290 Mr. William Sutherland on the 



to body are the velocity and the domain and volume of the 

 ions, so that we can say 



" frictional " resistance = <f>(V, w, U), 



or y = F(u, u). 



Now the simplest connexion that one can imagine between 

 the velocity and the domain and volume of the ion is that 

 the velocity will be greatest when the free domain or the 

 difference between the domain and the volume is greatest, 

 or, to be more general, when the difference between the 

 domain and some multiple of the volume is greatest ; but 

 if N is the sanie for all combined atoms, then U is proportional 

 to the refraction-equivalent q. Hence the form of F is such 

 that it contains u—aq, where a is a constant. On studying 

 the experimental data I found that a might be considered 

 unity, and that Y is a linear function of u — q. There is a 

 little difficulty in determining with accuracy the domain of an 

 ionic atom in a solution. Nicol, in his work (Phil. Mag. xvi., 

 xviii.) on the molecular domains of inorganic compounds in 

 solution, has confined his attention almost entirely to differ- 

 ences of domains, making the assumption suitable to his purpose 

 that the molecular domain of water is unaltered in solutions, 

 whereas we should expect that the greater part of the shrinkage 

 occurring on solution of an inorganic crystal happens in the 

 water, which is far more compressible than the crystal. 



Accordingly I take the molecular domains of salts in the 

 solid state, as given by Long in his paper on diffusion of 

 solutions (Wied. Ann.ix.), as nearer to the true domain when 

 they are in solution than Nicol's values ; but to allow to a 

 certain extent for the change of state on solution, I have assumed 

 that in each case the water experiences four fifths of the total 

 shrinkage and the dissolved salt one fifth. This is an arbitrary 

 adjustment, and is of no material importance to the comparison 

 to be made except as showing that the point has not been over- 

 looked. In the following Table are given under u the mole- 

 cular domains, under q the molecular refractions (Gladstone's), 

 in the next column their differences, under k the specific mole- 

 cular conductivities determined in highly dilute solution by 

 Kohlrausch and shown by him to be equal to the sum of the 

 velocities of the ions in each case. These are taken from his 

 paper (Wied. Ann. xxvi.), with a few additions from an 

 earlier one (Wied. Ann. vi.). Under k (calculated) are given 

 values of the conductivity calculated from the equation 



* = 68 + 2-2 (u-q), 





