1206 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



rearranging, we get 



1 I hit 

 pi 



P = Re 



47r^i^i 



(Tih coth ait\ + 



2pi_ 



{hit + Ith) 



pi 



+ 



1 - 



hh 



a - 



csch (Jiti 



(A26) 



aih coth aih — -^z— 



Pi L ^Pi_ 



up to first order in ij p\ . If we set 



0-1 = (1 + i)lh , 



(A27) 



then on expanding the right side of (A26) in powers of ti/8i up to the fourth, 

 we obtain 



P = 



h - h 



47r£?iii I V, 



PlP2 



+ 



.4 r T T* 



4/1 hh , 7(hi; + /r/2) , hh 



8\ L45p, 



+ 



+ 



45piJ 



(A28) 



360\/pip2 



where we have approximated pi(l + /i/2pi) by \/pip2 in the interest of 

 symmetry. 



Now writing APj for P, Alj for h — h , Pj-i for pi , and /y_i for h , 

 and neglecting curvature corrections of the order of 4/pi entirely, we have, 

 on setting h and h both equal to Ij-i in the coefficient of (h/di) , the ap- 

 proximate relation 



^Pj = F^T^ [l ^^i I' + ^ I ^i-^ I'l ' (A29) 



4irgriiipy_i L 35i J 



which is just equation (472) of Section XI. 



