Self-induction of Wires. 27 



which is, except as regards the terminal functions I introduce, 

 quite an old formula. It is what we get bj regarding the 

 line as having only resistance and electrostatic capacity. But, 

 still regarding the line as an Atlantic or similar cable, worked 

 nearly up to its limit of speed, VI is large, say 10 at most, so 

 that we may take this approximation to (265), 



C =2y o (Sn/R)*6- pz xGo"*xGr^ . . . (27b) 



where the first of the three factors is the line-factor, the 

 second that due to the apparatus at the 2 = end, and the 

 third to that at the z = l end of the line ; thus, by (20 5) and 

 (255), with L' = and R' = R in the former, 



Oo = l + ^{2PIi(Ro'-L 'n) + 2P 2 (Il ' 2 + W)}/ 



h (285) 

 G 1 = l + i{2PR(R 1 '-L» + 2P 2 (R 1 ' 2 + L 1 'V)}. 



This reduction to (27 b) is of course not possible when the 

 line is very far from being worked up to its possible limit ; in 

 fact, all three terms in the { } of (26 5), or, more generally, of 

 (19 5), require to be used in general. For this reason a full 

 examination of the effect of terminal apparatus is very labo- 

 rious. Most interesting results maybe got out of (19 5), 

 especially as regards the relative importance of the line and 

 terminal apparatus at different speeds, complete reversals 

 taking place as the speed is varied whilst the line and appa- 

 ratus are kept the same. The general effect is that, as the 

 speed is raised, the influence of the apparatus increases much 

 faster than that of the line. For instance, to work a land- 

 line of, say, 400 miles up to its limit, we must reduce the 

 inertia of the instruments greatly to make it even possible. 

 In fact electromagnets seem unsuitable for the purpose, unless 

 quite small, and chemical recording has probably a great 

 future before it. But it would be too lengthy a digression to 

 go into the necessarily troublesome details. 



The following relates to some properties of the terminal 

 function Gr, which have application when (27 5) is valid. Con- 

 sider the G x of (28 5). Let it be simply a coil that is in ques- 

 tion. Then R x is its resistance and L x its inductance, dropping 

 the accent. Keep the resistance constant, whilst varying the 

 inductance so as to make Gc ± a minimum, and therefore the 

 current amplitude a maximum. The required value of L x is 



L^R^P/i, (295) 



depending only upon the line-constants and the speed, inde- 



