What immediately precedes is not given as new, but merely on account of the extreme simplicity of the analysis employed. We shall, moreover, be able thence to deduce a singular consequence which has not before been noticed, that I am aware of.

Let (a, b, c) be the co-ordinates of any particle P of the fluid when in equilibrium. Then, since

and therefore any particle P revolves continually in a circular orbit, of which the radius is

H 2π
v'

round the point which it would occupy in a state of equilibrium. The radius of this circle, and consequently the agitation of the fluid particles, decreases very rapidly as the depth c increases, and much more rapidly for short than long waves, agreeably to observation.

Moreover, the direction of the rotation is such, that in the upper part of the circle the point P moves in the direction of the motion of the wave. Hence, as in the propagation of the Great Primary Wave, the actual motion of the fluid particles is direct where the surface of the fluid rises above that of equilibrium, and retrograde in the contrary

case.

V. On the Nature of the Molecular Forces which regulate the Constitution of the Luminiferous Ether. By S. EARNSHAW, M. A. of St. John's College, Cambridge.

[Read March 18, 1839.]

THERE are already before the world by various authors several Memoirs, which, collaterally or incidentally, embrace the subject of the present communication. There is observable in them, however, much disagreement of results, which seems chiefly to arise from the extreme length and complexity of the investigations by which those results are obtained; to avoid which, as much as possible, their authors are compelled to adopt means of simplification, which we cannot always be certain à priori are sufficiently approximative. In the following pages the subject will be found to be treated in a manner perfectly new and direct, and, it is hoped also, satisfactory, inasmuch as the analytical operations employed are brief and simple, involving no principles of a difficult or doubtful character.

The authors to which I have just alluded have generally adopted, as a most extensive means of simplification, symmetrical arrangements of the particles of the ethereal medium. This may be necessary and even allowable in some cases: but as it has never been shewn that such arrangements actually do exist in Nature, nor even that they can exist in Nature, I have been careful to confine myself to the investigation of properties which are independent of arrangement, or rather, which do not involve the hypothesis of a peculiar arrangement.

I may also remark that the investigations which follow are in other respects of a very general character. For, in this attempt to discover the laws of molecular action of the ether, amongst the experimental properties, assumed as the basis of analytical investigation, are, I believe, none which are peculiar to the luminiferous ether. I think it probable, that most terrestrial bodies possess in a greater or less degree of perfection the properties here assumed and consequently, the title of this paper might have been made more comprehensive. It might, perhaps, not improperly be, "An Investigation of the Nature of the Molecular Forces, which regulate the Internal Constitution of Bodies." This might, however, be disputed, and therefore in the investigations I have referred only to the luminiferous ether. Nevertheless, that the reader may more easily judge what degree of claim the following pages have to that general character which is here ascribed to them, I shall, in as few words as possible, introduce a statement of the experimental assumptions, and the results respectively derived from them.

I. It is assumed that the ether consists of detached particles; each of which is in a position of equilibrium, and when slightly disturbed is capable of vibrating in any direction. (Many solid as well as aerial bodies transmit sound, which is generally supposed to imply the existence of the same properties in them as are here assumed to be true of the ether.)

The most curious and perhaps least expected result of this assumption is, that the molecular forces which regulate the vibrations of the ether do not vary according to Newton's law of universal gravitation: and it is not a little remarkable, that a force, whether attractive or repulsive, varying according to this law, is the only one which cannot possibly actuate the particles of a vibrating medium.

II. It is next assumed, that the motion of a vibrating particle is more affected by the influence of the particles which are near to it than of those which are more remote. (This is certainly true of many other substances besides the ether.) The result which is sought to be derived from this assumption is, that the molecular forces which regulate the vibra

tion of the particles are REPULSIVE, and vary according to an inverse power of the distance greater than 2.

III: It is lastly assumed, that the ether exists (or at least is capable of existing) as one mass held together by the attraction of its elementary molecules. This assumption is necessary, in order that the dispersion of the medium which would naturally result from the repulsive forces which regulate the vibration of its particles, may be thereby prevented.

The result which is derived from this necessary assumption is, that each particle exerts (in addition to the repulsive force before mentioned) an attractive force, which varies according to Newton's Law of universal gravitation.

By reversing the problem, I have been able to shew, that though Newton's law is the only one which cannot enable the particles to vibrate, yet it is the only law of force which can enable them to constitute and maintain themselves a permanent medium, without endangering, or in any way affecting their vibrating or luminiferous property.

I have on these grounds not hesitated to express my opinion, that the particles of the luminiferous ether are each endued with two forces of distinct characters and uses; one attractive, to preserve themselves a permanent medium, varying inversely as the square of the distance; and the other repulsive, to which is due their luminiferous property, varying in a higher inverse ratio of the distance than the square.

A SYSTEM OF DETACHED PARTICLES.

1. If V denote the sum of the quotients formed by dividing each attracting body by its distance from the attracted body; then V = C is the equation of a surface at any point of which if the attracted body be placed, it will begin to move in the direction of a normal.