2-56-16. William Thomson to H. Poincaré

March 2nd. 1901.11 1 This letter was penned by a copyist; there is also a draft (LB 9, 66, Cambridge University Library).

15, Eaton Place, S.W.

Dear Mr. Poincaré,

I am sorry to say it is too true that there are, as you tell me in your letter which I have received this morning, several mistakes in respect to magnitude and to sign in my statements regarding the nutation which would exist if the earth consisted of a rigid ellipsoidal shell filled with frictionless liquid.22 2 Poincaré’s letter has not been located, such that the precise context of his remarks remains obscure. Plausibly, Poincaré was motivated to examine Thomson’s theory of nutation while studying Oskar Backlund’s calculation of the secular variations of the Earth’s equator due to secular variations of the ecliptic. On the latter topic, see O. Backlund to Poincaré, 05.02.1901 (§ 3-1-1). Ever since 1876 when that statement of results was published, I have been looking for time to go through the mathematical work again and publish it.33 3 W. Thomson 1863, 1867, §§ 878–879), later corrected (W. Thomson 1876), and reedited with minor changes (W. Thomson 1882, Volume 3, 312–336). Poincaré’s and Orr’s remarks are aimed at the 1876 version. If I had succeeded in finding the time, no doubt I would have corrected the errors myself; but in this I was anticipated by an Irish professor (W.J. Mc. F. Orr, of the Royal College of Science, Dublin), in a paper published in the Philosophical Magazine for December 1898.44 4 Orr 1898. William McFadden Orr (1866–1934), professor of applied mathematics. The corrections which you will find in this paper agree, I believe, with those you now give me. The subject is most interesting, and I hope yet to return to it, but meantime I hope you will publish your own work with your corrections of my errors.55 5 The fact that Poincaré did not publish his corrections of Thomson’s calculation suggests that they agreed with those published by Orr (1898).

In my mathematical work I suppose for simplicity the ideal interior liquid to be frictionless. No assumption of viscosity in the liquid would be, to my mind, very interesting. It certainly could not show any way of escaping my main conclusion that the earth is on the whole an elastic solid of high rigidity; though probably or possibly not so high as to cause practically perfect resistance against change of shape by the tide-generating influences of the sun and moon.

I thank you warmly for your kindness in writing to me and telling me of the errors you have found.

Believe me, with kind regards, Yours very truly,

Kelvin

TLS 1p. Private collection, Paris 75017.

Time-stamp: " 1.09.2018 11:30"

References

  • W. M. Orr (1898) On the forced precession and nutations of a rotating ellipsoidal shell containing liquid. Philosophical Magazine 46, pp. 545–553. External Links: Link Cited by: footnote 4, footnote 5.
  • W. Thomson and P. G. Tait (1867) Treatise on Natural Philosophy. Clarendon, Oxford. External Links: Link Cited by: footnote 3.
  • W. Thomson (1863) On the rigidity of the earth; shiftings of the earth’s instantaneous axis of rotation; and irregularities of the earth as a timekeeper. Philosophical Transactions of the Royal Society of London 153, pp. 573–582. Cited by: footnote 3.
  • W. Thomson (1876) Presidential address. Report–British Association 46, pp. 1–12. External Links: Link Cited by: footnote 3.
  • W. Thomson (1882) Mathematical and Physical Papers. Cambridge University Press, Cambridge. External Links: Link Cited by: footnote 3.