772 Mr. H. D. Arnold on Stokes's Laic for\ 



diameter measurements. A simple computation shows, how- 

 ever, that the factor of increase in apparent viscosity due to 

 a film of thickness t surrounding a sphere of radius r is t/r; 

 hence to account for the observed increase the thickness of 

 the film would have to be equal to half the radius of the 

 sphere. Moreover, on such an assumption the apparent 

 viscosity would become abnormally large for very small radii, 

 and this is not the case. 



A more probable assumption seems to be that with large 

 bubbles there is no appreciable film separating the air from 

 the oil, but the oil next in contact with the air holds fast to 

 a thickness of air approximately equal to the radius of the 

 sphere of action of the oil molecules. The actually moving 

 part of the air bubbles is therefore, on this assumption, 

 moving in contact with a stationary air surface, and w T e 

 would expect the coefficient of sliding friction to be the 

 same as the coefficient of viscosity of the air. This latter 

 value would be too small to detect in this experiment. If 

 we assume, however, that as the sphere becomes smaller a 

 film gradually forms, eventually enclosing the air in a per- 

 manent sack, we see that this sack would move upwards as 

 a solid sphere, and we would have approximately the con- 

 ditions of no slip. 



This matter of the formation of films has recently been 

 investigated by Schutt and by Ramsden. The latter assumes 

 that films are formed from material which is in the liquid, 

 and which enters the film because in doing so it tends to 

 minimize the energy of the film. It is apparent on this 

 hypothesis that the smaller the bubble the thicker and more 

 permanent the film would become. In addition, the slower 

 motion of the small bubbles would be less likely to result in 

 a tearing away of the film when once it was formed. An 

 assumption of this kind accounts readily for the maximum 

 and minimum values of the viscosity curve in olive oil, but 

 it is not so evident that the curve would pass continuously 

 between the two values. One would rather expect that there 

 would be a point of discontinuity corresponding to the first 

 formation of a permanent film. 



This idea of a permanent film fits particularly well the 

 results in linseed oil. Of all the oils used this one has the 

 greatest film-forming power. Indeed, films may be formed 

 on a wire loop and remain intact for twenty minutes in the 

 open air. Correspondingly, we notice that there is no marked 

 evidence of slip between the air and this oil, a result which 

 would follow if the surface film remained intact even with 

 laro-e bubbles. 



