PROBLEM OF WHEATSTONE's BRIDGE. 



341 



force + E, which annuls the preceding, a fresh distribution of 

 currents is produced ; but from the principle of the superposition 

 of the conditions of equilibrium (202) the strength of the current 

 which traverses the conductor r is defined by the equation 



The two points A and A' of the primitive system behave then 

 in reference to a new conductor by which they are connected, as 

 a single conductor of resistance p, equal to that which at first 

 existed between them, and containing an electromotive force equal 

 to the difference of potential in the primitive state. 



This important relation might be utilised for determining 

 either the resistance between two points, or the differences of 

 their potentials, fi "A^- 



947. PROBLEM OF WHEATSTONE'S BRIDGE. In Wheatstone's 

 arrangement the six conductors present the same relations of 



A R B 



Fig. 185. 



position as the six edges of a triangular pyramid (Fig. 185), for 

 each conductor is adjacent to four others and opposed to the 

 sixth. As the general case, it might be assumed that all the sides 

 contain electromotive forces; we shall denote them by the same 



letter E^ E a > , affected by an index which indicates the 



resistance of the side in which it is placed. 



We observe, in the first place, that two opposite sides R and r 

 are conjugate, if the four others satisfy equation (17). Further, 

 if two couples of opposite sides R and r, a and b' are respectively 

 conjugate, the two others are so likewise, for the equations 







