82 C. V. L. Cliarlier 



(Jonsidering, that the two terms iu the denominator must have the same 

 dimensions, we gei 



(196*) KWlU-\ 



It follows that 

 (196**) T-Hfrr^ 

 and 



a* 



The quantity Aq^,^ denotes the number of stars per cub. siriometer and has 

 the dimensions 



so that 



Hence : The inverse value o f 3v denotes a time — the time of relaxation. 

 For numerical computation of T we may use either the tables of Glaisher 

 for the integralsine and the integralcosiue and the expression (171) for i}*, whereupon 



^ = 1 - 2g ^ (2 + q^) f , 



or developments into series. The latter method is alone practicable for very large 

 and for very small values of q. For very small values we get from (78) 



<K^) = cosa.|- - ^+y|3 --5|5 +yjy ~-| + 



1 • Id I 1 x^ \ 



+ smx p + logx- + - -q^ + 



and 



x'^ , X* x'° 



<\\x) = (to^x\\ogx^B- 1 — Yjg- + 475 ""6]T + ••• r + 



which give 



(198) 



1 + cos X { — Tlx — 2 log X — log x — 2{B — I) -\- x^ . Powerseries} + 

 2 



-I- sin { — 2x log x ^ 'k x{- -28 — 2) + . Powerseries} . 



X 



For very small values of x we have 

 (199) -^ = -2\ogx. 



