upon an insulated metal disc, of a diameter a little larger than its own; it is electrised, and its exterior surface alone gives signs of electricity. It is surrounded exteriorly with small brass columns, higher than itself, and which rest by their base upon the same metal disc; all the electricity is immediately disposed upon the exterior surface of these small columns. A third experiment consists in fixing to an insulated metal wire, bent into the form of a ring, a conical muslin bag, which forms in fact a butterfly net. It is to be electrised: no electricity is found upon its interior surface by the proof-plane. By means of two insulated silk threads, fixed to the apex of the cone, one withinside and the other without, the bag is turned inside out without being deprived of the electricity with which it is charged, so that the surface which was exterior becomes interior, and reciprocally and it is always the surface that is outside which is alone found to be charged with electricity (Fig. 40.).

Fig. 40.

Electric Reaction of the Points of a Surface.

It is therefore fairly proved, that upon the exterior surface of a conducting body is disposed all the electricity with which it is charged. Each point of this surface will have a certain quantity of electricity, which is termed a certain electric reaction; an expression by which we designate the condition of an electrised point or surface that, in the static state, does not exercise any action, but would virtually be capable of exercising one. The electric reaction of each point of the surface of a conducting body must depend, for the same quantity of electricity given to this body, upon the extent of its surface, and must be inversely to it, because all the electricity is disposed upon the surface alone. We may

machines in action, the electroscopes experience no effect, the electricity that reaches them being entirely disposed upon the exterior surface of the tissue by which they are enveloped.

Fig. 41.

prove directly by experiment this self-evident principle, by means of a metal riband wound around an insulated metallic axis. An electroscope composed of two elder-pith balls, suspended to linen threads, is fixed at the extremity of the metal axis (Fig. 41.). The whole is to be electrised; and the electroscope diverges powerfully. We then unroll the riband by means of an insulating silk thread fixed at the free extremity; the balls of the electroscope approach and come almost into contact. The riband is then wound up again by means of an insulated handle fixed at the end of the axis; the balls of the electroscope immediately begin again to diverge. This double operation, which may be repeated several times without the electricity being dissipated, if the air is tolerably dry and the supports good insulators, shows that the electric reaction of the point of the surface to which the electroscope is fixed is less according as the total surface is greater, and, reciprocally, is stronger, as the surface is smaller. The mass of the body remains the same, its surface alone is varied; but as the electricity is disposed upon the surface alone, it is clear that the same quantity of electricity, in distributing itself over a greater surface, will give to each of the points of which it is composed a less electric reaction than would be possessed by each of the points when the surface was smaller.

Distribution of Electricity upon the Points of different Surfaces.

The electric reaction of a point, for the same surface, does not depend simply upon the absolute intensity of the electricity, but also upon the general form of the surface to which this point belongs. The influence of this form on the manner in which the electricity distributes itself over a surface, has been the object of numerous and interesting researches by Coulomb. It was also by touching successively with the

proof-plane the different points of the surface of an electrised conducting body, and bringing it each time to the torsion balance, that he succeeded in determining the laws which the distribution of electricity obeys. In fact, when the proofplane is tangent to a point of the surface, it is confounded with the point that it touches; it becomes itself part of the surface, and consequently takes the same charge of electricity that was possessed by the element that it covers. When the plane is taken away, it is as if there had been cut from the surface an element of the same extent as itself, and it had been conveyed to the balance with the electricity that it possessed, when it formed part of the surface. Consequently, when we wish to operate, we begin by charging the disc of the movable needle with the same electricity as that of the body subjected to experiment; we then touch with the proof-plane a point of the surface of the electrised conductor, and carry the plane to the torsion balance; we determine the angle of torsion necessary to establish equilibrium at a constant distance; we now take it away, and discharge its electricity, and then convey it to another point of the same conducting body; it takes electricity from it, is carried over to the balance; we determine the angle necessary to produce equilibrium still at the same distance. The relation existing between this angle and the preceding one, expresses the relation that exists between the two electric charges taken successively by the plane, consequently, between the electric charges of the two portions of the surface that have been successively touched.

By applying the method to determining the distribution of electricity over the surfaces of insulated conductors of different forms, we arrive at the following results:

Sphere. We find that the angles of torsion are all equal, whatever point is touched; whence we conclude, that the distribution of electricity is uniform on a spherical surface.

Ellipsoide.—This uniformity ceases to exist so soon as the spherical surface becomes slightly spheroidal; experiment gives the angles of torsion greater when the proof-plane has touched a point of the surface of an ellipsoïde of revolution near to the ends of the longer axis, than when the point

touched is near to the ends of the short axis. The electric reaction is greatest at the very extremities of the great axis, and least at the extremities of the small one; and the difference between the two reactions is the more considerable as there is a greater difference between the length of the two

axes.

Cylinders. A cylinder of 2 in. in diameter and 33 long, terminated by two hemispheres, when touched successively by the proof-plane at the middle, or at one of its extremities, manifests electric reaction, of which the first is to the second as 1 is to 2.30. By comparing the middle point of the cylinder with a point taken at 9.8 in. from the extremity, the relations of the electric reactions were found to be as 1 to 1.25. It follows from this that the electric reaction varies but little from the middle of the cylinder to 2 in. from its extremities; and that it increases from this distance to the very extremity, where it is at its maximum.

Plane Surfaces and Prismatic Bodies.

Thin plates, whose length is at least double their width, present an electric reaction which is very nearly constant from the middle to about an inch from the extremity; this reaction goes on increasing, from this distance, to the extremity itself. At the extremities of the plate, the reaction is double of what it is in the middle; and, if the proof-plane is placed on the prolongation of the plate, it is quadrupled. In a circular plate the electric reaction goes on increasing from the centre to the edges; however, this increase does not become very sensible till about an inch from the edge: at about a third of an inch from the edge the reaction is double what it is at the centre; it is triple at the edge itself. The increase of the electricity towards the extremities is found in prismatic bodies, especially when they are very elongated. It exists, in like manner, toward their edges.

Spheres in contact.

If the spheres are equal, the distribution of the electricity

greatly resembles what it is upon a cylinder. Thus in a series of twenty-four globes, placed in contact in a straight line, the electric reaction varies very little in the middle globes from those which precede the latter ones, but considerably between the two extremes and those which immediately follow. Thus the electric reaction of the extreme globes is to that of the middle globes as 1·75: 1·00. With two equal spheres in contact, the electricity goes on increasing from the point of contact, where it is null, to the extremities of the common diameter that passes through this point,-extremities where it is at its maximum. If the spheres in contact go on diminishing in size, from one end to the other, the electric reaction goes on increasing from the largest to the smallest, where it is most considerable.

Power of Points.

The electric reaction is so considerable at the extremity of a point that the electricity escapes from it, to be carried through the air to the nearest bodies, or to diffuse itself simply in the atmosphere. This effect of points is a consequence of the distribution of electricity. We have seen, indeed, that in an ellipsoïde the electric reaction is greater at the extremity of the greater axis than at the extremity of the small one; and that the difference is the more considerable as the two axes differ the more from each other. It is the same with respect to a cylinder, which, when it is extremely long in regard to its diameter, presents at its extremities a very great electric reaction. In this case, as in that of the very elongated ellipsoïde, this reaction may become such that the electricity escapes. This is exactly what happens with a point, which may be regarded as being the extremity of a very elongated ellipsoïde or cylinder, or rather of a series of spheres in contact, whose dimensions go on gradually decreasing.

Methods for taking account of the Loss of Electricity.

The experiments upon the distribution of electricity are subject to a source of errors, which we must know how to take