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In other letters John Stuart Mill is 666 if the a be left out; Chasuble is perfect. John Brighte is a fait accompli; and I am asked whether intellect can account for the final e. Very easily: this Beast is not the M. P., but, another person who spells his name differently. But if John Sturt Mill and John Brighte choose so to write themselves, they may.

A curious collection; a mystical phantasmagoria! There are those who will try to find meaning: there are those who will try to find purpose.

And some they said-What are you at?

And some-What are you arter?

My account of Mr. Thom and his 666 appeared on October 27: and on the 29th I received from the editor a copy of Mr. Thom's sermons published in 1863 (he died Feb. 27, 1862) with best wishes for my health and happiness. The editor does not name himself in the book; but he signed his name in my copy: and may my circumference never be more than 3 of my diameter if the signature, name and writing both, were not that of my Ding friend Mr. James Smith! And so I have come in contact with him on 666 as well as on π ! I should have nothing left to live for, had I not happened to hear that he has a perpetual motion on hand. I returned thanks and kind regards: and Miss Miggs's words-Here's forgivenesses of injuries! here's amicablenesses!'-rang in my ears. But I was made slightly uncomfortable: how could the war go on after this armistice? Could I ever make it understood that the truce only extended to the double Vahu and things thereunto relating? It was once held by seafaring men that there was no peace with Spaniards beyond the line: I was determined that there must be no concord with J. S. inside the circle; that this must be a special exception, like Father Huddleston and old Grouse in the gun-room. I was not long in anxiety; twenty-four hours after the book of sermons there came a copy of the threatened exposure-The British Association in Jeopardy, and Professor De Morgan in the Pillory without hope of escape. By James Smith, Esq.' London and Liverpool, 8vo., 1866 (pp. 94). This exposure consists of reprints from the Athenæum and Correspondent: of things new there is but one. In a short preface Mr. J. S. particularly recommends to read to the end. At the end is an appendix of two pages, in type as large as the work; a very prominent peroration. It is an article from the Athenæum, left out of its place. In the last sentence Mr. J. Smith, who had asked whether his character

J. S.'S SYMBOLICAL REASONING.

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as an honest Geometer and Mathematician was not at stake, is warned against the fallacia plurium interrogationum. He is told that there is not a more honest what's-his-name in the world: but that as to the counter which he calls his character as a mathematician, he is assured that it had been staked years ago, and lost. And thus truth has the last word. There is no occasion to say much about reprints. One of them is a letter [that given above] of August 25, 1865, written by Mr. J. S. to the Correspondent. It is one of his quadratures; and the joke is that I am made to be the writer: it appears as what Mr. J. S. hopes I shall have the sense to write in the Athenæum and forestall him. When I saw myself thus quoted-yes! quoted! double commas, first person-I felt as I suppose did Wm. Wilberforce when he set eyes on the affectionate benediction of the potato which waggish comrades had imposed on a raw Irish reporter as part of his speech. I felt as Martin of Galway-kind friend of the poor dumb creatures!—when he was told that the newspapers had put him in Italics. I appeal to you, Mr. Speaker! I appeal to the House! Did I speak in Italics? Do I ever speak in Italics?' I appeal to editor and readers, whether I ever squared the circle until a week or two ago, when I gave my charitable mode of reconciling the discrepant cyclo

meters.

The absurdity of the imitation of symbolic reasoning is so lusciously rich, that I shall insert it when I make up my final book. Somebody mastered Spanish merely to read Don Quixote: it would be worth while to learn a little algebra merely to enjoy this a b-istical attack on the windmills. The principle is, Prove something in as roundabout a way as possible, mention the circle once or twice irrelevantly in the course of your proof, and then make an act of Q. E. D. in words at length. The following is hardly caricature:-

To prove that 2 and 2 make 5. Let a = 2, b = 5 let c = 658, the number of the House: let d = 666, the number of the Beast. Then of necessity d = a + b + c + 1; so that 1 is a harmonious and logical quantification of the number of which we are to take care. Now, b, the middle of our digital system, is, by mathematical and geometrical combination, a mean between 5+1 and 2 + 2. Let 1 be removed to be taken care of, a thing no real mathematician can refuse without serious injury to his mathematical and geometrical reputation. It follows of necessity that 2 + 2 = 5, quod erat demonstrumhorrendum. If Simpkin & Marshall have not, after my notice, to account for

a gross of copies more than would have gone off without me, the world is not worthy of its James Smith!

The only fault of the above is, that there is more connexion than in the process of Faber Cyclometricus: so much, in fact, that the blunders are visible. The utter irrelevance of premises to conclusion cannot be exhibited with the requisite obscurity by any one who is able to follow reasoning: it is high art displayed in a certain toning down of the agri somnia, which brings them. to a certain look of approach to reasoning which I can only burlesque. Mr. J. S. produces something which resembles argument much as a chimpanzee in dolour, because balked of his dinner, resembles a thinking man at his studies. My humble attempt at imitation of him is more like a monkey hanging by his tail from a tree and trying to crack a cocoa-nut by his

chatter.

I could forgive Mr. J. S. anything, properly headed. I would allow him to prove for himself that the Quadrature of the Circle is the child of a private marriage between the Bull Unigenitus and the Pragmatic Sanction, claiming tithe of onions for repeal of the Mortmain Act, before the Bishops in Committee under the kitchen table: his mode of imitating reason would do this with ease. But when he puts his imitation into my mouth, to make me what he calls a real mathematician,' my soul rises in epigram against him. I say with the doll's dressmaker-such a job makes me feel like a puppet's tailor myself— He ought to have a little pepper? just a few grains? I think the young man's tricks and manners make a claim upon his friends for a little pepper?' De Fauré and Joseph Scaliger come into my head: my reader may look back for them.

Three circlesquarers to the manner born,

Switzerland, France, and England did adorn,
De Fauré in equations did surpass, (p. 89)
Joseph at contradictions was an ass. (p. 67)
Groaned Folly, I'm used up! What shall I do

To make James Smith? Grinned Momus, Join the two!

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

Bien posé sur un coussinet.

Joanna Southcott never had a follower who believed in her with more humble piety than Mr. James Smith believes in himself. After all that has happened to him, he asks me with high confidence

A SCHOOLBOY'S DEFENCE.

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to' favour the writer with a proof' that I still continue of opinion that the best of the argument is in my jokes, and the best of the joke is in his arguments.' I will not so favour him. At the very outset I told him in plain English that he has the whiphand of all the reasoners in the world, and in plain French that il a perdu le droit d'être frappé de l'évidence; I might have said pendu. To which I now add, in plain Latin, Sapienti pauca, indocto nihil. The law of Chancery says that he who will have equity must do equity: the law of reasoning says that he who will have proof must see proof.

The introduction of things quite irrelevant, by way of reproach, is an argument in universal request: and it often happens that the argument so produced really tells against the producer. So common is it that we forget how boyish it is; but we are strikingly reminded when it actually comes from a boy. In a certain police court, certain small boys were arraigned for conspiring to hoot an obnoxious individual on his way from one of their school exhibitions. This proceeding was necessary, because there seemed to be a permanent conspiracy to annoy the gentleman; and the masters did not feel able to interfere in what took place outside the school. So the boys were arraigned; and their friends, as silly in their way as themselves, allowed one of them to make the defence, instead of employing counsel; and did not even give them any useful hints. The defence was as follows; and any one who does not see how richly it sets off the defences of bigger boys in bigger matters has much to learn. The innocent conviction that there was answer in the latter part is delightful. Of course fine and recognizance followed.

A said the boys had received great provocation from BHe was constantly threatening them with a horsewhip which he carried in his hand [the boy did not say what had passed to induce him to take such a weapon], and he had repeatedly insulted the master, which the boys could not stand. B- - had in his own drawing-room told him (A) that he had drawn his sword against the master and thrown away the scabbard. B— knew well that if he came to the college he would catch it, and then he went off through a side door-which was no sign of pluck; and then he brought Mrs. B— with him, thinking that her presence would protect him.

My readers may expect a word on Mr. Thom's sermons, after my account of his queer doings about 666. He is evidently an honest and devout man, much wanting in discrimination. He has a sermon about private judgment, in which he halts between

the logical and legal meanings of the word. He loathes those who apply their private judgment to the word of God: here he means those who decide what it ought to be. He seems in other places aware that the theological phrase means taking right to determine what it is. He uses his own private judgment very freely, and is strong in the conclusion that others ought not to use theirs except as he tells them how; he leaves all the rest of mankind free to think with him. In this he is not original: his fame must rest on his senary tripod.

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

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When a man is regularly snubbed, bullied, blown up, walked into, and put down, there is usually some reaction in his favour, a kind of deostracism, which cannot bear to hear him always called the blunderer. I hope it will be so in this case. There is nothing I more desire than to see sects of paradoxers. There are fully five thousand adults in England who ought to be the followers of some one false quadrature. And I have most hope of 3, because I think Mr. James Smith better fitted to be the leader of an organised infatuation than any one I know of. He wants no pity, and will get none. He has energy, means, good humour, strong conviction, character, and popularity in his own circle. And, most indispensable point of all, he sticks at nothing; In cœlum jusseris, ibit.

When my instructor found I did not print an acceptance of what I have quoted, he addressed me as follows (Corr., Sept. 23):

'In this life, however, we must do our duty, and, when necessary, use the rod, not in a spirit of revenge, but for the benefit of the culprit and the good of society. Now, Sir, the opportunity has been thrown in your way of slipping out of the pillory without risk of serious injury; but, like an obstinate urchin, you have chosen to quarrel with your opportunity and remain there, and thus you compel me to deal with you as schoolmasters used to do with stupid boys in bygone days -that is to say, you force me to the use of the critic's rod, compel me to put you where little Jack Horner sat, and, as a warning to other naughty boys, to ornament you with a dunce's cap. The task I set

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