3-15-30. George Howard Darwin to H. Poincaré
Sep. 1. 01
Newnham Grange – Cambridge
Dear Monsieur Poincaré,
In order to save you trouble I hasten to make confession.11 1 Voir (§ 3-15-29). My work is right but insufficient. It is necessary to include 4th powers of so that you are right. I see this in the following way. If I change the sign of , I change the stalk into the blunt end of the pear & vice versa. This cannot change the value of and hence must be absent. I found this to be the case with the transition from the Maclaurin to the Jacobian Ellipsoid, but I was delayed by (my usual) small algebraic mistake which prevented the term from vanishing. In this case the change of sign of changes the azimuth of the Jacobian and the same result follows. But in the case of the sphere and Maclaurin the change of sign of changes oblate into prolate ellipsoid and therefore is not the same in the two cases.
I must admit that at present I do not see how to calculate the term in in my way. Your method will probably indicate it to me. But the calculation of the term was so troublesome that I suppose the term will be enormously worse. I do not think I can attempt it now.
I had written thus far when I received your letter in which you point out the same thing. I am sorry to have given you so much trouble.
I shall be much interested to see what you write.
I remain, Yours very sincerely,
G. H. Darwin
ALS 3p. Collection particulière, Paris 75017.
Time-stamp: "21.01.2016 02:03"