744 



' jr<3V2 



(la) 



which (luanlity increases with v. Other well-known corrections have 

 been left out of consideration. 



Accordingly for liquids we shall not principally have to think of 

 transport of monientun» by the diffusing molecules, but we shall 

 have to explain the friction by forces which the molecules exert on 

 each other. If at an arbitraiy moment we could suddenly check the 

 motion of the molecules, and if we could arrest them in the position 

 which they occupied at that moment, the friction by means of 

 transport would at the same moment be destroyed, so that we 

 should not have any means to study the friction in those resting 

 molecules. 



The case is different for "friction through molecular forces". At 

 least when we think the molecular forces independent of the velo- 

 city, the frictioiuil forces would continue to exist also after the 

 immobilisation of the molecules. They would be a consequence of 

 the grouping of the molecide?? in space. It is now the question : of 

 what nature ai-e the molecular forces and what is the grouping of 

 the molecules, which gives rise to the existence of the tensor of 

 tension as we meet with it for the friction of liquids. The following 

 three answers might be given to this question : 



I. Friction through impact forces or throiKjIi an instantaneoas 

 transfer of inoinentuni. We might assume that the forces that 

 the molecules exert on each other at an impact would furnish the 

 explanation of viscosity. Let us consider the sim|)le case of a 

 liquid in which the current oidy moves in a single direction, which 

 has been chosen as .c-direction of a cartesian system of coordinates, 

 this velocity {it) being a linear function of z, hence: 



n — az, (with a > 0) (2) 



Then the layers with greater z will move towards the righthand 

 side with regard to the underlying layers, if the system of axes is 

 orientated in space in the usual way. A consequence will be that the 

 line connecting the centres of two collidiiig molecules, which 1 shall 

 call the central line, will be found more often in the second quadrant 

 of the .r2-surface than in the first. When the system of coordinates is 

 turned over an angle of 45 " ',, so that the -f- ,r-axis moves towards 

 the -\- j-axis, and when the new axes are called ,v' and z\ the 

 pressure that the molecules exert on each other will be greater in 

 the z' direction than in the ./■' direction. It is evident that this 

 agrees with (he value of the tensor of tension in this case. 



