1189 



»,' = u^^ + - (/ X 2.- dx = «,' -f I ^' . . . . («) 



o 



Oil contact of the two molecules u^i s 'las therefore become 



2/ 

 = ?//-["' ('^ — •''■)*' ^vliile — ill consequence of the appearance of 

 ni 



the ie|)nl8ive force, given l)y (the qnasi-elastic force being represented 



by 2ê) 



/^' = 2f(.i- — (/-.)), 



when P is within llie distance .<? (on contact) — the velocity is 

 henceforth represented by 



2/ 2 r 





i.e. by 



Ur' = u/ -I -^ (/ - .)'' ix-il-s)y . . . . (b) 



m m 



Hence we have, u being *'/(/< : 



dx dx 



dt, — ____ • f/t, ^= 



2/ ( / 2/ 2f 



7n V m m 



i.e. for the times t^ and ^^ resp. between M and the collision, and 



during the collision up to the culminating point, where n. has 

 become = : 



'-« dx '-•"' dx 



"-'V-.-f^-^ ^'^li^-' 



2/ 28 



when / represents the distance of the molecule centres at the 

 highest point of the compression. 



For the mean square of velocity, i.e. the time-nverac/e, which also 

 occurs in the Virial equation, and to which the temperature is pro- 

 portional, we evidently have now quite generally : 



i.e. with 



1 r\ 2f 2s 



- "o* f -^-^ {x~{i-s)y 







dx 

 dt 



(It, 



V 



2f 26 



in m 



77 

 Proceedings Royal Acad. Amsterdam. Vol. XXI. 



