3-15-21. George Howard Darwin to H. Poincaré

Aug. 8.01

Newnham Grange–Cambridge

Dear Monsieur Poincaré,

I am glad you have found my letters worthy of attention.11See Poincaré to Darwin (§ 3-15-20), where Poincaré acknowledges Darwin’s two letters to Poincaré, of 31.07.1901 (§ 3-15-17) and 03.08.1901 (§ 3-15-18). I feel more & more confident of my correctness. There is [a] portion of your letter which I could not follow & therefore I am not clear of the physical meaning of your h.22See Poincaré to Darwin (§ 3-15-19). I feel no doubt that I have included all the sources of energy & moment of inertia and therefore I believe your h is included. The h has its counterpart in the problem I have solved & the result is correct in that case. How can it be that I have omitted [it] in the pear problem?

I find it very hard to look at the problem through your eyes, as I feel as urgent a necessity to continually keep the physical meaning before me, as you (I fancy) feel it a relief to dismiss it from your mind & betake yourself to analysis.

Nevertheless I have no doubt that you will arrive at the truth, & I feel pretty confident you will agree with me.

I find that it is unnecessary to regard the shift in the centre of inertia of the pear because the terms involved are of the fourth order.

I have gone a long way towards the determination of the mass of the layer – which corresponds to the determination of a in terms in a0 – and I have no words to describe the immensity of the task.

I have not made an exact estimate but I think there will be 20 or 30 integrals to evaluate by quadratures. The integrals are all of this type

0π2sin2nθdθ(1-k2sin2ysin2θ)p1-k2sin2θ

and there is another group of the type

0π2cos2nϕdϕ(1+k2tan2ycos2ϕ)p1-k2cos2ϕ

These will have to be found for n=0, 1, 2, 3, 4 combined with p=0, 1, 2, 3. It would seem that there are then 40 integrals of this kind.

There are others which I suspect will fall into the same type but I have not got so far yet. Have I patience for the task? I suppose I shall not feel contented until I have done it – and that is the only reason I have for thinking I shall persevere.

I shall be much interested to hear what you think, altho’ as I have said we look at this thing from different points of view. Shall I return your original letter.

Yours sincerely,

G. H. Darwin

ALS 4p. Collection particulière, Paris.

Time-stamp: "21.01.2016 01:47"