Mr. 0. Heaviside on Duplex Telegraphy. 41 



by making /= ^ . We then have 



9— o> J~~~A 



as the best resistances for each coil and the battery. Now 

 although this admits of application in testing with the differ- 

 ential galvanometer (when x is constant), yet it cannot be 

 applied to duplex working, since x becomes infinite, which 

 may receive an interpretation similar to that in the correspond- 

 ing case of Wheatstone's bridge. 



It is an interesting practical question whether with a given 

 instrument and battery it is possible to obtain stronger signals 

 by the bridge than by the differential system. To make the 

 comparison fairly, in the former case the arrangement must 

 give the maximum current. In the differential system the 

 strength of the signal is (10) 



Em 

 and in the bridge system 



2Em 



/+ * + 3g + V2fy + ( ^/+ V2^) (V^ + \Z*0J 



which is obtained from (8) by changing g into 2g and multi- 

 plying by 2m. In (10) and (14) x has not the same significa- 

 tion; but the difference is not great. Effective comparison 

 can easily be made numerically in any particular case. As 

 general results, we may say that when / and g are very small 

 in comparison with I, the advantage is in favour of the bridge 

 system ; but when f and g are taken larger, the advantage 

 becomes rapidly in favour of the differential system. It may 

 also be observed that in the latter the strength of signal is 

 always less than one half the strength when the same instru- 

 ments are used for single working, whereas in the former 

 system the strength of the signal may be, but generally is not, 

 more than one half. 



If the practical success of duplex telegraphy were dependent 

 on the continuous maintenance of an exact balance at each 

 station, then would duplex telegraphy exist only on paper. 

 The variations, sometimes large and rapid, which are always 

 taking place in the resistance and insulation of overland wires 

 would necessitate such frequent changes of the balancing re- 

 sistances as to render efficient working the exception rather 

 than the rule. But it is found practically that, instead of an 



