Self-induction of Wires. 439 



It is clear that when S is made to vanish, making m' = oo , 

 the current oscillations wholly vanish, reducing the C solution 

 to the first of (193). But the Y oscillations remain in full 

 force, though of infinitely short period, and subside at a defi- 

 nite rate. This means that the mean value of Y at any place 

 has to be taken to represent its actual value, and this mean 

 value is its final value. That is, if Y denote the mean value, 

 about which Y oscillates, we have 



v=« (i-z/o=v . 



Introduce LS = v~ 2 , where v is constant, making 



ra'=2mLv/R 



very nearly, when the line is short ; then the second of (194) 

 becomes 



V==e (l-j\^~°€-^^X S ^^cosmv^ . (195) 



which must very nearly show the subsidence of the oscillations. 

 First ignore the subsidence factor, replacing it by unity, then 

 (195) represents a wave of Y travelling to and fro at velocity 

 v, as thus expressed, 



Y = e from z—0 to z = vt, 1 . , 



Y = beyond z = vt. ) 



When vt = l, the whole line is charged to Y=--e . The wave 

 then moves back in the same manner as it advanced, so that 

 the state of things at time t = l/v + t is the same, until t reaches 

 2l/v, when we have Y=0 as at first. This would be repeated 

 over and over again if there were no resistance, which, through 

 the exponential factor, causes the range of the oscillations of 

 Y at any place about the final value to diminish according to 

 the time constant 2L/R. Also, the resistance has the effect 

 of rounding off the abrupt discontinuity in the wave of Y. 



I have given a fuller description of this case elsewhere 

 (Journal S. T. E. and E. vol. ix., " On Induction between 

 Parallel Wires "), and only bring it in here in connection 

 with the interpretation according to my present views regard- 

 ing the transfer of energy. As it is clear that this oscillatory 

 phenomenon is, primarily, a dielectric phenomenon, and only 

 affects the conductor secondarily, it is necessary that the L in 

 the above should not at the beginning be the full L of dielec- 

 tric and wires, but only L , that of the dielectric, making v 

 the velocity of undissipated waves, although as the oscillations 

 subside the velocity must diminish, tending towards v = (LS)~ 2 , 

 which may, however, be far from being reached, especially in 



2H2 



