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 circ.u.mference never be more than 3-1/8 of my diameter if the signature, name and writing both, were not that of my [circle square]

ing friend Mr. James Smith! And so I have come in contact with him on 666 as well as on [pi]! 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 {236} 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 a.s.sociation 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 _Athenaeum_ 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 _Athenaeum_, left out of its place. In the last sentence Mr. J.

Smith, who had asked whether his character as an honest Geometer and Mathematician was not at stake, is warned against the _fallacia plurium interrogationum_.[377] 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 a.s.sured that it has been staked years ago, and lost. And thus truth has the last word. There is no occasion to say much about reprints. One of them is a letter [that given above] of August 25, 1865, written by Mr. J. S. to the _Correspondent_. It is one of his quadratures; and the joke is that I am made to be the writer: it appears as what Mr. J. S. hopes I shall have the sense to write in the _Athenaeum_ and forestall him. When I saw myself thus quoted--yes! quoted!

double commas, first person--I felt as I suppose did Wm. Wilberforce[378]

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[379] of {237} Galway--kind friend of the poor dumb creatures!--when he was told that the newspapers had put him in Italics. "I appeal to you, Mr. Speaker! I appeal to the House! Did I speak in Italics?

Do I ever speak in Italics?" I appeal to editor and readers, whether I ever squared the circle until a week or two ago, when I gave my charitable mode of reconciling the discrepant cyclometers.

The absurdity of the imitation of symbolic reasoning is so lusciously rich, that I shall insert it when I make up my final book. Somebody mastered Spanish merely to read Don Quixote: it would be worth while to learn a little algebra merely to enjoy this a 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 {238} connection 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 _aegri somnia_, which brings them to a certain look of reproach to reasoning which I can only burlesque. Mr. J. S. produces something which resembles argument much as a chimpanzee in dolor, because balked of his dinner, 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 t.i.the of onions for repeal of the Mortmain Act, before the Bishops in Committee under the kitchen table: his mode of imitating reason would do this with ease. But when he puts his imitation into my mouth, to make me what _he_ calls a "real mathematician," my soul rises in epigram against him. I say with the doll's dressmaker--such a job makes me feel like a puppet's tailor myself--"He ought to have a little pepper? just a few grains? I think the young man's tricks and manners make a claim upon his friends for a little pepper?" De Faure[380] and Joseph Scaliger[381] come into my head: my reader may look back for them.

"Three circlesquarers to the manner born, Switzerland, France, and England did adorn, De Faure in equations did surpa.s.s, Joseph at contradictions was an a.s.s.

Groaned Folly, I'm used up! What shall I do To make James Smith? Grinned Momus, _Join the two_!"

{239}

As to my _locus poenitentiae_,[382] the reader who is fit to enjoy the letter I have already alluded to will see that I have a soft and easy position; that the thing is really a _pillowry_; and that I am, like Perrette's pot of milk,

"Bien pose sur un coussinet."[383]

Joanna Southcott[384] never had a follower who believed in her with more humble piety than Mr. James Smith believes in himself. After all that has happened to him, he asks me with high confidence to "favor the writer with a proof" that I still continue of opinion that "the best of the argument is in my jokes, and the best of the joke is in his arguments." I will not so favor him. At the very outset I told him in plain English that he has the whiphand of all the reasoners in the world, and in plain French that _il a perdu le droit d'etre frappe de l'evidence_[385]; I might have said _pendu_.[386] To which I now add, in plain Latin, _Sapienti pauca, indocto nihil_.[387] 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 {240} masters did not feel able to interfere in what took place outside the school. So the boys were arraigned; and their friends, as silly in their way as themselves, allowed one of them to make the defence, instead of employing counsel; and did not even give them any useful hints. The defence was as follows; and any one who does not see how richly it sets off the defences of bigger boys in bigger matters has much to learn. The innocent conviction that there was answer in the latter part is delightful. Of course fine and recognizance followed.

A---- said the boys had received great provocation from B----. He was constantly threatening them with a horsewhip which he carried in his hand [the boy did not say what had pa.s.sed 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 G.o.d: 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. {241}

JAMES SMITH ONCE MORE.

Mr. James Smith's procedures are not caricature of reasoning; they are caricature of blundering. The old way of proving that 2 = 1 is solemn earnest compared with his demonstrations. As follows:[388]

Let x = 1 Then x^2 = x And x^2 - 1 = x - 1 Divide both sides by x - 1; then x + 1 = 1; but x = 1, whence 2 = 1.

When a man is regularly snubbed, bullied, blown up, walked into, and put down, there is usually some reaction in his favor, a kind of deostracism, which cannot bear to hear him always called the blunderer. I hope it will be so in this case. There is nothing I more desire than to see _sects_ of paradoxers. There are fully five thousand adults in England who ought to be the followers of some one false quadrature. And I have most hope of 3-1/8, because I think Mr. James Smith better fitted to be the leader of an organized infatuation than any one I know of. He wants no pity, and will get none. He has energy, means, good humor, strong conviction, character, and popularity in his own circle. And, most indispensable point of all, he sticks at nothing;

"In coelum jusseris, ibit."[389]

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 {242} 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 you was a very simple one, as I shall make manifest at the proper time."

In one or more places, as well as this, Mr. Smith shows that he does not know the legend of little Jack Horner, whom he imagines to be put in the corner as a bad boy. This is curious; for there had been many allusions to the story in the journal he was writing in, and the Christmas pie had become altered into the Seaforth [pi].

Mr. Smith is satisfied at last that--what between argument and punishment he has convinced me. He says (_Corr._, Jan. 27, 1866): "I tell him without hesitation that he knows the true ratio of diameter to circ.u.mference as well as I do, and if he be wise he will admit it." I should hope I do, and better; but there is no occasion to admit what everybody knows.

I have often wished that we could have a slight glimpse of the reception which was given to some of the old cyclometers: but we have nothing, except the grave disapprobation of historians. I am resolved to give the New Zealander a chance of knowing a little more than this about one of them at least; and, by the fortunate entrance into life of the _Correspondent_, I am able to do it. I omit sober mathematical answers, of which there were several. The following letter is grave earnest:

"Sir,--I have watched Mr. James Smith's writings on this subject from the first, and I did hope that, as the more {243} he departs from truth the more easy it must be to refute him, [this by no means always true] some of your correspondents would by this time have done so. I own that I am unable to detect the fallacy of his argument; and I am quite certain that '[Pi]'

is wrong, in No. 23, where he declares that Mr. Smith is 'ignorant of the very elements of mathematical truth.' I have observed an immense amount of geometrical reasoning on his part, and I cannot see that it is either fair or honest to deny this, which may be regarded as the 'elements' of mathematical truth. Would it not be better for '[Pi]' to answer Mr. Smith, to refute his arguments, to point out their fallacies, and to save learners from error, than to plunge into gross insult and unmanly abuse? Would it not be well, also, that Professor De Morgan should favour us with a little reasoning?

"I have hitherto seen no attempt to overthrow Mr. Smith's arguments; I trust that this will not continue, since the subject is one of immense importance to science in general, especially to nautical science, and all that thereto belongs.

Yours, etc.,

A CAPTAIN, R.N."

On looking at this h.o.m.oeopathic treatment of the 3-1/8 quadrature--remember, h.o.m.oeopathic, _similia similibus_,[390] not infinitesimal--and at the imputation thrown upon it, I asked myself, what _is_ vulgarity? No two agree, except in this, that every one sees vulgarity in what is directed against himself. Mark the world, and see if anything be so common as the description of the other side's remarks as "vulgar attempt at wit." "I suppose you think that very witty:" the answer is "No my friend! your remark shows that you feel it as wit, so that the purpose is answered; I keep my razor for something else than cutting blocks;" I am inclined to think that "out of place" is a necessary attribute of true vulgarity. And further, it is to be noticed that nothing is {244} unproducible--_salvo pudore_[391]--which has cla.s.sical authority, modern or ancient, in its favor. "He is a vulgar fellow; I asked him what he was upon, and what do you think he answered, My legs!"--"Well, and has he not justification? what do you find in Terence? _Quid agitur? Statur._"[392] I do not even blench from my principle where I find that it brings what is called "taking a sight" within permissible forms of expression: Rabelais not only establishes its antiquity, but makes it English. Our old translation[393] has it thus (book 2. ch. 19):

"Then made the Englishman this sign. His left hand, all open, he lifted up into the air, then instantly shut into his fist the four fingers thereof; and his thumb extended at length he placed upon the tip of his nose.

Presently after he lifted up his right hand all open and abased and bent it downwards, putting the thumb thereof in the very place where the little finger of the left hand did close in the fist, and the four right hand fingers he softly moved in the air. Then contrarily he did with the right hand what he had done with the left, and with the left what he had done with the right."

An impressive sight! The making of a fist of the left hand is a great addition of power, and should be followed in modern practice. The gentle sullation of the front fingers, with the clenched fist behind them, says as plainly as possible, Put _suaviter in modo_ in the van, but don't forget to have _fort.i.ter in re_[394] in the rear.

{245}

My Budget was announced (March 23, 1867) for completion on the 30th. Mr.

James Smith wrote five letters, one before the completion, four after it; the five contained 68 pages of quarto letter paper. Mr. J. S. had picked up a clerical correspondent, with whom he was in the heat of battle.

"_March 27._--Dear Sir. Very truly yours. Duty; for my own sake; just time left to retrieve my errors; sends copy of letter to clergyman; new proof never before thought of; merest tyro would laugh if I were to stifle it, whether by rhodomontade or silent contempt; keep your temper. I shall be convinced; and if world be right in supposing me incapable of a foul act, I shall proclaim glorious discovery in the _Athenaeum_.

"_April 15._--Sir,... My dear Sir, Your sincere tutelary. Copy of another letter to clergyman; discovery tested by logarithms; reasons such as none but a knave or a sinner can resist. Let me advise you to take counsel before it is too late! Keep your temper. Let not your _pride_ get the better of your discretion! Screw up your courage, my good friend, and _resolve_ to show the world that you are an _honest_ man....

"_April 20._--Sir ... Your very sincere and favorite tutelary. I have long played the _cur_, snapping and snarling...; suddenly lost my power, and became _half-starved_ dog without _spirit_ to bark; try if air cannot restore me; calls himself the _thistle_ in allusion to my other tutelary, the _thorn_; Would I prefer his next work to be, 'A whip for the Mathematical Cur, Prof. De M.' In some previous letter which I have mislaid, he told me his next would be 'a muzzle for the Mathematical Bull dog, Prof. De M.'

"_April 23._--Sir. Very sincerely yours. More letters to clergyman; you may as well knock your head against a stone wall to improve your intellect as attempt to controvert my proofs. [I thought so too; and tried neither].

{246}

"_May 6._--My dear Sir. Very sincerely yours. All to myself, and nothing to note.

"_July 2._--No more in this interval. All that precedes is a desperate attempt to induce me to continue my descriptions: notoriety at any price."

I dare say the matter is finished: the record of so marked an instance of self-delusion will be useful.