order that the balls shall separate positively as much as they did

4

negatively, be 16-1; for, if this surface is given to it, it is plain

x

that the redundant fluid in B will as much exceed the deficient in the trial plate as it before fell short of it. The mean between 4(x-1) these two surfaces is 16+ whereas it ought to have been 16, so that the error which will proceed from thence in finding the

> 2x

is less than half of the error which we are liable to in finding it the other way (or that in which we endeavour to find that surface of the trial plate with which the balls do not separate at all), though x is ever so great; for in that way it was before said that we were liable to an error of four. But if x is equal to 4, which is as great an error of strength as I think can well arise in charging the vials, even when the first mentioned electrometer is used, the error in finding the required surface is only of the whole surface, or only part of what might arise the other way.

251] Having thus found what surface must be given to the trial plate, in order that the deficience of fluid in it shall be equal to the redundance in B, I take away the body B and put the other body b, which I want to compare with it, in its room, and if I find on repeating the experiment that the trial plate must be drawn out to the same surface as before, in order that the deficience of fluid in it shall be equal to the redundance in b, or, in other words, if the required surface of the trial plate is the same in trying b as in trying B, I am well assured that if B and b were successively made to communicate with one of the vials, or with any other third body, and were positively electrified, they would each of them contain the same quantity of redundant fluid, supposing the quantity of redundant fluid in the third body to remain the same each time. On the other hand, if I find that the required surface of the trial plate is greater in trying b than in trying Bin the ratio of t to T, I am well assured that the quantity of redundant fluid in b would exceed that in B in the ratio of t to T, supposing, as was said before, that the deficience of fluid in the trial plate is in proportion to the square root of its surface.

252] If the reader should think that this conclusion requires any proof it may be thus demonstrated :

Suppose that in trying B it was found that the required surface of the trial plate was T2 and that in trying b it was ť2, and let us first suppose that the vials are charged in exactly the same degree in trying b as in trying B, then is the conclusion evident, for then are B and b successively made to communicate with the vial A, the charge of this vial being exactly the same each time, and the quantity of redundant fluid communicated to b is, actually, to that communicated to B as t to T. But it is plain that the conclusion is equally just, though the vials are charged higher in trying one than in trying the other. For though, in this case, the redundant fluid actually communicated to b will not be to that communicated to B in the ratio of t to T, yet we are sure that it would have been so if the vials had been charged in the same degree each time, for the required surfaces which must be given to the trial plate in trying b must evidently be the same whether the vials are charged to the same degree as they were in trying B, or to a different degree.

253] Though it is of no signification whether the vials are charged to the same degree in trying b as in trying B, yet it is necessary, as I said before, that in trying either B or b the vials should be charged nearly with the same strength when the balls are to separate positively as when they are to separate negatively, as otherwise a small error will arise in finding the required surface of the trial plate.

254] In all the following experiments I took care to proportion the size of the bodies B and b in such manner that the quantity of redundant fluid in one should not be very different from that in the other, so that, though the deficience of fluid in the trial plate should not be very nearly as the square root of its surface, it would make very little error in the conclusion.

255] The usual distance of the centers of B and J in these experiments was 83 inches, the distance of B from the vial A 106 inches, and that of T from a 86 inches, and the distance of the two vials about 10 inches*. The usual height of the body B and the trial plate above the ground was 50 inches; they were commonly supported upon pillars such as are represented in fig. 16, [See plan at Art. 265, details at Art. 466, and theory in Note 17.]

*

where Ee, Bb and Dd are three upright pillars of baked wood about 40 inches long, and ee, bß, and dƐ are sticks of glass 10 inches long and inch thick let into the wood, and covered with sealing-wax. ACGF is a piece of board which the pillars are fastened into. The points M, N, R, and S were each supported by a pillar of the same kind, and the point D was supported nearly in the same manner. In some experiments, however, the body B was suspended by silk strings. The wires dDS, rRSs, and mMNn were about inch thick.

256] It is well known that the air of a room is easily rendered over- or undercharged, in particular if a wire such as rRSs [Fig. 14] is positively electrified, though even in no greater degree than in these experiments, and kept so for a second or two, and its electricity then destroyed, the air near it will be sensibly overcharged, as may be thus shewn. Take a pair of pith balls, like those hung at D, and suspend them within a few feet of the wire from some body communicating with the ground. The balls will instantly separate on electrifying the wire on account of the repulsion of the redundant fluid in it, but they will also continue to separate, though in a less degree, after the electricity of the wire is destroyed, which can be owing only to the air being rendered overcharged by it.

257] It may be suspected that this electrification of the air by the wires may affect the separation of the pith balls at D and thereby cause an irregularity in the experiments, but it must be considered that the wire mMNn is made as much undercharged as rRSs is overcharged, and the pith balls are placed about equally distant from both, so that the undercharged air near one wire will nearly balance the effect of the overcharged air near the other. Besides that, if it had any effect upon the separation of the balls, it would have much the same effect in trying B as in trying b, and therefore could hardly cause any error in the result of the experiment. However, still further to obviate any error from that cause, I had a contrivance by which the electricity of the wires rRSs and mMNn, as well as that of the vials, was destroyed as soon as the wires rR and mM were lifted up from B and T.

258] It is necessary that the outside of the bottle A and the wire yz should have as perfect a communication with the ground as possible, as otherwise it might happen that the body B and the trial plate might not receive their full degree of electrification before the wires rR and mM were lifted up. I therefore made them to communicate by a piece of wire with the outside wall of the house. This I found to be sufficient, for if I charged a vial, making the outside to communicate with the outside wall, and then made a communication by another wire between the inside of the vial and another portion of the outside wall of the house at several feet distance from the other, I found the vial to be discharged instantly; but if I made the wires to communicate only with the floor of the room instead of the wall of the house, I found it took up some time before the vial was discharged.

It must be observed that in this case, where you want to carry off the electricity very fast by an imperfect conductor, such as the wall, the best way is to apply a pretty broad piece of metal to the wall, so as to touch it in a considerable surface, and to fasten the wire to that, which was the way I last made use of, for if you only apply the wire against the wall, as it will touch the wall only in a few points, the electricity will not escape near so fast.

259] In dry weather the linen threads by which the pith balls are suspended are very imperfect conductors, so that the balls are apt not to separate or close immediately on giving or

taking away the electricity. To remedy this inconvenience I moistened the threads with a solution of sea-salt, which I found answered the end perfectly well, for the threads after having been once moistened conveyed the electricity ever after very well, though the air was ever so dry.

260] As the charge of the vials A and a is continually diminishing from the time that the communication between them and the electrical machine is taken away, both by the electricity running along the surface of the vial from the inside to the outside, and by the waste of electricity from the wires rRSS and mMNn and their supports, it is necessary that the operation of electrifying B and T and lifting up the wires rR and mM should be performed as soon as possible, and, above all, it is necessary that the communication should be made between B and T as soon as possible after lifting up the wires rR and mM. This end was obtained very well by the manner, already described, of performing the operation.

261] Before I begin to relate the experiments, it will be proper to say something more about the accuracy that is to be expected in them. I before said that increasing or diminishing the surface of the trial plate by of what I called the required surface, i. e., that surface in which the deficience was equal to the redundance in B, made a sensible alteration in the distance to which the pith balls separated. In reality I found that increasing or diminishing it by only part of the required surface would in general make a sensible alteration, but I could not be certain to nearly so small a quantity, for it would frequently happen that after having determined the surface of the trial plate at which the balls separated to a given degree, that on repeating the experiment a little after, the balls would separate differently from what they did before, and that I was obliged to alter the surface of the trial plate by and sometimes even of the required surface in order to make the balls separate in the same degree as before. Therefore, as increasing the surface of the trial plate by part increases the deficience of fluid therein by 24 part, it appears that if the bodies B and b really contain the same quantity of redundant fluid, it might seem from the experiments as if B contained or even part more or less redundant fluid than b, so that I am liable to make an error of