2l6 VARIABLE STATE. 



origin of the wire, and at the time / from the establishment of 

 contact, is given by the expression 



V _ew -e-> __L_ = n '*', . TZTT 



o =i 



which, if the loss may be neglected, becomes 



V _t-X ^ M=C I 27r % . W7T 



225. DURATION OF THE RELATIVE PROPAGATION. The second 

 equation shows that if there is no loss by the sides, the ratio of the 

 potential at a distance x, to the potential at the origin, is the same for 

 two different wires, at two points whose distances from the origin are 



proportional to the total lengths of the wires, when the ratio - has 



or/- 1 



the same value. 



The time / necessary for the potential at any given point (in the 

 middle of the wire, for instance) to attain a definite fraction of the 

 initial potential or of the final potential, is therefore proportional to 

 a 2 / 2 or y/>/ 2 that is to say, to the square of the length of the wire, to 

 the capacity, and to the resistance of unit length. This condition 

 gives what may be called the time of relative propagation of 

 electricity. 



There is not, therefore, in the preceding conditions, a deter- 

 minate velocity for the propagation of electricity as there is for sound, 

 or for light. The apparent velocity which it has sometimes been 

 attempted to estimate, by supposing the propagation uniform, and 

 determining the time necessary for the electrification produced at 

 one end of a wire to have a sensible effect at a certain distance, 

 depends on constants characteristic of the wire, and on the 

 sensitiveness of the means by which these electrical effects are 

 made evident. 



226. UNLIMITED WIRE. Fourier's general integral lends itself 

 with difficulty to numerical applications; but we may choose simpler 

 conditions, which really correspond to several of the observed 

 phenomena, and enable us to find again the principal results 

 obtained by Sir W. Thomson, 



