1 289 



ill whic'li It repieseiits the velocity of (Min-eul and ,/,/, llie velocity 

 of the heat motion, and lei us take into consideration that 



ƒ 



2 2m n xtii ■= 0. 



and 



V „i „» 4- m (a-,— .1-,) //' Ifix) <lr = (). 



Equation (18) then assumes the following forni : 



2 m x*ih -\- 2 X K-\- {x^ — x^) in j .v*th /(a') dx ■=: 



Let us further split up X into A, and A\, in which A, refers to 

 the mutual forces of the molecules in the considered volume and 

 A, to the forces exerted by bodies lying outside the volume on the 

 molecules contained in it. We shall only have to take forces A, 

 into account that act in the planes ;Ci = r and .r, = c ; the others 

 will be zero on an average. We shall further be allowed to put : 



{2X,)^^~^mO fxth\f{x)d:v=p,,.0 .... (19) 



in which (SA,).t, represents the sum of all tiie forces A', that act 

 in the plane ,i\ = c, and p^cx an element of the stress tensor in the 

 well-known way. The lefthand member of (19), jiamely, indicates 

 the total change of momentum which is caused by the substance on 

 the lefthand side of the plane x^ =z c in that on the righthand side 

 both in consequence of transport by the molecules in their heat 

 motion and in consequence of forces. As 0{.v, — r,) = T^we find: 



p^ig V = 2 m x' |- 2 X X, 

 or 



.;>xx=y-:s'.^^x, (20) 



when the sign .2" in the last equation represents a summation o\ er 

 all the molecules in a c.c.m. 



^ 7. The stress tensor in a fiowing liquid. When we now calcu- 

 late p^i according to equation (20), we find: 



RT rrb<f (s^-§,r . , ,,,.. 



