﻿1871.] L. Scliwendler — On the General Tlieorij of Duplex Tcle(jraj)hi/ . 223 



-—8.^4.-— ■ 82+-— -Si 

 ^, ax a I dL 



But as Zx, Si and 8L are very small, and, as neither ■- — > , nor 



can become infinite, it follows that So' must be always very small in pro- 

 portion to & itself, and more so as compared with p' -+- o\ 

 Thus we have at last 



cix ill aJj 



p + & p + g[ p + c' 



and therefore to make 0\ for independent variations Sx, Si, and SL, as small 

 as possible, each term should be made as small as possible. Now, taking p' 

 and p" as independent variables, it will be seen that the total differential of 

 each term is negative. Thus $' becomes smaller the larger p' and p" are 

 selected, and the same of course is the case for 0" (Station II). 



Now the complex resistance of any one station can be expressed as 

 follows : — 

 p* _ (^4-/)(.y4- ^) (^cI-ijfY 



Thus for any given sum of resistances, i. e., a-^-f-^-d-^rg^^ const., 

 p will be largest if 



. ad-gf=o (VI) 



which is the " immediate balance condition^ 



Now 



m* -^ K* m* 



1? T'' 1? 



feubstituting for — its value we get 



h' n' ^ 



but N' = c' n' + a' 



— = c' -I- — , but -: = p 



N' 



n' 



= ^' + P' 



or — Tj- = c» + p' + 5 c' 



*• This expression is nothing else hut the resistance of a Wlieatstone's Bridge 

 between the two battery electrodes. It is most easily obtained by the ai^plication of 

 Kirchoff's rules. 

 29 



