﻿lS7i.] L. Sehwendler — On the Oeneral Theory of DiqAcx Tclrrjraphj. 221 



Now that D' approxinicates also rapidly towards zero by making 



A' 



'ill' ij/' 

 as small as possible can be proved as follows : — 

 By detinition we have 



Furfclier, as c^' =^ (//' (on account of the Icey equation), we have 

 p' =z >S" invariably 



Thus D' for any given P' approximates towards zero at the same rate 

 as S' does, i. e., the smaller 0' becomes. 



Therefore the whole problem is actually most generally solved by 

 making 



as small as possible for both stations. 



Now for Station (I), if balance in the g' branch for the outo'oino- 

 current be established, we have 



a' d' — h' c' = 

 where c' is the '■'-measured circuif from Station (I), and supposinp- that all 

 variations in the system are chiefly due to variations in the line resistance * 

 we have at once : 



— 5' 8 c' = A' 



8 <?' the total variation of the line resistance may be either positive or 

 negative, and supposing that 8 & contains its sign we have : 



on' \p' 



"V 



to be made as small as possible. 



Now in case of the line being perfect (i = oo) Sc' = 8Z (a constant 

 with respect to the different resistances of each arrangement, and which 

 was the case in the first solution). At present however Sc' is a function 



* The variations in c' may he due to variations in the line, or to variations in the 

 duplex arrangements. In the latter case they may be due either to an alteration of 

 temperature in the station and then the effect can be only small, or to an accident (wire 

 or connection breaking) and then the influence will become so great that nothing short 

 of actual repairs could help. Thus practically the problem has onl}- to be solved for 

 vui'iations in the line. 



