498 BELL SYSTEM TECHNICAL JOURNAL 



It remains to choose the coefficients mi, nio, ni\ , and nio' so that for 

 moderate propagation lengths, y = 7/, the composite network will give 



Tc approximately = >» = 7/. (84) 



At this point let us introduce an important simplification by writing 

 the function 



1 - 2:y + gr - 48^ +384^ - 3840^^ + " " ' 



Then upon comparing (83) and (85) we see that fortunately for small 

 values of y we can satisfy (84) providing we identify the coefficients 

 of powers of y in (83) as 



Wi + mi =2' 



mim2 + mitni + nii'mi' = q, (86) 



o 



mim2mi' + mimi'm^ = xo , 

 4o 



and 



, , 1 



The solution of the equations gives a sixth degree equation for mi, 

 namely, 



mi« - |mi^ + ^,4 _ 3^^3 +^^^. _ _1_^,^ +_±_ = 0; 



and for the others 



_ 6mi — 48mi^mi' — 1 



^ 48mi(mi — m/) ' 



mi' = .5 — mi, 

 and 



1 + 48mi(mi')2 - 6w/ 



1712 — 



48mi'(mi — m/) 



From these we get this set of real positive coefficients, determined 

 once for all, namely, 



mi = .45737; mo = .14456; 



(87) 

 m/ = .04263; ni^' = .92403. 



