THE MEASUREMENT OF RESISTANCE 



183 



points brought out by a study of the theory of the instrument 

 must receive attention. 



Galvanometer Current. The general expression for the current 

 through the galvanometer in terms of the resistances of the vari- 

 ous bridge arms and the electromotive force and resistance of 

 the battery is readily deduced. However, a simpler and more 

 useful formula is that connecting the total bridge current with 

 the current through the galvanometer, for in many cases the 

 bridge current is regulated by a rheostat rather than controlled 

 solely by the e.m.f . of the battery and by the various resistances. 



Suppose the connections to be those given in Fig. 104A, atfd 

 assume, following Maxwell, that the meshes are traversed by 

 currents (x -\- y), x and I B as shown in the figure, also that the 



N 



FIG. 104. Mesh diagrams for Wheatstone bridge. 



resistances of the various branches are M, N, X, P, R G and 

 B and that the electromotive force of the battery is E. By 

 KirchofTs corollaries 



(x + y) (M + R G + X) - xR G - I B X = 



(x) (N + P + R G ) - (x + y) R G - I B P = 0. 



Solving for ?/, which is the true galvanometer current, gives 



T I*(NX - MP) 



IGI R G (M + N + X + P) + (N + P)(M + X) 



The important case is when the bridge is nearly balanced. Then 

 if B is the total resistance in the battery circuit outside of the 

 bridge, 



, 



" 



M + N + X + P 



