774 Stokes's Law for the Motion of Spheres in Liquids. 



Radii of Molecular Attraction, 



It is interesting to consider the significance of the rate of 

 diminution of the air bubbles. As has been stated, this is 

 but slightly dependent upon the rate of diffusion of the air 

 in the oil, but seems, on the contrary, to depend for the most 

 part on the adhesion of a film of air to the oil surface. If 

 this is the case, the film would be of a thickness proportional 

 to the sphere of action of the oil molecules, and indeed would 

 be expected to be to a first approximation equal to the radius 

 of the sphere of action. It is easy to get an idea of the 

 thickness of this film. We have seen that if we represent 

 by x the distance traversed by the sphere, 



dr 2 /dx = c, 



whence 



9 dr* d(%m*) 9 



2irr — — — ^ L =2irrc. 



ax ax 



This states that the diminution in volume is just sufficient 

 to provide a lining of thickness c for the tube of radius r 

 through which the sphere is moving. The value of c 

 actually obtained from the curves is of the right magnitude 

 to verify our assumptions, as will be seen from the following 

 values : — 



Olive oil 3-6 xlO" 6 



Colza oil. 8-5 xlO" 6 



Castor oil 1O0 x 10" 6 . 



Although there are several factors whose omission prevents 

 us from concluding that these values are actually the radii 

 of molecular attraction in the different oils, the close agree- 

 ment of these values with those ordinarily assigned from the 

 results of utterly different types of experiments is quite re- 

 markable. It may be that further experiments along this 

 line will result in a method of determining at least the ratio 

 of the spheres of attraction in some of the oils which are 

 most amenable to this process. 



Summary. 



It is possible to make metallic spheres sufficiently small 

 and uniform in density and in surface texture to allow of the 

 verification of Stokes's law in the less viscous oils. 



One of these spheres may be used instead of the capillary 

 tube method to test the rate of variation of viscosity with 

 temperature or with pressure, with probably greater accuracy, 

 and certainly with greater ease and rapidity. 



