382 COMPARISON OF RESISTANCES. 



resistances in the form of coils which can be put on either side, 

 without their sum being changed ; PQ is the wire of a bridge. The 

 contacts are made on each of the conductors by means of two 

 points, or of two knife edges mounted on an insulating plate, and 

 at a constant distance and measured exactly. Each of the points 

 communicates with a small mercury cup in which dips one of the 

 galvanometer wires, the other end of which is at D. The resistances 

 X and Y and the point D are adjusted so that the needle of the 

 galvanometer is at zero. If a is the resistance MA, S the total 

 resistance from M to N, / the resistance of the wire PQ, x that 

 of PD, and T the sum X + /+Y. If contact be made successively 

 at A and A', the values X and X', x and x' relative to the two 

 equilibriums, give 



S a a+0 a 



T X + x X' + x' X'-X + x'-x 



If in like manner the contacts are at B' and B, the values X' x 

 and Xj, x\ and x 1 give similarly 



S b 



T* "V *V' i ' ^ 



consequently 



a X f -X + x f -x 

 ~b X l -X' l + x l -x' l ' 



As the resistances of the points of contact only act in the 

 branch of the galvanometer, they do not come into play in the 

 equations of equilibrium; the only condition to be fulfilled is that 

 the resistances S and T are unchanged. 



981. USE OF THE DIFFERENTIAL GALVANOMETER. Professor^ 

 Tait* has used a differential galvanometer with great advantage in 

 comparing the resistances of stout metal rods. One of the coils 

 of the galvanometer is connected with the points A and A' of the 

 first conductor, the other to the points B and B' of the second, 

 while the two conductors placed in succession in the circuit are 

 traversed by the same current. The points are chosen so that the 

 needle is at zero; if the galvanometer is adjusted, we have a = b. 



* TAIT. Trans. Roy. Soc. Edinburgh, Vol. xxvni., p. 717. 1877-78. 



