4 Mr. W. Sutherland on Ionization in Solutions 



where T is the time of relaxation characteristic of the 

 substance. If s is constant, 



F = Ese ~ t/T , 



and the stress gradually disappears. If ds/dt is constant, 

 that is, if there is steady motion tending to increase the 

 displacement, 



F = ~ETds/dt + Ce- tIT , 



which shows that F tends to a value proportional to ds/dt 

 with ET as the coefficient of viscosity of the substance. 



For our polarized medium of ions we have to calculate ET, 

 and E is the rigidity of this medium, while for the electrons 

 of a metal at absolute zero it is denoted by N in my paper on 

 rigidity. If p is the density of the metal, m its molecular 

 mass, so that mjp is the domain of a molecule and (m/p)* 

 measures the diameter of a molecule and also the distance 

 between the electrons % and b which form the doublet that 

 causes rigidity, while K is the dielectric capacity of the 

 molecule, then it was shown that 



N = — -^- 4 (2) 



3K (m/ P y 



Hence for an electrolytic solution containing q positive .and 

 q negative ions per c.c. the instantaneous rigidity N of the 

 ions is given by 



N = 3kM • . (3) 



in which K is the dielectric capacity of the solution. This is 

 the required value of E in Maxwell's ET. We have now to 

 find T. It may be taken to be proportional to the resistance 

 experienced by each ion as all return to uniform distribution. 

 For a given solute it will be proportional to l/\ where \ 

 is the molecular conductivity of the solute at infinite dilution. 

 As we shall find 1/X proportional to rj the viscosity of the 

 solvent, this makes T proportional to the viscosity of the pure 

 solvent, and not to the viscosity of the solution. This is a 

 very important distinction, as it limits the dependence of T 

 to the molecules of solvent, and excludes any mutual influence 

 of the ions on one another as regards T. We shall find it 

 essential in explaining the variation of molecular conductivity 

 with concentration. As regards other physical quantities 

 upon which T depends, we can see that strain in our distri- 

 bution of ions will be accompanied with instantaneous strain 

 in the solvent, which possesses an instantaneous rigidity, so 



