the center, and the matter near the surface will be entirely deprived of fluid. It is likely too, if the repulsion is inversely as some higher power of the distance than the square, that all parts of the body will be undercharged: if it is inversely as the square, that all parts, except near the surface, will be saturated and if it is inversely as some less power than the square, that all parts, except near the surface, will be overcharged.

43] PROP. X. Let the bodies A and D (Fig. 5) communicate Fig. 5.

with each other by the canal EF; and let one of them, as D, be overcharged; the other body A will be so also.

For as the fluid in the canal is repelled by the redundant fluid in D, it is plain, that unless A was overcharged, so as to balance that repulsion, the fluid would run out of D into A.

In like manner, if one is undercharged, the other must be so too.

44] PROP. XI. Let the body A (Fig. 6) be either saturated or over or undercharged; and let the fluid within it be in equilibrio. Let now the body B, placed near it, be rendered overcharged, the fluid within it being supposed immoveable, and disposed in such manner, that no part of it shall be undercharged; the fluid in A will no longer be in equilibrio, but will

Fig. 6.

M

R

B

A

be repelled from B: therefore, the fluid will flow from those parts of A which are nearest to B, to those which are more distant from it; and, consequently, the part adjacent to MN (that part of the surface of A which is turned towards B) will be made to contain less electric fluid than it did before, and that adjacent to the opposite surface RS will contain more than before.

48]

ELECTRIFICATION BY INDUCTION.

19

It must be observed, that when a sufficient quantity of fluid has flowed from MN towards RS, the repulsion which the fluid in the part adjacent to MN exerts on the rest of the fluid in A, will be so much weakened, and the repulsion of that in the part near RS will be so much increased, as to compensate the repulsion of B, which will prevent any more fluid flowing from MN to RS.

The reason why I suppose the fluid in B to be immoveable is, that otherwise a question might arise, whether the attraction or repulsion of the body A might not cause such an alteration in the disposition of the fluid in B, as to cause some parts of it to be undercharged; which might make it doubtful, whether B did on the whole repel the fluid in A. It is evident, however, that this proposition would hold good, though some parts of B were undercharged, provided it did on the whole repel the fluid in A.

45] COR. If B had been made undercharged, instead of overcharged, it is plain that some fluid would have flowed from the further part RS to the nearer part MN, instead of from MN to RS.

46] PROP. XII. Let us now suppose that the body A communicates by the canal EF, with another body D, placed on the contrary side of it from B, as in Fig. 5; and let these two bodies be either saturated, or over or undercharged; and let the fluid within them be in equilibrio. Let now the body B be overcharged: it is plain that some fluid will be driven from the nearer part MN to the further part RS, as in the former proposition; and also some fluid will be driven from RS, through the canal, to the body D; so that the quantity of fluid in D will be increased thereby, and the quantity in A, taking the whole body together, will be diminished; the quantity in the part near MN will also be diminished; but whether the quantity in the part near RS will be diminished or not, does not appear for certain; but I should imagine it would be not much altered.

47] COR. In like manner, if B is made undercharged, some fluid will flow from D to A, and also from that part of A near RS, to the part near MN.

48] PROP. XIII. Suppose now that the bodies A and D communicate by the bent canal MPNnpm (Fig. 7) instead of the straight one EF: let the bodies be either saturated or over or under

charged as before; and let the fluid be at rest; then if the body B

B

Fig. 7.

N

is made overcharged, some fluid will still run out of A into D; provided the repulsion of B on the fluid in the canal is not too great.

The repulsion of B on the fluid in the canal will at first drive some fluid out of the leg MPpm into A, and out of NPpn into D, till the quantity of fluid in that part of the canal which is nearest to B is so much diminished, and its repulsion on the rest of the fluid in the canal is so much diminished also as to compensate the repulsion of B: but as the leg NPpn is longer than the other, the repulsion of B on the fluid in it will be greater; consequently some fluid will run out of A into D, on the same principle that water is drawn out of a vessel through a siphon.

49] But if the repulsion of B on the fluid in the canal is so great, as to drive all the fluid out of the space GPHPG, so that the fluid in the leg MGpm does not join to that in NHpn; then it is plain that no fluid can run out of A into D; any more than water will run out of a vessel through a siphon, if the height of the bend of the siphon above the water in the vessel, is greater than that to which water will rise in vacuo.

50] COR. If B is made undercharged, some fluid will run out of D into A; and that though the attraction of B on the fluid in the canal is ever so great.

Fig. 8.

51] PROP. XIV. Let ABC (Fig. 8) be a body overcharged with immoveable fluid, uniformly spread; let the bodies near ABC on the outside be saturated with immoveable fluid; and let D be a body inclosed within ABC, and communicating by the canal DG with other distant bodies saturated with fluid; and let the fluid in D and the canal and

F

D

54]

ELECTRIFICATION BY INDUCTION.

21

those bodies be moveable; then will the body D be rendered undercharged.

For let us first suppose that D and the canal are saturated, and that D is nearer to B than to the opposite part of the body, C'; then will all the fluid in the canal be repelled from C by the redundant fluid in ABC; but if D is nearer to C than to B, take the point F, such that a particle placed there would be repelled from C with as much force as one at D is repelled towards C; the fluid in DF, taking the whole together, will be repelled with as much force one way as the other; and the fluid in FG is all of it repelled from C: therefore in both cases the fluid in the canal, taking the whole together, is repelled from C'; consequently some fluid will run out of D and the canal, till the attraction of the unsaturated matter therein is sufficient to balance the repulsion of the redundant fluid in ABC.

52] PROP. XV. If we now suppose that the fluid on the outside of ABC is moveable; the matter adjacent to ABC on the outside will become undercharged. I see no reason however to think that that will prevent the body D from being undercharged; but I cannot say exactly what effect it will have, except when ABC is spherical and the repulsion is inversely as the square of the distance; in this case it appears by Prob. I. that the fluid in the part DB of the canal will be repelled from C, with just as much force as in the last proposition; but the fluid in the part BG will not be repelled at all: consequently D will be undercharged, but not so much as in the last proposition.

53] COR. If ABC is now supposed to be undercharged, it is certain that D will be overcharged, provided the matter near ABC on the outside is saturated with immoveable fluid; and there is great reason to think that it will be so, though the fluid in that matter is moveable.

54] PROP. XVI. Let AEFB (Fig. 9) be a long cylindric body, and D an undercharged

body; and let the quantity of

Fig. 9.

fluid in AEFB be such, that the part near EF shall be saturated. It appears from what has been

α

D

said before, that the part near AB will be overcharged; and more

over there will be a certain space, as AabB, adjoining to the plane AB, in which the fluid will be pressed close together; and the fluid in that space will press against the plane AB, and will endeavour to escape from it; and by Prop. II. the two bodies will attract each other: now I say that the force with which the fluid presses against the plane AB, is very nearly the same with which the two bodies attract each other in the direction EA; provided that no part of AEFB is undercharged.

Suppose so much of the fluid in each part of the cylinder as is sufficient to saturate the matter in that part, to become solid; the remainder, or the redundant fluid remaining fluid as before. In this case the pressure against the plane AB must be exactly equal to that with which the two bodies attract each other in the direction EA for the force with which D attracts that part of the fluid which we supposed to become solid, is exactly equal to that with which it repels the matter in the cylinder; and the redundant fluid in Eab F is at liberty to move, if it had any tendency to do so, without moving the cylinder; so that the only thing which has any tendency to impel the cylinder in the direction EA is the pressure of the redundant fluid in AabB against AB; and as the part near EF is saturated, there is no redundant fluid to press against the plane EF, and thereby to counteract the pressure against AB. Suppose now all the electric fluid in the cylinder to become fluid; the force with which the two bodies attract each other will remain exactly the same; and the only alteration in the pressure against AB, will be, that that part of the fluid in AabB, which we at first supposed solid and unable to press against the plane, will now be at liberty to press against it; but as the density of the fluid when its particles are pressed close together may be supposed many times greater than when it is no denser than sufficient to saturate the matter in the cylinder, and consequently the quantity of redundant fluid in AabB many times greater than that which is required to saturate the matter therein, it follows that the pressure against AB will be very little more than on the first supposition.

N.B. If any part of the cylinder is undercharged, the pressure against AB is greater than the force with which the bodies attract. If the electric repulsion is inversely as the square or some higher power of the distance, it seems very unlikely that any part of the