^Eolotropic Potential. 437 



J,' being the statical value of J'. Write 



C standing for #/16ir or 3e?/4:(hr, with conductor or volume- 

 distribution. Then 



-|i= c J."^[»-( , -^ x ^ +x ^ +x )/ J ']' (,05 > 



and since 



2J' — (1 - Sp 2 ) X ( A 1 ' + X) (c 2 + X) 

 = 2«W +\{6V(1 + 2p 2 ) + 2« 2 (c 2 F^ + b 2 l -V) \ 



+ X-{/.-(l + ./)+c-(l + r 2 )+2rt-(l- 7 --r-)}+X 3 (l-%rX 



- which is Y 2 F/u is essentially positive if £» 2 <1, 



i. e. ' electromagnetic mass ' is positive *. 

 From (105) with (104) we get 



T=2P«=-2^=cj;^=[j'(l + V)-Ji(l-V)] ! (106) 



In terms of c/> L , • • • the simplest expression of P is 



VP = ^ (Wo +7>L « 2 + rMJc 2 + y N7'") , . (107) 



and Nq contains the factors ]ig explicitly. To obtain this 

 form we make use of 



pj' = | pa?a + 7 //- 7 ' -f rc 2 /3')J' +y*(l -l]r)\(h 2 + X) (r + X). 



The relation 



y> 7 (L,r-M^)=X:,i,r(l- y 2 -r-)-/r(l-^- / ^j} + .VO>L / - 7 M0 



is also of service in working with (107). 



How does S compare with the statical value S s or E s ? 

 Going back to first principles, in the element of integral 1/r 

 is replaced by (1— 2p 2 )/R, where 



R 2 = (1 -V; Ste-*') 2 *^*-*')) 2 . 



* With 2y/->l, the bracket in (lOo) is positive as long as J' is 

 positive. The integral is then curtailed at the upper limit (v. infra) and 

 the condition i? not necessary. 



