llü 



put in the place of tlie ecpiation of Langevin-Einstein, Miss Snethlage 

 differentiates equation (1) according to t. This yields 



V — = - K— — — — (3 



dt dt M 



dK , J m 



From which she rightly concludes that — is not independent ot v. The 

 nature of this dependence will . be known, if for each value of v 



V 



dK 

 one knows the average — :=F{v). Then there may be written for 



dt 



one system : 



— = F (v) -^w . . (4) 



dt 



where w is an accidental quantity which on the average is zero 



(i7"L 0). 



If we want to determine i'^(?;l it is apparently necessary to consider 

 the group of systems with a detinite value of v. We shall further 

 on indicate an average in such a "?;-group", the same as above 

 bj — v^ i. e. the average over the systems where in 07ie definite 

 moment v has a prescribed value, whilst the symbol — will indicate 

 the average for the whole ensemble. As is proved by the following 

 calculation equation (3) in not applicable, as (4) and (2), to every 

 v-group in particular; and this Miss Snethlagk has left out of 

 consideration. 



liet K represent the force acting in the ^'-direction on the particle, 

 V the velocity of this particle in that direction. Equation (1) is then 

 found for the canonical ensemble, when K does not depend upon 

 the velocities, and is exclusively a function of the coordinates 



7, • • • qn- 



Let 7i be the x coordinate of the particle, so that q^ = v. Then 



we have 



dK dK dK . dK. 



dt Oq, Oq, Oqu 



and for the average at definite v 



dK" _dk'' M'^" ^^^ 

 dt dq^ dq^ 



In order to reduce the last term we have made use of the well- 

 known independence of the extension in velocity and configuration. 



These terms fall out because q," = 0. The same independence 

 has as its result that 



