6 Mr. "W. Sutherland on Ionization in Solutions 



effect in the whole solution around it. In this case the time 

 of relaxation is proportional to the viscosity of the solution 

 and not that of the solvent. Thus the ET of Maxwell, which 

 we shall denote by 6 for this induced viscosity, may be 

 written 



6 = CV/47rKa 3 ZA (5) 



where C is a constant. We shall consider the expression 

 for the resistance acting on the ion from this induced viscosity 

 -after we have written down that due to the ordinary viscosity 

 of the solution. According to Stokes, the resistance to a 

 sphere of radius a moving with velocity u through a liquid 

 of viscosity rj and whose coefficient of slipping friction is ft, 

 is 



F = 6Trwna(l + 2 v /fta)/( 1 + ty/fta). ... (6) 



In "A Dynamical Theory of Diffusion for Non-Electro- 

 lytes 5 " (Phil. Mag. [6] ix. p. 781) I showed that this applies 

 to diffusing molecules only if the factor of slipping 



(l + 2y/fta)l(l + 3 V /fta) 



is replaced by the empirical factor 1/(1 -f cja 2 ) in which c is 

 a constant. For small values of y/fta the theoretical factor 

 becomes l/(l-t-ri/fta). Now, if ft is proportional to rj, as we 

 should expect, and if further it is proportional to a, then the 

 empirical factor takes the same form as the theoretical in 

 the limit when rj/fta is small. But the empirical factor holds 

 when 7)1 fta is no longer small compared with 1. I conclude, 

 therefore, that the empirical factor provides for molecular 

 effects not contemplated in the theoretical formula, namely 

 an amount of slipping which becomes greater the smaller the 

 diffusing sphere becomes, the intermolecular interstices of 

 the solvent making the amount of slipping larger for smaller 

 spheres. Just as it has been shown above that the ionic 

 charge causes an induced viscosity, the charges forming the 

 electric doublets of molecular attraction must cause an induced 

 viscosity which is a function of the distance from a diffusing 

 molecule. For these reasons I shall write the resistance of 

 ordinary viscosity to the motion of an ion in the form 



F = 6t™ W '(1 + c/a?) (7) 



instead of (6). This is necessary to keep the theories of 

 conduction and diffusion inconsistent relation, as will appear 

 in Sections 7 and 8. 



For the resistance due to our induced viscosity we ought 

 strictly to repeat the investigation of Stokes with viscosity 



