3-15-21. George Howard Darwin to H. Poincaré
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 .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 is included. The 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 in terms in – 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
and there is another group of the type
These will have to be found for , , , , combined with , , , . 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.
G. H. Darwin
ALS 4p. Collection particulière, Paris.