For suppose that the canal NRS, instead of communicating with the plate DF, is bent back just before it touches it, and continued infinitely along the line Ss; the force with which the two plates impel the fluid in Ss, is the same with which they impel that in EL, supposing Ss to be of the same breadth and thickness as EL; and is therefore nothing; therefore the force with which they impel the fluid in NRS, is the same with which they impel that in NRSs; which is the same with which they impel that in CG.

89] PROP. XXVI. Let now xyz [Fig. 17] be a body of an infinite size, containing just fluid enough to saturate it; and let a communication be made between h and xyz, by the canal hy of incompressible fluid, of the same breadth and thickness as gc or GC; the fluid will flow through it from h to xyz; and the force with which the fluid in that canal is impelled along it, is equal to that with which the fluid in NRS is impelled by the two plates.

If the canal hy is of so great a length, that the repulsion of h thereon is the same as if it was continued infinitely, then the thing is evident: but if it is not, let the canal hy, instead of communicating with xyz, so that the fluid can flow out of the canal into xyz, be continued infinitely through its substance, along the line yv now it must be observed that a small part of the body xyz, namely, that which is turned towards h, will by the action of h upon it, be rendered undercharged; but all the rest of the body will be saturated; for the fluid driven out of the undercharged part will not make the remainder, which is supposed to be of an infinite size, sensibly overcharged: now the force with which the fluid in the infinite canal hyv is impelled by the body h and the undercharged part of xyz, is the same with which the fluid in gc is impelled by them; but as the fluid in all parts of xyz is in equilibrio, a particle in any part of yv cannot be impelled in any direction; and therefore the fluid in hy is impelled with as much force as that in hyv; and therefore the fluid in hy is impelled with as much force as that in gc; and is therefore impelled with as much force as the fluid in NRS is impelled by the two plates.

90] It perhaps may be asked, whether this method of demonstration would not equally tend to prove that the fluid in hy was impelled with the same force as that in NRS, though xyz did not

contain just fluid enough to saturate it. I answer not; for this demonstration depends on the canal yv being continued, within the body xyz, to an infinite distance beyond any over or undercharged part; which could not be if xyz contained either more or less fluid than that *.

91] PROP. XXVII. Let two bodies B and b (Fig. 13) be joined by a cylindric or prismatic canal Aa, filled with real fluid; and not by any imaginary canal of incompressible fluid as in the 20th proposition; and let the fluid therein be in equilibrio : the force with which the whole or any given part of the fluid in the canal is impelled in the direction of its axis by the united repulsions and attractions of the redundant fluid or matter in the two bodies and the canal, must be nothing; or the force with which it is impelled one way in the direction of the axis of the canal, must be equal to that with which it is impelled the other way.

For as the canal is supposed cylindric or prismatic, no particle of fluid therein can be prevented from moving in the direction of the axis of it, by the sides of the canal; and therefore the force with which each particle is impelled either way in the direction of the axis, by the united attractions and repulsions of the two bodies and the canal, must be nothing, otherwise it could not be at rest; and therefore the force with which the whole, or any given part of the fluid in the canal, is impelled in the direction of the axis, must be nothing.

92] COR. I. If the fluid in the canal is disposed in such manner, that the repulsion or attraction of the redundant fluid or matter in it, on the whole or any given part of the fluid in the canal, has no tendency to impel it either way in the direction of the axis; then the force with which that whole or given part is impelled by the two bodies must be nothing; or the force with which it is impelled one way in the direction of the axis, by the body B, must be equal to that with which it is impelled in the contrary direction by the other body; but not if the fluid in the canal is disposed in a different manner.

93] COR. II. If the bodies, and consequently the canal, is overcharged; then, in whatever manner the fluid in the canal is disposed, the force with which the whole quantity of redundant fluid in the canal is repelled by the body B in the direction Aa,

[* Note 5.]

must be equal to that with which it is repelled by b in the contrary direction. For the force with which the redundant fluid is impelled in the direction Aa by its own repulsion, is nothing; for the repulsions of the particles of any body on each other have no tendency to make the whole body move in any direction.

94] REMARKS. When I first thought of the 20th and 22nd propositions, I imagined that when two bodies were connected by a cylindric canal of real fluid, the repulsion of one body on the whole quantity of fluid in the canal, in one direction, would be equal to that of the other body on it in the contrary direction, in whatever manner the fluid was disposed in the canal; and that therefore those propositions would have held good very nearly, though the bodies were joined by cylindric canals of real fluid; provided the bodies were so little over or undercharged, that the quantity of redundant or deficient fluid in the canal should be very small in respect of the quantity required to saturate it; and consequently that the fluid therein should be very nearly of the same density in all parts. But from the foregoing proposition it appears that I was mistaken, and that the repulsion of one body on the fluid in the canal is not equal to that of the other body on it, unless the fluid in the canal is disposed in a particular manner: besides that, when two bodies are both joined by a real canal, the attraction or repulsion of the redundant matter or fluid in the canal has some tendency to alter the disposition of the fluid in the two bodies; and in the 22nd proposition, the canal CG exerts also some attraction or repulsion on the canal EM: on all which accounts the demonstration of those propositions is defective, when the bodies are joined by real canals. I have good reason however to think, that those propositions actually hold good very nearly when the bodies are joined by real canals; and that, whether the canals are straight or crooked, or in whatever direction the bodies are situated in respect of each other: though I am by no means able to prove that they do: I therefore chose still to retain those propositions, but to demonstrate them on this ideal supposition, in which they are certainly true, in hopes that some more skilful mathematician may be able to shew whether they really hold good or not. [See Note 3.]

95] What principally makes me think that this is the case, is that as far as I can judge from some experiments I have made*, [* Exp. III., Art. 265.]

the quantity of fluid in different bodies agrees very well with those propositions, on a supposition that the electric repulsion is inversely as the square of the distance. It should also seem from those experiments, that the quantity of redundant or deficient fluid in two bodies bore very nearly the same proportion to each other, whatever is the shape of the canal by which they are joined, or in whatever direction they are situated in respect of each other.

96] Though the above propositions should be found not to hold good when the bodies are joined by real canals, still it is evident, that in the 22nd proposition, if the plates AB and DF are very near together, the quantity of redundant fluid in the plate AB will be many times greater than that in the body H, supposing H to consist of a circular plate of the same size as AB, and DF will be near as much undercharged as AB is overcharged.

97] Sir Isaac Newton supposes that air consists of particles which repel each other with a force inversely as the distance: but it appears plainly from the foregoing pages, that if the repulsion of the particles was in this ratio; and extended indefinitely to all distances, they would compose a fluid extremely different from common air. If the repulsion of the particles was inversely as the distance, but extended only to a given very small distance from their centers, they would compose a fluid of the same kind as air, in respect of elasticity, except that its density would not be in proportion to its compression: if the distance to which the repulsion extends, though very small, is yet many times greater than the distance of the particles from each other, it might be shewn, that the density of the fluid would be nearly as the square root of the compression. If the repulsion of the particles extended indefinitely, and was inversely as some higher power of the distance than the cube, the density of the fluid would be as some power of the compression less than . The only law of repulsion, I can think of, which will agree with experiment, is one which seems not very likely; namely, that the particles repel each other with a force inversely as the distance; but that, whether the density of the fluid is great or small, the repulsion extends only to the nearest particles: or, what comes to the same thing, that the distance to which the repulsion extends, is very small, and also is not fixed, but varies in proportion to the distance of the particles *.

[* Note 6.]

PART II.

CONTAINING A COMPARISON OF THE FOREGOING THEORY WITH EXPERIMENT.

98] 1. IT appears from experiment, that some bodies suffer the electric fluid to pass with great readiness between their pores; while others will not suffer it to do so without great difficulty; and some hardly suffer it to do so at all. The first sort of bodies are called conductors, the others non-conductors. What this difference in bodies is owing to I do not pretend to explain.

It is evident that the electric fluid in conductors may be considered as moveable, or answers to the definition given of that term in page 6. As to the fluid contained in non-conducting substances, though it does not absolutely answer to the definition of immoveable, as it is not absolutely confined from moving, but only does so with great difficulty; yet it may in most cases be looked upon as such without sensible error.

99] Air does in some measure permit the electric fluid to pass through it; though, if it is dry, it lets it pass but very slowly, and not without difficulty; it is therefore to be called a nonconductor.

:

It appears that conductors would readily suffer the fluid to run in and out of them, were it not for the air which surrounds. them for if the end of a conductor is inserted into a vacuum, the fluid runs in and out of it with perfect readiness; but when it is surrounded on all sides by the air, as no fluid can run out of it without running into the air, the fluid will not do so without difficulty.

100] If any body is surrounded on all sides by the air, or other non-conducting substances, it is said to be insulated if on the