## 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.^{1}^{1}Voir (§ 3-15-29).
My work is right but insufficient. It is necessary to include 4^{th}
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 ${e}^{3}$ 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
${e}^{3}$ 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 ${e}^{4}$ in my way. Your method will probably indicate it to me. But the calculation of the ${e}^{3}$ term was so troublesome that I suppose the ${e}^{4}$ 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"