20 ELECTRICITY [DISTRIBUTION. Hollow sphere experi- juent. Frank lin s experi ment. Blot s experi ment. covers. If now we remove the proof-plane in the direction of the normal, keeping it, as nearly as possible, parallel to the surface, the electricity will not leave it; but we shall carry safely away all that it had when iu contact with the surface of the body. We may return to the con sideration of the proof-plane when we come to study mathematically the laws of electrical distribution. In the experiment with which we are now concerned, Coulomb used a very delicate balance (a force of -j-jVo of a milligramme was sufficient to keep the wire twisted through 90). When the proof-plane was applied to any point of the external surface of the wooden cylinder, and then introduced into the torsion balance, it repelled the electrified ball of the balance with great force. When it was carefully introduced into one of the holes, made to touch the bottom, and then carefully withdrawn so as not to .touch the edge of the hole, it produced no appreciable effect on the balance. Coulomb varied this experiment as follows. He insu lated and electrified a hollow sphere of metal (fig. 7), and by carefully introducing a proof-plane through a small opening tested the electrical condition of the interior surface. He found no sensible trace of electricity inside, except very near the edge of the small opening. Hence we conclude that if the sphere had been closed entirely there would have been no electrification in side. Many experiments have been made to illustrate the proposition that electricity resides entirely on the surface of conductors. Franklin put a long chain inside a metal teapot, which he insulated and electrified. When he seized the chain by a hook at the end of a glass rod and pulled it out of the teapot Fi S- "< he observed that a pair of pith balls, suspended side by side from the teapot, collapsed more and more as the chain was drawn out, and he concluded that the electrification of the teapot, being now spread over a greater surface, had become weaker. The folio wing experiment of Biot s has become classical. A spherical conductor A (fig. 8) is supported on an insulat ing stem D. B and C are two hollow hemispheres fastened to insulating handles E and F. When these are fitted together they form a sphere some what larger than A, with a small hole in it through which the stem D can pass. If we electrify A very strongly, so that when put in the electric Fi 8- 8 - cage it powerfully deflects the electrometer, and then close B and C over A. and make either B or C touch it, then separate B and C, and test A, B, and C in the cage, we shall find that all the electricity has gone from A and spread itself over B and C. The following is an ingenious experiment of Faraday s, involving the same principle. AB (fig. 9) is a wire ring sup- jj ported on an insulating stand; C is a conical muslin bag da fitted to the ring with two strings fastened to the vertex of P 6 the cone, giving the experimenter the means of quickly turning the bag inside out. If the bag be electrified in the first position in the figure and tested with the proof- plane and electric cage, it will be found that the outside only is electrified. If we turn the bag inside out and test it, we shall find as before that what is now the outside, and was formerly the inside, is alone electrified. The electricity has thus passed through the bag so as to be on the outside in both cases. Before leaving for a time the question of the distribution of electricity on conductors, it may be well to warn the student to accept with due reserve the proposition that electricity resides entirely on the surface of conductors, and to remind him that such a proposition is from the nature of the case incapable of direct experimental proof, for we cannot operate in the substance of a mass of metal. Some of the experiments we have quoted bear more directly on the question than others. Coulomb s experiment, for instance, shows, strictly speaking, merely that electri city avoids cavities and re-entrant angles. Again, in Fara day s experiment with the linen bag, we have not clearly defined what we mean by the outside of the body. The proposition has on the whole been suggested rather than proved. Its meaning will become clearer as we go more and more into the theory of distribution, 1 and we shall meet with it by-and-by as one of the first propositions in the mathematical theory. Laivs o/* Electric Force. Before proceeding to give an account of Coulomb s quantitative experiments on electrical distribution, we shall describe shortly the methods by which he arrived at the laws of electric force, and did for electricity what Newton did for astronomy, i.e., laid the foundation for a mathema tical theory of the subject based on tb.3 hypothesis of action at a distance. In this research Coulomb used the form of balance EJ which we described above. The clamp holding the fixed m> ball of the balance is so adjusted that the centre of the de ball falls in a horizontal line through zero of the gradua- of tion on the glass cylinder and the prolongation of the sus- el* pending wire; the torsion button is turned till its arm is ta. at zero; the disc, button and all, is then turned till the disc on the arm and the centre of the movable ball are in a line with the zero of the lower graduation. The fixed ball, which had been removed to allow of the last adjust ment, being replaced, and the movable ball having come to rest in contact with it, both are electrified by means of a small metal ball carried on an insulating stem of shellac. The balls repel each other, and the movable ball takes up a certain position of equilibrium; the corresponding angle is read off. The torsion button is then turned through an angle which is noted, so as to bring the balls nearer together. The new position of the beam is again read off; this may be repeated a third time. We are then in pos session of data from which we can draw conclusions as to the law of electrical force at different distances. Let us assume that the force between two elements of positive electricity (supposed collected at two points, technically speaking, "regarded as physical points") varies inversely as the square of the distance between them. It will be shown in the mathematical theory that two spheres uniformly* electrified, as we shall at present 1 One additional caution may be useful, viz., not to confound this proposition with another of fundamental importance, -of which we can give direct experimental proof of the most conclusive nature "that there is no electrical action inside a hollow conductor containing no charged bodies." 4 This condition is not absolutely satisfied in any experiment; it i
approximately satisfied in Coulomb s experiment.