702 



THE HELL SV8TEM TECHNICAL JOUKXAL, MAY 195G 



the first factor on th(> h ft of (7")), and obtain the siniplei- form 



7 - 7(1 



/oo y/Ry- + cosh 



CO 



(79) 



which is the generalization of (31). 



The drop ^Vp in the middle region given by (()o) can be written 



^^^ = r^ ^^ ^ + J-^Tx yj;^ V/^y + cosh 0, FM (80) 



AN'here Fc^ii) comes from / dx/ n and is defined 



p ( \ _ f Mill 



Jo 7 siiih fw(l — u)] + sinh [ww] 



In 



7 snm [(jo(] 



1 + Q 

 1 + Q 



(n 



1 + e"Q 

 1 - e^Q 



(81) 



or 



2 



\/l — 27 cosh CO + 7- 



tan~' e"Q — tan~^ Q 

 \/27 cosh CO — 1 — 7- 



The first form applies when 7 > r", or 7 < c~", and the second applies 

 when e"" < 7 < <»", and Q is the (luantity 



Q = 



1 — ye' 



■\/\ 1 — 27 cosh CO + 7^ 

 It can readily b(> shown that when co -^ 



In 7 



/'^o(7) = 

 Thus when co = (80) reduces to 



7 - 1 



(82) 



(83) 



/3T> 



Ch 7 /> — 1 



r, (7 - 1) + 



7-16 + 2 

 (n 7 (7/700)' - 1 



6+ 1 



-^ \//?7- + 1 



l/i 



(84) 



.7-1 Ry- -{- I 



which is identical with (il). It is also clear that (7!J) reduces to (31) as 

 the recombination goes to zc ro. f'inally we write from (58) 



^(Fo + V„.) = tn yt = (n /- + (n ^ ., / . (85) 



1 p, Ry- + cosh CO 



