Chapter 13

"Treason does never prosper: what's the reason?Why, when it prospers, none dare call it treason."

"Treason does never prosper: what's the reason?

Why, when it prospers, none dare call it treason."

Language is in constant fermentation, and all that is thrown in, so far as it is not fit to assimilate, is thrown off; and this without any obvious struggle. In the meanwhile every one who has read good authors, from Shakspeare downward, knows what is and what is not English; and knows, also, that our language is not one and indivisible. Two very different turns of phrase may both be equally good, and as good as can be: we may be relieved of the consequences of contempt of one court byhabeas corpusissuing out of another.

TEST OF LANGUAGE.

Hallam remarks that the Authorized Version of the Bible is not in the language of the time of James the First: that it is not the English of Raleigh or of Bacon. Here arises the question whether Raleigh and Bacon are the true expositors of the language of their time; and whether they were not rather the incipient promoters of a change which was successfully resisted by—among other things—the Authorized Version of the Testaments. I am not prepared to concede that I should have given to the English which would have been fashioned upon that of Bacon by imitators, such as they usually are, the admiration which is forced from me by Bacon's English from Bacon's pen. On this point we have a notable parallel. Samuel Johnsoncommands our admiration, at least in his matured style: but we nauseate his followers. It is an opinion of mine that the works of the leading writers of an age are seldom the proper specimens of the language of their day, when that language is in its state of progression. I judge of a language by the colloquial idiom of educated men: that is, I take this to be the best medium between the extreme cases of one who is ignorant of grammar and one who is perched upon a style. Dialogue is what I want to judge by, and plain dialogue: so I choose Robert Recorde[609]and his pupil in theCastle of Knowledge, written before 1556. When Dr. Robert gets into his altitudes of instruction, he differs from his own common phraseology as much as probably did Bacon when he wrote morals and philosophy. But every now and then I come to a little plain talk about a common thing, of which I propose to show a specimen. Anything can be made to look old by such changes asmakesintomaketh, with a little old spelling. I shall invert these changes, using the newer form of inflexion, and the modern spelling: with no other variation whatever.

"Scholar.Yet the reason of that is easy enough to be conceived, for when the day is at the longest the Sun must needs shine the more time, and so must it needs shine the less time when the day is at the shortest: this reason I have heard many men declare.

Master.That may be called a crabbed reason, for itgoes backward like a crab. The day makes not the Sun to shine, but the Sun shining makes the day. And so the length of the day makes not the Sun to shine long, neither the shortness of the day causes not [sic] the Sun to shine the lesser time, but contrariwise the long shining of the Sun makes the long day, and the short shining of the Sun makes the lesser day: else answer me what makes the days long or short?

Scholar.I have heard wise men say that Summer makes the long days, and Winter makes the long nights.

Master.They might have said more wisely, that long days make summer and short days make winter.

Scholar.Why, all that seems one thing to me.

Master.Is it all one to say, God made the earth, and the earth made God? Covetousness overcomes all men, and all men overcome covetousness?

Scholar.No, not so; for here the effect is turned to be the cause, and the agent is made the patient.

Master.So is it to say Summer makes long days, when you should say: Long days make summer.

Scholar.I perceive it now: but I was so blinded with the vulgar error, that if you had demanded of me further what did make the summer, I had been like to have answered that green leaves do make summer; and the sooner by remembrance of an old saying that a year should come in which the summer should not be known but by the green leaves.

Master.Yet this saying does not import that green leaves do make summer, but that they betoken summer; so are they the sign and not the cause of summer."

I have taken a whole page of our author, without omission, that the reader may see that I do not pick out sentences convenient for my purpose. I have done nothing but alter the third person of the verb and the spelling: but great is the effect thereof. We say "the Sun shining makes the day"; Recorde, "the Sonne shynynge maketh the daye."These points apart, we see a resemblance between our English and that of three hundred years ago, in the common talk of educated persons, which will allow us to affirm that the language of the authorized Bible must have been very close to that of its time. For I cannot admit that much change can have taken place in fifty years: and the language of the version represents both our common English and that of Recorde with very close approximation. Take sentences from Bacon and Raleigh, and it will be apparent that these writers will be held to differ from all three, Recorde, the version, and ourselves, by differences of the same character. But we speak of Recorde's conversation, and of our own. We conclude that it is the plain and almost colloquial character of the Authorized Version which distinguishes it from the English of Bacon and Raleigh, by approximating it to the common idiom of the time. If any one will cast an eye upon the letters of instruction written by Cecil[610]and the Bishop of London to the translators themselves, or to the general directions sent to them in the King's name, he will find that these plain business compositions differ from the English of Bacon and Raleigh by the same sort of differences which distinguish the version itself.

PRONUNCIATION.

The foreign word, or the word of a district, or class of people, passes into the general vernacular; but it is long before the specially learned will acknowledge the right of those with whom they come in contact to follow general usage. The rule is simple: so long as a word is technical or local, those who know its technical or local pronunciation may reasonably employ it. But when the word has become general, the specialist is not very wise if he refuse to followthe mass, and perfectly foolish if he insist on others following him. There have been a few who demanded that Euler should be pronounced in the German fashion:[611]Euler has long been the property of the world at large; what does it matter how his own countrymen pronounce the letters? Shall we insist on the French pronouncingNewtonwithout that finaltongwhich they never fail to give him? They would be wise enough to laugh at us if we did. We remember that a pedant who was insisting on all the pronunciations being retained, was met by a maxim in contradiction, invented at the moment, and fathered upon Kaen-foo-tzee,[612]an authority which he was challenged to dispute. Whom did you speak of? said the bewildered man of accuracy. Learn your own system, was the answer, before you impose it on others; Confucius says that too.[613]

The old English hasfote,fode,loke,coke,roke, etc., forfoot, etc. Andaboverhymes in Chaucer toremove. Suspecting that the broader sounds are the older, we may surmise thatremoveandfoodhave retained their old sounds, and thatcook, oncecoke, would have rhymed to ourLuke, the vowel being brought a little nearer, perhaps, to theoin our presentcoke, the fuel, probably so called as used by cooks. If this be so, the Chief JusticeCook[614]of our lawyers, and theCoke(pronounced like the fuel) of the greater part of the world, are equally wrong. The lawyer has no right whatever to fasten his pronunciation upon us: even leaving aside the general custom, he cannot prove himself right, and is probably wrong. Those whoknow the village of Rokeby (pronounced Rookby) despise the world for not knowing how to name Walter Scott's poem: that same world never asked a question about the matter, and the reception of the parody ofJokeby, which soon appeared, was a sufficient indication of their notion. Those who would fasten the hodiernal sound upon us may be reminded that the question is, not what they call it now, but what it was called in Cromwell's time. Throw away general usage as a lawgiver, and this is the point which emerges. ProbablyRūke-bywould be right, with a little turning of the Italian ū towards ō of modern English.

[Some of the above is from an old review. I do not always notice such insertions: I take nothing but my own writings. A friend once said to me, "Ah! you got that out of theAthenæum!" "Excuse me," said I. "theAthenæumgot that out of me!"]

APOLOGIES TO CLUVIER.

It is part of my function to do justice to any cyclometers whose methods have been wrongly described by any orthodox sneerers (myself included). In this character I must noticeDethlevus Cluverius,[615]as the Leipzig Acts call him (probably Dethleu Cluvier), grandson of the celebrated geographer, Philip Cluvier. The grandson was a Fellow of the Royal Society, elected on the same day as Halley,[616]November 30, 1678: I suppose he lived in England. Thisman is quizzed in the Leipzig Acts for 1686; and, if Montucla insinuate rightly, by Leibnitz, who is further suspected of wanting to embroil Cluvier with his own opponent Nieuwentiit,[617]on the matter of infinitesimals. So far good: I have nothing against Leibnitz, who though he was ironical, told us what he laughed at. But Montucla has behaved very unfairly: he represents Cluvier as placing the essence of his method in the solution of the problemconstruere mundum divinæ menti analogum, to construct a world corresponding to the divine mind. Nothing to begin with: no way of proceeding. Now, it ought to have beenex data linea construere,[618]etc.: there is a given line, which is something to go on. Further, there is a way of proceeding: it is to find the product of 1, 2, 3, 4, etc. for ever. Moreover, Montucla charges Cluvier withunsquaringthe parabola, which Archimedes had squared as tight as a glove. But he never mentions how very nearly Cluvier agrees with the Greek: they only differ by 1 divided by 3n2, wherenis the infinite number of parts of which a parabola is composed. This must have been the conceit that tickled Leibnitz, and made him wish that Cluvier and Nieuwentiit should fight it out. Cluvier, was admitted, on terms of irony, into the Leipzig Acts: he appeared on a more serious footing in London. It is very rare for one cyclometer to refute another:les corsaires ne se battent pas.[619]The only instance I recall is that of M. Cluvier, who (Phil. Trans., 1686, No. 185) refuted M. Mallemont de Messange,[620]whopublished at Paris in 1686. He does it in a very serious style, and shows himself a mathematician. And yet in the year in which, in thePhil. Trans., he was a geometer, and one who rebukes his squarer for quoting Matthew xi. 25, in that very year he was the visionary who, in the Leipzig Acts, professed to build a world resembling the divine mind by multiplying together 1, 2, 3, 4, etc. up to infinity.

THE RAINBOW PARADOX.

There is a very pretty opening for a paradox which has never found its paradoxer in print. The philosophers teach that the rainbow is not material: it comes from rain-drops, but those rain-drops do nottakecolor. They onlygiveit, as lenses and mirrors; and each one drop givesallthe colors, but throws them in different directions. Accordingly, the same drop which furnishes red light to one spectator will furnish violet to another, properly placed. Enter the paradoxer whom I have to invent. The philosopher has gulled you nicely. Look into the water, and you will see the reflected rainbow: take a looking-glass held sideways, and you see another reflection. How could this be, if there were nothing colored to reflect? The paradoxer's facts are true: and what are called the reflected rainbows areotherrainbows, caused by thoseotherdrops which are placed so as to give the colors to the eye after reflection, at the water or the looking-glass. A few years ago an artist exhibited a picture with a rainbow and its apparent reflection: he simply copied what he had seen. When his picture was examined, some started the idea that there could be no reflection of a rainbow; they were right: they inferred that the artist had made a mistake; they were wrong. When it was explained, some agreed and some dissented. Wanted,immediately, an able paradoxer: testimonials to be forwarded to either end of the rainbow, No. 1. No circle-squarer need apply, His Variegatedness having been pleased to adopt 3.14159... from Noah downwards.

TYCHO BRAHE REVIVED.

The system of Tycho Brahé,[621]with some alteration and addition, has been revived and contended for in our own day by a Dane, W. Zytphen,[622]who has publishedThe Motion of the Sun in the Universe, (second edition) Copenhagen, 1865, 8vo, andLe Mouvement Sidéral, 1865, 8vo. I make an extract.

"How can one explain Copernically that the velocity of the Moon must be added to the velocity of the Earth on the one place in the Earth's orbit, to learn how far the Moon has advanced from one fixed star to another; but in another place in the orbit these velocities must be subtracted (the movements taking place in opposite directions) to attain the same result? In the Copernican and other systems, it is well known that the Moon, abstracting from the insignificant excentricity of the orbit, always in twenty-four hours performs an equally long distance. Why has Copernicus never been denominated Fundamentus or Fundator? Because he has never convinced anybody so thoroughly that this otherwise so natural epithet has occurred to the mind."

Really the second question is more effective against Newton than against Copernicus; for it upsets gravity: the first is of great depth.

JAMES SMITH WILL NOT DOWN.

TheCorrespondentjournal makes a little episode in the history of my Budget (born May, 1865, died April, 1866). It consisted entirely of letters written by correspondents. In August, a correspondent who signed "Fair Play"—and who I was afterwards told was a lady—thought it would be a good joke to bring in the Cyclometers. Accordingly a letter was written, complaining that though Mr. Sylvester's[623]demonstration of Newton's theorem—then attracting public attention—was duly lauded, the possibly greater discovery of the quadrature seemed to be blushing unseen, and wasting etc. It went on as follows:

"Prof. De Morgan, who, from his position in the scientific world, might fairly afford to look favourably on less practised efforts than his own, seems to delight in ridiculing the discoverer. Science is, of course, a very respectable person when he comes out and makes himself useful in the world [it must have been a lady; each sex gives science to the other]: but when, like a monk of the Middle Ages, he shuts himself up [it must have been a lady; they always snub the bachelors] in his cloistered cell, repeating his mumpsimus from day to day, and despising the labourers on the outside, we begin to think of Galileo,[624]Jenner,[625]Harvey,[626]and other glorious trios, who have been contemned ..."

The writer then called upon Mr. James Smith[627]to comeforward. The irony was not seen; and that day fortnight appeared the first of more than thirty letters from his pen. Mr. Smith was followed by Mr. Reddie,[628]Zadkiel,[629]and others, on their several subjects. To some of the letters I have referred; to others I shall come. TheCorrespondentwas to become a first-class scientific journal; the time had arrived at which truth had an organ: and I received formal notice that I could not stifle it by silence, nor convert it into falsehood by ridicule. When my reader sees my extracts, he will readily believe my declaration that I should have been the last to stifle a publication which was every week what James Mill[630]would call a dose of capital for my Budget. A few anti-paradoxers brought in common sense: but to the mass of the readers of the journal it all seemed to be the difference between Tweedledum and Tweedledee. Some said that the influx of scientific paradoxes killed the journal: but my belief is that they made it last longer than it otherwise would have done. Twenty years ago I recommended the paradoxers to combine and publish their views in a common journal: with a catholic editor, who had no pet theory, but a stern determination not to exclude anything merely for absurdity. I suspect it would answer very well. A strong title, or motto, would be wanted: not so coarse as was roared out in a Cambridge mob when I was an undergraduate—"No King! No Church! No House of Lords! No nothing, blast me!"—but something on thatprinciple.

At the end of 1867 I addressed the following letter to theAthenæum:

Pseudomath, Philomath, and Graphomath.

December 31, 1867

Many thanks for the present of Mr. James Smith's lettersof Sept. 28 and of Oct. 10 and 12. He asks where you will be if you read and digest his letters: you probably will be somewhere first. He afterwards asks what theWEof theAthenæumwill be if, finding it impossible to controvert, it should refuse to print. I answer for you, that We-We of theAthenæum, not being Wa-Wa the wild goose, so conspicuous in "Hiawatha," will leave what controverts itself to print itself, if it please.

Philomathis a good old word, easier to write and speak thanmathematician. It wants the words between which I have placed it. They are not well formed:pseudomatheteandgraphomathetewould be better: but they will do. I give an instance of each.

Thepseudomathis a person who handles mathematics as the monkey handled the razor. The creature tried to shave himself as he had seen his master do; but, not having any notion of the angle at which the razor was to be held, he cut his own throat. He never tried a second time, poor animal! but the pseudomath keeps on at his work, proclaims himself clean-shaved, and all the rest of the world hairy. So great is the difference between moral and physical phenomena! Mr. James Smith is, beyond doubt, the great pseudomath of our time. His 3⅛ is the least of a wonderful chain of discoveries. His books, like Whitbread's barrels, will one day reach from Simpkin & Marshall's to Kew, placed upright, or to Windsor laid length-ways. The Queen will run away on their near approach, as Bishop Hatto did from the rats: but Mr. James Smith will follow her were it to John o' Groats.

Thephilomath, for my present purpose, must be exhibited as giving a lesson to presumption. The following anecdote is found in Thiébault's[631]Souvenirs de vingt ans de séjours à Berlin, published in 1804. The book itself got a high character for truth. In 1807 Marshal Mollendorff[632]answered an inquiry of the Duc de Bassano,[633]by saying that it was the most veracious of books, written by the most honest of men. Thiébault does not claim personal knowledge of the anecdote, but he vouches for its being received as true all over the north of Europe.[634]

Diderot[635]paid a visit to Russia at the invitation of Catherine the Second. At that time he was an atheist, or at least talked atheism: it would be easy to prove him either one thing or the other from his writings. His lively sallies on this subject much amused the Empress, and all the younger part of her Court. But some of the older courtiers suggested that it was hardly prudent to allow such unreserved exhibitions. The Empress thought so too, but did not like to muzzle her guest by an express prohibition: so a plot was contrived. The scorner was informed that an eminent mathematician had an algebraical proof of the existence of God, which he would communicate before the whole Court, if agreeable. Diderot gladly consented. The mathematician, who is not named, was Euler.[636]He came to Diderot with the gravest air, and in a tone of perfect conviction said, "Monsieur!

donc Dieu existe; répondez!"[637]Diderot, to whom algebra was Hebrew, though this is expressed in a very roundabout way by Thiébault—and whom we may suppose to have expected some verbal argument of alleged algebraical closeness, was disconcerted; while peals of laughter sounded on all sides. Next day he asked permission to return to France, which was granted. An algebraist would haveturned the tables completely, by saying, "Monsieur! vous savez bien que votre raisonnement demande le développement dexsuivant les puissances entières den".[638]Goldsmith could not have seen the anecdote, or he might have been supposed to have drawn from it a hint as to the way in which the Squire demolished poor Moses.

Thegraphomathis a person who, having no mathematics, attempts to describe a mathematician. Novelists perform in this way: even Walter Scott now and then burns his fingers. His dreaming calculator, Davy Ramsay, swears "by the bones of the immortal Napier." Scott thought that the the philomaths worshiped relics: so they do, in one sense. Look into Hutton's[639]Dictionary forNapier's Bones, and you shall learn all about the little knick-knacks by which he did multiplication and division. But never a bone of his own did he contribute; he preferred elephants' tusks. The author ofHeadlong Hall[640]makes a grand error, which is quite high science: he says that Laplace proved the precession of the equinoxes to be a periodical inequality. He should have said the variation of the obliquity. But the finest instance is the following: Mr. Warren,[641]in his well-wrought tale of the martyr-philosopher, was incautious enough to invent the symbols by which hissavantsatisfied himself Laplace[642]was right on a doubtful point. And this is what he put together—

√-3a2,rectangley2/z2+ 9 -n= 9,n× loge.

Now, to Diderot and the mass of mankind this might be Laplace all over: and, in a forged note of Pascal, wouldprove him quite up to gravitation. But I know of nothing like it, except in the lately received story of the American orator, who was called on for some Latin, and perorated thus: "Committing the destiny of the country to your hands, Gentlemen, I may without fear declare, in the language of the noble Roman poet,

E pluribus unum,Multum in parvo,Ultima Thule,Sine qua non."[643]

E pluribus unum,

Multum in parvo,

Ultima Thule,

Sine qua non."[643]

But the American got nearer to Horace than the martyr-philosopher to Laplace. For all the words are in Horace, exceptThule, which might have been there. Butrectangleis not a symbol wanted by Laplace; nor can we see how it could have been; in fact, it is not recognized in algebra. As to the junctions, etc., Laplace and Horace are about equally well imitated.

Further thanks for Mr. Smith's letters to you of Oct. 15, 18, 19, 28, and Nov. 4, 15. The last of these letters has two curious discoveries. First, Mr. Smith declares that he hasseenthe editor of theAthenæum: in several previous letters he mentions a name. If he knew a little of journalism he would be aware that editors are a peculiar race, obtained by natural selection. They are never seen, even by their officials; only heard down a pipe. Secondly, "an ellipse or oval" is composed of four arcs of circles. Mr. Smith has got hold of the construction I was taught, when a boy, for a pretty four-arc oval. But my teachers knew better than to call it an ellipse: Mr. Smith does not; but he produces from it such confirmation of 3⅛ as would convince anyhonesteditor.

Surely the cyclometer is a Darwinite development of a spider, who is always at circles, and always begins again when his web is brushed away. He informs you that hehas been privileged to discover truths unknown to the scientific world. This we know; but he proceeds to show that he is equally fortunate in art. He goes on to say that he will make use of you to bring those truths to light, "just as an artist makes use of a dummy for the purpose of arranging his drapery." The painter's lay-figure is for flowing robes; the hairdresser's dummy is for curly locks. Mr. James Smith should read Sam Weller's pathetic story of the "four wax dummies." As tohisuse of a dummy, it is quite correct. When I was at University College, I walked one day into a room in which my Latin colleague was examining. One of the questions was, "Give the lives and fates of Sp. Mælius,[644]and Sp. Cassius."[645]Umph! said I, surely all know that Spurius Mælius was whipped for adulterating flour, and that Spurius Cassius was hanged for passing bad money. Now, a robe arranged on a dummy would look just like the toga of Cassius on the gallows. Accordingly, Mr. Smith is right in the drapery-hanger which he has chosen: he has been detected in the attempt to pass bad circles. He complains bitterly that his geometry, instead of being read and understood by you, is handed over to me to be treated after my scurrilous fashion. It is clear enough that he would rather be handled in this way than not handled at all, or why does he go on writing? He must know by this time that it is a part of the institution that his "untruthful and absurd trash" shall be distilled into mine at the rate of about 3⅛ pages of the first to one column of the second. Your readers will never know how much they gain by the process, until Mr. James Smith publishes it all in a big book, or until they get hold of what he has already published. I have six pounds avoirdupois of pamphlets and letters; and there is more than half a pound of letterswritten to you in the last two months. Your compositor must feel aggrieved by the rejection of these clearly written documents, without erasures, and on one side only. Your correspondent has all the makings of a good contributor, except the knowledge of his subject and the sense to get it. He is, in fact, only a mask: of whom the fox

"O quanta species, inquit, cerebrum non habet."[646]

I do not despair of Mr. Smith on any question which does not involve that unfortunate two-stick wicket at which he persists in bowling. He has published many papers; he has forwarded them to mathematicians: and he cannot get answers; perhaps not even readers. Does he think that he would get more notice if you were to print him in your journal? Who would study his columns? Not the mathematician, we know; and he knows. Would others? His balls are aimed too wide to be blocked by any one who is near the wicket. He has long ceased to be worth the answer which a new invader may get. Rowan Hamilton,[647]years ago, completely knocked him over; and he has never attempted to point out any error in the short and easy method by which that powerful investigator condescended to show that, be right who may, he must be wrong. There are some persons who feel inclined to think that Mr. Smith should be argued with: let those persons understand that he has been argued with, refuted, and has never attempted to stick a pen into the refutation. He stated that it was a remarkable paradox, easily explicable; and that is all. After this evasion, Mr. James Smith is below the necessity of being told that he is unworthy of answer. His friends complain that I do nothing butchaffhim. Absurd! I winnow him; and if nothing but chaff results, whose fault is that? I am usefully employed: for he is the type of a class which ought to be known, and which I have done much to make known.

Nothing came of this until July 1869, when I received a reprint of the above letter, with a comment, described as Appendix D of a work in course of publication on the geometry of the circle. TheAthenæumjournal received the same: but the Editor, in his private capacity, received the whole work, beingThe Geometry of the Circle and Mathematics as applied to Geometry by Mathematicians, shown to be a mockery, delusion, and a snare, Liverpool, 8vo, 1869. Mr. J. S. here appears in deep fight with Professor Whitworth,[648]and Mr. Wilson,[649]the author of the alleged amendment of Euclid. How these accomplished mathematicians could be inveigled into continued discussion is inexplicable. Mr. Whitworth began by complaining of Mr. Smith's attacks upon mathematicians, continued to correspond after he was convinced that J. S. proved an arc and its chord to be equal, and only retreated when J. S. charged him with believing in 3⅛, and refusing acknowledgment. Mr. Wilson was introduced to J. S. by a volunteer defense of his geometry from the assaults of theAthenæum. This the editor would not publish; so J. S. sent a copy to Mr. Wilson himself. Some correspondence ensued, but Mr. Wilson soon found out his man, and withdrew.

There is a little derision of theAthenæumand a merited punishment for "that unscrupulous critic and contemptible mathematical twaddler, De Morgan."

MR. REDDIE'S ASTRONOMY.

At p. 183 I mentioned Mr. Reddie,[650]the author ofVis Inertiæ Victaand ofVictoriatotocœlo,[651]which last is notan address to the whole heaven, either from a Roman Goddess or a British Queen, whatever a scholar may suppose. Between these Mr. Reddie has publishedThe Mechanics of the Heavens, 8vo, 1862: this I never saw until he sent it to me, with an invitation to notice it, he very well knowing that it would catch. His speculations do battle with common notions of mathematics and of mechanics, which, to use a feminine idiom, he blasphemes so you can't think! and I suspect that if you do not blaspheme them too,youcan't think. He appeals to the "truly scientific," and would be glad to have readers who have read what he controverts, i.e., Newton'sPrincipia: I wish he may get them; I mean I hope he may obtain them. To none but these would an account of his speculations be intelligible: I accordingly disposed of him in a very short paragraph of description. Now many paradoxers desire notice, even though it be disparaging. I have letters from more than one—besides what have been sent to the Editor of theAthenæum—complaining that they are not laughed at; although they deserve it, they tell me, as much as some whom I have inserted. Mr. Reddie informs me that I have not said a single word against his books, though I have given nearly a column to sixteen-string arithmetic, and as much to animalcule universes. What need to say anything to readers of Newton against a book from which I quoted that revolution by gravitation isdemonstrablyimpossible? It would be as useless as evidence against a man who has pleaded guilty. Mr. Reddie derisively thanks me for "small mercies"; he wrote me private letters; he published them, and more, in theCorrespondent. He gave me,pro viribus suis,[652]such a dressing you can't think, both for my Budget non-notice, and for reviews which he assumed me to have written. He outlawed himself by declaring (Correspondent, Nov. 11, 1856) that I—in a review—had made a quotation which was "garbled, evidently on purposeto make it appear that" he "was advocating solely a geocentric hypothesis, which is not true." In fact, he did his best to get larger "mercy." And he shall have it; and at a length which shall content him, unless his mecometer be an insatiable apparatus. But I fear that in other respects I shall no more satisfy him than the Irish drummer satisfied the poor culprit when, after several times changing the direction of the stroke at earnest entreaty, he was at last provoked to call out, "Bad cess to ye, ye spalpeen! strike where one will, there's noplasingye!"

Mr. Reddie attaches much force to Berkeley's[653]old arguments against the doctrine of fluxions, and advances objections to Newton's second section, which he takes to be new. To me they appear "such as have been often made," to copy a description given in a review: though I have no doubt Mr. Reddie got them out of himself. But the whole matter comes to this: Mr. Reddie challenged answer, especially from the British Association, and got none. He presumes that this is because he is right, and cannot be answered: the Association is willing to risk itself upon the counter-notion that he is wrong, and need not be answered; because so wrong that none who could understand an answer would be likely to want one.

Mr. Reddie demands my attention to a point which had already particularly struck me, as giving the means of showing toallreaders the kind of confusion into which paradoxers are apt to fall, in spite of the clearest instruction. It is a very honest blunder, and requires notice: it may otherwise mislead some, who may suppose that no one able to read could be mistaken about so simple a matter,let him be ever so wrong about Newton. According to his own mis-statement, in less than five months he made the Astronomer Royal abandon the theory of the solar motion in space. The announcement is made in August, 1865, as follows: the italics are not mine:

"The third (Victoria ...), although only published in September, 1863, has already had its triumph.It is the book that forced the Astronomer Royal of England, after publicly teaching the contrary for years, to come to the conclusion, "strange as it may appear," that "the whole question of solar motion in space is at the present time in doubt and abeyance."This admission is made in the Annual Report of the Council of the Royal Astronomical Society, published in the Society'sMonthly Noticesfor February, 1864."

It is added that solar motion is "full of self-contradiction, which "the astronomers" simply overlooked, but which they dare not now deny after being once pointed out."

The following is another of his accounts of the matter, given in theCorrespondent, No. 18, 1865:

"... You ought, when you came to put me in the 'Budget,' to have been aware of the Report of the Council of the Royal Astronomical Society, where it appears that Professor Airy,[654]with a better appreciation of my demonstrations, had admitted—'strange,' say the Council, 'as it may appear,'—that 'the whole question of solar motion in space [and here Mr. Reddie omits some words] is now indoubt and abeyance.' You were culpable as a public teacher of no little pretensions, if you were 'unaware' of this. If aware of it, you ought not to have suppressed such an important testimony to my really having been 'very successful' in drawing the teeth of the pegtops, though you thought them so firmly fixed. And if you still suppressit, in your Appendix, or when you reprint your 'Budget,' you will then be guilty of asuppressio veri, also of further injury to me, who have never injured you...."

Mr. Reddie must have been very well satisfied in his own mind before he ventured such a challenge, with an answer from me looming in the distance. The following is the passage of the Report of the Council, etc., from which he quotes:

"And yet, strange to say, notwithstanding the near coincidence of all the results of the before-mentioned independent methods of investigation, the inevitable logical inference deduced by Mr. Airy is, that the whole question of solar motion in space,so far at least as accounting for the proper motion of the stars is concerned, [I have put in italics the words omitted by Mr. Reddie] appears to remain at this moment in doubt and abeyance."

Mr. Reddie has forked me, as he thinks, on a dilemma: if unaware, culpable ignorance; if aware, suppressive intention. But the thing is atrilemma, and the third horn, on which I elect to be placed, is surmounted by a doubly-stuffed seat. First, Mr. Airy has not changed his opinion about thefactof solar motion in space, but only suspends it as to the sufficiency of present means to give the amount and direction of the motion. Secondly, all that is alluded to in the Astronomical Report was said and printed before the Victoria proclamation appeared. So that the author, instead of drawing the tooth of the Astronomer Royal's pegtop, has burnt his own doll's nose.

William Herschel,[655]and after him about six other astronomers, had aimed at determining, by the proper motions of the stars, the point of the heavens towards which the solar system is moving: their results were tolerably accordant. Mr. Airy, in 1859, proposed an improved method, and, applying it to stars of large proper motion, producedmuch the same result as Herschel. Mr. E. Dunkin,[656]one of Mr. Airy's staff at Greenwich, applied Mr. Airy's method to a very large number of stars, and produced, again, nearly the same result as before. This paper was read to the Astronomical Society inMarch, 1863, was printed in abstract in theNoticeof that month, was printed in full in the volume then current, and was referred to in the Annual Report of the Council inFebruary, 1864, under the name of "the Astronomer Royal's elaborate investigation, as exhibited by Mr. Dunkin." Both Mr. Airy and Mr. Dunkin express grave doubts as to the sufficiency of the data: and, regarding the coincidence of all the results as highly curious, feel it necessary to wait for calculations made on better data. The report of the Council states these doubts. Mr. Reddie, who only published inSeptember, 1863, happened to see the Report of February, 1864, assumes that the doubts were then first expressed, and declares that his book of September had the triumph of forcing the Astronomer Royal to abandon thefactof motion of the solar system by the February following. Had Mr. Reddie, when he saw that the Council were avowedly describing a memoir presented some time before, taken the precaution to find outwhenthat memoir was presented, he would perhaps have seen that doubts of the results obtained, expressed by one astronomer in March, 1863, and by another in 1859, could not have been due to his publication of September, 1863. And any one else would have learnt that neither astronomer doubts thesolar motion, though both doubt the sufficiency of present means to determine itsamountanddirection. This is implied in the omitted words, which Mr. Reddie—whose omission would have been dishonest if he had seen their meaning—no doubt took for pleonasm, superfluity, overmuchness. The rashness which pushed him headlonginto the quillet thathisthunderbolt had stopped the chariot of the Sun and knocked the Greenwich Phaeton off the box, is the same which betrayed him into yet grander error—which deserves the full word,quidlibet—about thePrincipiaof Newton. There has been no change of opinion at all. When a person undertakes a long investigation, his opinion is that, at a certain date, there isprima facieground for thinking a sound result may be obtained. Should it happen that the investigation ends in doubt upon the sufficiency of the grounds, the investigator is not put in the wrong. He knew beforehand that there was an alternative: and he takes the horn of the alternative indicated by his calculations. The two sides of this case present an instructive contrast. Eight astronomers produce nearly the same result, and yet the last two doubt the sufficiency of their means: compare them with the what's-his-name who rushes in where thing-em-bobs fear to tread.

I was not aware, until I had written what precedes, that Mr. Airy had given a sufficient answer on the point. Mr. Reddie says (Correspondent, Jan. 20, 1866):

"I claim to have forced Professor Airy to give up the notion of 'solar motion in space' altogether, for he admits it to be 'at present in doubt and abeyance.' I first made that claim in a letter addressed to the Astronomer Royal himself in June, 1864, and in replying, very courteously, to other portions of my letter, he did not gainsay that part of it."

Mr. Reddie is not ready at reading satire, or he never would have so missed the meaning of the courteous reply on one point, and the total silence upon another. Mr. Airy must be one of those peculiar persons who, when they do not think an assertion worth notice, let it alone, without noticing it by a notification of non-notice. He would never commit the bull of "Sir! I will not say a word on that subject." He would put it thus, "Sir! I will only say ten words on that subject,"—and, having thus said them, wouldproceed to something else. He assumed, as a matter of form, that Mr. Reddie would draw the proper inference from his silence: and this because he did not care whether or no the assumption was correct.

TheMechanics of the Heavens, which Mr. Reddie sends to be noticed, shall be noticed, so far as an extract goes:

"My connection with this subject is, indeed, very simply explained. In endeavoring to understand the laws of physical astronomy as generally taught, I happened to entertain some doubt whether gravitating bodies could revolve, and having afterwards imbibed some vague idea that the laws of the universe were chemical and physical rather than mechanical, and somehow connected with electricity and magnetism as opposing correlative forces—most probably suggested to my mind, as to many others, by the transcendent discoveries made in electro-magnetism by Professor Faraday[657]—my former doubts about gravitation were revived, and I was led very naturally to try and discover whether a gravitating body really could revolve; and I became convinced it could not, before I had ever presumed to look into the demonstrations of thePrincipia."

This is enough against the book, without a word from me: I insert it only to show those who know the subject what manner of writer Mr. Reddie is. It is clear that "presumed" is a slip of the pen; it should have beencondescended.

Mr. Reddie represents me as dreaming over paltry paradoxes. He is right; many of my paradoxes are paltry: he is wrong; I am wide awake to them. A single moth, beetle, or butterfly, may be a paltry thing; but when a cabinet is arranged by genus and species, we then begin to admire theinfinite variety of a system constructed on a wonderful sameness of leading characteristics. And why should paradoxes be denied that collective importance, paltry as many of them may individually be, which is accorded to moths, beetles, or butterflies? Mr. Reddie himself sees that "there is a method in" my "mode of dealing with paradoxes." I hope I have atoned for the scantiness of my former article, and put the demonstrated impossibility of gravitation on that level with Hubongramillposanfy arithmetic and inhabited atoms which the demonstrator—not quite without reason—claims for it.

In the Introduction to a collected edition of the three works, Mr. Reddie describes hisMechanism of the Heavens, from which I have just quoted, as—

"a public challenge offered to the British Association and the mathematicians at Cambridge, in August, 1862, calling upon them to point to a single demonstration in thePrincipiaor elsewhere, which even attempts to prove that Universal Gravitation is possible, or to show that a gravitating body could possibly revolve about a center of attraction. The challenge was not accepted, and never will be. No such demonstration exists. And the public must judge for themselves as to the character of a so-called "certain science," which thus shrinks from rigid examination, and dares not defend itself when publicly attacked: also of the character of its teachers, who can be content to remain dumb under such circumstances."

ON PARADOXERS IN GENERAL.

The above is the commonplace talk of the class, of which I proceed to speak without more application to this paradoxer than to that. It reminds one of the funny young rascals who used, in times not yet quite forgotten, to abuse the passengers, as long as they could keep up with thestage coach; dropping off at last with "Why don't you get down and thrash us? You're afraid, you're afraid!" They will allow the public to judge for themselves, but with somewhat of the feeling of the worthy uncle inTom Jones, who, though he would let young people choose for themselves, wouldhave themchoose wisely. They try to be so awfully moral and so ghastly satirical that they must be answered: and they are best answered in their own division. We have all heard of the way in which sailors cat's-pawed the monkeys: they taunted the dwellers in the trees with stones, and the monkeys taunted them with cocoa-nuts in return. But these were silly dendrobats: had they belonged to the British Association they would have said—No! No! dear friends; it is not in the itinerary: if you want nuts, you must climb, as we do. The public has referred the question to Time: the procedure of this great king I venture to describe, from precedents, by an adaptation of some smart anapæstic tetrameters—your anapæst is the foot for satire to halt on, both in Greek and English—which I read about twenty years ago, and with the point of which I was much tickled. Poetasters were laughed at; but Mr. Slum, whom I employed—Mr. Charles Dickens obliged me with his address—converted the idea into that of a hit at mathematicasters, as easily as he turned the Warren acrostic into Jarley. As he observed, when I settled his little account, it is cheaper than any prose, though the broom was not stolen quite ready made:

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