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Document number: 6438
Date: 08 Jul 1851
Recipient: TALBOT William Henry Fox
Author: SYLVESTER Joseph James
Collection: British Library, London, Manuscripts - Fox Talbot Collection
Collection number historic: LA51-27
Last updated: 21st April 2014

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 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


1. Remarks on M. Foucault’s Pendulum Experiment by H.F. Talbot, privately printed by Cox and Wyman, London, 1851. In March 1851 Jean Bernard Léon Foucault (1819–1868), French physicist, suspended a metal ball, weighing 28 kg, in a wire from the dome of the Panthéon in Paris. The ball was set in a pendulous motion, and over a span of hours it would exhibit a slow rotation in the direction of the pendulous motion, but what seemed to be the gradual rotation of the direction of the pendulous motion would actually be the rotation of the earth in space. In his paper WHFT suggested a different experiment, in which a horizontal bar balancing on a vertical bar would have to revolve within the span of 24 hours if Foucault’s reasoning was true. WHFT was convinced that this experiment would fail and thereby prove Foucault wrong, and the experiment would have failed, but perhaps not for the reasons WHFT thought. WHFT’s experiment would fail because he operated with an object, which was at rest with respect to the earth, whereas Foucault operated with an object, or rather a movement, which was at rest with respect to the frame defined by the stars. In the defence of WHFT only the fewest contemporary observers perceived this difference, among these few were Sylvester. [See Tobin, William, The Life and Science of Léon Foucault: the man who proved the earth rotates (Cambridge and New York: Cambridge University Press, 2003), pp. 133–172.].

2. Arthur Cayley (1821–1895), mathematician.

3. Possibly E. A. Baudrimont (1806–1880), French scientist.

4. James Challis (1803–1882), clergyman and astronomer at Cambridge.

5. Sir Charles Wheatstone (1802–1875), scientist.

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