and Two Keic Types of Viscosity. 29 



disappearing. Hence for large ions we have 1/A 01 propor- 

 tional to a ly and for small ones to K^. But for the large 

 compound radical ions K x falls to a nearly constant value 

 averaged from those of the component atoms, so that at both 

 limits we may say 1/A 01 is proportional to a v If the con- 

 stants of proportionality are suitably related, we can include 

 both limits approximately in the one formula, making 1/A 01 

 proportional to K^/i/!. As this is approximately true in the 

 limits, it has a good chance of being approximately true in 

 general. In this way we come back to (30) as an empirically 

 convenient simplification of (31). The proof from experience 

 that this is so was given in my previous paper on Ionization, 

 where it was shown that this formula (30) applies to the 

 fatty acid ions from HCOO to C 5 H n COO as well as to atomic 

 ions. This relation has since been investigated by Carse and 

 Laby (' Nature,' lxxv. 1906, p. 189), who find Ao^ sensibly 

 constant for the ions of 22 amines with a mean value 20*2. 

 For 7 anilines the mean value is 18*8, for 13 pyridines and 

 quinolines 20*3, and for 5 phosphines 17*6. These results 

 confirm the conclusion that with an appropriate value of K x 

 treated as an approximate constant for large ions (30) 

 becomes a useful formula for obtaining the size of large ions 

 whose molecular mass cannot be measured by the usual 

 methods. I have applied it to Hardy's ionic velocity of 

 globulin (loc. cit.), obtaining a result in reasonable agreement 

 with that obtained by (28) when applied to the diffusion 

 coefficient of egg-albumin (Phil. Mag. [6] ix. p. 781). For 

 small ions of measured A 01 , (30) becomes a means of finding 

 K x the effective dielectric capacity in electric fields which 

 change with a frequency small compared with that of light. 

 For changes of the frequency of light we have Maxwell's 

 relation K = N 2 , where N is the index of refraction of the 

 stuff of the atom. For most ordinary ions I have shown 

 that K x from (30) and N 2 from refraction equivalents show 

 a fair general agreement, but that the halogen ions are quite 

 exceptional, K x varying inversely as N 2 . This exceptional 

 behaviour of the halogens I attribute to the large amount of 

 latent valency in their atoms. 



We shall now consider (31) in detail. The main problem 

 is to determine from the experimental results the relative 

 magnitude of the two terms on the right-hand side, that is to 

 determine 0'. Now we shall see that for small ions the first 

 term becomes large compared to the second. In the first 

 7; /A stands for 1/A , and approximately for 1/2A 01 , so that for 

 these ions (31) reduces almost to the identity 1/A 01 =1/A 01 

 and becomes unsuitable for giving reliable values of A 01 , 



