be made more accurately than any other, and with such an electrometer P, should be adjusted to zero. But the only electrometer which Cavendish possessed was the pith ball electrometer, in which the repulsion between the balls when at any given distance depends on the square of the electrification, and in which therefore the indications are very feeble for low degrees of electrification. Cavendish therefore first adjusted his trial plate so as to produce a given amount of separation of the balls by positive electrification, and then altered the trial plate so as to produce an equal separation by negative electrification. In each case he has recorded a number expressing the side of a square electrically equivalent to the trial plate, together with the difference and the mean of the two values.

He seems to have adopted the arithmetical mean as a measure of the charge of the body to be tried. It is easy to see, however, that the geometrical mean would be a more accurate value. For, if we denote the values of the final potential of the trial plate by accented letters in the second trial, we have

P2' ([C3] + [D'3] + [E3]) = P。 ([C2] − [D ́2]).

Since P+P=0, we find by (6) and (7)

[C3] ([C3] + [E3]) = [D2] [D′3] + } [E2] ([D2] + [D'2]).

(7)

If we neglect the capacity of the pith ball electrometer, which is much less than that of the bodies usually tried, this equation becomes

[C2]2 = [D3] [D''],

or the capacity of the body tried is the geometrical mean of the capacities of the trial-plate in its positive and negative adjustments.

NOTE 18, ART. 216.

On the "Thoughts Concerning Electricity," and on an early draft of the Propositions in Electricity.

The theory of electricity sketched in the "Thoughts" is evidently an earlier form of that developed in the published paper of 1771. We must therefore consider the "Thoughts" as the first recorded form of Cavendish's theory, and this for the following reasons.

(1) Nothing is said in the "Thoughts" of the forces exerted by ordinary matter on itself and on the electric fluid. The only agent considered is the electric fluid itself, the particles of which are supposed to repel each other. This fluid is supposed to exist in all bodies whether apparently electrified or not, but when the quantity of the fluid in any body is greater than a certain value, called the natural quantity for the body, the body is said to be overcharged, and when the quantity is less than the natural quantity the body is said to be undercharged.

The forces exerted by undercharged bodies are ascribed, not, as in the later theory, to the redundant matter in the body, but to the repulsion of the fluid in other parts of space.

The theory is therefore simpler than in its final form, but it tacitly assumes that the fluid could exist in stable equilibrium if spread with uniform density over all space, whereas it appears from the investigations of Cavendish himself that a fluid whose particles repel each other with a force inversely as any power of the distance less than the cube would be in unstable equilibrium if its density were uniform.

This objection does not apply to the later form of the theory, for in it the equilibrium of the electric fluid in a saturated body is rendered stable by the attraction exerted by the fixed particles of ordinary matter on those of the electric fluid.

(2) The hypotheses are reduced in the later theory to one, and the third and fourth hypotheses of the "Thoughts" are deduced from this.

(3) In the "Thoughts" Cavendish appears to be acquainted only with those phenomena of electricity which can be observed without quantitative experiments. Some of his remarks, especially those on the spark, he repeats in the paper of 1771, but in that paper (Art. 95) he refers to certain quantitative experiments, the particulars of which are now first published [Art. 265].

The "Thoughts," however, though Cavendish himself would have considered them entirely superseded by the paper of 1771, have a scientific interest of their own, as showing the path by which Cavendish arrived at his final theory.

He begins by getting rid of the electric atmospheres which were still clinging to electrified bodies, and he appears to have done this so completely that he does not think it worth while even to mention them in the paper of 1771.

He then introduces the phrase "degree of electrification" and gives a quantitative definition to it, so that this, the leading idea of his whole research, was fully developed at the early date of the "Thoughts."

Several expressions which Cavendish freely used in his own notes and journals, but which he avoided in his printed papers, occur in the "Thoughts."

Thus he speaks of the "compression" or pressure of the electric fluid.

Besides the "Thoughts," which may be considered as the original form of the introduction to the paper of 1771, there is a mathematical paper corresponding to the Propositions and Lemmata of the published paper, but following the earlier form of the theory, in which the forces exerted by ordinary matter are not considered, and referring directly to the "Hypotheses" of the "Thoughts."

The first part of this paper is carefully written out, but it gradually becomes more and more unfinished, and at last terminates abruptly, though, as this occurs at the end of a page, we may suppose that the end of the paper has been lost. I think it probable, however, that when

Cavendish had advanced so far, he was beginning to see his way to the form of the theory which he finally published, and that he did not care to finish the manuscript of the imperfect theory.

The general theory of fluids repelling according to any inverse power of the distance is given much more fully than in the paper of 1771, and the remarks on the constitution of air are very interesting.

I have therefore printed this paper, but in order to avoid interrupting the reader with a repetition of much of what he has already seen, I have placed it at the end of this Note.

CAVENDISH'S FIRST MATHEMATICAL THEORY *.

α

B

Let a fluid whose particles mutually repel each other be spread uniformly through infinite space. Let a be a particle of that fluid; draw the cone baß continued infinitely, and draw the section bẞ: if the repulsion of the particles is inversely as any higher power of the distance than the cube, the particle a will be repelled with infinitely more force from the particles between a and bẞ than from all those situated beyond it, but if their repulsion is inversely as any less power than the cube, then the repulsion of the particles placed beyond bẞ is infinitely greater than that of those between a and bẞ.

If the repulsion of the particles is inversely as the n power of the distance, n being greater than 3, it would constitute an elastic fluid of the same nature as air, except that its elasticity would be inversely as the n+2 power of the distance of the particles, or directly as the n+2 power of the density of the fluid.

3

But if n is equal to, or less than 3, it will form a fluid of a very different kind from air, as will appear from what follows.

B

COR. 1. Let a fluid of the above-mentioned kind be spread uniformly through infinite space except in the hollow globe BDE, and let the sides of the globe be so thin that the force with which a particle placed contiguous to the sides of the globe would be repelled by so much of the fluid as might be lodged within the space occupied by the sides of the globe should be trifling in respect of the repulsion of the whole quantity of fluid in the globe.

If the fluid within the globe was of the same density as without, the particles of the fluid adjacent to either the inside or outside

P

7

surface of the globe would not press against those surfaces with any sensible force, as they would be repelled with the same force by the fluid on each side of them. But if the fluid within the globe is denser

* From MS. bundle 17.

than that without, then any particle adjacent to the inside surface of the globe will be pressed against by the repulsion of so much of the fluid within the globe as exceeds what would be contained in the same space if it was of the same density as without, and consequently will be greater if the globe be large than if it be small. Consequently the pressure against a given quantity (a square inch for example) of the inside surface of the globe will be greater if the globe is large than if it is small.

If the particles of the fluid repel each other with a force inversely as their distance, the pressure against a given quantity of the inside surface would be as the square of the diameter of the globe. So that it is plain that air cannot consist of particles repelling each other in the above-mentioned manner.

If the repulsion of the particles was inversely as some higher power of the distance than the cube, then any particle of the fluid would not be sensibly affected except by the repulsion of those particles which were almost close to it, so that the pressure of the fluid against a given quantity of the inside surface would be the same whatever was the size of the globe, but then the elasticity [would] be in a greater proportion than that of the power of the density.

If the repulsion of the particles is inversely as some less power than the cube of the distance, and the density of the fluid within the globe is less than it is without, then the particles on the outside of the globe will press against it, and the force will be greater if the globe is large than if it be small.

If the density of the fluid within the globe be greater than without, then the density will not be the same in all parts of the globe, but will be greater near the surface and less near the middle, for if you suppose the density to be everywhere the same, then any particle of the fluid, as d, would be pressed with more force towards a, the nearest part of the surface of the sphere, than it would [be] in the contrary direction.

If the repulsion of the particles is inversely as the square of the distance, I think the inside of the sphere would be uniformly coated with the fluid to a certain thickness, in which the density would be infinite, or the particles would be pressed close together, and in all the space within that, the density would be the same as on the outside of the sphere.

The pressure of a particle adjacent to the inside surface against it is equal to the repulsion of all the redundant matter in the sphere collected in the center, and the force with which a particle is pressed towards the surface of the sphere diminishes in arithmetical progression in going from the inside surface to that point at which its density begins to be the same as without, therefore the whole pressure against the inside of the sphere is equal to that of half the redundant matter in the sphere pressed by the repulsion of all the redundant matter collected in the center of the sphere.

Therefore, if the quantity of fluid in the sphere is such that its

density, if uniform, would be 1+d, and the radius of the sphere be called r, the whole pressure against the inside surface will be as dr.3 dr.3

2

and the pressure against a given space of the inside surface will be as d2r2.

JP

If this pressure be called P, d is as and dr3 is as r2 P. Con

sequently, supposing the fluid to be pumped into different sized globes, the quantity of fluid pumped in will be as the square root [of the force] with which it is pumped, multiplied by the square of the diameter of the globe.

If the density within the sphere is less than without, then the density within the sphere will not be uniform, but will be greater towards the middle and less towards the outside, and if the repulsion of the particles is inversely as the square of the distance, there would be a sphere concentric to the hollow globe in which the density would be the same as on the outside of the globe, and all between that and the inside surface of the globe would be a vacuum.

From these corollaries it follows that if the electric fluid is of the nature here described, and is spread uniformly through bodies, except when they give signs of electricity, that then if two similar bodies of different sizes be equally electrified, the larger body will receive much less additional electricity in proportion to its bulk than the smaller one, and moreover when a body is electrified, the additional electricity will be lodged in greater quantity near the surface of the body than near the middle.

Let us now suppose the fluid within the globe BDE to be denser than without, and let us consider [in what manner] the fluid without will be affected thereby.

1st. There will be a certain space surrounding the globe, as ẞde, which will be a perfect vacuum, for first let us suppose that the density without the globe is uniform, then any particle would be repelled with more force from the globe than in the contrary direction.

2ndly. Let us suppose that the space ẞde, BDE is not a vacuum, but rarer than the rest of the fluid; still a particle placed close to the surface of the globe would be repelled from it with more force than in the contrary direction.

3rdly. Let us [suppose that] the density in the space between BDE and Boe is greater than without, then according to some hypothesis of the law of repulsion a particle placed at B might be in equilibrium, but one placed at ẞ could by no means be so.

So that there is no way by which the particles can be in equilibrium, unless there is a vacuum all round the globe to a certain distance. How the density of the fluid will be affected beyond this vacuum I cannot exactly tell, except in the following case:

If the repulsion of the particles is inversely as the square of the distance, there will be a perfect vacuum between BDE and ẞde, and