GEXi:UALlZi;i) rKl.KOKAlMllST S EQUATIONS 



795 



- Too 



+ r,,//., 



j<^ 





7'(„o r/N (44) 



^ ^7'[p] a7'[„] 



t;H I Cj,. - — — 



('2 5/' f^i f>?/. 



7\„o r/N. 



If we solve the last two e(iiiatioiis for /,,[„] and !%,(«) and substitute 

 in the preceding four ecjuatioiis, we shall obtain the telegraphist's ecjua- 

 tions ill their final form (30). Tims, let 



'Z['n][n] = jj ju}tX,^Xln]Tln]Tl„,]dS, 



(45) 



From these coefficients we obtain another set 



""Z[„][„,] = normalized co-factor of ~Z[„,][n] , 

 'Z(„)(m) = normalized co-factor of 'Y(^m-)(^n-, . 



Then, 



(4(0 



+ 7'(p)'F[n][m] jj 

 — I[p]'Yin][m] jj 

 V2,(n) = —i(m) Z(„)(,„) 



+ y[p]'Z^n)(.m) jj ji 



J^ 



yco 



(Pi _ 



e-2 dv '" ei du _ 



dT[p] dT[p] 



Ci du 



62 dv 



d T(p) dT(^p) 



Cidu 62 dv 



7V«] dS 

 T,„, dS, 



7^(m) dS 



(47) 



_ dTip] dTip] 



62 dv 



Bi du 



(m) 



d.S. 



Before substituting in e(iuations (39) to (42), the summation index m 

 in (47) should be changed to avoid conflict with m in the former equa- 

 tions. It does not seem necessary to make these final substitutions in 

 their most general form. The results are very complicated and in prac- 

 tice the various coefficients are not independent. Some coefficients may 



