Physics. — ''On the Theory of the Friction of Liqaids II." By 

 Prof. J. D. VAN DKR Waai.s Jr. ('(^ouiiiimiicaled by Prof. J. D. 

 VAN DER Waals). 



(Communicated in the meeting of March 29, 1919). 



§ 4. Distribution of density in a liquid jioxnng in a field of 

 J-orces. Before proceeding to the "friction bv formation of groups", 

 we shall discuss a simpler problem. We shall namely imagine that 

 a gas streams in a field of force, and then examine what modifi- 

 cations are brought about by the streaming in the distribution of 

 density as it would arise in a field of forces when there was no 

 current. For this purpose we shall again imagine the simple case 

 that the streaming takes place in the ,r-direction, and that the 

 velocity may be represented by u = az. We shall further suppose 

 that we have to do with a stationary current, so that in a point 

 at rest in space the density and the velocity of the current are 

 constant. 



In order to examine the distribution of density which will present 

 this stationary character, we shall assume that there are two causes 

 that might give rise to a change in the density in a given point : 

 the "molar" current, and the "diffusion" curient. It is not to be 

 denied that this distinction is artificial, and that the change of the 

 quantity of substance in an element of space can of course always 

 be found from the total current that flows in through the boundary 

 surfaces. 1 shall, however, suppose that this total current may be 

 thought composed of a molar current, to which 1 shall assign the 

 unmodified velocity u = az, and a current which is the consequence 

 of the inhomogeneous density in connection with the heat motion. 

 The latter will be denoted by the name of diffusion current. I shall 

 further assume that the change brought about by each of these two 

 causes, can be computed independent of the other cause. 



The quantity which enters a volume element per second through 

 the molar current is : 



dn dn 



— rf.r dy dz -^ — u ^-~ dx dy dz (10) 



dt ' Ö.X - ' 



In order to calculate the contribution of the diffusion cuirent we 

 shall assume that the distribution of the velocities of the gas-mole- 



