250 ANNUAL EEPOET SMITHSONIAN INSTITUTION, 1910. 



gas molecule and the radius of the drop. 1 Since it is conceivable, 

 however, that there is some other cause for slip than that assigned 

 by the kinetic theory, it will be well to make this discussion as 

 independent as possible of all theoretical considerations. 



From whatever point of view, then, the phenomenon of external 

 slip be regarded, it is clear that the very existence of any surface 

 effect of this sort between the medium and the drop must tend to 

 produce an actual velocity higher than that computed from the 

 simple form of Stokes's law, i. e., it must tend to produce departures 

 from Stokes's law of the kind actually shown in the experiments 

 herewith recorded. Furthermore, it will be evident from the analysis 

 underlying Stokes's law that any surface effect whatever between oil 

 and air which might modify the velocity given by Stokes's law must 

 be more and more effective in so modifying it the more the radius 

 of the drop is diminished, and that when the radius is taken suffi- 

 ciently large the term which represents this surface effect must be- 

 come negligible. We could then write a corrected form of Stokes's 

 law, which would take into account any kind of surface phenomenon 

 which might alter the speed, in the general form 



X = G^1 +/(£)}" (5) 



in which I is a constant of the medium and a the radius of the drop. 

 If we were in complete ignorance of the form of the function / we 

 could express it in terms of the undetermined constants, A, B, C, 



etc., thus 



fQ= 



l + A^ + B ; - 2 + C-3, etc. (6) 



and so long as the departures from the simple form of Stokes's law 

 were small, we could neglect the second order terms in l/a and have 

 therefore 



X=6*/iaJl + A-] * (7) 



or 



2qa 2 (ff-p)l 7] 



0i= ' 



9 m i 1+A «r (8) 



Using this form of equation to combine with (1) and denoting now 

 by e the absolute value of the elementary charge and by e 15 as here- 

 tofore, the value of the charge obtained from the use of (4), there 

 results at once 



e(l + A~f = e x or #(l + A*) = e£. (9) 



1 See O. E. Meyer, Kinetische Theorie der Gase, p. 211, for the correction of Poiseuille's 

 law for slip, and Cunningham, Proc. Roy. Soc, 83, p. 57, 1910, for the corresponding 

 correction of Stokes's law. 



