Self-induction of Wires. 73 



and whose further side is connected to earth, as symbolized 

 by the arrow-head*. Let R 2 be the resistance of the secondary 

 coil, and L l3 L 2 , M the inductances, self and mutual, of the 

 primary and the secondary. At the distant end of the line, 



H 1 x=o 



* — \S\S\f\J\f\j — ©=*=•=« 



nj\AJ\j\r\ 



»a 



where z=l, we may have another arrangement of apparatus, 

 also joined through to earth, though this is not necessary. 

 The line and the two terminal arrangements form the com- 

 plete system, supposed to be independent of all other systems. 



Now suppose there to be no impressed force in any part 

 of the system, so that its state at a given moment depends 

 entirely upon its initial state at the time of removal of the 

 impressed forces ; after which, owing to the existence of 

 resistance, it must subside to a state of zero electric force and 

 zero magnetic force everywhere (with some exceptional cases 

 in which there is ultimately electric force, though not mag- 

 netic force), the manner of the subsidence to the final state 

 depending upon the connexions of the system. The course 

 of events at any place depends upon the initial state of every 

 part, including the terminal apparatus, which may be arbi- 

 trarv, since any values may be given to the electrical variables 

 which serve to fully specify the amount and distribution of 

 the electric and magnetic energies. 



Suppose that V, the potential difference, and C, the current 

 in the line, are sufficient to define its state, i. e. as electrical 

 variables, when the nature of the line is given, and that u 

 and w are the normal functions of V and C in a normal 

 system of subsidence. Then, at time t, we have 



Y = SAue pt , C = 2AW', .... (le) 



* It is not altogether improbable that the arrangement shown in the 

 figure, with the receiving instrument placed in the secondary circuit, 

 would be of advantage. A preliminary examination of the foini of the 

 arrival-curve when this arrangement is used for receiving at the end of a 

 long cable, with K =0, yields a favourable result. But the examination 

 did not wholly include the influence of the resistances on the form of the 

 curve. 



