692 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



or 



A'^\C-L) 



forB>l. 



Fortunately, because of the assumptions (40a, b) the formidable 

 relations (70a-71b) can be simplified to 



HB) ^ A"'C + 2e-''" 



and 



*(B) « A"\L -C)+ 2e-'"\ 



where 



*(B)^ 



'4(^)"'] 



for -1 < 5 < 1 

 f or B = 1 



[{^T^Umi '- 



> 1 



-F/2 



Subtracting (73) from (72) we obtain 



= 2A"'C - A"'L + 26-""' - 2e , 

 whence, substituting (66) and (69), 



Finally, substitution of (66) and (74) into (72) gives 



or, by virtue of (40c, d), 





(72) 



(73) 



(74) 



(75) 



Equations (66), (69), (74), and (75) are the desired expressions for 

 determining A, B, C, and V when values are assigned to A, L, and U 

 (subject to (40)). (If nectossary, some or all of the restrictions (40) could 



