of a Telegraph ReceicuKj-uistr anient. 453 



which is ;i inaxiiiuiiu for 



kl 



that is, the resistance of the recoiving-instriiment in the case 

 of a perfectly insulated and uniform line should be one fifth 

 of the resistance of the line *. 



Takinor into consideration the resistance of the siffnallins;- 

 battery, which has hitherto been neglected, the result is mo- 

 dified as follows. 



Suppose we are given a certain number of cells (all of equal 

 electromotive force and resistance) and arrange them so that 

 the total resistance of the battery =/; then it may easily be 

 shown that the total electromotive force of the battery will be 

 proportional to \/f. 



Thus the expression for the sensibility of the receiving- 

 instrument becomes (employing the same notation as before) 



M= const. X ^f'^ ; 

 and the expression for the retardation characteristic becomes 



kc 



i'-'^r 



RC= const. X 2 iog^ (I) ; 



and, finally, the expression for the receiving-efiiciency of the 

 instrument becomes 



KE = const. X /j; , 

 (f+r + kly 



which has a maximum both with respect to / and to r, namely 

 for 



r = l(r+kl)J 

 These maxima conditions are simultaneously fulfilled by 



* Singularly enough, this is the precise value selected, on experimental 

 grounds, by Professor Hughes. 



