Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/316

 within $$A$$ and partly within $$B$$, and the supporting radii should be near the middle of the quadrants of the hollow base, so that the divisions of the box and the extremities and supports of $$C$$ may be as far from each other as possible.

The conductor $$C$$ is kept permanently at a high potential by being connected with the inner coating of the Leyden jar which forms the case of the instrument. $$B$$ and $$A$$ are connected, the first with the earth, and the other with the body whose potential is to be measured.

If the potential of this body is zero, and if the instrument be in adjustment, there ought to be no force tending to make $$C$$ move, but if the potential of $$A$$ is of the same sign as that of $$C$$, then $$C$$ will tend to move from $$A$$ to $$B$$ with a nearly uniform force, and the suspension apparatus will be twisted till an equal force is called into play and produces equilibrium. For deflexions within certain limits the deflexions of $$C$$ will be proportional to the product

$(A-B)\left(C-\frac{1}{2}(A+B)\right) $

By increasing the potential of $$C$$ the sensibility of the instrument may be increased, and for small values of $$\tfrac{1}{2}(A+B) $$ the force will be nearly proportional to $$(A-B)C $$.

On the Measurement of Electric Potential.

220.] In order to determine large differences of potential in absolute measure we may employ the attracted disk electrometer, and compare the attraction with the effect of a weight. If at the same time we measure the difference of potential of the same conductors by means of the quadrant electrometer, we shall ascertain the absolute value of certain readings of the scale of the quadrant electrometer, and in this way we may deduce the value of the scale readings of the quadrant electrometer in terms of the potential of the suspended part, and the moment of torsion of the suspension apparatus.

To ascertain the potential of a charged conductor of finite size we may connect the conductor with one electrode of the electro meter, while the other is connected to earth or to a body of constant potential. The electrometer reading will give the potential of the conductor after the division of its electricity between it and the part of the electrometer with which it is put in contact. If $$K$$ denote the capacity of the conductor, and $$K'$$ that of this part