1862. Mr. Smith replies to me, still signing himself Nauticus: I give an extract:
"By hypothesis [what, again!] let 14 deg. 24' be the chord of an arc of 15 deg. [but I wont, says 14 deg. 24'], and consequently equal to a side of a regular polygon of 24 sides inscribed in the circle. Then 4 times 14 deg. 24' = 57 deg. 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_:
"Si quem dura manet sententia judicis, olim Damnatum aerumnis suppliciisque caput, Hunc neque fabrili lassent ergastula massa, Nec rigidas vexent fossa metalla manus. Circus quadrandus: nam--caetera quid moror?--omnes Poenarum facies hic labor unus habet."[273]
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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 [pi] the letters l and g are closely related: this appears in the well-known formula for the time of oscillation [pi] [sqrt](l : g). Hence g may be written for l, but only once: do it twice, and you require the time to be [pi] [sqrt](l^2 : g^2). 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 3-1/8 diameters to {156} the circumference--in [pi]-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.
