

Nature of Dielectric Capacity. 9 



average intensity throughout v due to the induced moment 

 (4) is that moment divided by v. Now the average intensity 

 of the electrization induced by F is F(K / — l)/47r, where K / 

 is the dielectric capacity caused on the average throughout v 

 by the presence o£ the atom, to be distinguished from K the 

 average dielectric capacity through the volume 47ra 3 /3 of 

 the atom. Consider the case where the atoms form a gas 

 whose index of refraction N' is connected with K' by the 

 law of Maxwell K' = N /2 , then since K' and N' differ little 

 from 1, we have K'-1 = 2(N'-1). But if N is the index 

 of refraction of the atom, so that K = N 2 , we have by the 

 chief law of molecular refraction (N' — l)u= (N — l)47ra 3 /3, 

 so that F(K'-l)/47r becomes 2F(N-l)a 3 /3r, which, when 

 equated to (4) divided by v, gives the desired relation 



^-1)^/3=^(1-,^^). • (5) 



In comparing the results of this equation with the experi- 

 mental ones we shall have to consider the metallic elements 

 in one group and the non-metallic in another. In the metals 

 it appears that a is constant in a natural family. Since 2i 

 is the mass of a pair of constitutive electrons, then 2in = m 

 the mass of the atom, and 2in/(2a) z is the density of the 

 atom, which may be denoted by p. By (1) we have ?'/R 3 = s/a 3 . 

 It has been shown above that in the Li family s is propor- 

 tional to <x, —ca say, and since v is the samo for all atoms 

 compared under the same conditions of pressure and tempe- 

 rature, and may be replaced by V for a gramme-atom, (5) 

 for the atoms of metals in their compounds takes the form 



(N'-l)V=(N-l)B = CB5 + DB§(N 2 -l)/ /3 , . (6) 



where C = 2Ra 2 /Bsc and D = iC/2a% 



C and 1) being parameters characteristic of the family, and 

 B the volume of a gramme-atom taking the place of (2a) z , 

 the actual volume of the smallest cube containing an atom. 

 Table II. contains the data for testing (6) in the Li family 

 of metals in their compounds, the values of B being already 

 given in Table I. The values of p are obtained by dividing 

 atomic weight by B. The refraction equivalents (N — 1)B 

 are taken from Gladstone's latest list (Proc. Roy. Soc. 189G). 

 From these by means of B the values of N have been calcu- 

 lated, those of K = N 2 being added for completeness. From 

 these data I find that in (6) 0=0*835 and D = 0735. The 

 values of N yielded by (6) with these values of C and D are 

 given in the table as N calc. 



