38 Mr. 0. Heaviside on Duplex Telegraphy. 



Either of these equations by itself can be made use of to de- 

 termine g when/ is constant or/ when g is constant. When 

 they are combined, we have 



Now, although this result can be applied to the construction 

 of instruments for testing purposes where x is constant, there 

 is one insuperable difficulty that prevents its use in duplex 

 working ; and that is, x becomes infinite. We can only con- 

 clude that the finer the wire of the relay and the greater the 

 number of convolutions, the smaller the cells are made, and the 

 greater their number, the greater will be the strength of the 

 signals — a fact which might be safely predicted without mathe- 

 matical examination. 



A comparison of the strength of the received current in 

 ordinary single working and duplex working with the bridge 

 will be interesting. In single working the received current is 



/+f+r <»> 



and in duplex working, when the arrangement is such as to 

 give the maximum current, its value is given in equation (8) 

 above as 



C = E 



where x is the external resistance, rather greater than I + s/fg. 

 When I is very great compared with/ and g, these expressions 

 (8) and (9) are nearly equal, the duplex current being a little 

 less than the other. (In the extreme case /=0, <7 = 0, they 

 are identical.) Numerical comparison, taking the most gene- 

 ral values of /and g occurring in practice, will show that the 

 duplex current is about one half or one third the strength of 

 the current obtained when the same instruments and batteries 

 are used for single working ; so that in general more than 

 double the electromotive force will be required to obtain sig- 

 nals of the same strength in both cases. 



The third principal difference between one arrangement of 

 the bridge and another, viz. that different amounts of artificial 

 capacity are required, is of some importance as regards cables. 

 Condensers of large capacity are such cumbrous and expensive 

 affairs, that the smaller the artificial capacity can be conve- 

 niently made the better. Now c ly the required capacity, equals 



-It, where \ is the capacity of the line ; consequently, to make 



