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atmospheric atoms, of which a few only are represented by the circles ade, 1, 2, 3, &c. Let the lines rs, t u, vx, yz, mn, represent vertical planes perpendicular to an imaginary straight line, passing through the centres of b and c, and each adjacent pair inclosing equal spaces. Let the two outer of those spaces be called respectively the outer b and.c spaces, and the others the inner b and c spaces. Let also the imaginary planes, tu and yz, passing through the centres of b and c, be imagined also to recede when, and as those balls recede; and the planes rs, mn, to do the like, but twice as rapidly; so as to preserve the same equality of distance between every two adjacent planes, at each instant during the recession of the balls.
(36.) Let the electricity be-- First, (supposed for the sake of argument,) equally diffused over each ball, even when the balls are brought near each other.
Secondly, distributed unequally by inductive action; and
(37.) First, The electricity supposed equally diffused over each ball, as I suppose it would be, if left to the undisturbed action of the balls alone, and under this head
As to atom e, midway between b and c. The solid matter of b and c, being required to exert increased attraction by an additional quantity of free electricity upon themselves, loses a portion of its natural attraction for the free natural electricity of e (prop. 10). That electricity is therefore left at liberty to exert increased attraction for the common matter of all the circle of next adjacent atmospheric atoms (which includes atom i,) in the plane vx, and other atoms next adjacent to e, near that plane, (proposition 13,) under the words vice versa.
The electricity of e will thereby be partly accumulated in a circle round it, in and near the medial plane vx, and evince a tendency to escape to atom i, and the other atoms similarly situated (prop. 15.) This atom, e, will thus be attracted by means of its electricity, by equal forces towards every atom next adjacent to it in the plane vx, and by other equal forces by means of its common matter towards
b and c.
(38.) The electricity of atom 2, and the other atmospheric atoms, whose common matter is thus acted upon by atom e, will at the same time act on the next larger circle of atoms, including atom 2, and those adjacent to such circle last mentioned, (prop. 14 and 13.)
(39.) As to atom d. The common matter of this atom corresponds to that of c, in figs. 2 and 5, and is subject to the same observations, and therefore is attracted by the electricity of c, fig. 6, with great force, in that direction ; while its own electricity is attracted with great force in the opposite direction, or away from c, by the other atoms in that direction, which are acted upon in a similar manner by the next in succession, and so forth. The same observations apply to atom a, with respect to the ball b.
(40.) As to atoms 1 and 2. These atoms, and all other situate
in the plane vx, equidistant from b and c, form the boundary dividing the respective ranges of predominant inductive action exerted by b and c; both 1 and 2, and their electricity, being as equally subject to the separate inductive action of 6 and its electricity, as to that of c and its electricity.
(41.) As to atom 3. The electricity of atom 3, and all others situate in the plane, y z, must lean a little to the right of y z, as represented, there being a preponderance of atmospheric atoms on that side, capable of being acted upon, and reacting, by induction.
(42.) This preponderance may perhaps appear more distinctly, by observing that the outer c space is equal to the inner c space; but the action of the electricity of c, on the atoms in its inner space, being counteracted by the inductive action of the electricity of b, while there is little or no such counteraction in the outer c space, the action of the atoms in the latter space may be certainly concluded to exceed the action of those in the inner space. The whole of the atoms to the right of m n may then be considered as adding to this excess, by exerting a great preponderating force, both in direct and oblique directions, only from c, without any counterbalancing force tending towards c.
(43.) Were there such a counter force, it could only be found to the left of v x; but, that such a compensating force cannot be found there, appears certain ; for the electricity of b must act on the common matter of the atoms there, and neutralise, or at least balance, by their propinquity, all the effects, either immediate or inductive, of that common matter, on the electricity of c. The preponderating force, to the right of m n, will consequently incline the deepest part of the film of electricity of atom 3 to the right of yz.
(44.) So far as to the electricity of b and c, considered as equally diffused.--Now,
Secondly, As to a new distribution by induction.—Before this new distribution, the electricity on the two contiguous hemispheres of the balls, acting conjointly on all the atmospheric atoms in the plane v x, while the atoms in the plane m n were acted on (at least, near the balls) by the outer hemisphere of c only, a greater amount of induction, or disturbance of equilibrium, must take place on the atoms in the plane v x, than on those in the plane m n; and consequently, give the former the stronger tendency to part with their electricity.
(45.) Though there be this joint action of the electricity of the two inner hemispheres of the balls on the atoms in the plane v x, yet a moiety of this action cannot equal the action capable of being exerted by the electricity of one of such inner hemispheres, if acting alone and unopposed; and, consequently, such moiety will not equal the action exerted between the electricity of the outer hemisphere of c and the atoms in the plane m n; and, in the same manner, a moiety of the actions of the electricity of the two inner
spaces, will not equal the action of the electricity of the outer hemisphere of c, on the atoms in the outer c space.
(46.) Therefore, on the electricity of b and c being released from the unnatural assumed distribution, and the natural forces allowed to operate, the preponderance of inductive force in the outer c space, must draw a greater portion than half of the electricity of c to its outer hemisphere; and when, to this drawing force, we add the totally unbalanced attractive force of the atoms to the right of mn, very little electricity can be left on the inner hemisphere of c. All the foregoing observations, as to the ball c, &c., apply, of course, equally to the ball b, &c.
(47.) Thirdly, As to the ultimate effect, the recession of the balls from each other.—The said preponderant force, existing on the right of m n, acting, by its inductive influence, through the atoms in the outer c space, and drawing the electricity of c in that direction, and the continual attraction of the electricity of c for the solid matter of c itself operating as shewn by fig. 4, (25, 6, 7,) tending to draw that solid matter into the centre of its film of electricity, while exactly similar forces are exerted on the ball b, and its electricity in the opposite direction, the recession of b and c from each other necessarily results.
(48.) As the ball c, and, consequently, the plane y z, recede from the stationary medial plane v x, an increased number of atmospheric atoms must become included between those two planes, that is, in the inner c space, and require a doubly rapid removal of the imaginary plane, m n, to include an equal additional number of atmospheric atoms in the outer c space, to balance the increased numbers in the increased inner c space. This process lessens the preponderant force to the right of mn, or beyond the outer c space, by increasing the distance of the atoms which, for the time, exert that force, and will so continue to lessen that preponderant force, till it is so far reduced as to be balanced by the gravity of the ball and the action of the thread supporting it.
(49.) To assist in such process, there is of course, at the same time, a progressive return of electricity to the contiguous sides of the balls, in proportion to the increased number of atoms, capable of induction, which have become included in their inner b and c spaces, as explained with respect to the receding halves of the cylinder, fig. 4, (30, 31.)
(50.) It may not be entirely useless, nor uninteresting, to inquire how far the balls might possibly recede from each other, supposing the supporting thread removed, the balls in an atmosphere of indefinite extent in every direction, of equal density, and perfect mobility.
(51.) If the law (which, I believe, is generally considered as settled), that electrical attraction, and what is called repulsion, are inversely as the square of the distance, be true, then a single electrified ball, placed in the supposed indefinite atmosphere, must
hemispheres on the atmospheric atoms in the two inner b and c extend its influence or disturbance of equilibrium indefinitely in every direction. Let the inner circle, fig. 7, represent a section of such ball, and the spaces between each two adjacent rings, the sections of spherical strata of atmospheric atoms, with their centres coinciding with the centre of the ball.
(52.) The sum of the attractions of the free active electricity of the atoms in any one spherical stratum, for the common matter of those in the next more remote stratum would (if the law be as above stated) equal that between the electricity of the ball and the common matter of the first stratum; and, consequently, the sum of such attractions between any one pair of next adjacent strata, (strata 2 and 3, for instance,) would exactly equal the sum of those between any other pair of strata next adjacent to each other, however distant those pairs of strata might be from the ball, or one pair of strata from the other pair.
(53.) Thus calling the number of atoms in the first stratum =9, and the sum of their attractions for the electricity of the ball = the forces would stand thus :
Number of Force in each Aggregate of
of atoms. each stratum.
1 And so forth, for any number of strata whatever. (54.) But I suppose the attractions exerted by the electricity of the ball on the common matter of the atoms of the first stratum is (contrary to the supposed law) lessened, or partly neutralised, at that and every subsequent stratum, by the attraction between each atom and its own electricity, such attraction tending to an equal diffusion of that electricity over every part of its surface.
(55.) This continual deduction from the original force, I presume, would, at some finite distance, entirely overcome it, and that force would, in that case, be divided equably, though not equally, amongst all the atoms, in a limited spherical space, having the electrified ball for its centre. The ball would thus be opposed by all the surrounding atoms, in a struggle, as it were, for the possession of the electricity added to it. The force of the ball would be exerted on such electricity in a direction towards the ball's centre, and the forces of all the atmospheric atoms exerted on the same electricity, would be from the centre of the ball ; but the forces of each stratum after the first, would not be immediate, but be exerted, as before shewn, through the medium or inductive agency of all the strata nearer to the ball; as the lower links of suspended chains do
not act immediately on the higher, but only by communication through those intermediate.
(56.) Admitting the law and the imaginary conditions above mentioned, and applying them to the balls b and c, fig. 6, the before mentioned preponderant force to the right of mn, or beyond the outer c space, would never be wholly destroyed, however far the balls might recede from each other. Many of the spherical strata of atmospheric atoms, within the influence of each ball, must impinge on and intersect similar spherical strata round the other ball at the plane ox, and prevent the inductive influence of either ball being exerted with the same effect in the portions of its spherical strata, which shall be cut off from the larger portion by the plane vx, and of course prevent the inductive influence of each from being exerted with the same force, on its side nearer to the other ball, as on its remoter side.
(57.) But excluding the law, and even admitting the other imaginary conditions (prop. 50), then the balls will recede only till the inductive force of the electricity of each ball, exerted in every direction, is equalled and balanced exactly by the resisting attractions of the common matter of such balls, and the surrounding atmospheric atoms, for their own several electricities, and perhaps by other retarding or opposing causes.
(58.) Then, also, two perfect spheres of disturbed equilibrium, having the two balls for their centres, will meet at the atom e, without being able to cause its electricity to recede towards the next adjacent atoms, 1, 2, &c., in the plane v x, so as to act upon them by induction.—Vide note at the end.
(59.) The dissipation of electricity, whether positive or negative, from points to atmospheric atoms, is an instance of recession apparent]y explainable in the same manner, as the recession of one electrified ball from another.
By fig. 3, it is shown how one ball (or atom), as c 2, in its natural state, becomes, by its neighbourhood to an electrified ball, more changed in its electrical condition than another, as c1; that is to say, by its induction being assisted by, or transmitted to a greater mass of matter, on its side remote from the electrified ball, as by or to d2 and d 3, and the two lines of balls through which they are supposed to transmit their inductive influence.
(60.) Fig. 4 (19, et. seq.) furnishes a further illustration of this; and the ends of the cylinder are similar in principle to points, especially when we consider such cylinder as becoming more elongated than in the figure, and also reduced in thickness ; the whole cylindrical surface approaching the axis fk, and the surface of the right hemispherical termination contracting equally towards its central point k, till the radius of both cylinder and hemisphere are reduced to (say) onefourth of their original length.
(61.) By this change, the number of balls forming the first stratum round the cylindrical part of the cylinder, (supposing them