﻿1874.] L. Schwendler — On ilie General Theory of Buiilex Tclcgraphj. 219 



any given variation in the system must he as small as posffihie, and approxi- 

 mate rapidly toioards zero as the variation in the system becomes smaller and 

 smaller. 



Further these two functions I) and >S' were expressed, say for Station 

 (I), as follows : 



and 



S'=:j<:"^,i.'f-^I + <T'.p- (iv) 



These two expressions are quite general, i. e.,they do not as yet contain 

 any restrictive conditions (beyond those inv^olved by the mode of arrange- 

 ment of the system of conductors) between the different variables ; and the 

 signification of the abbreviated terms can be found from the First Part.* 



Now the first relation that we shall introduce is 

 to + /3==f 

 for both stations, which may be called most appropriately " the key equa- 

 tion.''^ 



The introduction of this relation at the outset is quite justified, for say 

 that S' = D' = is rigidly fulfilled in Station (I), when Station (I) is 

 sending and the key in Station (II) is at rest, and suppose the electromotive 

 force in Station (II) equals o (the e. m. f. of all elements annulled and only 

 their resistance /5" left), then, moving the key in Station (II) from its rest 

 contact to its working contact, the regularity condition S' =^ D' = o would 

 be (i. e. balance in Station I) at once disturbed \i id" + /?" ^f" during the 

 motion of the key, even if no variation in the line took place. Thus it is 

 paramount to have w -{• (3 = f for each station during the movement of 

 the key.f 



* For convenience of reference I shall give here all the terms of which use will be 

 made hereafter. 



n = b {a ^ d .{• ff +f) + {a ^ ff) if + d.) 

 m = b {g ■\- d) -\- d {a -\- g.) 

 h = b{a.\-f) ^a{f^d.) 

 k 



a = b{g^d) («+/) ^ag{d^f)^fd{aJ^g.) 

 These expressions have been obtained by the application of Kirchoff's rules to the 

 Bridge Arrangement as represented in Fig. 1, and they are quite general, as no other 

 relations beyond those represented by the diagram have been introduced as yet. 



t To fulfil the key equation most exactly during the movement of the key, I have 

 constructed a key (constant resistance key) based on the following principle : During 



