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.11Voir (§ 3-15-29). My work is right but insufficient. It is necessary to include 4th powers of e so that you are right. I see this in the following way. If I change the sign of e, I change the stalk into the blunt end of the pear & vice versa. This cannot change the value of E and hence e3 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 e3 term from vanishing. In this case the change of sign of e 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 e changes oblate into prolate ellipsoid and therefore E is not the same in the two cases.

I must admit that at present I do not see how to calculate the term in e4 in my way. Your method will probably indicate it to me. But the calculation of the e3 term was so troublesome that I suppose the e4 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"