statistical mechanics 51 



SO that 



-^'^'i — — ^ ' -^2 = 



Ü ' 'il J> ' ^ 



2 



aud 



+ r: — r—r^^ — + ^2 ^■^1 — ^ _ Q 



a 



because, according to the integral of the centre of gravity for equal masses 



Mj' -|- U^' = ~\- . 



We arrive at the same conclusion if the expressions (18) for and u^' are used. 

 Similar relations are obtained for the other components, and we get 



VlOO ~ VolO ~ VoOl ~ ^ • 



The development of the passage function contains no terms of a degree lower than 

 the second. 



40. Terms of higher order. 



For obtaining Vyi- we have to perform 8 integrations, viz. regarding the 

 variables u^, v^, w^; u^, v^, b, Let us first perform the integration regarding 

 4» aud use the following notations: 



Let F be an arbitrary function of the velocities and put 



2tc 



(107) [F] 

 where 



= 2^ (^i' + F2' - - F,), 

 0 



F, = F(u,, V,, wj, 



-^2 = -^K' «2' ^(^2 )' 

 F^'= F{u^\ y/, w/), 



i^2'= -^("2'' ^2'' '''^2') 



then we have 



^^2i+2J+2t f 



(108) Vp- = |. I ■ ^ j[Ri;fc]/i/2 dh. 

 We get evidently 



where /c denotes any arbitrary constant, and further 



(109) [u] = ^ j(M/ + m/ - «1 — «2) = 0 



0 



and 



[?;] = 0 = \w]. 



