210 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



In working out the details we see that division by 



M /I — cos x^ 

 m \ t{c) 



puts the first two terms on the right hand side of (70) in a simple form. 

 The coefficient of the field term becomes then 



am am 



^/l-cos^\ 3^/ 1- COS x \ 



\ t{c) I \ t{c) /c=(c,} 



(¥)■ 



The first factor is just (cz) by the identity (71). For the second factor we 

 have up to linear small terms 



^ = Vcl +4 + cl = Vcl + cl-\- «c.) + c. - {Cz)Y 



Cz — (Cz) 



and hence for the coefficient of the field term 



(c.) (^^J ' « (C.) - (1 - a)(c. - (c.)) 



After division by 



M/1 — cos x\ 

 m\ t{c) /, 



the square terms still contain another small factor M/m; it appears 

 sufficient, therefore, to keep only the leading terms which are the ones 

 containing {c^f as factor. All these terms are multiplied with the ratio 

 of two angular averages over dx', these may be taken as independent of 

 c to a good approximation. Equation (70) thus takes the form 



(4 - a)h{c) + C^ -^ + Cy —^ + (2 - a){cz - (c)) — ^ 



dCx OCy dCz 



/sinScX 

 + 1 ^ \ r I , .2 fa^) a^) 

 ■^ 4 m /I - cos x\ I dcj "^ ac^, / (72) 



\ — ; — / 



/ (I - cos x)\ 



. 1M \ r / . ,2 a'/^(c) 



■^ 2 m /(l_-_cosjOy ""'^ ac^ 



