602 Mr. L. Vegard : Contributions to 



We shall now consider some special cases : 



(1) The solution is exposed to the influence of Gravity. 

 Then we have 



U = r/h + constant ; 



g is the acceleration of gravity, h the height above a fixed 

 horizontal plane. This being introduced into equation (14 a), 



^_M£±£)|£ dK . . . {lld) 



(2) The solution is placed in a vessel that turns round a 

 vertical axis with constant velocity. It is supposed that the 

 fluid follows the motion of the vessel. It is desired to find 

 the potential Ui referred to a coordinate system, where the 

 Z-axis coincides with the axis of rotation and the two other 

 axes follow the motion. Then 



dTl —gdz — 7 2 [scdx + ydy), 

 and consequently 



The force-intensity at the considered point is expressed by 

 the following term : 



7 is the angular velocity and H the distance from the point 

 to the axis of rotation. 



As the concentration gradient is proportional to the force, 



we see that when c and ^ are not very small, we might 



make R, and 7 sufficiently great to obtain a considerable 

 change of concentration from place to place. In other 

 words, we might expect to be able to separate the solutions 



for which sj- has a considerable value, as milk is separated 



dc -JL 



from cream in a separator. The separation will, however, 

 never be complete. Besides it would be very difficult to 

 carry out the experiment practically. In order that the 

 separation might be made visible, the rotation would have to 

 be continued for a long time — since the rate of diffusion is 

 very small — and the motion would have to be perfectly even. 

 Furthermore, temperature differences would have to be 

 avoided, as otherwise currents would arise in the fluid. 



