DISTRIBUTION OF ENERGY. 731 



If we replace the intermediate resistances y by their values, we 

 get for the total resistance y n , between the two poles A and B, 



Finally, let e lt e. 2 , ... e n be the differences of potential at the corre- 

 sponding points of contact; t\, i' 2 , . . . i n the currents in the resistances 

 a lt a 2 . .. a n . We' have generally 



or 



Fig. 262. 



The disposable difference of potential in the successive parts 

 decreases as we get away from the machine; the fall is only ne- 

 gligable provided the sum of the resistances is very small compared 

 with that of any one of the parts p. 



1278. A somewhat more satisfactory solution of the problem is 

 obtained by connecting the poles of the machine with the opposite 

 ends A and B (Fig. 262) of two principal conductors. 



Let a 19 2 > a n-l be the resistances A^, A 2 A 3 , . . . A n _ l A n ; 

 n 2 "'^n-i t ^ ie corresponding resistances of the conductors B; 

 a 1? a 2 , . . . a n _ 1 and fa, fi 2 , . . . ft n -i the respective currents ; I the 

 current We have evidently 



for the sum of the currents which traverse any plane cut by the prin- 

 cipal conductors is constant, and equal to I ; we get from this 



