## 3-15-26. George Howard Darwin to H. Poincaré

Aug. 25.01

Newnham Grange–Cambridge

Dear Monsieur Poincaré,

Since I last wrote I have continued to work at my subject & have met with unexpected success. The most troublesome integrals disappear automatically and a number of others can be obtained rigorously without elliptic integrals. I have now arranged the work in a very convenient form & have started a professional computer at the integrals. The work will not be very long. It would be tedious though not difficult to express them all in $E$ and $F$.

I find also that, by proper interpretation of the symbols and change of third harmonic to second, this result is applicable to this initial Jacobian considered as a deformation of an ellipsoid of revolution. I expect to have the result in a day or two, and if it is correct it seems to me absolutely impossible that I can be wrong in the problem of the pear.

It has been a very troublesome piece of analysis. I found it convenient to join part of my ${E}_{2}$ to ${E}_{1}$, then to join the other part to ${E}_{3}$; to join ${E}_{5}$ with part of ${E}_{4}$. The remaining part of ${E}_{4}$ is deducible by means of ${E}_{3}$. All this was not discovered until I had made many trials & failures.

I look forward to your letter with much interest.

Yours sincerely,

G. H. Darwin

ALS 3p. Collection particulière, Paris 75017.

Time-stamp: "13.01.2016 19:15"