tric stream, transmitted through the metal be sufficiently strong to effect a total alteration of the relative situation of its parts, the circulation of the magnetic stream will remain constant. However, the permanence of the circulation of the magnetic stream does not seem so much to depend upon the intensity of the electric stream, as to its direction, with respect to the internal structure of the metal through which it has been transmitted.

542. Under the impression that all metals contained the magnetic principle in some degree, and also that the conducting wire, connected with the two sides of a battery, is actually magnetic during the transmission of the electric fluid, as is demonstrated by several indubitable experiments, I was led to suppose, that the deflection of a magnetic needle, and the other phenomena of electro-magnetism, were not the immediate effects of electricity, but of the temporary magnetism excited in the conducting wire, during the transmission of the electric fluid.

543. With this view, I undertook a series of experiments with different conductors of galvanism (avoiding the metals as being capable of magnetic excitation), supposing that as these non-metallic conductors were incapable of exerting magnetic influence, they would produce no disturbance in the needle during their transmission of the electric fluid; and these expectations were very satisfactorily realised; for on attaching any of these conductors to the poles of the battery, and presenting the needle, not the least sensible deflection was produced; but, on removing these, and substituting metallic conductors, a deflection of 90° immediately ensued. 544. In applying this position to electromagnetism, it will not be necessary to recapitulate the experiments which have not only appeared in most of the journals of science, but have also appeared compiled in a volume. Neither will it be necessary to apply it minutely to any of the experiments, as from its simplicity the experimenter may, by substituting artificial magnets upon a wire, instead of exciting its inherent magnetism by means of the transmission of the electric fluid, perform several of the most pleasing experiments; and this would obtain universally, were he capable of adjusting his magnets with as much precision as is effected by electricity.

545. It will, however, be necessary to mention one peculiarity which takes place with respect to the direction of the route of the magnetic fluid, in a piece of metal during the transmission of the electric by which it has been excited; the direction of the route of the magnetic fluid seems to be at right angles, or nearly so, with the direction of the route of the electric: thus, when the electric fluid is transmitted in the longitudinal direction of the metal, the magnetic will move at right angles with it, and consequently transverse of the metal; but if the electric stream take its course transverse of the metal, as by means of the spiral conducting wire, the magnetic stream will still move at right angles with the electric, and consequently in the longitudinal direction of the metal, each extre

mity of which will possess a different magnetic pole.'

546. When two electrified spheres are made gradually to approach each other, and when there does not exist between the species and the quantities of electricity which they possess, the particular relation which would be established by their contact, the thickness of the electric stratum at the points nearest each other, on the two surfaces, becomes greater and greater, and increases indefinitely as their distance diminishes. It is the same with the pressure exerted by the electricity against the mass of air intercepted between the two spheres; since the pressure, as we have mentioned above, is always proportional to the square of the thickness of the electric strata. It must at last then overcome the resistance of the air, and the fluid, in escaping under the form of a spark or otherwise, must pass, previous to the contact, from the one surface to the other. The fluid thus accumulated, before the spark takes place, is of a different nature, and of nearly equal intensity on each of the spheres. If they are electrified, the one vitreously and the other resinously, it is vitreous in the first and resinous in the second; but when they are both electrified in the same manner, vitreously for example, there arises a decomposition of the combined electricity upon the sphere which contains less of the vitreous fluid than it would have in the case of contact; the resinous electricity, resulting from this decomposition, flows towards the point where the spark is preparing, and, on the contrary, the other sphere, which contains more vitreous electricity than it would have after the contact, remains vitreous over its whole extent.

547. The phenomena are no more the same after the two spheres have been brought in contact together, and are then removed, however little, from each other. The ratio which then exists between the total quantities of electricity with which they are charged, causes to disappear in the expression of the thickness, the term which before became infinitely great for a distance infinitely small, and no spark takes place. The electricity of the points nearest each other upon the two spheres is then very feeble, for very small distances, according to a law which calculation determines, and its intensity is nearly the same on both spheres; but, when they are unequal, this electricity is vitreous on the one, resinous on the other; and it is always upon the smallest that it becomes of a nature contrary to the total electricity, which is conformable to the observations related above.

548. In general, all the varieties of these phenomena depend on the relation which we establish between the radii of the two spheres, and also between the quantities of electricity with which they are charged. We may even determine these proportions in such a manner, that, at a certain distance, the thickness of the electric stratum on the small sphere may be almost constant, so that this sphere may remain near the other, almost as if it were not exposed to any action, not from the weakness of the electricity on the other sphere, but in consequence of a sort of equilibrium which is then established between ·

560. If the distance a were altogether infinite, compared with the radius r', the second member of this equation would be reduced to cos. u'; consequently, this cosine would be 0, which would give u 90°. The line of separation of the two fluids would then be the circumference of the great circle, of which the plane is perpendicular to the line of the centres.

561. But if a is not infinite, it is at least very great relatively to r'. Thus, the factor will

5 r

6 a

c to a, towards the electrified sphere C.

562. In considering only the degree of the equation which determines generally cos. u', there would seem to be two values of this cosine which would satisfy the conditions of our problem; but it will clearly appear, that one of those roots should necessarily be greater than unity, and, consequently, will not have here any real application, as it would correspond to an arc u', which is imaginary.

563. When we now consider how various, how delicate, and how detached from each other, are the phenomena this theory embraces; with what exactness, also, it represents them, and follows, in a manner, all the windings of experiment, we must be convinced that it is one of the best established in physics, and that bestows on the real existence of the two electric fluids the highest degree of probability, if not an absolute certainty. But what is not less valuable for science, it teaches us to fix, by exact definitions, the true meaning which we must attach to certain elements of the electrical phenomena, which are too often vaguely enunciated, or even confounded, with others; although the knowledge of each of them, individually, is indispensable to form a correct and general idea of the phenomena.

564. The first of these elements is the species, vitreous or resinous, of the electricity which exists at the surface of an electrified body, and at every point of this surface. This is determined by touching it with the proof plane, and presenting this to the needle of the electroscope,

already charged with a known species of electricity.

565. The second element is the quantity of this electricity accumulated on every point, or, what comes to the same thing, the thickness of the electric stratum. This we still measure by touching the body with the proof plane, and communicating the electricity acquired by this contact to the fixed ball of the electric balance; the moveable one having been previously charged The force with electricity of the same nature. of torsion necessary to balance the electric reaction communicated by the plane to the fixed ball, is at equal distances proportional to the quantity of electricity which it possesses, or, what is the same thing, to the thickness of the electric stratum on the element of the surface which it has touched.

566. The third element which it is of importance to consider in the phenomena, is the attractive or repulsive action exerted by each element of the electric stratum upon a particle of the fluid situated at its exterior surface or beyond this surface. This attraction or repulsion is directly proportional to the thickness of the electric stratum on the superficial element which attracts or repels, and is inversely proportional to the square of the distance which separates this element from the point attracted or repelled.

567. In fine, the last element to be considered, and which is a consequence of the preceding ones, is the pressure which the electricity exerts against the external air in each point of the surface of the electrified body. The intensity of this pressure is proportional to the square of the thickness of the electric stratum.

568. By adhering strictly to these denominations, there will be no risk of falling into error from vague considerations; and if we also keep in mind the development of electricity by influence at a distance, we shall then find no difficulty in explaining all the electric phenomena.

569 To place this truth in its full light, we shall apply it to some general phenomena which, viewed in this manner, can be conceived with perfect clearness, but which, otherwise, do not admit but of vague and embarrassed explications. These phenomena consist in the motions which electrified bodies assume, or tend to assume, when they are placed in presence of each other, and in which they appear as if they really acted upon each other by attraction or by repulsion. But it is extremely difficult to conceive the cause of these movements, when we consider that, according to the experiments, the attraction and repulsion are only exerted between the electric principles themselves, without the material substance of the body, provided it be a conductor, having any influence on their distribution or their displacement. We cannot hence admit, that the particles of the electric principles, whatever they may be, really attract or repel the material particles of the bodies. It is absolutely necessary, therefore, that the attractive and repulsive actions of these principles, whatever they are, be transmitted indirectly to the material bodies, by some mechanism which it is of extreme importance to discover, as it is the true

key to these phenomena. But we shall see that this mechanism consists in the re-action produced by the resistance which the air and non-conducting bodies in general oppose to the passage of electricity.

570. For the sake of greater simplicity, we may first confine ourselves to the consideration of two electrified spheres A and B; the one A fixed, the other B moveable. Three cases may arise which it is necessary to discuss separately. 1. A and B non-conductors.

2. A a non-conductor, B a conductor. 3. A a conductor, and B a conductor. 571. In the first case, the electric particles are fixed upon the bodies A and B, by the unknown force which produces the non-conductibility. Unable to quit these bodies they divide with them the motions which their reciprocal action tends to impress upon themselves.

572. The forces then which may produce the motion of B, are, (1.) The mutual attraction or repulsion of the fluid of A upon the fluid of B. (2.) The repulsion of the fluid of B on itself. But it is demonstrated in mechanics, that the mutual attractions and repulsions exerted by the particles of a system of bodies on each other, Cannot impress any motion on its centre of gravity; the effects of this internal action then destroy themselves upon each of the spheres; there cannot result from it any motion of the one towards the other; and the first kind of force, therefore, is the only one to which we need pay any attention. If the electricity is distributed uniformly over every sphere, each of them attracts or repels the other as if its whole electric mass were collected in its centre. Thus, if we call a the distance of their centres; r,, their radii; e, e', the thicknesses of the electric strata formed upon their surfaces by the quantities of electricity introduced into them; the electric mass of each of them will be 4 e, 4, being the semi-circumference of which the radius is equal to unity, and the attractive or repulsive force will be expressed by 152 Kr2 re e K being a co-efficient which

a*

75

expresses the intensity of the force when the quantities a, e, e', are each equal to the unity of their species. This force transmits itself directly to the two spheres, in consequence of the adhesion by which they retain the electric particles. We see, from this expression, that the force must become nothing, if e or e' be nothing, that is, if the one of the two spheres be not primitively charged with electricity. During the motion it suffers no alteration but what arises from the distance, because the two spheres being supposed of a perfectly non-conducting substance, their reciprocal action produces upon them no new development of electricity.

573. In the second case, where A is a nonconductor, and B a conductor, the sphere B suffers a decomposition of its natural electricities by the influence of A. The opposite electricities which result from this decomposition unite with the new quantity which has been introduced, and dispose themselves together according to the laws of the electric equilibrium.

Here the motion of B towards A may be regarded under two points of view.

The

574. Suppose, first, that without disturbing the electric equilibrium of B, we extend over its surface an insulating stratum, solid, without weight, and which may remain invariably attached to it. The electricity of B, unable to escape, will press as it were against this stratum, and, by this means, transmit to the particles of the body the forces by which it is urged. forces which then act upon the system will be, (1.) The mutual attraction or repulsion of the fluid of A on the fluid of B. (2.) The repulsion of the fluid of B upon itself, a repulsion, however, which cannot produce any motion upon the centre of gravity of B. (3.) The pressure of the fluid of B upon the insulating envelope, a pressure, again, which being exactly counterbalanced by the re-action of this coating, produces still no motion whatever. The first force, then, is still the only one to which we need pay any attention.

575. When the distance a of the two spheres is very great, relatively to the radii of their surfaces, the decomposed electricities of B, are distributed almost equally over the two hemispheres situated on the side of A, and on the opposite. In that case the actions which they suffer on the part of A are nearly equal, and destroy each other; all the force then is produced by the quantities of external electricity, 4re, 4πre introduced into the two spheres, which, acting as if they were wholly collected in their centres, the 16π2K222ee'. force becomes still

a2

576. When the two spheres are very far from each other, the co-efficient K may be considered as constant, and the attractive or repulsive force varies not but in consequence of a change in the distance 4. But this is only an approximation; for, to consider the matter rigorously, the electrical state of the conducting sphere B varies in proportion as it approaches A, on account of the separation which this produces in its natural electricities. Hence also the reciprocal action of the two spheres ought to vary in a very complicated manner, and it is probably to this that we must ascribe the error which appears in the experiments of Coulomb, at very small distances, when calculated by the simple law of the square of the distance.

577. The supposition of an insulating envelope, without weight, serves here merely to connect the electric fluid with the material particles of the body B, and we may always regard as such the little stratum of air with which bodies are ordinarily enveloped, and which adheres to their surfaces. Yet the same result may be obtained without the aid of this intermediary; but, in that case, we must consider the pressures produced upon the air by the electricities which exist at liberty in B. These electricities, in effect, as well those that have been introduced, as those that are decomposed on it, move towards the surface of B, where the air stops them by its pressure, and prevents their escape; they dispose themselves then under this surface, as their mutual action and the influence of the body A require, resting, for this purpose, against the