of contributors on science, has grown 'small by degrees and beautifully less,' until it has dwindled down to one—'a last rose of summer left withering alone.' The one contributor has contributed one paper 'On Ancient and Modern Usage in Reckoning.'

"The learned critic's chef d'œuvre, is considered, by competent judges, to be an Essay on Old Almanacks printed a few years ago in this annual, and supposed to be written with the view of surpassing a profound memoir on the same subject by James O. Halliwell,^[263] Esq., F.R. and A.S.S., but the tremendous effort which the learned writer then made to excel many titled competitors for honors in the antique line appears to have had a sad effect upon his mental powers—at any rate, his efforts have since yearly become duller and duller; happily, at last, we should suppose, 'the ancient [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-examination will find some strange conclusions arrived at by us.' The writer never wrote a more correct sentence—it admits of no kind of dispute.

"'Language and counting,' says the learned author, 'both came before the logical discussion of either. It is not allowable to argue that something is or was, because it ought to be or ought to have been. That two negatives make an affirmative, ought to be; if no man have done nothing, the man who has done nothing does not exist, and every man has done something. But in Greek, and in uneducated English, it is unquestionable that 'no man has done nothing' is only an emphatic way of saying that no man has done anything; and it would be absurd to reason that it could not have been so, because it should not.'—p. 5.

"'But there is another difference between old and new times, yet more remarkable, for we have nothing of it now: whereas in things indivisible we count with our fathers, and should say in buying an acre of land, that the result has no parts, and that the purchaser, till he owns all the ground, owns none, the change of possession being instantaneous. This second difference lies in the habit of considering nothing, nought, zero, cipher, or whatever it may be called, to be at the beginning of the scale of numbers. Count four days from Monday: we should now say Tuesday, Wednesday, Thursday, Friday; formerly, it would have been Monday, Tuesday, Wednesday, Thursday. Had we asked, what at that rate is the first day from Monday, all would have stared at a phrase they had never heard. Those who were capable of extending language would have said, Why it must be Monday itself: the rest would have said, there can [150]be no first day from Monday, for the day after is Tuesday, which must be the second day: Monday, one; Tuesday, two,'—p. 10.

"We assure our readers that the whole article is equally lucid, and its logic alike formal.

"There are some exceedingly valuable footnotes; we give one of the most interesting, taken from the learned Mr. Halliwell's profound book on Nursery Rhymes^[264]—a celebrated production, for which it is supposed the author was made F.R.S.

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

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

In December, 1846, the Mechanics' Magazine published a libel on Airy in the matter of the discovery of Neptune. In May, 1849, one * * * was to have been brought forward for election at the Astronomical Society, and was opposed by me and others, on the ground that he was the probable author of this libel, and that he would not, perhaps could [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.]^[265]

Accordingly, * * * was withdrawn, and a discussion took place, for which see the Athenæum, No. 1126, May 26, 1849, p. 544. The Mechanics' Magazine was very sore, but up to this day has never ventured beyond an attack on Airy, private whisperings against Adams—(see ante, p. 147),—and the above against myself. In due time, I doubt not my name will appear as one of the âmes damnées^[266] of the Mechanics' Magazine.^[267]

T. S. DAVIES ON EUCLID.

First, as to Mr. Halliwell. The late Thomas Stephens Davies,^[268] excellent in geometry, and most learned in its history, was also a good hand at enmity, though not implacable. He and Mr. Halliwell, who had long before been very much one, were, at this date, very much two. I do not think T. S. Davies wrote this article; and I think that by giving my reasons I shall do service to his memory. It must have been written at the beginning of February; and within three days of that time T. S. Davies was making over to me, by his own free act, to be kept until claimed by the relatives, what all who knew even his writings knew that he considered as the most precious deposit he had ever had in his keeping—Horner's^[269] papers. His letter announcing the transmission is dated February 2, 1850. This is a strong point; but there is another quite as strong. Euclid and [152]his writings were matters on which T. S. Davies knew neither fear nor favor: he could not have written lightly about a man who stood high with him as a judge of Euclid. Now in this very letter of Feb. 2, there is a sentence which I highly value, because, as aforesaid, it is on a point on which he would never have yielded anything, to which he had paid life-long attention, and on which he had the bias of having long stood alone. In fact, knowing—and what I shall quote confirms me,—that in the matter of Euclid his hand was against every man, I expected, when I sent him a copy of my 22-column article, "Eucleides" in Smith's Dictionary,^[270] to have received back a criticism, that would have blown me out of the water: and I thought it not unlikely that a man so well up in the subject might have made me feel demolished on some points. Instead of this, I got the following: "Although on one or two minor points I do not quite accord with your views, yet as a whole and without regard to any minor points, I think you are the first who has succeeded in a delineation of Euclid as a geometer." All this duly considered, it is utterly incredible that T. S. Davies should have written the review in question. And yet Mr. Halliwell is treated just as T. S. Davies would have treated him, as to tone and spirit. The inference in my mind is that we have here a marked instance of the joining of hatreds which takes place in journals supported by voluntary contributions of matter. Should anything ever have revived this article—and no one ever knows what might have been fished up from the forgotten mass of journals—the treatment of Mr. Halliwell would certainly have thrown a suspicion on T. S. Davies, a large and regular contributor to the Magazine. It is good service to his memory to point out what makes it incredible that he should have written so unworthy an article.

The fault is this. There are four extracts: the first [153]three are perfectly well printed. The printing of the Mechanics' Magazine was very good. I was always exceedingly satisfied with the manner in which my articles appeared, without my seeing proof. Most likely these extracts were printed from my printed paper; if not the extractor was a good copier. I know this by a test which has often served me. I use the subjunctive—"if no man have done nothing," an ordinary transcriber, narrating a quotation almost always lets his own habit write has. The fourth extract has three alterations, all tending to make me ridiculous. None is altered, in two places, into nine, denial into decimal, and comes into aims; so that "none, the denial of one, comes to be associated with the denial of plurality," reads as "nine, the decimal of one, aims to be associated with the decimal of plurality." This is intentional; had it been a compositor's reading of bad handwriting, these would not have been the only mistakes; to say nothing of the corrector of the press. And both the compositor and reader would have guessed, from the first line being translated into "one is not one," that it must have been "one's none," not "one's nine." But it was not intended that the gem should be recovered from the unfathomed cave, and set in a Budget of Paradoxes.

We have had plenty of slander-paradox. I now give a halfpennyworth of bread to all this sack, an instance of the paradox of benevolence, in which an individual runs counter to all the ideas of his time, and sees his way into the next century. At Amiens, at the end of the last century, an institution was endowed by a M. de Morgan, to whom I hope I am of kin, but I cannot trace it; the name is common at Amiens. It was the first of the kind I ever heard of. It is a Salle d'Asyle for children, who are taught and washed and taken care of during the hours in which their parents must be at work. The founder was a large wholesale grocer and colonial importer, who was made a Baron by Napoleon I for his commercial success and his charities. [154]

JAS. SMITH AGAIN.

1862. Mr. Smith replies to me, still signing himself Nauticus: I give an extract:

"By hypothesis [what, again!] let 14° 24' be the chord of an arc of 15° [but I wont, says 14° 24'], and consequently equal to a side of a regular polygon of 24 sides inscribed in the circle. Then 4 times 14° 24' = 57° 36' = the radius of the circle ..."

That is, four times the chord of an arc is the chord of four times the arc: and the sum of four sides of a certain pentagon is equal to the fifth. This is the capital of the column, the crown of the arch, the apex of the pyramid, the watershed of the elevation. Oh! J. S.! J. S.! groans Geometry—Summum J. S. summa injuria!^[271] The other J. S., Joseph Scaliger,^[272] as already mentioned, had his own way of denying that a straight line is always the shortest distance between two points. A parallel might be instituted, but not in half a column. And J. S. the second has been so tightly handled that he may now be dismissed, with an inscription for his circular shield, obtained by changing Lexica contexat into Circus quadrandus in an epigram of J. S. the first:

[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 detected by an effort of reasoning which I never could have made except by following in his steps. In all matters connected with π the letters l and g are closely related: this appears in the well-known formula for the time of oscillation π √(l : g). Hence g may be written for l, but only once: do it twice, and you require the time to be π √(l² : g²). This may be reinforced by observing that if as a datum, or if you dislike that word, by hypothesis, the first l be a g, it is absurd that it should be an l. Write g for the first l, and we have un fait accompli. I shall be in pillory; and overhead, in a cloud, will sit Mr. James Smith on one stick laid across two others, under a nimbus of 3⅛ diameters to [156]the circumference—in π-glory. Oh for a drawing of this scene! Mr. De Morgan presents his compliments to Mr. James Smith, and requests the honor of an exchange of photographs.

July 26.—Another printed letter.—Mr. James Smith begs for a distinct answer to the following plain question: "Have I not in this communication brought under your notice truths that were never before dreamed of in your geometrical and mathematical philosophy?" To which, he having taken the precaution to print the word truths in italics, I can conscientiously answer, Yes, you have. And now I shall take no more notice of these truths, until I receive something which surpasses all that has yet been done.

A FEW SMALL PARADOXERS.

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

Newton and others think that in a revolving sphere the [157]loose surface matter will tend to the equator: Mr. Bakewell thinks it will tend to the poles.

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

[158]

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

DR. THORN AND MR. BIDEN.

This is much about Thorn, and its connected words, Thor, Thoth, Theta, etc. It is a very mysterious vagary. The author of it is the person whom I have described elsewhere as having for his device the round man in the three-cornered hole, the writer of the little heap of satirical anonymous letters about the Beast and 666. By accident I discovered the writer: so that if there be any more thorns to crackle under the pot, they need not be anonymous.

Nor will they be anonymous. Since I wrote the above, I have received onymous letters, as ominous as the rest. The writer, William Thorn, M.D., is obliged to reveal [159]himself, since it is his object to prove that he himself is one 666. By using W for double Vau (or 12) he cooks the number out of his own name. But he says it is the number not of a beast but of a man, and adds, "Thereby hangs a tale!" which sounds like contradiction. He informs me that he will talk the matter over with me: but I shall certainly have nothing to say to a gentleman of his number; it is best to keep on the safe side.

In one letter I am informed that not a line should I have had, but for my "sneer at 666," which, therefore, I am well pleased to have given. I am also told that my name means the "'garden of death,' that place in which the tree of knowledge was plucked, and so you are like your name 'dead' to the fact that you are an Israelite, like those in Ezekiel 37 ch." Some hints are given that I shall not fare well in the next world, which any one who reads the chapter in Ezekiel will see is quite against his comparison. The reader must not imagine that my prognosticator means Morgan to be a corruption of Mortjardin; he proves his point by Hebrew: but any philologist would tell him the true derivation of the name, and how Glamorgan came to get it. It will be of much comfort to those young men who have not got through to know that the tree of knowledge itself was once in the same case. And so good bye to 666 for the present, and the assumption that the enigma is to be solved by the united numeral forces of the letters of a word.

It is worthy of note that, as soon as my Budget commenced, two guardian spirits started up, fellow men as to the flesh, both totally unknown to me: they have stuck to me from first to last. James Smith, Esq., finally Nauticus, watches over my character in this world, and would fain preserve me from ignorance, folly, and dishonesty, by inclosing me in a magic circle of 3⅛ diameters in circumference. The round man in the three-cornered hole, finally William Thorn, M.D., takes charge of my future destiny, [160]and tries to bring me to the truth by unfolding a score of meanings—all right—of 666. He hints that I, and my wife, are servants of Satan: at least he desires us both to remember that we cannot serve God and Satan; and he can hardly mean that we are serving the first, and that he would have us serve the second. As becomes an interpreter of the Apocalypse, he uses seven different seals; but not more than one to one letter. If his seals be all signet-rings, he must be what Aristophanes calls a sphragidonychargocometical fellow. But—and many thanks to him for the same—though an M.D., he has not sent me a single vial. And so much for my tree of secular knowledge and my tree of spiritual life: I dismiss them with thanks from myself and thanks from my reader. The dual of the Pythagorean system was Isis and Diana; of the Jewish law, Moses and Aaron; and of the City of London, Gog and Magog; of the Paradoxiad, James Smith, Esq., and William Thorn, M.D.

September, 1866. Mr. James Biden^[280] has favored me with some of his publications. He is a rival of Dr. Thorn; a prophet by name-right and crest-right. He is of royal descent through the De Biduns. He is the watchman of Ezekiel: God has told him so. He is the author of The True Church, a phrase which seems to have a book-meaning and a mission-meaning. He shall speak for himself:

"A crest of the Bidens has significance. It is a lion rampant between wings—wings in Scripture denote the flight of time. Thus the beasts or living creatures of the Revelations have each six wings, intimating a condition of mankind up to and towards the close of six thousand years of Bible teaching. The two wings of the crest would thus intimate power towards the expiration of 2000 years, as time is marked in the history of Great Britain.

[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 language of Daniel is prophetic, and Darius has in another an antitype. The writer was born July 18th, 1803; and the claim was asserted at the close of 1865, when he was about sixty-two years of age.

"The claims which have been asserted demand a settled faith, and which could only be reached through a long course of divine teaching."

When I was a little boy at school, one of my school-fellows took it into his head to set up a lottery of marbles: the thing took, and he made a stony profit. Soon, one after another, every boy had his lottery, and it was, "I won't put into yours unless you put into mine." This knocked up the scheme. It will be the same with the prophets. Dr. Thorn, Mr. Biden, Mrs. Cottle,^[281] etc. will grow imitators, until we are all pointed out in the Bible: but A will not admit B's claim unless B admits his. For myself, as elsewhere shown, I am the first Beast in the Revelations.

Every contraband prophet gets a few followers: it is a great point to make these sequacious people into Buridan's asses, which they will become when prophets are so numerous that there is no choosing.

[162]

SIR G. C. LEWIS.

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

How then comes the history of astronomy among the paradoxes? Simply because the author, so admirably when writing about what he knew, did not know what he did not know, and blundered like a circle-squarer. And why should the faults of so good a writer be recorded in such a list as the present? For three reasons: First, and foremost, because if the exposure be not made by some one, the errors will gradually ooze out, and the work will get the character of inaccurate. Nothing hurts a book of which few can fathom the depths so much as a plain blunder or two on the surface. Secondly, because the reviews either passed over these errors or treated them too gently, rather implying their existence than exposing them. Thirdly, because they strongly illustrate the melancholy truth, that no one knows enough to write about what he does not know. The distinctness of the errors is a merit; it proceeds from the clear-headedness of the author. The suppression in the journals may be due partly to admiration of the talent and energy which lived two difficult lives at once, partly to respect for high position in public affairs, partly to some of the critics being themselves men of learning only, unable to detect the errors. But we know that action and reaction are equal and contrary. If our generation take no notice of defects, and allow them to go down undetected among merits, the next generation will discover them, will perhaps believe us incapable of detecting them, at least will pronounce our judgment good for nothing, and will form an [164]opinion in which the merits will be underrated: so it has been, is, and will be. The best thing that can be done for the memory of the author is to remove the unsound part that the remainder may thrive. The errors do not affect the work; they occur in passages which might very well have been omitted: and I consider that, in making them conspicuous, I am but cutting away a deleterious fungus from a noble tree.

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

Upon this determination two remarks may be made. First, the error with respect to Mercury and Venus is considerable; with respect to Mercury, it is, in round numbers, 365 instead of 88 days, more than four times too much. Aristotle remarks that Eudoxus distinguishes Mercury and Venus from the other three planets by giving them one sphere each, with the poles in common. The proximity of Mercury to the sun would render its course difficult to observe and to measure, but the cause of the large error with respect to Venus (130 days) is not apparent.

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

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

If there be one thing more prominent than another in the work of Copernicus himself, in the popular explanations of it, and in the page of Delambre^[288] cited, it is that the parallelism of the earth's axis is a glaring part of the [166]theory of Copernicus. What Kepler^[289] did was to throw away, as unnecessary, the method by which Copernicus, per fas et nefas,^[290] secured it. Copernicus, thinking of the earth's orbital revolution as those would think who were accustomed to the solid orbs—and much as the stoppers of the moon's rotation do now: why do they not strengthen themselves with Copernicus?—thought that the earth's axis would always incline the same end towards the sun, unless measures were taken to prevent it. He did take measures: he invented a compensating conical motion of the axis to preserve the parallelism; and, which is one of the most remarkable points of his system, he obtained the precession of the equinoxes by giving the necessary trifle more than compensation. What stares us in the face at the beginning of the paragraph to which the author refers?

"C'est donc pour arriver à ce parallelisme, ou pour le conserver, que Copernic a cru devoir recourir à ce mouvement égal et opposé qui détruit l'effet qu'il attribue si gratuitement au premier, de déranger le parallelisme."^[291]

Parallelism at any price, is the motto of Copernicus: you need not pay so dear, is the remark of Kepler.

The opinions given by Sir G. Lewis about the effects of modern astronomy, which he does not understand and singularly undervalues, will now be seen to be of no authority. He fancies that—to give an instance—for the determination of a ship's place, the invention of chronometers has been far more important than any improvement in astronomical theory (p. 254). Not to speak of latitude,—though the omission is not without importance,—he ought to have known that longitude is found by the difference between what o'clock it is at Greenwich and at the ship's place, at [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 observation, aided by the best knowledge of the heavenly motions.

I think I have done Sir G. Lewis's very excellent book more good than all the reviewers put together.

I will give an old instance in which literature got into confusion about astronomy. Theophrastus,^[292] who is either the culprit or his historian, attributes to Meton,^[293] the contriver of the lunar calendar of nineteen years, which lasts to this day, that his solstices were determined for him by a certain Phaeinus of Elis on Mount Lycabettus. Nobody else mentions this astronomer: though it is pretty certain that Meton himself made more than one appointment with him for the purpose of observing solstices; and we may be sure that if either were behind his time, it was Meton. For Phaeinus Helius is the shining sun himself; and in the astronomical poet Aratus^[294] we read about the nineteen years of the shining sun:

Some man of letters must have turned Apollo into Phaeinus of Elis; and there he is in the histories of astronomy to [168]this day. Salmasius^[296] will have Aratus to have meant him, and proposes to read ἠλείοιο: he did not observe that Phaeinus is a very common adjective of Aratus, and that, if his conjecture were right, this Phaeinus would be the only non-mythical man in the poems of Aratus.

[When I read Sir George Lewis's book, the points which I have criticized struck me as not to be wondered at, but I did not remember why at the time. A Chancellor of the Exchequer and a writer on ancient astronomy are birds of such different trees that the second did not recall the first. In 1855 I was one of a deputation of about twenty persons who waited on Sir G. Lewis, as Chancellor of the Exchequer, on the subject of a decimal coinage. The deputation was one of much force: Mr. Airy, with myself and others, represented mathematics; William Brown,^[297] whose dealings with the United States were reckoned by yearly millions, counted duodecimally in England and decimally in America, was the best, but not the only, representative of commerce. There were bullionists, accountants, retailers, etc. Sir G. L. walked into the room, took his seat, and without waiting one moment, began to read the deputation a smart lecture on the evils of a decimal coinage; it would require alteration of all the tables, it would impede calculation, etc. etc. Of those arguments against it which weighed with many of better knowledge than his, he obviously knew nothing. The members of the deputation began to make their statements, and met with curious denials. He interrupted me with "Surely there is no doubt that the calculations of our books of arithmetic are easier [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 contrast when he had greater depth.]

DECIMAL COINAGE.

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

In the debate on decimal coinage of July 12, 1855, Mr. Lowe,^[298] then member for Kidderminster, an effective speaker and a smart man, exhibited himself in a speech on which I wrote a comment for the Decimal Association. I have seldom seen a more wretched attempt to distort the points of a public question than the whole of this speech. Looking at the intelligence shown by the speaker on other occasions, [170]it is clear that if charity, instead of believing all things, believed only all things but one, he might tremble for his political character; for the honesty of his intention on this occasion might be the incredible exception. I give a few paragraphs with comments:

"In commenting on the humorous, but still argumentative speech of Mr. Lowe, the member for Kidderminster, we may observe, in general, that it consists of points which have been several times set forth, and several times answered. Mr. Lowe has seen these answers, but does not allude to them, far less attempt to meet them. There are, no doubt, individuals, who show in their public speaking the outward and visible signs of a greater degree of acuteness than they can summon to guide their private thinking. If Mr. Lowe be not one of these, if the power of his mind in the closet be at all comparable to the power of his tongue in the House, it may be suspected that his reserve with respect to what has been put forward by the very parties against whom he was contending, arises from one or both of two things—a high opinion of the arguments which he ignored—a low opinion of the generality of the persons whom he addressed. [Both, I doubt not].

But he cannot mean that Englishmen in general are so easily managed. And as to Jonathan, who is but John lengthened out a little, he would see creation whittled into chips before he would even split what may henceforth be called the Kidderminster difference. The House, not unmoved—for it laughed—with sly humor decided that the introduction of the florin had been "eminently successful and satisfactory."

The truth is that Mr. Lowe here attacks nothing except the coexistence of the florin and half-crown. We are endeavoring to abolish the half-crown. Let Mr. Lowe join us; and he will, if we succeed, be relieved from the pressure on his pocket which must arise from having the turn of the market always against him.

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Now, if Mr. Lowe insists on it that our integer is the pound, he is bound to admit that the present integer is the pound, of which a shilling, etc., are fractions. The next time he has a chop and a pint of stout in the city, the waiter should say—"A pound, sir, to you," and should add, "Please to remember the waiter in integers." Mr. Lowe fancies that when he pays one and sixpence, he pays in integers, and so he does, if his integer be a penny or a sixpence. Let him bring his mind to contemplate a mil as the integer, the lowest integer, and the seven cents five mils which he would pay under the new system would be payment in integers also. But, as it happens with some others, he looks up the present system, with Cocker,^[299] and Walkingame,^[300] and always looks down the proposed system. The word decimal is obstinately associated with fractions, for which there is no need. Hence it becomes so much of a bugbear, that, to parody the lines of Pope, which probably suggested one of Mr. Lowe's phrases—

To the poor, who keep no books, the whole secret is "Sixpence farthing to the half shilling, twelve pence halfpenny to the shilling." The new twopence halfpenny, or cent, will be at once five to the shilling.

In conclusion, we remark that three very common misconceptions run through the hon. Member's argument; and, combined in different proportions, give variety to his patterns.

First, he will have it that we design to bring the uneducated into contact with decimal fractions. If it be so, it will only be as M. Jourdain was brought into contact with prose. In fact, Quoi! quand je dis, Nicole, apportez-moi mes pantoufles, c'est de la prose?^[305] may be rendered: "What! do you mean that ten to the florin is a cent a piece must be called decimal reckoning?" If we had to comfort a poor man, horror-struck by the threat of decimals, we should tell him what manner of fractions had been inflicted upon him hitherto; nothing less awful than quarto-duodecimo-vicesimals, we should assure him.

Secondly, he assumes that the penny, such as it now is, will remain, as a coin of estimation, after it has ceased to be a coin of exchange; and that the mass of the people will continue to think of prices in old pence, and to calculate them in new ones, or else in new mils. No answer is required to this, beyond the mere statement of the nature of the assumption and denial.

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Thirdly, he attributes to the uneducated community a want of perception and of operative power which really does not belong to them. The evidence offered to the Committee of the House shows that no fear is entertained on this point by those who come most in contact with farthing purchasers. And this would seem to be a rule,—that is, fear of the intelligence of the lower orders in the minds of those who are not in daily communication with them, no fear at all in the minds of those who are.

A remarkable instance of this distinction happened five-and-twenty years ago. The Admiralty requested the Astronomical Society to report on the alterations which should be made in the Nautical Almanac, the seaman's guide-book over the ocean. The greatest alteration proposed was the description of celestial phenomena in mean (or clock time), instead of apparent (or sundial) time, till then always employed. This change would require that in a great many operations the seaman should let alone what he formerly altered by addition or subtraction, and alter by addition or subtraction what he formerly let alone; provided always that what he formerly altered by addition he should, when he altered at all, alter by subtraction, and vice versa. This was a tolerably difficult change for uneducated skippers, working by rules they had only learned by rote. The Astronomical Society appointed a Committee of forty, of whom nine were naval officers or merchant seamen [I was on this Committee]. Some men of science were much afraid of the change. They could not trust an ignorant skipper or mate to make those alterations in their routine, on the correctness of which the ship might depend. Had the Committee consisted of men of science only, the change might never have been ventured on. But the naval men laughed, and said there was nothing to fear; and on their authority the alteration was made. The upshot was, that, after the new almanacs appeared, not a word of complaint was ever heard on the matter. Had the House of Commons had to [181]decide this question, with Mr. Lowe to quote the description given by Basil Hall^[306] (who, by the way, was one of the Committee) of an observation on which the safety of the ship depended, worked out by the light of a lantern in a gale of wind off a lee shore, this simple and useful change might at this moment have been in the hands of its tenth Government Commission.

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

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THE TONAL SYSTEM.

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

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

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

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

Let us translate—

And again, Fylander thrown into our December! What is [183]to become of those lines of Praed, which I remember coming out when I was at Cambridge,—

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

SOME SMALL PARADOXERS.

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

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

A paper read—but, according to the report, not understood—at the British Association. There is a notion that political economy is entirely mathematical; and its negative quantity is strongly recommended for study: it contains "the whole of the Funds, Credit, 32 parts out of 33 of the value of Land...." The mathematics are described as consisting of—first, number, or Arithmetic; secondly, the theory of dependent quantities, subdivided into dependence by cause and effect, and dependence by simultaneous variations; thirdly, "independent quantities or unconnected events, which is the theory of probabilities." I am not ashamed, having the British Association as a co-non-intelligent, to say I do not understand this: there is a paradox in it, and the author should give further explanation, especially of his negative quantity. Mr. Macleod has gained [185]praise from great names for his political economy; but this, I suspect, must have been for other parts of his system.

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

In a paper on the beats of organ-pipes and on temperament published some years ago, I said that equal temperament appeared to me insipid, and not so agreeable as the effect of the instrument when in progress towards being what is called out of tune, before it becomes offensively wrong. There is throughout that period unequal temperament, determined by accident. General Thompson, taking me one way, says I have launched a declaration which is likely to make an epoch in musical practice; a public musical critic, taking me another way, quizzes me for preferring music out of tune. I do not think I deserve either one remark or the other. My opponent critic, I suspect, takes equally tempered and in tune to be phrases of one meaning. But by equal temperament is meant equal distribution among all the keys of the error which an instrument must have, which, with twelve sounds only in the octave, professes to be fit for all the keys. I am reminded of the equal temperament which was once applied to the postmen's jackets. The coats were all made for the average man: the [186]consequence was that all the tall men had their tails too short; all the short men had them too long. Some one innocently asked why the tall men did not change coats with the short ones.