TC TO ROBERT MITCHELL; 3 August 1816; DOI: 10.1215/lt-18160803-TC-RM-01; CL 1:81-84.
TC TO ROBERT MITCHELL
Annan, 3d August 1816.
My Dear lad,
You will easily guess, by the speediness with which I have answered your letter, that I am anxious to be reinstated in your favour. We have indeed written to one another much too seldom, of late. I suppose a good part of the blame is my own—but I will not take it all. Let us try to be more regular in future. I was at a loss what to make of the first part of your letter. I could have laughed at the causes which your sagacity has pointed out for the mistake—had I not been grieved at the mistake itself. You expect my explanation; but in truth I am unable to give any explanation of the matter. I am altogether unconscious of having mentioned any particular Saturday,1 for our excursion; and had I done so, I cannot conceive, how I should have hit on that day you speak of—for I must have known that the tide would not serve. If you have not destroyed that letter, I think you will find in it, that I wished you to come, on the first Saturday that would suit our purpose. But in reality it was late at night, or rather early in the morning before I finished that immense epistle—and I dare say I was half asleep over the latter part of it; and so I cannot vouch for its contents. But let us be of comfort. I have looked into the Belfast Town and Country Almanack2—and consulted several cunning men upon the subject—and from all quarters, I collect— that the moon will be full about one of the clock on the morning of Thursday the 8th inst.—so that in all human probability—the time of full sea, next Saturday after that, will be between 1 and 2 o'clock:—a time that will answer our purpose very well. Now if notwithstanding your late disappointment, you could be induced to come to Annan about twelve o'clock, that day—we could eat a morsel of dinner together and forthwith embark for Cumberland. I am anxious that you should come—for I wish to see you; and this will be a pleasant enough way of spending the time; and besides It will do no harm to you—it may happen to be of service.— Write on Tuesday if you can; and at any rate on Thursday—& let me know if you can come.
With regard to the division of the circle into 360 parts,—I think it cannot be done by elementary Geometry—at least if M. Gauss3 is right—who (Leslie tells us)4 has demonstrated that a polygon can be inscribed in a circle—directly—by means of circles and straight lines—only—when the number of its sides is a prime number and can be denoted by 2n + 1. This with the exception of the polygons described in the common books of Geometry.— Therefore this cannot be done directly. If we attempt to accomplish it by the method explained in Prop. 23.IV—I know of no polygons—of which, if [if appears to have been crossed out] the number of sides multiplied together will produce 360 [word obscured or 360/2n possibly overwritten] except 12 & 15 or 30—and these require the trisection of an arc;—or 18 and 20; and these require the inscription of a nine sided polygon—which cannot be done by any known method of plane Geometry.— To artists this is of little consequence— Indeed Delambre tells us that many of them have adopted a different plan of division. He say[s]—‘Pour diviser par de bisections continuelles, des artistes célèbres ont trouvé plus commode de partager le quart d[u] circle en 96 parties qui, par bisection donnent les arcs de 48, 24, 12, 6, 3. L'arc d[e] 60° vaut 64 parties et donne 32, 16, 8, 4, 2, 1; ce degré vaut 15/16 = 0.9375 = 0°-56'-15"; il se sousdivisé en quatre parties de 14'-3".75, et chachun de ces parties e[n] 16, q[ui] valent 52"·734375.’5— In your second difficulty6 I am not without hopes of being able to shew you a flaw in your reasoning—not doubting that you are very open to conviction. It appears, that in your speculations about this spiral, you forget that the ship's track is perpendicular to any7 two meridians—and therefore that one has no mor[e] right to be called the hypotenuse than the other. reflect upon the circle and all perpendicular radii: consider that if the plane of the ship's path (for since it is always directed to one point—it lies all in one plane) were produced to meet the earth's axis—being by hypothesis perpendicular to every meridian, it must be perpendicular to their common intersection. And in that case how can it avoid being paralell to the equator— which is also perpendicular to the same straight line? Your reasoning indeed applies to the equator as well as to any paralell circle. But you are sufficiently convinced by this time, I am well aware:—and therefore I make no more remarks upon the subject.
I am very glad that you have met with a book of natural philosophy that you like.— Send me your demonstration (or bring it) of the accelerated motion.— I return always to the study of Physics with more pleasure—after trying ‘The Philosophy of Mind.’8 It is delightful, after wandering in the thick darkness of metaphysics—to behold again the fair face of truth. When will there arise a man who shall do for the science of mind—what Newton did for that of matter—establish its fundamental laws on the firm basis of induction—and discard forever those absurd theories—that so many dreamers have devised?— I believe this is a foolish question—for its answer is—never.— I am led to talk in this manner—by having lately read M[r.] Sweart's [Stewart's] History of Philosophy in the supplement to the Encyclopedia Britannica[.]9 I doubt I am going to displease you—but I must say—that I do not recollect of ever having bestowed as much attention with so little effect—upon any author as upon Profr Stewart. Let me study his writings as I like—my mind seems only to turn on its axis—but without progressive or retrograde motion at all. [Dur]ing these eighteen months, for example, have I been at times, labouring to comprehend the difference between the primary & secondary qualities of [bodies, and m]y labour has always been in vain.— Can you resolve me, thi[s dif]ficulty? I can easily see that heat (a secondary quality) has two meanings—either it means the sensation in our mind—or it means the disposition of the particles of the body—that causes this sensation: but is not hardness (& th[e] other primary qualities) in the same predicament?
I designed to say many other things—but Post John is about to set out—and I must hold my hand. Write me at the time—I mentioned and see if you can come—at the time specified. I have many things to shew you & tell you—and ask you. I remain in the mean time (in great haste)
My Dear friend / Yours truly /