44 



C. V. L. Cliarlier 



SO that 



(77) • |3 0.% = - '6[L-^M) [X, - [L-Mf^, + 3a^(L-M) . 



\± a^T, = l^, - 4(L--.¥) ^, + 6(Z-ilf)V2 + (i-i»^)*H-o 

 -6a,(tx, + (L-.V)X) + 3aVo. 



For L = M these relations take the form 



To ~ [^0' 

 Ti = 0, 



(78) L£ ^•'T2 = !J'2 ^ Sl^o ' 



1^ a*T4 = [J^4 — 6^-^P'2 + 3'^*!J'o, etc. 



Were in addition a? = 0^ = [j,^ : jj.^, so should also the coefficient Y2 vanish and 

 we should get the usual formulae. 



34. ^-series with several variables. 



In statistical mechanics we have to do with the frequency function of the 

 three com])onents of velocity (paying for the moment no regard to the positional 

 coordinates). In stellar statistics this frequency function is evidently of type A. 

 We have hence here to consider the development 



du' dv^ dw^ ' 



where 9 may be any function of the form 



(f(«, V, w) — Ce 



where (i[u, v, tv) is a polynôme of the second degree in u, v and w. 

 Putting 



so is Rijk a polynôme, of the degree i-\-j-\-k, in the variables u, v, w. 

 The coefficients Ayk have the form 



(81) A = C'ijt III F Riß. du riv dîv , 



--C 



where Cyk is a certain factor, the value of which it is not for the present necessary 

 to know (Compare Meddel. N:o 58 and Ser. II N:o 12). 



