d^" _dK 



dq, dq^ ' 



The last average is easily calculated from Gibbs' formulae. 



Integrating by parts the tlenominater yields 



— \K-- e \lq, . . . dqn 



dq, 



as the integrated part falls out (6=00 at the limits). 

 Now 



de dK 1 



^—=-K and therefore ^- = A" 



dq, ^ dq^ f) 



Considering that O = M v' , we obtain 



dK' 



^K^ • . {^ 



dt M v"" 



And so F iv) has been found; equation (4) becomes 



dK kT' 



= r=: V \~ W (Oa) 



dt ,]/^» 



i. e. the very form given to this equation without further proof by 



V. D. Waals and iVliss Snkthlage. (Miss Snkthlage e(puition 24, sees 



however the note of these Proc. 24, 1278 where a cah-ulation 



remotely analogous to ours is found, without however our conclusions 



beine drawn from it.) 

 ♦ : 



The fact that _ = and ^=-^^ K' or 1^ = — — --= v 

 dt dt Mv' dt' APv' 



has great inportance for the theory of canonical ensembles. If 

 at a given moment one chooses a group of systems in which the 

 suspended particle has a definite velocity-component v, then the 

 formulae found are applicable to this group. Now one ought to 

 consider, that, if one follows these systems in the lime, the velocity 

 of the particles does not remain the same for all of them, but that 

 different velocities are going to arise. Moreover our formulae iïidicale 

 that, if we take the average velocity a very shoi-t time t 

 after the selection of the gioup, it has become smaller than v. Bj 



