MOMENTARY CONTACTS. 221 



two states, the first due to the permanent potential V , established at 

 the origin of the wire at the beginning of the time, the second to 

 the permanent potential - V , set up after the time r. The value of 

 the potential at the distance x, corresponding to each of those states, 

 is the same function of the time which elapses from establishing at 

 the origin of the wire the corresponding potential; the resultant poten- 

 tial U is therefore equal to V(/) - V(/-r). If we suppose that the 

 time r is infinitely short, we get 



From this we deduce 



The value of U is no longer then a simple function of z*. If < 

 stands for the function 



z fix _ 



- e r** = e t 

 t 2/1 



we may write 

 (8) 



230. We may, moreover, determine graphically the value of , 



v o 



by taking the difference of the ordinates of the curve A, and of 

 another identical curve which has been displaced towards the right 

 by a quantity T. The curves I, II, III, IV, V, represent the result 

 of this superposition for values of r equal respectively to a, 20, 30, 

 40, $a. 



This construction and the formula will show that the momentary 

 connection of the end of the wire with a source of constant poten- 

 tial, gives rise to a sort of electrical wave, which is propagated 

 according to a somewhat complex law, and which spreads itself out 

 as it travels. 



