"'=-2 



+ * 



»<< _ £ 



2 



+ r 



= _ / v 



2V2I'+5 

 1 / F~ 



1875.] Theory of Duplex Telegraphy . 59 



Now bj inference we get for a line with leakage, i. e, i < go 

 i' 6' 1 



> Approximately. 



J 



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

 application they are quite correct enough. 



The physical reason that this solution for the differential method gives 

 an indeterminate result, is simply due to the fact that the force which pro- 

 duces the signals in the differential method is due to the combined magnetic 

 actions 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 passing 

 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 con- 

 dition 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 ft, i. e., on the 

 constancy of the resistance 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 internal re- 

 sistance of 10 B. A. v. per single cell. Their minimum resistance, obtained 

 by working, is never less than 5 b. a. tj., and if the zincs are changed from 

 time to time, their maximum resistance will scarcely ever be higher then 



10 B. A. V. 



Hence to make b about 50% 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 instru- 

 ment through a given line, when the circuit Kg. 2 is adopted. This abso- 

 lute 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. 



