On the Connexion of the Physical Sciences

The quantity of electricity bodies are capable of receiving does not follow the proportion of their bulk, but depends principally upon the form and extent of their surface. It appears from the experiments of Sir W. S. Harris that a given quantity of electricity, divided between two perfectly equal and similar bodies, exerts upon external bodies only one fourth of the attractive force apparent when disposed upon one of them; and if it be distributed among three equal and similar bodies, the force is one ninth of that apparent when it is disposed on one of them. Hence, if the quantity of electricity be the same, the force varies inversely as the square of the surface on which it is disposed; and if the surface be the same, the force varies directly as the square of the quantity of electricity. These laws however do not hold when the form of the surface is changed. A given quantity of electricity disposed on a given surface has the greatest intensity when the surface has a circular form, and the least intensity when the surface is expanded into an indefinite straight line. The decrease of intensity seems to arise from some peculiar arrangement of the electricity depending on the extension of the surface. It is quite independent of the extent of the edge, the area being the same; for Sir W. S. Harris found that the electrical intensity of a charged sphere is the same with that of a plane circular area of the same superficial extent, and that of a charged cylinder the same as if it were cut open and expanded into a plane surface.