113 



(5nf), which accordingly ninsi not be holed upon ,is a ilijf'erential 

 equation, Or: if we do consider (5^0 right for later moments, we 



do not get in connection with it w = 0, as it is made use of by 

 Miss Snethlagk. 



We ■ are able to refute the second objection, viz. that statistical 

 mechanics should not allow that the fluid moves with tlie particle 

 in an analogous way. For this purpose we shall calculate the 

 derivatives of 



V 



vv' —0 

 where v' is the .r-velocity of an arbitrary molecule situated in the 

 neighbourhood of the particle. 

 We have 



c? , rff , dv' K -" K' 



— vv =-;-?' -\- V = — v' A- V 



dt dt dt M ^ M' 



as v' as well as K' are zero. Furtlier 



d"- , d^v , dv dv' d'v' 



— v v' = V -]- 2 \- v =z - 



W df dt dt de I 



The average of the first term yields 



d"- , d'^v . ^dv dv' d'v' 1 dK , KK' v dK' 



vv = V -{- Ó [- V -=: Ü -4- 2 1 



df df dt dt de M dt MM' M' dt ' 



1 |ö^ , , ^^^ ,. , I löA^-TT KK'-^ KK' 



\^vv'-\-.— v"" 



V- == — v" = — 



M\dq dq' '") Mdq' M0 MM' 



and of the third term 



v \dK' 0^' , ) v' dK' v' KK' v' KK' 



idK' dK' 



^^/' I 0^ Oq' ' ' ] M' dq M' -2 MM' 



so that 



d^ -V ICK' f v^\ 



^^'^' --MM'V-^) ^^) 



For the change of?;' with the time we have according to the preceding 



dv' 



— = 

 dt 



^''_ KK^ 



'^i' ~ MM'V- 

 Novy K is the sum of the forces in the .I'-direction, which all 

 other particles exercise on the first, K' the corresponding sum for 

 the second particle. 



If we develop the product of these sums, we shall obtain the 

 average of the product of action and reaction that may beassunied 



8 

 Proceedings Royal Acad.. Amsterdam. Vol. XXI. 



