386 



municated at the point O' at a distance - a _ on the negative side 



Vkc 



of O, the consequent potential at any time t, at a distance z _ 



Vkc 

 along the wire from O, will be 



and if a be infinitely small, this becomes 



_ 

 Qa ze 4 < 



which with positive values of z, expresses obviously the effect of 

 communicating the point O with the positive pole for an infinitely 

 short time, and then instantly with the ground. 

 " The strength of the current at any point of the wire, being equal to 



. -, as shown above, in equation (2), will vary proportionally 

 A ax 



to or to -. The time of the maximum electrodynamic effect 

 dx dz 



of impulses such as those expressed by (11) or (13) will be found 

 by determining t, in each case, to make a maximum. Thus 



G>2 



we find 



as the time at which the maximum electrodynamic effect of connect- 

 ing the battery for an instant at O, and then leaving this point in- 

 sulated, is experienced at a distance x. 



" In these cases there is no regular ' velocity of transmission.' 

 But, on the other hand, if the potential at O be made to vary regu- 

 larly according to the simple harmonic law (sin 2n), the phases are 



propagated regularly at the rate 2 * / , as is shown by the well- 

 known solution 



v=e~* n * sm(2nt-zn k ) ..... (14). 



* We may infer that the retardations of signals are proportional to the squares 

 of the distances, and not to the distances simply ; and hence different observers, 

 believing they have found a " velocity of electric propagation," may well have 

 obtained widely discrepant results ; and the apparent velocity would, ceeteris part- 

 bus, be the less, the greater the length of wire used in the observation. 



