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electricity of the latter ball, a portion of electricity will dart in a spark to c, or other ball more remote from b than, but next to, the ball giving the spark. Under these circumstances, the free electricity of all the balls, on their sides farthest from b, as well as their solid matter on their sides nearest to b, may be termed active.

(13.) In further illustration of propositions 9, 10, 13, 14, 15, vide fig. 3, where a and cl each represent the commencement of an indefinite line of balls, and c2 the commencement of two indefinite lines through d2 and 23. Here the attraction for the electricity of an electrified ball, b, being divided between a only on the one side, and both cl and c2 (a double quantity of next adjacent solid attracting matter) on the other side, the quantity of electricity accumulated on the c side of b must be much greater than on the a side.

(14.) This preponderance on the c side will also be further increased by c 2 being assisted in its inductive action by two lines of balls, d2 and d3. For this latter reason, the quantity of electricity on the part of b, opposite to c2, (as at f,) will be greater than the quantity opposite cl, (as at e,) which is but the commencement of a single line of balls. Nevertheless, as the c1 and c2 lines are adjacent to each other, they will act inductively upon each other's electricity in some degree, and so far lessen the difference of their action on the electricity of b. Such mutual inductive action will, however, be small, being indirect or curvilinear.

(15.) The preponderant inductive influence exercised by c 2 on the electricity of b, through the assistance rendered it by the two lines of balls commencing with d 2 and d 3, would be rendered still more preponderant by the assistance of another line or lines of balls concurring with them, or by those two lines themselves branching into three or more lines.

(16.) The converse of the foregoing explanations as to positive electricity, appears (if they be true) so evident in its applications to the negative state of electricity, that I shall not trouble the Society with a separate exposition of it.

(17.) The foregoing propositions are also as applicable to parts of bodies as to different bodies, and which parts may be considered as represented by the balls in the figures given; for, supposing those balls in contact, the only difference would be, that the balls which tended to part with their electricity, or discharged it by a spark only to others when separate, would, when in contact, part at once with it by conduction; and the same observation applies, if the balls in fig. 2, considered as in contact, be replaced by a cylinder; or in fig. 3, by a branching cylindrical body, each divided into imaginary sections as counterparts of the balls.

(18.) A non-conducting body, electrified on one point, would be in a situation more analogous to that of the balls when separate than when in contact.

(19.) In further illustration of propositions 9, 10, 13, 14, 15, vide also fig. 4, where fghi indicate the vertical longitudinal section of a fixed and insulated metallic cylinder, the terminations being hemispheres of the same radius as the cylinder. This cylinder imagined to be surrounded indefinitely, in every direction, by small metallic balls, insulated, of equal size, and equidistant. It does not seem to require an argument to shew, that a large body electrified may act inductively on smaller ones. If the whole surface of the cylinder be imagined so for the present) equally electrified in excess, a particle of free electricity at fgh or i, will have no direct and immediate tendency to change its situation on the cylinder, being in each case attracted, in every two opposite directions, by the solid matter of an equal number of the balls, and surrounded in every such two directions by equal portions of other free active electricity.

(20.) Not so as to any other particles. Take, first, those on the line gph only, (being one quarter of the longitudinal circumference of the cylinder,) for simplicity's sake, in the first instance, and compare those on the straight part, gp, with those on the curved part, ph, of that line.* While the plane, lmgp, continues of the same breadth at all distances from the straight line, 9p, the plane, mphoq, increases continually in the length of its lines parallel to its curvilinear sides, in arithmetical proportion to distance from the curve ph; so the number of balls through which that plane passes, and consequently its quantity of solid attracting matter, is greater, in each line across it, at each greater distance, than at any lesser distance from the cylinder, in the like proportion ; while the number of balls, and consequently the quantity of solid attracting matter, in any line across the plane Img p, parallel to the line gp, do not become greater at any distance, however remote. These conditions will tend to place the first line of balls, adjacent and parallel to the line gp, in a similar inductive state to ci in fig. 3 ; while the first line of balls adjacent and parallel to ph, will tend to acquire a similar inductive state to c 2 in that fig. There will consequently be produced an unequal distribution of the electricity; a similar excess or preponderance of it on ph, as at f, in fig. 3; and a similar deficiency on gp, as at e, in fig. 3.

(21.) There will, at the same time, be an inductive action exerted upon the electricity of each other, by the solid matter of the balls in the two planes, about the line of their junction, mp, making their films of electricity to coincide there, and regularly increase in depth from g to h.

(22.) Take, secondly, the particles of electricity on the whole of the surface of the right-hand half of the cylinder, and consider the relations between the cylindrical part, gpis, of that half, and the

I take the liberty of frequently using the words line, plane, and section, as if they had thickness. The context will sufficiently indicate when they are used thus, or in a strictly methematical sense ouly.

remainder or hemispherical part, kphs, and between their portions of electricity. In this case, the number of balls in each stratum, opposite and parallel to the surface of the cylindrical portion of the half cylinder, increase in arithmetical proportion to distance from that part of the surface ; while the number of balls in the strata, opposite and parallel to the hemispherical part, increase in geometrical proportion to distance from the surface. This greater increase of matter by distance, opposite the hemispherical portion of the cylinder, enables each ball, in the first or nearest stratum, to exert a greater amount of attraction on the electricity of such hemispherical portion, than can be exerted by any ball in the first stratum opposite the cylindrical portion. The film of electrical liquid' must, therefore, necessarily be deeper on the hemispherical portion of the surface kphs, and more shallow on the cylindrical portion gpis, in such proportion, that the excess in the quantity or depth of the film of electricity on the former portion, neutralises or balances the excess of attraction shewn to exist in that direction.

(23.) The balls in the cylindrical and hemispherical portions will nevertheless act upon each other's electricity, and render their films of electricity coincident in depth at the transverse section ps, and gradually increasing all the way from the transverse section or plane yi to h.

(24.) So far the electricity has been disturbed from the equable arrangement that would have been natural to it, (if attracted by the cylinder alone,) by the opposing attraction of matter exterior to the cylinder, and projects horizontally from the end of the cylinder towards the volume of air which attracts it, as a drop of water, hanging from the end of the finger by which it is attracted upwards, projects downwards by the opposing attraction of the earth. It now becomes requisite to consider what forces are exerted, in what directions, and with what tendencies, under these circumstances, between the unequally diffused electricity of the cylinder, and the solid matter of the cylinder itself.

(25.) The depth of the film of electricity being greater on any transverse section of the cylinder nearer to h, than on any other parallel section nearer to the section gci, (as on v v, compared with nn, for instance,) that greater proportional quantity or depth of film of the electricity over v v, and within the range of its influence, will require the solid matter of that section to exert a greater proportional amount of attraction than is required to be exerted by that of the section nn, on the smaller depth of electricity over it, and within the range of its influence.

(26.) The solid matter at section n n, will therefore be at liberty to exert a greater proportional amount of attraction or inductive influence, than the solid matter at section vv, on a portion of electricity equidistant from them, as is the electricity round the section pks. The tendency of this greater amount of attraction

will therefore be to move the electricity, situate round pks, towards nn, and would do so, were it not for the opposing attractive force of the air, as above explained.

(27.) Action and reaction being equal, this greater amount of attraction also tends to draw the solid matter at section nn towards the electricity round pks, and, as a consequence of the union of section nn with the rest of the cylinder, to move the whole of the cylinder in the line or direction towards o.

(28.) Causes exactly similar, and equal to those considered as operating on one-half the cylinder, operating also on the other half, the tendency of the cylinder to move towards o is counteracted and balanced by an equal and contrary tendency of such other half, in the opposite direction.

(29.) The two halves of the cylinder, being separated through the transverse plane lcr, and suspended by silk threads, will then no longer oppose and restrain each other's motion; but obeying their separate and opposite tendencies, RECEDE from each other. Thus might take place a perfect recession of two electrised bodies from each other, without reference to a power so anomalous as is that of repulsion, particularly when referred to the negative state of electricity.

(30.) As the right half of the cylinder moves towards o, the balls included between the stationary medial plane lcr, and the parallel plane mkt, considered as moving with the cylinder, become increased in number, and less and less influenced by the inductive action of the electricity of the other, now more distant, half of the cylinder ; while the quantity of solid attracting matter exterior to the cylinder, on the side ou of the plane mkt, is not increased.

(31.) Several consequences flow from this increase in the number of balls or quantity of solid matter between the medial stationary plane lcr, and the moving plane mkt, and each of such consequences flows from the other or others before it, in the following order :

(a) An increase in the attraction or inductive influence exerted on the electricity of the first stratum of balls round nn, by the solid matter of the increased number of more remote balls.

(6) An increase in the attraction of the solid matter of such first stratum of balls, for the electricity of the cylinder about nn.

(c) An increase in the depth of the film of electricity about nn, at the expense of the mass of it at vv, and elsewhere on the side of mki, towards h.

(d) A diminution of the excess in the depth of the electrical film at ov, over that at nn.

(e) A diminution of the excess of attraction exerted between the solid matter of section vv, of the cylinder and its electricity, over that exerted between section nn and its electricity.

() A diminution of the excess of the attraction of such solid matter at nn, for the electricity round the plane or section pks, over that of the solid matter at vv, for the same electricity.

(g) A diminution of the tendency of that electricity, and the solid matter of the section nn, to approach each other.

(h) And, lastly, a dimin on of the tendency of this half of the cylinder to recede from the other.

(32.) In lieu of the two half cylinders, I will now examine the case of two balls, equally electrified positively, b 1 and b 2, fig. 5, which (the foregoing explanations being admitted) must divide the inductive attractions of the balls a and c between them. Here 6 1 will be in the situation of an adjacent ball to b 2, as also b2 to b1, and the observations on propositions 9 (3), 10 (4, 5, 6), 13 (7), 14 (8), 15 (10), and fig. 2 (11, 12), where c was a body adjacent to b, apply in the same manner to shew that the free and increased electricity of b 1, fig. 5, must now stand out or be elongated on its side remote from b 2, as the free and natural portion of a and c, fig. 2, stood out on the sides remote from b; b 1 and b 2, fig. 5, being equally electrified, any observation applying to one must apply equally to the other.

(33.) The two balls, bl and b2, if kept in contact, act very nearly as if they were one elongated body, like the above-mentioned cylinder, fig. 4; and well known experiments having proved that such a body has a deeper bed, or accumulation of electricity, at its ends than elsewhere, support the foregoing partly theoretical conclusions. Let the two halves of the cylinder in fig. 4, and the balls b1 and 62, in fig. 5, change places, and it will be seen that the above observations will, with a trifling allowance, still apply to each figure under such a change of circumstances.

(34.) I have thus far spoken of metallic balls for the sake of more easy comprehension, (without noticing the influence of the air,) but think the observations hitherto made will apply equally to the atoms of the atmosphere, which are, by some yet unexplained means, insulated from each other. That they, in their natural state, possess free electricity, is shewn by a point on a conductor electrified negatively, and I suppose it adheres to them as it does to a metallic ball. If they be chemically compounded, and consequently not spherical (speaking of their component atoms of oxygen and nitrogen only), those component atoms probably present spherical or otherwise curved terminations, and answer every purpose of the present question. I shall therefore take the circles in the figures given as their representatives, and consider either a metallic ball, or one of such atmospheric atoms, positively electrified, will produce the same inductive influence, or disturbance of equilibrium, amongst other atmospheric atoms, as one electrified metallic ball amongst others unelectrified, and consequently the same elongations of their films of free electrical liquid, in a direction from the positively electrified ball or atom, towards each next adjacent atom.

(35.) Returning to the case of two electrified balls. Let two such balls as b and c, fig. 6, be positively electrified, suspended as the common pith ball electroscope, and surrounded as usual by

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