ANY GIVEN LINEAR CONDUCTORS. 193 



In order that the potential may be constant, dR. must also be 

 proportional to the time ; let us put 



We have then 



udt ru ' 



and therefore 



i 



r=- 

 u 



Thus the resistance r of a given conductor is the inverse of the 

 velocity u with which the radius of a sphere must decrease for its 

 potential to remain constant, notwithstanding the loss of electricity, 

 when it is connected with the earth by the conductor in question. 



207. ANY GIVEN LINEAR CONDUCTORS. We have supposed the 

 conductors to be rectilinear, but the same reasoning evidently applies 

 to linear conductors bent in any manner whatever, the flow of elec- 

 tricity being perpendicular at each point to the cross section of the 

 conductor. 



Y* 



T7 



Fig. 50- 



If the circuit consists of two or more cylindrical portions of 

 different kinds and sections joined end to end, these various parts 

 may be considered separately. 



If Vj and V 2 are the potentials at the points A and B (Fig. 50), 

 the first in a conductor of section S, and whose coefficient of conduc- 

 tivity is c, and the second belonging to a conductor in which these 

 quantities are S' and c'. Let V be the point of contact O of the 

 two cylinders, at distances / and /' from A and B respectively, and 

 let us for the present disregard the electromotive force of contact of 

 the two conductors, to which we shall subsequently return. On each 

 side of the point O we have 



r+r 1 



The current is therefore inversely as the sum of the resistances 



o 



