504 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



w 



By definition, tjW = {1 + i) — - We can therefore write approximately, 



cos^,W^[l-l{^J]^i{^) (III-32) 



(rjW) sinh vWc^ -^^ (jj + i2 (^^ (III-33) 



Using expressions (III-32) and (III-33), equation (III-31) becomes 

 cosh" ^ 



-- W + t 



Provided that (1 + 2P) ( — j « 1, equation (III-34) can be expanded in 

 orders of magnitude. Thus, for 



W /dV 



1-^ 



we find approximately 



"" (W + V 5 / (111-36) 



• ( V- / + Vf^+j^ ± i V/TvF+TO 



where 



and 



g = 1 + 2P (III-38) 



The plus sign is to be used when g is positive and the minus sign when g is 

 negative. 



Equations (III-36) for «,„ and (11-24) for ao are very similar. With a little 

 manipulation we can rewrite equation (11-24) as 



-i/-(?)rT)V(?)'(?)"-('-?)") 



