﻿1874.] L. Schv^'cncllor — On tlie General Theory of Duplex Telegraphy. 227 



Put l" + T— — Yf ^= ■^" measured conduction from Station (II), 



i I" 

 and V -f- ■ .„ = Tf measured conduction from Station (I). 



t -J- L 



Thus, the two equations which determine the absolute magnitude of 

 g' and g" respectively, are 



and 



from which g' and g" can be expressed, namely, 



y' = — i ^' + i V" 2' (3 X"+ q) (X') 



and 



/=-i/ + i\//(3i." + /) (X'O 



where 



q' =i-{-l' 

 and 



^'' -= z + r 



Supposing now ^ = oo, or the insulation perfect, we have L' = L" == 



L, and 



9 =9=9 = -^ 



the former special solution. 



But so long as i is not infinite, L' and L" may be different from each 

 other ; and, therefore, also g' different from g\ and, further, 



and 



will be somewhat too large. These values will, however, represent a very 

 close approximation in the case of any line in tolerably good electrical con- 

 dition ; and, as a line worked duplice represents two lines, it can be alwa3's 

 afforded to select the best sections, when the above values for g' and g" 

 will be sufficiently correct for all practical purposes, especially if it be 

 remembered that when once g' and g" have been fixed, they cannot be 

 easily altered, and that, therefore, L' and L" must be invariably certain 

 averages, either for the whole year or for certain seasons. This, however, 

 belongs more to the practical application than to the theory of Duplex 

 Telegraphy. 



