3-15-35. George Howard Darwin to H. Poincaré

Oct. 12.01

Newnham Grange–Cambridge

Dear Monsieur Poincaré

I have no doubt you are substantially right,¹¹ 1 Poincaré had recently charged Darwin with error (§ 3-15-34). and I cannot now recall the argument which made me think as I did. Is not it at least partially true? At any rate I have made the first calculation of my coeff^ts (other than $\mathfrak{K}_{3}$ ) for $y=75^{\circ}$ , $\kappa=\sin 81^{\circ}5^{\prime}$ and find

\displaystyle\mathfrak{K}^{1}_{3}

\displaystyle=.130

\displaystyle\mathbf{K}^{1}_{3}

\displaystyle=.224

\displaystyle\mathfrak{K}^{2}_{3}

\displaystyle=.460

\displaystyle\mathbf{K}^{2}_{3}

\displaystyle=.465

\displaystyle\mathfrak{K}^{3}_{3}

\displaystyle=.604

\displaystyle\mathbf{K}^{3}_{3}

\displaystyle=.614

I shall go on and compute for $\kappa=\sin 81^{\circ}4^{\prime}$ – for the Jacobian is $\kappa=\sin 81^{\circ}4.4^{\prime}$ . In this way I have an independent calculation & verification.

I have found an error in my calculation of $\mathbf{K}^{1}_{3}$ for $y=69^{\circ}50$ , $\kappa=\sin 73^{\circ}56^{\prime}$ . It sh^d be $.299$ & not $.236$ . This does not disturb the order in which the $K$ ’s are arranged.

If it would be of any help to you I will send you my compⁿ of the critical Jacobian.

Having struggled so much with arithmetic and realised its extreme difficulty, it is a comfort to me to hear you confess yourself a bad calculator.²² 2 See Poincaré to Darwin (§ 3-15-34).

Yours sincerely,

G. H. Darwin

ALS 2p. Collection particulière, Paris 75017.

Time-stamp: "18.09.2016 01:36"