6-1-322. Albert Gauthier-Villars à H. Poincaré

Paris, le 28-12 1909

Gauthier-Villars Éditeur
55, Quai des Grands-Augustins, Paris 6e{}^{\text{e}}

MEMORANDUM

M. Gauthier-Villars présente ses compliments à M. Poincaré et a l’honneur de l’informer qu’il a bien tous les bons à tirer nécessaires pour le Bin{}^{\text{in}} Astronomique, no{}^{\text{o}} de Janvier.11endnote: 1 The verso features calculations from lunar theory in Poincaré’s hand, seemingly unrelated to the publication of the January, 1910 issue of Bulletin astronomique by Gauthier-Villars.


A⁢p′+A1⁢p1′+r⁢(B⁢q+B1⁢q1)−q⁢(C⁢r+C1⁢r1)=−L,\displaystyle Ap^{\prime}+A_{1}p_{1}^{\prime}+r(Bq+B_{1}q_{1})-q(Cr+C_{1}r_{1}% )=-L,
A1⁢(p′+p1′)−B1⁢r1⁢(q+q1)+C1⁢q1⁢(r+r1)=0.\displaystyle A_{1}(p^{\prime}+p_{1}^{\prime})-B_{1}r_{1}(q+q_{1})+C_{1}q_{1}(% r+r_{1})=0.

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−L=K⁢cos⁡k⁢t,−M=−K⁢sin⁡k⁢t,N=0.-L=K\cos kt,\qquad-M=-K\sin kt,\qquad N=0.

p,q,p1,q1p,\ q,\ p_{1},\ q_{1} très petits 1er{}^{\text{er}} ordre,  r12dr_{1}\quad 2^{\textrm{d}} ordre.

r1=0r_{1}=0, r=r=const

A⁢p′+A1⁢p1′+r⁢(A⁢q+A1⁢q1)−q⁢C⁢r=K⁢cos⁡k⁢t,\displaystyle Ap^{\prime}+A_{1}p_{1}^{\prime}+r(Aq+A_{1}q_{1})-qCr=K\cos kt,
A1⁢(p′+p1′)+C1⁢q1⁢r=0\displaystyle A_{1}(p^{\prime}+p_{1}^{\prime})+C_{1}q_{1}r=0
p\displaystyle p =α⁢sin⁡k⁢t,q\displaystyle=\alpha\sin kt,\qquad q =α⁢cos⁡k⁢t,\displaystyle=\alpha\cos kt,
p1\displaystyle p_{1} =α1⁢sin⁡k⁢t,q1\displaystyle=\alpha_{1}\sin kt,\qquad q_{1} =α1⁢cos⁡k⁢t\displaystyle=\alpha_{1}\cos kt
(A⁢α+A1⁢α1)⁢(k+r)−α⁢C⁢r=K,(A\alpha+A_{1}\alpha_{1})(k+r)-\alpha Cr=K,
A1⁢k⁢(α+α1)+C1⁢α1⁢r=0A_{1}k(\alpha+\alpha_{1})+C_{1}\alpha_{1}r=0

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α1=A1⁢r⁢αA1⁢k+C1⁢r−A1⁢(k+r)⁢αA1⁢k+C1⁢r\alpha_{1}=\frac{A_{1}r\alpha}{A_{1}k+C_{1}r}-\frac{A_{1}(k+r)\alpha}{A_{1}k+C% _{1}r}
A1⁢k+C1⁢r=A1⁢(k+r)+(C1−A1)⁢rA_{1}k+C_{1}r=A_{1}(k+r)+(C_{1}-A_{1})r
α⁢r⁢(−C+A12⁢(k+r)A1⁢k+C1⁢r−A12⁢(k+r)r⁢(A1⁢k+C1⁢r)néglig.+A⁢k+rrnéglig.)=K\alpha r\left(-C+\frac{A_{1}^{2}(k+r)}{A_{1}k+C_{1}r}-\frac{\frac{A_{1}^{2}(k+% r)}{r(A_{1}k+C_{1}r)}}{\text{néglig.}}+\frac{A\frac{k+r}{r}}{\text{néglig.}}% \right)=K
α0=−KC⁢r\alpha_{0}=-\frac{K}{Cr}
α0α=1−A1C⁢A1⁢(k+r)A1⁢(k+r)+(C1−A1)⁢r.\frac{\alpha_{0}}{\alpha}=1-\frac{A_{1}}{C}\frac{A_{1}(k+r)}{A_{1}(k+r)+(C_{1}% -A_{1})r}.
−rk+r\displaystyle\frac{-r}{k+r} =N;A1C1−A1=ε\displaystyle=N;\qquad\frac{A_{1}}{C_{1}-A_{1}}=\varepsilon
α0α\displaystyle\frac{\alpha_{0}}{\alpha} =1−A1C⁢εε−N\displaystyle=1-\frac{A_{1}}{C}\frac{\varepsilon}{\varepsilon-N}
A1\displaystyle A_{1} =Cαα0=N−εN\displaystyle=C\qquad\frac{\alpha}{\alpha_{0}}=\frac{N-\varepsilon}{N}
ε\displaystyle\varepsilon =Nnut. nulle\displaystyle=N\qquad\text{nut. nulle}
ε\displaystyle\varepsilon >Nnut. change de signe.\displaystyle>N\qquad\text{nut. change de signe.}
∞⁢ pour ⁢A1C=ε−Nε\displaystyle\infty\text{ pour }\frac{A_{1}}{C}=\frac{\varepsilon-N}{\varepsilon}

AL 1p. Private collection, Paris.

Time-stamp: "24.10.2026 20:17"

Notes

  • 1 The verso features calculations from lunar theory in Poincaré’s hand, seemingly unrelated to the publication of the January, 1910 issue of Bulletin astronomique by Gauthier-Villars.