unequal distribution. Thirdly, that the whole action of two opposed spherical surfaces depends on the distance of each pair of corresponding points, and may thus be reduced to a very simple formula, depending on their radii and mutual distance.

The contrast between these conclusions, and some of the results of other experimenters, seems to prove the need of further inquiry, before the facts can be viewed as thoroughly ascertained. Estimates of electrical force require peculiar accuracy and care for their determination. But the conclusions of Sir W. S. Harris agree in substance with the consequences of the present theory.

First, it seems incredible that each point of two electrized surfaces acts only on one point of the other, singling it out by a kind of elective affinity. On the other hand, a calculation based on this principle will approach to the case where the action diminishes with the inclination as well as the distance, more nearly than the complex calculation from fluids of equal force in all directions. It will not be difficult to solve the simplest cases, with an assumed law of decrement for the inclination, and to shew that they approach nearly to Sir W. S. Harris's empirical rule.

Again, the present theory agrees with the conclusions of Sir W. Harris, in viewing the influx of a charge as resembling more nearly the influx of water than of air. On the theory of two fluids, the whole internal space of the body is equally receptive of the fluid, and it is driven to the surface by its self-repulsion alone. On this view, also, the higher intensity at the minor axes of an ellipsoid is due to the repulsion of the whole charge, acting in straight lines through the substance of the body. The

present theory, on the contrary, supposes that the change resides on the surface, because it is only at the surface that the relations of the matter and ether are discontinuous, and the distribution resembles the case of a soluble gas, admitted into a space of very small height over a large liquid surface. The self-repulsion of the charge will be insensible for all sensible distances; and hence its distribution, apart from secondary action or pressure, will be sensibly uniform, so far as it depends on central forces alone. But the equilibrium required between the lateral pressures and the retaining force will cause it to be denser where the curvature is greater, and most of all at edges and angles, though in a less ratio than in the fluid theory.

107. Particular Cases of Electric Distribution.

The statements of De la Rive and Sir W. Harris, compared, answer to the conclusions that appear to flow naturally from the present hypothesis, though a full comparison would require complex calculations, and a reference to the conducting or coercing power of different substances.

(1) "In the Ellipsoid the charge at the ends," according to De la Rive, "is proportional to the axes."

(2) "Those plates, whose length is at least double the breadth, have the charge nearly constant, till about an inch from the end. It is double at the end, and if the proof plane is put in the prolongation of the plate, fourfold." The retentive force on the ether, at the edge, has to counteract two equal pressures from the two sides in the same direction, and must therefore, it would seem, be double the force along the side of the plate. At the corners, for a like reason, it would be fourfold, and the proof plane held in the prolongation of the plate, is under the same condition, and will naturally receive a fourfold

charge, that is, an amount of ether causing a fourfold resistance or tension.

(3) "In a circular plate, it increases slightly to an inch from the edge, at one third of an inch is double, and at the edge is triple." The resolved part of the pressure of the edge which meets and balances the pressure on each

2

ᅲ

side is sin 980, and the total pressure 80. Hence it

0

0

would seem that the charge at the sharp edge will be π or 34 when the charge along the surface is unity; while its diminution inward will probably vary with the size of the plate, and the conducting or coercing power.

(4) "In a cylinder 331⁄2 inches long, and 2 in diameter, the charge being unity in the middle, it is 11 at 1.8 from the end, and 21% at the end." The charge at the circumference of the end, where there is a right angle, it seems a probable conclusion, from the theory, and the balance of pressures, should be: 1, compared with that along the cylinder. But the end being small compared with the whole surface, this charge may be diffused over the whole end, and thus require the same ratio at the circumference to balance its own increased pressure. The extreme value would then be =246, as its limiting value when the

πT2

4

radius of the end is small, compared with the length. At a distance from the end equal to the radius, it would probably be=1.57, and hence a value 1-25 at the distance of 1.8 seems to agree with this approximate result of the theory.

(5) "In twenty-four equal spheres in contact, it is

nearly constant for the middle ones, and 175 for the extremes." Such a series evidently approaches to the case of a long cylinder with hemispherical ends. In this case, we should expect a double strength of the charge at the ends, to meet the opposite pressures, reducing itself to unity a little beyond the first hemisphere. Hence the mean charge of the spheres next to the ends may be expected to be 15, or nearly a mean between the limiting and central values; and the mean charge of the last spheres a mean between this and the limit, or 1·75.

Thus a first and rough application of the present theory to the best ascertained facts of electrical distribution yields results equally, and perhaps more conformable to experiment, than the fluid theory. At the same time, since it recognizes the double influence of induction and the conductivity or coercive power of the substance electrized, and requires us to distinguish the quantity of ether distributed along the surface from the elasticity or electric force which it occasions, it plainly admits of two elements being introduced into the formulæ of electric distribution, by which the harmony between theory and experiment may be rendered more complete than in the fluid theory, which takes no account of the varieties of coercing power, and makes the charge a direct measure of the external activity.

CHAPTER X.

ON THE ELECTRIC CURRENT.

108. THE Science of Dynamic Electricity, while it has made immense progress through the labours of Volta, Wollaston, Davy, Oersted, Ampère, Cumming, Becquerel, Faraday, De la Rive, and many others, still remains in a state not a little perplexing and obscure. Electricity, chemical affinity, magnetism, light and heat, are all proved to be intimately related to each other, and the relation of each pair of them supplies a large class of phenomena, but the exact nature of each and all continues unknown.

Electro-dynamics, or the theory of the electric current, and of the attendant chemical union and decomposition, stands first in order among these closely related branches of science. And here the unsolved questions are many. What is the meaning of an electric current? Is it the transfer of one or two fluids, properly electric, or of the luminous ether, or a transfer of forces alone? Why does it decompose chemical compounds, and some, not others? Why should such currents circulate, as the hypothesis of Ampère assumes, around the atoms of magnetic bodies? Why should electricity, in motion, have a power to attract or repel, which ceases when it is in repose? Why should