AN ATTEMPT TO EXPLAIN SOME OF THE PRINCIPAL PHÆNOMENA OF ELECTRICITY, BY MEANS OF AN ELASTIC FLUID.

1] SINCE I first wrote the following paper, I find that this way of accounting for the phænomena of electricity is not new. Æpinus, in his Tentamen Theorie Electricitatis et Magnetismi*, has made use of the same, or nearly the same hypothesis that I have; and the conclusions he draws from it agree nearly with mine, as far as he goes. However, as I have carried the theory much farther than he has done, and have considered the subject in a different, and, I flatter myself, in a more accurate manner, I hope the Society will not think this paper unworthy of their acceptance.

2] The method I propose to follow is, first, to lay down the hypothesis; next, to examine by strict mathematical reasoning, or at least, as strict reasoning as the nature of the subject will admit of, what consequences will flow from thence; and lastly, to examine how far these consequences agree with such experiments as have yet been made on this subject. In a future paper, I intend to give the result of some experiments I am making, with intent to examine still further the truth of this hypothesis, and to find out the law of the electric attraction and repulsion.

HYPOTHESIS.

3] There is a substance, which I call the electric fluid, the particles of which repel each other and attract the particles of all other matter with a force inversely as some less power of the distance than the cube: the particles of all other matter also, repel each other, and attract those of the electric fluid, with a force

* [Petropoli, 1759.]

varying according to the same power of the distances. Or, to express it more concisely, if you look upon the electric fluid as matter of a contrary kind to other matter, the particles of all matter, both those of the electric fluid and of other matter, repel particles of the same kind, and attract those of a contrary kind, with a force inversely as some less power of the distance than the cube.

4] For the future, I would be understood never to comprehend the electric fluid under the word matter, but only some other sort of matter.

5] It is indifferent whether you suppose all sorts of matter to be indued in an equal degree with the foregoing attraction and repulsion, or whether you suppose some sorts to be indued with it · in a greater degree than others; but it is likely that the electric fluid is indued with this property in a much greater degree than other matter; for in all probability the weight of the electric fluid in any body bears but a very small proportion to the weight of the matter; but yet the force with which the electric fluid therein attracts any particle of matter must be equal to the force with which the matter therein repels that particle; otherwise the body would appear electrical, as will be shewn hereafter.

To explain this hypothesis more fully, suppose that 1 grain of electric fluid attracts a particle of matter, at a given distance, with as much force as n grains of any matter, lead for instance, repel it: then will 1 grain of electric fluid repel a particle of electric fluid with as much force as n grains of lead attract it; and 1 grain of electric fluid will repel 1 grain of electric fluid with as much force as n grains of lead repel n grains of lead *.

6] All bodies in their natural state with regard to electricity, contain such a quantity of electric fluid interspersed between their particles, that the attraction of the electric fluid in any small part of the body on a given particle of matter shall be equal to the repulsion of the matter in the same small part on the same particle. A body in this state I call saturated with electric fluid: if the body contains more than this quantity of electric fluid, I call it overcharged if less, I call it undercharged. This is the hypothesis; I now proceed to examine the consequences which will flow from it.

* [Note 1.]

Fig. 1.

E

D

B

A

7] LEMMA I. Let EAe (Fig. 1) represent a cone continued infinitely; let A be the vertex, and Bb and Dd planes parallel to the base; and let the cone be filled with uniform matter, whose particles repel each other with a force inversely as the n power of the distance. If n is greater than 3, the force with which a particle at A is repelled

by EBbe or all that part of the cone beyond Bb is as

1 AB

в

For supposing AB to flow, the fluxion of EBbe is proportional to - ABX AB, and the fluxion of its repulsion on A is propor

- AB tional to ABR-23

the fluent of which is

1

(n − 3) AB-s; which when

AB is infinite is equal to nothing; consequently the repulsion of

1 is infinitely great; AB-3

8] COR. If AB is infinitely small, therefore the repulsion of that part of the cone between A and Bb, on A, is infinitely greater than the repulsion of all that beyond it.

9] LEMMA II. By the same method of reasoning it appears, that if n is equal to 3, the repulsion of the matter between Bb and Dd on a particle at A, is proportional to the logarithm of ; AB

AD

consequently, the repulsion of that part is infinitely small in respect of that between A and Bb, and also infinitely small in respect of that beyond Dd.

10] LEMMA III. In like manner, if n is less than 3, the repulsion of the part between A and Bb on A is proportional to AB": consequently the repulsion of the matter between A and Bb on A, is infinitely small in respect of that beyond it.

11] COR. It is easy to see from these three lemmata, that, if the electric attraction and repulsion had been supposed to be inversely as some higher power of the distance than the cube; a particle could not have been sensibly affected by the repulsion of any fluid, except what was placed close to it. If the repulsion was inversely as the cube of the distance, a particle could not be

sensibly affected by the repulsion of any finite quantity of fluid, except what was close to it. But as the repulsion is supposed to be inversely as some power of the distance less than the cube, a particle may be sensibly affected by the repulsion of a finite quantity of fluid, placed at any finite distance from it.

12] DEF. If the electric fluid in any body is by any means confined in such manner that it cannot move from one part of the body to the other, I call it immoveable: if it is able to move readily from one part to another, I call it moveable.

13] PROP. I. A body overcharged with electric fluid attracts or repels a particle of matter or fluid, and is attracted or repelled by it, with exactly the same force as it would, if the matter in it, together with so much of the fluid as is sufficient to saturate it, was taken away, or as if the body consisted only of the redundant fluid in it. In like manner an undercharged body attracts or repels with the same force, as if it consisted only of the redundant matter; the electric fluid, together with so much of the matter as is sufficient to saturate it, being taken away.

This is evident from the definition of saturation.

14] PROP. II. Two over or undercharged bodies attract or repel each other with just the same force that they would, if each body consisted only of the redundant fluid in it, if overcharged, or of the redundant matter in it, if undercharged.

For, let the two bodies be called A and B; by the last proposition the redundant substance in B impels each particle of fluid and matter in A, and consequently impels the whole body A, with the same force that the whole body B impels it for the same reason the redundant substance in A impels the redundant substance in B, with the same force that the whole body A impels it. It is shewn therefore, that the whole body B impels the whole body A, with the same force that the redundant substance in B impels the whole body A, or with which the whole body A impels the redundant substance in B; and that the whole body A impels the redundant substance in B, with the same force that the redundant substance in A impels the redundant substance in B; therefore the whole body B impels the whole body A, with

the same force with which the redundant substance in A impels the redundant substance in B, or with which the redundant substance in B impels the redundant substance in A.

15] COR. Let the matter in all the rest of space, except in two given bodies, be saturated with immoveable fluid; and let the fluid in those two bodies be also immoveable. Then, if one of the bodies is saturated, and the other either over or undercharged, they will not at all attract or repel each other.

If the bodies are both overcharged, they will repel each other. If they are both undercharged, they will also repel each other. If one is overcharged and the other undercharged, they will attract each other.

N.B. In this corollary, when I call a body overcharged, I would be understood to mean, that it is overcharged in all parts, or at least nowhere undercharged: in like manner, when I call it undercharged, I mean that it is undercharged in all parts, or at least nowhere overcharged.

16] PROP. III. If all the bodies in the universe are saturated with electric fluid, it is plain that no part of the fluid can have any tendency to move.

17] PROP. IV. If the quantity of electric fluid in the universe is exactly sufficient to saturate the matter therein, but unequally dispersed, so that some bodies are overcharged and others undercharged; then, if the electric fluid is not confined, it will immediately move till all the bodies in the universe are saturated.

For supposing that any body is overcharged, and the bodies near it are not, a particle at the surface of that body will be repelled from it by the redundant fluid within; consequently some fluid will run out of that body; but if the body is undercharged, a particle at its surface will be attracted towards the body by the redundant matter within, so that some fluid will run into the body.

N.B. In Prob. IV. Case 3, there will be shewn an exception to this proposition; there may perhaps be some other exceptions to it: but I think there can be no doubt, but what this proposition must hold good in general.