660 



BELL SYSTEM TECHNICAL JOURNAL 



By substituting the expression for 4(7r/3)^ given in equation (28) into 

 {33) we obtain 



f , . ga> / 



+ l ; — ;; cor 



eo + 2 



+ 2 



1 -J- • 1 



+ I ; — ^ wr 



eo + 2 



+ 2 



(34) 



or 



Co / . . . eo + 2 €00 / 



Co + 2 \ 600 + 2 €0 



«o + 2 \ Coo + 2 



Then, by setting 



we obtain 



(34a) 



(35) 



(36) 



and transforming this into polar form to faciHtate division gives 



^'^"' = Pi g'(.,-.,) = Pi 



€0 P2e"^2 p2 

 where 



Pi = 



pi 



cos {ipi — 1^2) + /sin (v5i — ip2) 



, (37) 



1 + I — I co-r- 

 60 



P2 == [1 + C0V-]% 



V^i = tan ^ — cor and ^2 = tan ^ cor. 

 to 



Equation (37) then gives 



1 + — co"r" 

 60 ~ 1 + coV^ "^ ' 



- 1 



or 



± _ ^ < 



eo 60 1 + 



1 + wV^ 



1 _ i» {( !f^ - I \^r 



60 



+ 



60 



1 + 



(38) 



(SSa) 



from which we obtain 



6 = €00 + 



60 — 6co _ ijep — €00) ( 

 1 + co^r^ 1 + coV' 



(39) 



