170 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



First, we will define a more simple set of parameters. We will denote 



Io(ya) by /oi and h{yh) by /02 , etc. 



Further let us use the notation introduced by Humphrey, Kite and 

 James" in his treatment of coaxial helices. 



Poi ^ laiKoi P02 = ToiKa2 Rq = I01K02 



Pn = InKn P12 = InKu Ri = /iii^i2 



and define a common factor (C.F.) by the equation 



r(/3oa cot hY p p (/3oa cot ^pif cot i/'z „ r, 



\_ (yay {jay cot t^i 



+ Ro' — PoiP 



(20) 



.,] 



(21) 



With all of this we can now write for the coefficients of equations 1 

 through 18: 





y ju j8oa cot \pi 1 02 



U iQoa cot 1^1 7oi/vi2 RiSoa cot i^i) 



y M ""to C.F. L 



^4 _ _ • / £_ /3oa cot 1^1 /pi/ii r( 



B^~ -^ T M 7^ C.F. L" (7a)^ 



5 

 5 





(7a)'^ 

 (/3oa cot 1^2)^ 



cot 1A2 p 

 cot ;^i J 



P12 — jPo2 



■] 



B5 



B, 

 Bt 



Ro 

 C.F. 



Ro — 



((Soa cot xl/iY cot 1/' 



(7a^) 

 (/3oa cot 1^2) 



cot l/' 



;«'] 



(7a)^ 



12 — -P02 



B7 _ • . /£ i3oa cot lAi 1 /oi r 

 5; ~ "^ y M 7a C.F. K12 L 



Bs _ (|8oa cot i/'i)" cot 1/^2 /pi "" 

 B2 {yay coT^i C.F.Po 



P02R1 — 

 P02R1 - 



cot l/'2 

 cot i/'i 



cot l// 

 cot \l/ 



2R0 

 - P12R0 



(22) 

 (23) 

 (24) 

 (25) 

 (26) 

 (27) 

 (28) 



The last equation necessary for the solution of our field problem is the 

 transcendental equation for the propagation constant, 7, which can be 



