﻿230 L. Sell wen dler—0;i the General Theory of Duplex Telegraphy. [No. 4, 



and, substituting these values in the expressions for Q' and G'\ we get 



a' g" 



G'* = E" i 



/' ^a" + g") + a" {g" + d") ] [ ^' {a' + g') + a' (/ + d') ] 

 a" g' 



where 



2'- = i + I' 



Put -^ = k 



9 

 and substitute in the first expression 



in the second 



when we get 



^ -h 



G'=Wih "'^' 



{a' -Vg'Tc)^- a!' {d" +g'h)][q («' ^g') + «' (y'+ d') } 



(?''==JE;'i. "^' 



Now it will be seen that G' has clearly a maximum with respect to g', 

 while 6^'' has a maximum with respect to g'' ; thus, if we take g' as the only 

 variable in G' (h constant) and differentiate with respect to g', we get 



d G" 

 dg' ~~ 

 and, if we take g" as the only variable in G" and differentiate, we get 



d G" _ 

 dg" ~^ 



* If in these two expressions we put 



e = 00 

 and remember that then 



a' = a" = a 

 d' = d" = d 



g' = g" = fj 



and c' = c" = Z -J- p 



O' in ■^ d') 

 whUe P = — H-P— .^ 



a-^ g 



we get G'-= G'* = G = E r ; -^ ^ ■ 



the expression of the current which produces the signals (single and duplex) through 

 a perfect line, as was given in the first part of tliis investigation (p. 1 9) . 



