24 

 and 



C. V. L. Charlier 



a:) = p sin jS cos A — pi 

 y = p sin B sin A = p m 

 s = p cos IB — pn . 



Then the transition from the variables i)-, to the variables B, A may be 

 performed according to the following scheme: 



= I 



= / 



P. I ^' ' 



(^iJ, A) \p, 71 J./ \Pi 2' '7 

 But, according to the formula (32)' we have 



X, Xl, z 



X / ■ 



X, y, z] \p, 4 



and 



■f^^' ^Ul/p^sin ,^ 



As to the remaining determinant we have, according to (16*) 



y = ßi P + p2 5 + ßs ^" 

 ^ = 'iiP + Ï2 î + Ta 



which formulae give 



X, y, z' 



so that 



as before. 



B, A 



«1, a,, ag 



ßl) ßs' ßs 



Ti > T2 ' T3 



sin 



= 1 



sin ■O- 



18. Final formula for V {i)- We have in § 5 obtained for the number 

 of stars »thrown in» into Jsj the expression 



(in) =A^Atf zle/' Ab^" d'Y' db" h" w" //' /^" 



where ^b^" = du^" dv^" dw^" and ^b.^" = du^" dv^" dw^" and the integration is to be 

 performed over all values of the variables 



/O O \ 1 1 1 1 n unit 



(00) , i\ , ; , ^2 1 ^^2 



such that after the passage the velocity components of one of the masses acquire 

 the values u^±\ du^, ± ^ dv^, ^ dw^ , i. e. are situated within the dominion Ae^ . 

 As we know from our above-mentioned theorem (Meddel. 69) that the variables 



(34) Mj', Vi', iu^'; n,/, I'j', 



