Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/440

course of experiments if any alteration of the position of the needle is suspected.

The other null method, in which Wheatstone's Bridge is used, requires only an ordinary galvanometer, and the observed zero deflexion of the needle is due, not to the opposing action of two currents, but to the non-existence of a current in the wire. Hence we have not merely a null deflexion, but a null current as the phenomenon observed, and no errors can arise from want of regularity or change of any kind in the coils of the galvanometer. The galvanometer is only required to be sensitive enough to detect the existence and direction of a current, without in any way determining its value or comparing its value with that of another current.

347.] Wheatstone's Bridge consists essentially of six conductors connecting

Fig. 31.

four points. An electromotive force $E$ is made to act between two of the points by means of a voltaic battery introduced between $B$ and $C$. The current between the other two points $O$ and $A$ is measured by a galvanometer.

Under certain circumstances this current becomes zero. The conductors $BC$ and $OA$ are then said to be conjugate to each other, which implies a certain relation between the resistances of the other four conductors, and this relation is made use of in measuring resistances.

If the current in $OA$ is zero, the potential at $O$ must be equal to that at $A$. Now when we know the potentials at $B$ and $C$ we can determine those at $O$ and $A$ by the rule given at Art. 274, provided there is no current in $OA$,

$O={\frac {B\gamma +C\beta }{\beta +\gamma }},\qquad A={\frac {Bb+Cc}{b+c}},$

whence the condition is

$b\beta =c\gamma ,$

where $b,\,c,\,\beta ,\,\gamma$ are the resistances in $CA,\,AB,\,BO\,{\mbox{and}}\,OC$ respectively.

To determine the degree of accuracy attainable by this method we must ascertain the strength of the current in $OA$ when this condition is not fulfilled exactly.

Let $A,\,B,\,C,$ and $O$ be the four points. Let the currents along $BC,\,CA\,{\mbox{and}}\,AB$ be $x,\,y\,{\mbox{and}}\,z,$ and the resistances of these