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(1.) Proposition 1.-I rest principally on the usual simplicity of natural operations, or paucity of causes employed in nature, to produce a multiplicity of effects.*

Prop. 2 and 3, I have before considered.

Prop. 4, 5, and 6, are, I believe, generally assented to.

Prop. 7 is not essential to the principal question discussed in this

paper.

(2.) To illustrate prop. 8, let the inner circles, a b c d, plate 1, fig. 1, represent a portion of an indefinite line of metallic balls, equidistant, extending in each direction from the ball b, and supposed insulated, and the dotted circles their natural films or coatings of free electric fluid or liquid. The electricity of b is here attracted by the solid matter of its own ball, and also by the solid matter of a and c, and their solid matter is likewise attracted by the electricity of b and their other next adjacent balls, and the like of each ball throughout the series. Now, a b c d and the other balls being equidistant, and possessed of equal portions of free electricity, the electricity of either, as b for instance, cannot be attracted by the solid matter of its next adjacent balls, as a and c, in one direction more than another, the quantities of solid attracting matter in each direction being equal. Likewise, the solid matter of b, or any other ball, cannot be attracted in one direction more than another, the quantities of electricity attracting it in each direction being equal. Under these circumstances, the electricity of each ball may be termed free electricity quiescent.

(3). Prop. 9.-To illustrate this proposition, let b, fig. 2, be one of the line of metallic balls before mentioned, having more than its natural share of free electricity, and a c d other such balls, having each its natural share only. Here, the free electricity of b, having been increased, must become active, and exert increased attractive influence on the solid matter of the adjacent balls, as a and c, whose free electricity has not been increased, and give those bodies an increased tendency to approach b. The free electricity of b may then be called free electricity active.

(4.) Prop. 10, fig. 2.-When the solid matter of b, which, in its

When I say one fluid, I rather mean to deny that the positive and negative states are the separation of a vitreous from a resinous fluid, and not to assert that the common electric stream is composed but of one fluid. I think that that stream may be one principal fluid, (which I call electricity,) accompanied by or combined with caloric in a liquid state, or holding it, and perhaps very minute portions of metallic and other substances, in solution. It appears to me not improbable that the atmospheric atoms, as well as the surfaces of other bodies, are surrounded by films of liquid electricity and caloric, and perchance different strata of the two united in different definite atomic proportions; thereby giving rise to the varieties of colour, (as I endeavoured to shew some reasons for in the "Mechanics' Magazine" of 13th May, 1837,) and also causing that elasticity, or expansion and recession from each other, of the atmospheric atoms, which is so confidently attributed to a power of homogeneous repulsion, a power assumed (most paradoxically) to belong to the same two particles of matter, when near together, which are known and admitted to possess that of homogeneous attraction when at a greater distance from each other.

natural or unelectrified state, exerts a certain force of attraction on the free electricity of c, is required to exert an attractive influence on an additional quantity of free electricity communicated to itself, it must lose some portion of its attraction for the free electricity of c.

(5.) We might infer this by analogy, from the instance of a magnet; one, for instance, supporting a pound weight of iron, and capable of supporting that weight only. On the approach of another piece of iron, the magnet transfers a portion of its attractive influence to that approaching piece, and therefore drops the pound weight, and this although the aggregate forces exerted by the magnet on both pieces together, would be increased so as to equal more than a pound.

(6.) Were this otherwise, the attraction of two masses of matter (a piece of iron and a magnet, for instance,) would, to a considerable extent, increase in arithmetical proportion to the increase of one of them, and either of them support an enormous mass of the other.

(7.) Prop. 13, fig. 2.-[Referring to the words vice versa.] The natural quantity of free electricity of the ball c (adjacent to b), being required to exert a lessened amount of attraction in the direction b, is left at liberty to, and must, exert an increased attraction for the solid matter of the ball d. It will then have become free electricity active, as well as that of the ball b.

(8.) Prop. 14, fig. 2.-The solid matter of c, being called upon to exert an increased attraction by the added electricity of b, and thereby become active on that side of it, must lose some portion of its attraction for electricity in the opposite direction, (that of d, for instance,) and must have an increased tendency to approach the electricity of b, by the preponderance of the attraction in that direction.

(9.) As to the changes of attraction mentioned in the propositions 13 and 14, between a body (adjacent to an electrified body) and its own electricity, those propositions go too far; they certainly contradict each other on that point. However, as I do not see my way clearly, and as the settlement of the point does not seem essential to the main question of recession, I pass it by for the present.

(10.) Prop. 15.-This appears by proposition 14 and fig. 2. The tendency of c to part with electricity to d, and to abstract it from b, and of d to part with electricity to e, and abstract it from c, and the like of every more remote ball, is evident.

(11.) A portion of electricity will have been removed further from its own ball, and consequently have diminished its attraction for that ball, while it will have approached nearer to the next more remote ball, and thereby have increased its attraction for that ball.

(12.) When this attraction for c, or any more remote ball, shall have been so far increased as to exceed the force of attraction of b, or the next ball towards b, and the homogeneous attraction of the

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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 c1 each represent the commencement of an indefinite line of balls, and c2 the commencement of two indefinite lines through d2 and d 3. Here the attraction for the electricity of an electrified ball, b, being divided between a only on the one side, and both c1 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 d 3. 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 c 1, (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, Imgp, continues of the same breadth at all distances from the straight line, gp, 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 Imgp, 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 p h, 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, m p, 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 p s, and gradually increasing all the way from the transverse section or plane y l 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 vv, 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

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