344 Mr. 0. Heaviside on the 



per unit length ; and, in the whole line 



2(U _ T)= [ C2 |J]< (125) 



We have to see how far these are affected by the longitudinal 

 transfer. We have 



-^V 1 C 2 =SV 1 V 2 + L C 2 C 1 + (B.-FOC, 



- A y.d = SV 2 V, + L CA + (E, -F^d ; 

 therefore, if the systems are normal, 



^(VA-V 2 C 1 )=te.-A)(SV 1 V 2 -L C 1 C 2 ) 



-(E 1 -F 1 )0 2 + (E 2 -F 2 )C 1 . 



It will be found that we cannot make the parts depending 

 upon E and F exactly represent the U 12 — T ]2 in the conduc- 

 tors except when m 2 is the same in both systems p^ and p 2 . 

 In that case, the parts (E r ) 1 (H) 2 and (J$ r ) 2 (Il) 1 of the longi- 

 tudinal transfer of energy in the conductors, depending upon 

 the mutual action of the two systems, are equal ; (E r ) x and 

 (E r ) 2 being proportional to sin mz, and B^ and H 2 propor- 

 tional to cos mz. So, in case p x and p 2 are values of p belong- 

 ing to the same m 2 , the influence of the longitudinal energy- 

 transfer in the conductors goes out from (122) and (123), 

 which are therefore true in spite of it. Similarly, provided 

 the w's can be settled independently of thep's, equations (124) 

 and (125) are true. 



Now the normal V and C functions, say u and w, as before, 

 may be taken to be 



iyv\ 



u ~ W ^ ai Jl ^ lG ^ "~ * ai ^ 1 ^ 1 ) ^ ia °^ Kl ( SlCl ^ Kl ^ Sl<z ^ \ sin ( mz + ^ 



w= -j ^cos(mz 



so that Y = AueP f , G = AweP t ; and 



J-S-gM-'+.'fc • • • -( i27 ) 



and the complete equations for the determination of m, 6, and 

 p are 



^tan# = Z , gp tan {ml + 0) = Z 1 , 

 P 2 P > • (128) 





