RESISTANCE OF A CONDUCTOR. 211 



Let us consider, as a more general case, a wire the different points 



in which P lf Pg, P 3 , are connected with the earth by conductors 



of resistance p v p# /> 3 , Let R x be the total resistance from 



the point P x to the ground, R 2 the resistance starting from the point 



P 2 , , ; finally r v r 2 , r 3 , . . . . the resistances of the wire between 



the successive points of contact P^, P 2 ^3' > etc - From the point 

 P! the total conductivity is equal to the sum of the conductivities 

 which the various paths offer, which gives the equation 



We should have a series of analogous equations, and ultimately 



I 



P2 



I 

 Pn r n 



This is the case of overhead telegraph wires when we take 

 into account the leakage by the insulators. If the leakage is 

 continuous, and R is the resistance starting from the point P, 

 R + </R the resistance from the adjacent point P' at the distance 

 dx, the coefficients p and p having the same meaning as above, 

 equation (12) becomes 



I I 

 T? ' 



dx 



or 



</R dx 



