The ratio q⧸V, of charge to potential, which is called the electrostatic capacity of the conductor, is thus 2a⧸π, that is a⧸1.571. It is, as Thomson notes in his paper, very remarkable that the Hon. Henry Cavendish should have found long ago by experiment with the rudest apparatus the electrostatic capacity of a disk to be 1⧸1.57 of that of a sphere of the same radius. [Illustration: FIG. 10.] [Illustration: FIG. 11.] Now invert this disk distribution with any point Q as centre of inversion, and with radius of inversion a. The geometrical inverse is a segment of a spherical surface which passes through Q. The inverse distribution is the induced distribution on a conducting shell uninsulated and coincident with the segment, and under the influence of a charge －aV situated at Q (Fig. 11). Call this conducting shell the "bowl." If the surface-densities at corresponding points on the disk and on the inverse, say points P and P', be s and s', then, as on page 51, s' = sa³⧸QP'³. If we put in the value of s given above, that of s' can be put in a form given by Thomson, which it is important to remark is independent of the radius of the spherical surface. This expression is applicable to the other side of the bowl, inasmuch as the densities at near points on opposite sides of the plane disk are equal. If v, v' be the potentials at any point R of space, due to the disk and to its image respectively, －v' = av⧸QR. If then R be coincident with a point P' on the spherical segment we have (since then v = V) V' = aV⧸QP', which is the potential due to the induced distribution caused by the charge －aV at Q as already stated. The fact that the value of s' does not involve the radius makes it possible to suppose the radius infinite, in which case we have the solution for a circular disk uninsulated and under the influence of a charge of electricity at a point Q in the same plane but outside the bounding circle. Now consider the two parts of the spherical surface, the bowl B, and the remainder S of the spherical surface. Q with the charge －aV may be regarded as situated on the latter part of the surface. Any other influencing charges situated on S will give distributions on the bowl to be found as described above, and the resulting induced electrification can be found from these by summation. If S be uniformly electrified to density s, and held so electrified, the inducing distribution will be one given by integration over the whole of S, and the bowl B will be at zero potential under the influence of this electrification of S, just as if B were replaced by a shell of metal connected to the earth by a long fine wire. The densities are equal at infinitely near points on the two sides of B.