of Duplex Telegraphy. 471 



L' b' ~) 



L" W_ 



2~ + 4' 



<-W- 



approximately. 



b' 



2L' + b" 



*-w t 



2 V 2L" + b"' J 



The above values for a and v are somewhat too large ; but in 

 practical application they are quite accurate enough. 



The physical reason that this solution for the differential me- 

 thod gives an indeterminate result, is simply due to the fact that 

 the force which produces the signals in the differential method 

 is due to the combined magnetic actioas of two separate coils 

 through which unequal currents pass, instead of to one coil as 

 in the bridge method. On account of b=f, it follows that the 

 current which passes through the b coil is only half of that pass- 

 ing through the a coil. Thus, in order to make the most of the 

 arrived currents, b and f should be both equal to zero, or, in 

 other words, placing all the convolutions in a and none in b must 

 clearly give the greatest magnetic force. Obviously, however, 

 such a solution could not fulfil the balance-condition in the 

 sending-station. 



The value of b should be chosen as small as practicable ; and its 

 minimum value is (3, the internal resistance of the signalling 

 battery. How much larger b should be taken depends on the 

 absolute variation of /3, t. e. on the constancy of the signalling 

 battery. If the battery is very constant with respect to internal 

 resistance, then b need be only very little larger than /3, which 

 determines the adjustable resistance w. 



For instance, minotto cells can be easily prepared with an in- 

 ternal resistance of 10 B.A. U. per single cell. Their minimum 

 resistance, obtained by working, is never less than 5 B.A. U. ; 

 and if the zincs are changed from time to time, their maximum 

 resistance will scarcely ever be higher than 10 B.A. U. 



Hence to make b about 50 per cent, larger than (3 will suffice, 

 by which, if /3 is known, the greatest value of w is fixed. 



The absolute value of /3 can be determined from the number 

 of cells which have to be connected up successively, in order to 

 work a given instrument through a given line, when the circuit 

 fig. 2 is adopted. This absolute value of /3 will therefore not 

 only depend on the electrical state of the line and the nature of 

 the cells, but also on the absolute sensitiveness of the differential 

 instrument employed. 



