296 BELL SYSTEM TECHNICAL JOURNAL 



The voltage between sheath and core conductors at x = then becomes: 



(102) 



7(0) =-L ^ ^22 - Zi2 



2 a^ -\- 13^ Zn + Z22 — 2Zi2 \ioi/ 



/ R /iV p + ao 



2 a^ + /3^ '^ \io:J p + ^0 



where 



77 = (L22 - Li2)/{Ln + L22 - 2L12) (103) 



ao = i?2/(i:22 - L12) (104) 



/3o = (i?i + i^2)/(i:n "t" 1-22 - 2L12) (105) 

 The function S' is in this case 



where the function h is defined as before. 



When the shield wires are at a sufficient distance from the sheath, so that 

 proximity effects may be neglected, the self and mutual inductances are 

 as follows: 



Ln - Ln=~ log -^ (107) 



27r rn 



L22 - Ln=~ log "^ (108) 



ZTT ^22 



where 



log = logc and: 



V — 1.256-10" henries per meter 

 rn = Radius of sheath 

 ^22 = Radius of shield wire 

 ri2 = Distance between sheath and shield wire. 



With more than one shield wire, ^22 is the geometric mean radius and rn 

 their geometric mean separation from the sheath. When there are two 

 cables, as is frequently the case, ru is the geometric mean radius of the cables 

 and R is their combined sheath resistance. 



The surge voltage obtained by solution of (1), for a current as given by 

 (19), is in this case: 



IRi] V a — (xq 

 2 (a* + fi) L^^7o 





(109) 



b h{b t ) + ^--7 ^0 «(/3oO 



- iSo (a - iSo)(o - )3o) J 



