134 Mr. L. Schwendler Gn the General Theory 



the same station are produced is equal in magnitude and sign to 

 the force by which balance in that station is disturbed. 



Consequently the rigid fulfilment of the first condition (D = 0) 

 will entail the rigid fulfilment of the second condition (S = 0) ; 

 and this, it will be clear, is only due to the fact that the complex 

 resistance p is independent of b, and that the key during signal- 

 ling does not alter p ; whence it follows that the perfection of 

 the key in this respect is of the greatest importance. There are, 

 however, no practical difficulties connected with the construction 

 of a key which fulfils condition (VII.) perfectly. 



By the aid of the relations given in equations (VI.) and (VII.) 

 we have therefore gained the^great practical advantage that du- 

 plex telegraphy will be entirely on a par with single telegraphy, 

 if the means of attaining rigid balance are sufficiently accurate, 

 convenient, and rapid. 



But, even supposing that we are unable to keep that balance 

 rigidly for any length of time (on account of L varying), we can 

 nevertheless bring the regularity of duplex working as near as 

 possible to that of single working by making D and S as small 

 as possible for any given variation of L. 



Rapid approximation of the two functions D and S towards zero. 

 For station I. we had 



S'^'^-^rt'-^r; .... (IV.) 

 which we may also write 



s '=''«™{itV-4' • • 



m'yjr' 



(IV.) 



Since 



and 



T rv 



Further, if we call V the value of b which in station I. esta- 

 blishes rigid balance for any given values a 1 , d', and L', we have 



A'=6'.SL', 



where BV is the variation of 1/ which throws the balance out, 

 and which variation may be either positive, zero, or negative 

 (hV shall contain the sign in itself). 



