406 M. G. Kirchhoff on {he Motion of Electrieiiy in Wires'. 



exponent of e^ according to the assumption already made, is in- 

 finitely small. In comparison to velocities which come within 

 the range of our conceptions> the diminution of the electricity 

 will certainly be always very speedy. If the wii-e were the 



standard wire of Jacobi, then -j- would be very nearly the 2 oV u*'^ 



of a second ; and hence in this small time the electric density 

 would diminish in the ratio of e : 1, that is, of 2*7 : 1. 



When a is not =0, or when the mean density of the electri- 

 city is not =0, the expression for e shows that the excess of 

 density over the average changes exactly as if the mean density 

 were equal 0. 



The velocity of propagation of an electric wave is here found 



to be = — =, hence it is independent of the cross section, of the 



conductivity of the wii-e, also, finally, of the density of the elec- 

 tricity : its value is 41950 German miles in a second, hence very 

 nearly equal to the velocity of light in vacuo. 



When the wire is not one which returns into itself, the quan- 

 tity b cannot be = 0, and the quantities n may have other 

 values than in the case just considered. As regards the ends 

 of the wire, certain equations are to be ftdfilled according to 

 the conditions to which the ends are subjected. If one end 

 be insulated, at this end i must always be =0; if the end be 

 placed in complete connexion with the earth, the potential V, 

 and also e for all values of t must here vanish. There is no dif- 

 ficulty in forming the expressions for e and i for the cases that 

 both ends are insulated, both connected with the earth, or one 

 of them insulated and the other connected with the earth. In 

 all cases a reflexion of the wave occurs at the end at which it 

 arrives. If the end is connected with the earth, a reversion of 

 the wave accompanies its reflexion, that is, negative electricity 

 proceeds from the end after it has been struck by positive ; at 

 an insulated end the reflexion takes place without reversion. 

 Hence when the end is connected with the earth, it corresponds 

 in some measure to the fixed end of a rod vibrating longitudi- 

 nally; the insulated end, on the contrary, corresponds to the 

 fi'ee end of the rod. 



We shall enter more fully here into the consideration of an- 

 other case. We shall examine how the electricity moves in the 

 connecting wire of a galvanic battery before the current has 

 become stationary. I will assume that the resistance of the bat- 

 tery is infinitely small in comparison with that of the wire con- 

 necting its poles, and that one of its poles stands in perfect con- 

 nexion with the earth. With this pole let the commencement 

 of the wire be connected, and with the other pole the end of the 



