Mr. 0. Heaviside on Duplex Telegraphy, 37 



from which we see that the sensitiveness of any exact balance 

 to disturbances in the resistance of the line, either in duplex 

 working or in testing, is proportional to 



be . 



{b(c + x)+g(J> + x)\ {c(b + x)+f(c + x)\ ' 



and this expression is a maximum when b and c have the values 

 given in (7) above. 



Hence it is perfectly hopeless to find any arrangement of 

 Wheatstone's bridge for duplex telegraphy which shall give 

 the maximum received current at both stations and at the same 

 time be least liable to disturbance. Generally speaking, the 

 more sensitive the balance the stronger the received current. 



Since x, the resistance external to one station, includes the 

 resistance at the other station, any alteration of adjustment at 

 one station will theoretically cause a disturbance in the other 

 station's balance ; and it is true that an infinite series of suc- 

 cessive adjustments must be made by each station to reobtain 

 an exact balance whenever balance is disturbed. But these 

 alterations are so excessively small that practically they have 

 no existence. By making bc=fg and adjusting solely by the 

 resistance a, each station's balance becomes independent of the 

 other's ; but this is introducing a greater difficulty to avoid a 

 lesser and inappreciable one, since to keep be—fg frequent mea- 

 surements would have to be made of/, the battery-resistance, a 

 variable quantity ; and besides, such an arrangement would not 

 give the maximum current, as is evident from equations (7). 



The above investigations apply to any instrument, battery, 

 and line, and therefore admit of immediate practical application 

 in any particular case. There are, however, two principles 

 frequently made use of by theoretical writers on electric cir- 

 cuits : — first, that if the space to be filled with wire in a galva- 

 nometer or relay is fixed, the greatest strength of signal is ob- 

 tained when the wire is of such a size that its resistance equals 

 the external resistance : and next, that if the quantity of me- 

 tallic surface of a battery is fixed, and also the distance between 

 the plates in each cell, to obtain the maximum current the cells 

 should be of such a size that the total resistance of the battery 

 equals the external resistance. These principles do not often 

 admit of practical application in telegraphy ; but we may just 

 see to what they lead us when we apply them to duplex work- 

 ing with the bridge. We shall have the following equations 

 to determine / and g : — 



x 2 Sg(x+f) + 2s/Mx+g) = 0, . 



