714 Boltzmanns Law of Probability e~ h x. 



and therefore since ~dh and "dv are mutually independent, 



du _ _ du _ rf^ 



dh~~~ X > dv~"~ dv' 



. , . rZ du d du , 



And since r -rr = ^ T , we have 

 au a/i ah dv 



dv dh\ dv) W 



Let now/ be the function of probability, so that %= \fxda, 



the integration for da including all configurations, also -^ = 



dv 



\f%la. Then (B) gives 



and the equation 

 becomes 



and since v is a function of v only, we may write -/ = -£- -A 

 " J J dv dxdv 9 



and we have I y f--^da= 1 h~J -%da. 



J A d X dv J d/ic/v ' 



which leads to #-f = ^j{ That is, /* is a function of the 



product hx- Also 



d£l dfl djogf dlogf 



X d x f h dhf 01 x dx ~ h dh . 



and log / is a function of /i^. The simplest solution of 

 which is f=e~' ! x. 



