Nature of Dielectric Capacity. 13 



as for instance in the halogens, if a z is used here for the first 

 member, fluorine, a z /2 is to be used for CI, a 3 /3 for Br, and 

 a 3 /4 for I, that is to say, that in F" the coefficient of F' is 

 proportional to (a d /u) ~ 2 / 3 , where u has the values 1, 2, 3, 4. 

 It appears then that in the CI atom two halves are strained 

 separately, in the Br atom three equal parts are strained 

 separately, and in the I atom four equal parts, and similarly 

 with other families of non-metals. In order to draw 

 attention to this phenomenon it is advisable to replace an a? 

 in F" by a' 2 , thus F" = 3£? 2 F's/47ra' 3 Wa 3 . 



This intensity acting upon the special pair of electrons 

 imparts to it in the direction of F a moment 3e 2 F l r/4:7ra 2 'W / , 

 in which W is the rigidity due to <?r. But as the electric 

 intensity F is acting in a region of dielectric capacity K, it 

 will produce a moment K times as great as that just calcu- 

 lated without reference to dielectric capacity. Thus we get 

 the following equation like (5) 



9/\- ia V3— 3K? 2 r 3e' 2 s Znfia , 



" l )a ' 4tira*W "49ra' 2 Wa 8 '4»(<0i*) W {) 



in which W = 27n?V73(2a) 6 and ^=27r^V;i 2 /3(2a) 6 . 



It is to be noticed that the rigbt-hand side of (7) is 

 obtained by acting on F with three successive operators of 

 the form 3e 2 x/4:7ra 2 w. Moreover, when we have derived F' 

 from F, we do not call the intensity F' + F, but simply F'. 

 The intensity F is intensiried three times in succession, the 

 final result being independent of the order in which the in- 

 tensifications are appliad. The whole affair recalls the 

 intensification of an ordinary force by a system of levers. 



In simplifying (7) we must remember that r is constant 

 because in (1) when applied to the non-metals es is propor- 

 tional to a 3 and R is constant. If then, as in the atoms of 

 metals, a is the same for all non-metals, and since 2i7i = m 

 and p = m/(2ay, we have, like (6), 



(N'-1)V = (N-1)B = EKB 2 ^ 23 / /3 13 ) . . (8) 



where E is the constant 3 7 2 2 (2?'//i) 13 /7r 5 ^?'o-, where ka z = s and 

 h is the mass of an atom of hydrogen. The most suitable 

 way to test this relation is to use the values of N' — 1 for the 

 non-metals as elements in the gaseous state investigated by 

 Cuthbertson since 1902 (' Nature,' Phil. Trans., and Proc. 

 Roy. Soc). The data for 0° C. and 1 atmo. (2 atmos. for 

 the monatomic gases of the inert He family) are collected 

 by Cuthbertson and Metcalfe (Phil. Trans.'ccvii. A. 1908, 



