946 Mr. A. M. Mosharrafa on the Appearance of 



§ 3. Calculations for Comparatively Large Fields. 



We shall treat the term in D in equation (7) as a corrective 



term. Let 0, /3 + A/3 = /3', £' + A'#=/8", etc., denote the 

 successive approximations to the value of /3 ; similarly for 

 A, B, and W. We see that to the first order of small 

 quantities 



B^fBj + AB^-tBj+moA/3] 2 from (5a) 



= B 1 * + 2m B 1 &l3, (Sa) 



and similarly 



B 2 2 =B 2 2 - 2m B 2 A/3 from (5 b). . . . (8 6) 



o 

 Now the equations for determining A/5 could easily be 

 solved, but as we are assuming Epstein's work we shall 

 merely give here the value obtained on solving his equations 

 (61) *. We have 



o N.F.A'fa + ^-t-n,) fq , 



A/ *~ 64m W7r* " ? * * * * (y; 



where 



N= (6n 2 2 + Qn 2 n 3 + n^) (2n x -f n B ) 



+ (6w 1 2 +6n 1 n 2 + n 3 2 )(2n 2 + ^ 3 ), (10) 

 so that we have from (8) and (9) 



B' E'li,„E .. y(n, + «, + n,)N , 



similarly 



JJ, - B 2 -2m c B 2 x - 64n , o , sEV , • F; (11 J) 







also, B 2 is obtained from (7) on neglecting the term in D, 

 thus : 



o 

 B 2 



= A( V C + fJ. .... (12) 



* Ann. d. Phys. 1. p. 508 (1916) ; our A/3 corresponds to Epstein's 

 (e 2 4/3). y 



