246. This way of making the experiment I found much more accurate than the other, for supposing the required surface of the trial plate to be expressed by the number 16, I found that its surface must be increased to about 20 before I could be certain that the pith balls would separate negatively, and that it must be diminished to about 12 before they would separate positively; whereas I found that increasing its surface from 20 to 21 would make the balls separate sensibly further, and that diminishing its surface from 12 to 11 would have the same effect; so that I could determine the required surface of the trial plate at least four times more exactly by the latter method than by the former.

247] It will be shewn hereafter* that the quantity of deficient fluid in the trial plate is in proportion to the square root of its surface; consequently the redundant fluid in B must exceed, or fall short of, the deficient fluid in the trial plate by about 4th part, in order that the balls should separate, and moreover the increasing or diminishing the deficience of fluid in the trial plate by about part will make a sensible difference in the separa

tion of the balls.

248] It is plain that this way of finding the required surface of the trial plate is not just, unless the vials are charged equally in both trials, namely, that in which the balls separate positively and that in which they separate negatively; I therefore fastened an electrometer to the wire Pp, at a sufficient distance from the vials, consisting of two paper cylinders about three-quarters of an inch in diameter and one inch in height, suspended by linen threads about eight inches long, and in changing the vials took care always to turn the globet till these cylinders just began to separate.

249] In all the later experiments, however, I made use of a more exact kind of electrometer, consisting of two wheaten straws, Aa and Bb (Fig. 30), eleven inches long, with cork balls A and B at the bottom, each one-third of an inch in diameter, and supported at a and b by fine steel pins bearing on notches in the brass plate C, and turning on these pins as centers. This electrometer was suspended by the piece of brass C from the prime conductor, and a piece of pasteboard, with two black lines drawn upon it, was placed six inches behind the electrometer on a level with the balls, in order to judge of the distance to which the balls separated, the eye being placed before the electrometer at thirty inches distance [Arts. 284, 479, 682.]

+ [Of Nairne's electrical machine, see Art. 563.]

from them (a guide for the eye being placed for that purpose*), and the electrical machine was turned till the balls appeared even

with those lines. By these means I could judge of the strength of the electricity to a considerable degree of exactness. In order to make the straws conduct the better they were gilt over.

250] In order to estimate what error may arise from the vials being not equally charged in both trials, let the required surface of the trial plate be called 16; then must the surface which must be given to it in order that the balls may separate negatively be 20, or 16+4, supposing the vials to be charged with the usual degree of strength. Suppose now that in the next trial, in which the balls are to separate positively, the vials are charged stronger than before, in the ratio of a to 1, so that the quantity of redundant fluid in B shall be greater than before, in the ratio of x to 1, and that the deficience in the trial plate should be greater than before in the same ratio, provided its surface remained unaltered; then must the surface which must be given to the trial plate, in

It is necessary that the eye should always be placed nearly at the same distance from the electrometer, as it is evident that the nearer the eye is placed the further the balls will appear to separate. But as the distance of the balls from the eye is so much greater than their distance from the pasteboard, a small alteration in the distance of the balls either from the eye or the pasteboard will make no sensible alteration in the distance to which the balls appear to separate.

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

4

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

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 these two surfaces is 16+ whereas it ought to have been

4(x-1)
2x

16, so that the error which will proceed from thence in finding the 2(x-1), and, consequently,

required surface of the trial plate is x

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 ť, 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 d8 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 dD8, rRSs, and mMNn were about inch thick.

Fig.16

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.