a perfect communication by metal between them and the inner globe, so that the electricity has free liberty to enter the inner globe if it has any disposition to do so, and moreover that this communication is not taken away till after the wire by which the hemispheres are electrified is removed. Secondly, before the hemispheres begin to be separated from each other, the wire which makes the communication between them and the globe is taken away, so that there is no longer any communication between them by any conducting substance. Thirdly, from the manner in which the operation is performed, it is impossible for the hemispheres to touch the inner globe while they are removing, or even to come within ths of an inch of it. And Fourthly, the whole time of performing the operation is so short, that no sensible quantity of electricity can escape from the inner globe, between the time of taking away the communication between that and the hemispheres, and the approaching the pith balls to it, so that the quantity of electricity in the globe when the pith balls are approached to it cannot be sensibly different from what it is when it is inclosed within the hemispheres and communicating with them. 227] The result was, that though the experiment was repeated several times*, I could never perceive the pith balls to separate or show any signs of electricity. 228] That I might perceive a more minute degree of electricity in the inner globe, I tried the experiment in a different manner, namely, before the hemispheres were electrified, I electrified the pith balls positively, making them separate about one inch. When the hemispheres were then separated, and the tinfoil, x, brought in contact with the globe, and consequently the electricity of the pith balls communicated to the globe, they still continued to separate, though but just sensibly. I then repeated the experiment in the same manner, except that the pith balls were negatively electrified in the same degree that they before were positively. They still separated negatively after being brought in contact with the globe, and in the same degree that they before did positively. [* Dec. 18—24, 1772, Arts. 512, 513, and April 4, 1773, Art. 562.] 230] ON THE LAW OF ELECTRIC FORCE. 109 229] It must be observed that if the globe was at all overcharged the pith balls should separate further when they were previously positively electrified than when negatively, as in the first case the pith balls must evidently separate further than they would do if the globe was not overcharged, and in the latter case less. Moreover, a much smaller degree of electricity may be perceived in the globe by this manner of trying the experiment than the former, for when the pith balls have already got a sufficient quantity of electricity in them to make them separate, a sensible difference will be produced in their degree of divergence by the addition of a quantity of fluid several times less than what was necessary to make them separate at first. It is plain that this method of trying the experiment is not just, unless the hemispheres are electrified in nearly the same degree when the pith balls are previously electrified positively as when negatively, which was provided for by the electrometer. 230] In order to find how small a quantity of electricity in the inner globe might have been discovered by this experiment, I took away the hemispheres with their frames, leaving the globe and the pith balls as before. I then took a piece of glass, coated as a Leyden vial, which I knew by experiment contained not more thanth of the quantity of redundant fluid on its positive side that the jar by which the hemispheres were electrified did, when both were charged from the same conductor. I then electrified this coated plate to the same degree, as shewn by the electrometer, that the jar was in the former experiment, and then separated it from the prime conductor, and communicated its electricity to the jar, which was not at all electrified. Consequently the jar contained only th part of the redundant fluid in this experiment that it did in the former, for the coated plate and jar together contained only th, and therefore the jar alone contained only th. By means of this jar, thus electrified, I electrified the globe in the same manner that the hemispheres were in the former experiment, and immediately after the electrifying wire was withdrawn, approached the pith balls. The result was that by previously electrifying the balls, as in the second way of trying the experi ment, the electricity of the globe was very manifest, as the balls separated very sensibly more when they were previously electrified positively than when negatively, but the electricity of the globe was not sufficient to make the balls separate, unless they were previously electrified. It is plain that the quantity of redundant fluid communicated to the globe in this experiment was less than th part of that communicated to the hemispheres in the former experiment, for if the hemispheres themselves had been electrified they would have received onlyth of the redundant fluid they did before, and the globe, as being less, received still less electricity. 231] It appears, therefore, that if a globe 121 inches in diameter is inclosed within a hollow globe 13.3 inches in diameter, and communicates with it by some conducting substance, and the whole is positively electrified, the quantity of redundant fluid lodged in the inner globe is certainly less than th of that lodged in the outer globe, and that there is no reason to think from any circumstance of the experiment that the inner globe is at all overcharged. 232] Hence it follows that the electric attraction and repulsion must be inversely as the square of the distance, and that when a globe is positively electrified, the redundant fluid in it is lodged intirely on its surface. For by Prop. V. [Art. 20], if it is according to this law, the whole redundant fluid ought to be lodged on the outer surface of the hemispheres, and the inner globe ought not to be at all over or undercharged, whereas, if it is inversely as some higher power of the distance than the square, the inner globe ought to be in some degree overcharged. 233] For let ADB (Fig. 13) be the hemispheres and adb the inner globe, and Aa the wire by which a communication is made between them. By Lemma IV. [Art. 18], if the electric attraction and repulsion is inversely as some higher power of the distance than the square, the redundant fluid in ABD repels a particle of fluid placed anywhere in the wire Aa towards the center, and consequently, unless the inner globe was sufficiently overcharged to prevent it, some fluid would flow from the hemispheres to the globe. But if the electric attraction and repulsion is inversely as some lower power of the distance than the square, the redundant fluid in ABD impels the particle in the contrary direction, that is, from the center, and therefore the inner globe must be undercharged. 234] In order to form some estimate how much the law of the electric attraction and repulsion may differ from that of the inverse duplicate ratio of the distances without its having been perceived in this experiment, let AT be a diameter of the two concentric spheres ABD and abd, and let Aa be bisected in e. Ae in this experiment was about 35 of an inch and Te 13.1 inches, therefore if the electric attraction and repulsion is inversely as the 2th power of the distance, it may be shewn that the force with which the redundant fluid in ABD repels a particle at e towards the center is to that with which the same quantity of fluid collected in the center would repel it in the contrary direction as 1 to 57. But as the law of repulsion differs so little from the inverse duplicate ratio, the redundant fluid in the inner globe will repel the point e with very nearly the same force as if it was all collected in the center, and therefore if the redundant fluid in the inner globe is th part of that in ABD the particle at e will be in equilibrio, and as e is placed in the middle between A and a, there is the utmost reason to think that the fluid in the whole wire Aa will be so too. We may therefore conclude that the electric attraction and repulsion must be inversely as some power of the distance between that of the 26th and that of the 2-th, and there is no reason to think that it differs at all from the inverse duplicate ratio*. 235] EXPERIMENT II. A similar experiment was tried with a piece of wood 12 inches square and 2 inches thick, inclosed between two wooden drawers each 14 inches square and 2 inches deep on the outside, so as to form together a hollow box 14 inches square and 4 thick, the wood of which it was composed being 5 to 3 of an inch thick. The experiment was tried in just the same manner as the former. I could not perceive the inner box to be at all over or undercharged, which is a confirmation of what was supposed at the end of Prop. IX. [Art. 41]-that when a body of any shape is overcharged, the redundant fluid is lodged entirely on the surface, supposing the electric attraction and repulsion to be inversely as the square of the distance t. DEMONSTRATION OF COMPUTATIONS IN [ART. 234]. Let aef be a sphere, c its center, bany point within it, af a diameter, Ee any plane perpendicular to af. Let cb=a, bad, bfs and ad=x, and let the repulsion be inversely as the n power of the distance. The convex surface of the segment Eae is to that of the whole globe as ad af, and therefore if the point d is supposed to flow towards f, the fluxion of the surface Eae is proportional to x, and the fluxion of its repulsion on b in the direction de is proportional to x (d-x) or may be represented thereby, but be2 = (d − x)2 + x (2a + 2d − x) = d2 + 2ax, therefore the fluxion of the repulsion is x (d-x) +19 |