Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/444

This result is easily obtained by considering the resistance from $A$ to $O$ through the system, remembering that $BC$, being conjugate to $AO$, has no effect on this resistance.

In the same way we should find that if the total area of the acting surfaces of the battery is given, the most advantageous arrangement of the battery is when

$B={\frac {RS}{R+S}}.$

Finally, we shall determine the value of $S$ such that a given change in the value of $n$ may produce the greatest galvanometer deflexion. By differentiating the expression for $\xi$ we find

$S^{2}={\frac {BR}{B+R}}\left(R+{\frac {G}{n(1-n)}}\right).$

If we have a great many determinations of resistance to make in which the actual resistance has nearly the same value, then it may be worth while to prepare a galvanometer and a battery for this purpose. In this case we find that the best arrangement is

$S=R,\qquad B={\frac {1}{2}}R,\qquad G=2n(1-n)R,$

and if $n={\frac {1}{2}},\;G={\frac {1}{2}}R$.

On the Use of Wheatstone's Bridge.

350.] We have already explained the general theory of Wheatstone's Bridge, we shall now consider some of its applications.

Fig. 32.

The comparison which can be effected with the greatest exactness is that of two equal resistances.