through Heterogeneous Telegraph Circuits. 221 



stant potential ; (6) shows the arrival-curve when a resistance 

 equal to the cable's is inserted at each end. 



It will be observed from an inspection of the curves, that, 

 when resistance is added at one end of a cable only, the effect 

 in increasing the retardation is very great when the added 

 resistance is small, but as more and more resistance is added 

 there is not much further effect. The limit is reached in 

 curve (5). But the insertion of resistance at both ends has a 

 much greater retarding influence, which increases without 

 limit. Compare (4) with (6): in (4) we have twice the 

 cable's resistance at one end and none at the other ; in (6) the 

 same resistance is equally divided at each end, and the retar- 

 dation is very greatly increased. 



With respect to the change in the form of the arrival-curves, 

 it will be seen that, when resistance is inserted, the first part 

 of the arrived current is proportionally less retarded than the 

 later parts. Thus, comparing (1) with (6), when there is no 

 resistance inserted the current reaches 5 per cent, of its maxi- 

 mum in 2*45 a, whereas (6) takes 6a, or 2*4 times as long ; 

 to reach 10 per cent. (6) takes 3*3 times as long as (1) ; to 

 reach 40 per cent, it takes 3' 7 times as long, and to reach 70 

 per cent. 4*5 times as long. 



Curves (1), (7), and (8) show the effect of different distri- 

 butions of the same amount of capacity in a line of given 

 resistance. (8) shows the arrival-curve when the capacity is 

 all collected at the centre of the line as a single condenser, 

 (7) when the capacity is uniformly distributed over the middle 

 third of the line, and (1) when it is uniformly distributed over 

 the whole length. The more the capacity is spread, the longer 

 is the time taken for the current to reach a sensible strength, 

 whereas the current rises rapidly the moment contact is made 

 when the capacity is collected at one place. Curve (7) is the 

 same as (6) with the abscissas of the latter reduced in the ratio 

 3:1; and curve (8) is the limiting form of the arrival-curve 

 when very great equal resistances are inserted at both ends of 

 the cable, the abscissas being reduced in the same proportion 

 as the resistance of the circuit is increased. Its equation is 



N ., _i< 



= 1—6 T. 



100 



