136 Mr. L. Schwendler on the General Theory 



But 



a'(cf + d<) _ 



a'+g' ~ p> 



the complex resistance of station I. (the expression for p has be- 

 come thus simple on account of the immediate-balance condition 



VI.). 



Further, 



a'd' . „ 



(on account of balance in station I. being established, equationV.). 

 Thus we have 



y'-p' + p'i + U 



for station I. ; and similarly 



y "=p' + p " + L" 

 for station II. 



Therefore the rapid approximation of both the functions D and 

 S towards zero in both stations is obtained if ice make the complex 

 resistances p 1 and p" maxima. 



Now the form of p shows at once that it has a maximum for 



(a+f)=(g+d), 



which, in consequence of equation (VI.), gives at last 



a=g_=d=f. (VIII.) 



From the development of this result it will be clear that the 

 relation expressed by equation (VIII.) must hold for either 

 station independent of L. 



All that now remains is to determine b } and further to fix the 

 absolute magnitude of any one of the branches. Before doing 

 this, however, it is necessary to inquire what the other factor of 

 S, namely G, becomes in consequence of fulfilling the regularity 

 condition as expressed by equation (VIII.). 



The current which passes through the receiving-instrument 

 to produce "single" as well as "duplex" signals is at balance 

 expressed by 



**-"' ■ (_a+g){h{a+g)+2a{g + d)} X """^ 



which expression has a maximum for either a or g. 



The maximum of G with respect to a, it will be seen, contra- 

 dicts the regularity condition, since a=g~d could only satisfy 



da 

 if d were negative, a physical impossibility. 



