now. When I was a boy, in some parts of the country at least, it ran thus:
"Tit for tat;
Butter for fat:
If you kill my dog,
I'll kill your cat."
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
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
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.