Let the bowl be a thin metal shell connected with the earth by a long thin wire and be surrounded by a concentric and complete shell of diameter f greater than that of the spherical surface, and let this shell be rigidly electrified with surface density －s. There will be no force within this shell due to its own electrification, and hence it will produce no change of the distribution in the interior. But the potential within will be －2πfs, for the charge is －πf²s, and the capacity of the shell is ½f. The potential of the bowl will now be zero, and its electrification will just neutralise the potential -2πfs, that is, will be exactly the free electrification required to produce potential 2πfs. To find this electrification let the value of f be only infinitesimally greater than the diameter of the spherical surface of which B is a part; then the bowl is under the influence (1) of a uniform electrification of density －s infinitely close to its outer surface, and (2) of a uniform electrification of the same density, which may be regarded as upon the surface which has been called S above. It is obvious that by (1) a density s is produced on the outer surface of the bowl, and no other effect; by (2) an equal density at infinitely near points on the opposite sides of the bowl is produced which we have seen how to calculate. Thus the distribution on the bowl freely electrified is completely determined and the density can easily be calculated. The value will be found in Thomson's paper. Interesting results are obtained by diminishing S more and more until the shell is a complete sphere with a circular hole in it. Tabulated results for different relative dimensions of S will be found in Thomson's paper, "Reprint of Papers," Articles V, XIV, XV. Also the reader will there find full particulars of the mathematical calculations indicated in this chapter, and an extension of the method to the case of an influencing point not on the spherical surface of which the shell forms part. Further developments of the problem have been worked out by other writers, and further information with references will be found in Maxwell's _Electricity and Magnetism_, loc. cit.