Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/314

but require for each observation an adjustment of a micrometer screw, or some other movement which must be made by the observer. They are therefore not fitted to act as self-registering instruments, which must of themselves move into, the proper position. This condition is fulfilled by Thomson s Quadrant Electrometer.

The electrical principle on which this instrument is founded may be thus explained:–

$A$ and $B$ are two fixed conductors which may be at the same or at different potentials. $C$ is a moveable conductor at a high potential, which is so placed that part of it is opposite to the surface of $A$ and part opposite to that of $B$, and that the proportions of these parts are altered as $C$ moves.

For this purpose it is most convenient to make $C$ moveable about an axis, and make the opposed surfaces of $A$, of $B$, and of $C$ portions of surfaces of revolution about the same axis.

In this way the distance between the surface of $C$ and the opposed surfaces of $A$ or of $B$ remains always the same, and the motion of $C$ in the positive direction simply increases the area opposed to $B$ and diminishes the area opposed to $A$.

If the potentials of $A$ and $B$ are equal there will be no force urging $C$ from $A$ to $B$, but if the potential of $C$ differs from that of $B$ more than from that of $A$, then $C$ will tend to move so as to increase the area of its surface opposed to $B$.

By a suitable arrangement of the apparatus this force may be made nearly constant for different positions of $C$ within certain limits, so that if $C$ is suspended by a torsion fibre, its deflexions will be nearly proportional to the difference of potentials between $A$ and $B$ multiplied by the difference of the potential of $C$ from the mean of those of $A$ and $B$.

$C$ is maintained at a high potential by means of a condenser provided with a replenisher and tested by a gauge electrometer, and $A$ and $B$ are connected with the two conductors the difference of whose potentials is to be measured. The higher the potential of $C$ the more sensitive is the instrument. This electrification of $C$, being independent of the electrification to be measured, places this electrometer in the heterostatic class.

We may apply to this electrometer the general theory of systems of conductors given in Arts. 93, 127.

Let $A,B,C$ denote the potentials of the three conductors respectively. Let $a,b,c$ be their respective capacities, $p$ the coefficient of induction between $B$ and $C$, $q$ that between $C$ and $A$, and $r$ that