28 Mr. W. Sutherland on Ionization in Solutions 



temperature. The bearings of this empirical formula in the 

 form 1 + c/a 2 representing 1 4- k/hB* have already been dis- 

 cussed in Section 2 and will further appear in 9. The 

 empirical factor w T ill be shown, in the next section, to have 

 an important application and verification in replacing the 

 theoretical one in our expression for ionic velocity. For 

 water at 16° C. b = 21 and k = 220. 



8. The Dielectric Capacity of Atoms. 



In my previous paper the formula given for ionic conduc- 

 tivity (with dropping of a constant) was 



A, 1 = v l e 2 'KJ^7r7 ] a 1 Yi 1 (29) 



This is erroneous through omission of the effect of the 

 dielectric polarization accompanying the ion. Yet it leads 

 to values of K x the dielectric capacity of the ionic atom 

 which are of the right relative magnitude for many atoms. 

 In the form 



Kx = 280^/^4^!* (30) 



it was used in "The Dielectric Capacitv of Atoms" (Phil- 

 Mag. [6] vii. p. 402 ; Austr. Assoc. Adv. Sci. 1904) for the 

 calculation of Kj for many atoms, and these values have 

 been used in " The Molecular Constitution of Aqueous 

 Solutions " (loc. cit.), and in " The Nature of Chemical and 

 Electrical Stimulation" (Amer. Journ. of Physiology, xvii. 

 p. 266). But now in place of (29) we have from (8), 



1/A 01 = 677770V* < C V* 2 /47rK 1 a 1 3 ZA + 1/(1 + c/aty/e 2 ^. (31) 



It is important to see clearly how these apparently incon- 

 sistent relations are really consistent. This comes to pass 

 through two remarkable relations. When giving values of 

 K 1? I pointed out that K 1 2 B 1 /v 1 2 is approximately constant, 

 suggesting in " The Electric Origin of Rigidity and Con- 

 sequences " (loc. cit.) how this might have a very fundamental 

 significance in the theory of matter. Using this in (31) we 

 see that the term in Vi/K^ can be written as a term in 

 Ki/j>i. We shall see that for ordinary atomic ions, especially 

 the small ones, this is the larger of the two terms. If we were 

 to neglect the other term, we should have 1/A 01 proportional 

 to K^/Vi as in (30). But for large ions the first term in 

 (31) is made small by l/«i 3 , and in the limit that equation 

 reduces to 



l/A 01 = 67T7} a 1 h/e 2 v 1 , (32) 



depending only on ordinary viscosity, the induced viscosity 



