TALBOT6438

26 Lincoln’s Inn Fields
8 July 1851

My dear Sir,

I acknowledge with my best thanks your interesting brochure ¹ on Foucault’s experiment of which you have had the kindness to send me a copy. Undoubtedly if the oscillations be considerable in amplitude & the length of the string small the law of the rotation may be [accurately?] & appreciably interfered with. It is desirable that the nature of the deviation from exact uniformity of motion should be reasoned out from the equations; I am not aware that in Paris it was all<?> to take an experimental quantitative measure of the effect phenomenon but the experiments in this country bring out results agreeing very closely with those indicated by analysis ( strict analysis – as you will see in a paper by one Mr <Thenber?> in the Phil. Mag of next month, who has gone over precisely the same ground as my friend Mr Cayley ² some months back) of the supposition of the motion of the pendulum being indefinitely small. On a cursory consideration of the case put by you, it appears to me to illeg resemble that proposed by Baudrimont, ³ to and inserted in the Comptes Rendus, viz to observe the oslatory motion of a sphere suspended at rest. But this appears to me to involve a fallacy; for the sphere would not appear to be at rest unless it were moving with the velocity of all the surrounding objects about the earths axis – & to reduce it to absolute rest it would be necessary to impart an apparent motion which is what would be observed and from which nothing could be inferred

I have discussed this very point with Professor Challis, ⁴ Arthur Cayley & Wheatstone ⁵ all of whom I think were thought were disposed to be satisfied with our view of the matter. Foucault however appears to have considered that the experiment suggested by Baudrimont would not be illusory or rather I should say negatory – but I cannot after much reflexion avoid adhering to my first view.

I am My dear Sir, Yours very truly
J J Sylvester

I beg your acceptance of my Essay on Canonical Forms, in which I have opened up some remarkable new ground in Algebra and given a fresh significance and field of application to the admirable discovery by Cayley of Hyp Hyperdeterminants
I beg to invite your attention to the general theorem page & of the supplement where I have shown how to Concoct any homogenous Function of an ord degree (2n – 1) into the form of the sum of or the of [sic] n, (2n-1)^th powers of linear functions of x and y. I should be most pleased to give you my explanations which might have the effect of interesting you in this most attractive field of Algebraical [numerals?] where the work is to be done is abundant & the laborers very few