through Heterogeneous Telegraph Circuits. 217 



g +a + g. Therefore the current dies away more quickly in 



a 



the latter case, and, by reason of the before-mentioned pecu- 

 liarities, the station A nearest the cable receives more slowly 

 than B. The explanation of the reduction of speed by leakage 

 is similar. The leakage lessens the retardation and conse- 

 quently quickens the signals. If every signal were quickened 

 in the same proportion, as would happen were the circuit 

 always complete, it is evident that the speed of working must 

 be increased ; but it is easily seen that the decrease in the re- 

 tardation caused by the loss is proportionally much less when 

 the circuit is complete than when the line is insulated at 

 the sending-end, thus increasing the irregularity in the re- 

 ceived signals due to the unequal intervals between the 

 sent signals, and consequently lowering the working-speed. 

 Again, the addition of resistance at the receiving-end, as 

 at A in fig. 2, when B sends to A, may increase the work- 

 ing-speed. Now, since the addition of resistance obviously 

 increases the retardation, nothing could result save a de- 

 crease of speed if the retardation of e\ery signal were in- 

 creased in the same ratio. But this is not the case ; for the 

 retardation is increased in a greater ratio when the line is in- 

 sulated at the sending-end than when the circuit is complete 

 — exactly the opposite to what occurs with leakage: then the 

 working-speed was lowered ; now it is increased. (This rea- 

 soning will not, of course, apply to other systems of transmis- 

 sion.) On the other hand, the speed is lowered by inserting 

 resistance at the sending-end, B, fig. 2 ; for the retardation is 

 unaltered with line insulated, and increased with complete 

 circuit. 



To ascertain the exact amount of retardation produced by 

 resistance at either or both ends of a submarine cable, each- 

 case must be calculated separately, because the form of the 

 curve of arrival of the current is altered, the law of the squares 

 only holding good when exactly similar systems are compared. 



Let B C be a cable of length I, resistance k per unit of 

 length, capacity c per unit of length ; and let A B and C D 

 be resistances equal to mkl and nkl respectively, connected to 

 the cable at B and C, and to earth at A and D. Let v be the 

 potential of the conductor of the cable at distance x from B 

 at the time t. Then, according to Sir W. Thomson's theory, 

 v must satisfy tf* v j v 



~d? =ck dt 



