of Duplex Telegraphy. 1 19 



and 



HI! 



I' + - r. = L', measured conduction from station I. 



i + l" 



Thus the two equations which determine the absolute magni- 

 tude of g' and g u respectively are 



and 



L"+/-3y(l + ^)=0; 



from which g' and g u can be expressed — namely, 



/"-W+ivW+a .... (X'.) 



and 



/=-> s "+'V / 2"(3L" + 9 "), . . . (X".) 

 where 



^• + /, 



and 



q'=i + l". 



Supposing now i— co, or the insulation perfect, we have 

 L'=L" = L, and 



i it ^ 



the former special solution. 



But so long as i is not infinite, 1/ and L" may be different 

 from each other, and therefore also g 1 different from g" ; and 

 further, 



, V 



s = w 



and 



will be somewhat too large. These values, however, will repre- 

 sent a very close approximation in the case of any line in tolerably 

 good electrical condition ; and as a line worked duplice represents 

 two lines, it can always be 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. 



