therefore, be the refraction due to the nucleus alone that gives rise to the formation of caustics, and thus produces, at a distance, the illusion of cometary tails. We have said enough, however, of an hypothesis which has little chance of rising again from the discredit into which it has fallen.

SECTION III.

THEORY OF THE IMPULSION OF THE SOLAR RAYS.

Ideas of Kepler concerning the formation of tails-Galileo, Hooke, and Euler-Hypthesis of Kepler formulated by Laplace-Where does the impulsion come from in the theory of undulations?

KEPLER, who for a moment suffered himself to be led away by the idea of Cardan,* soon abandoned it, and substituted in its place that of the action of the solar rays. According to this theory cometary tails have substance and are formed of materials borrowed from the comet, its nucleus, or at least its nebulosity. The sun,' says Kepler, 'strikes upon the spherical mass of the comet with direct rays, which penetrate its substance, and carrying with them a portion of this matter, issue thence to form that trace of light which we call the tail of the comet.

*It appears that Galileo was also a partisan of the same theory. 'We find,' says Arago, in a work entitled Il Trutinatore, 'that Galileo gave it his appro

bation.'

[It is worthy of remark that Kepler seems to have abandoned Cardan's theory mainly because it failed to explain the curvature of tails. He remarks that the laws of optics teach us that the paths of light-rays are rectilinear, so that, if produced as supposed by Cardan, the tail could not be curved. But if we take into account the fact that the velocity of light is finite-a fact not known in Kepler's time-it is easily seen that the tail will appear curved except when the earth should happen to be in the plane of the comet's orbit. M. W. de Fonvielle has recently called attention to this point in the history of Cardan's theory. See Monthly Notices of the Royal Astronomical Society, vol. 1875.-ED.] 408. p.

XXXV.

This action of the solar rays rarefies the particles which compose the body of the comet; it drives them away and dissipates them.'

Hooke, a contemporary of Newton, in order to explain the ascent of the light and tenuous matters which, emanating from the nucleus and flowing back in a direction opposite the sun, contribute to form the tail, assumes that these volatile matters are imponderable: to gravitation he opposes their levitation; according to him they have a tendency to fly from the sun. This amounts to assuming a repulsive force without explaining where this force resides.

The opinion of Kepler has been completed, extended, and modified. Admitted by Euler, and then by Laplace, it may be considered as the starting-point of the theory maintained by several contemporary astronomers, and notably by M. Fayethe theory according to which the solar rays exercise a repulsive action at a distance. We shall devote to it in its present form a separate section. In the meantime let us see how this theory has been formulated by Laplace in his Exposition du Système du Monde :

The tails of comets appear to be composed of the most volatile molecules which the heat of the sun raises from their surface and by the impulsion of his rays banishes to an indefinite distance. This results from the direction of these trains of vapour, which, always situated, as regards the sun, on the further side of the head of the comet, increase in proportion as the comet draws near to the sun, and only attain their maxima after the perihelion passage. The extreme tenuity of the molecules increasing the ratio of the surface to the mass, the impulsion of the solar rays becomes sensible, and causes nearly every molecule to describe a hyperbolic orbit, the sun being the focus of the corresponding conjugate hyperbola. The series of molecules moving in these curves

form, beginning from the head of the comet, a luminous train in a direction opposite the sun, and slightly curved towards that region which the comet has just quitted, whilst advancing in its orbit; and this is what observation shows to us to be the case. The rapidity with which cometary tails increase enables us to judge of the extraordinary velocity with which these molecules ascend. The different volatility, size, and density of the molecules must needs produce considerable differences in the curves which they describe: hence arise the great varieties of form, length, and breadth observed in the tails of comets. If we suppose these effects combined with others which may result from a movement of rotation in the comet itself, and the apparent changes arising from the illusions of the annual parallax, we may partly conceive the reason of the singular phenomena presented by the nebulosities and tails of comets.'

This hypothesis, it is evident, supposes two modes of action of the emanations from the sun. The first, which Kepler vaguely indicated, is an effect of dilatation due to the calorific activity of the solar rays, an effect doubtless itself preceded by an evaporation throughout the liquid parts of the surface of the nucleus. The nebulosity thus becomes more voluminous and the layers which form it more and more attenuated. Up to this point there is no difficulty-the known physical effects of heat justify this portion of the theory. The difficulty begins when it is necessary to assume that the same rays which have hitherto acted as calorific rays are endowed with another property, hitherto unknown, that of giving an onward motion or propulsion to all molecules reduced to a state of suitable tenuity. Does such a force exist?

To Laplace, who was justified in adopting the theory of emission at the epoch when he wrote, this repulsive force was

quite natural. The luminous molecules emitted by the sun, moving with enormous speed, communicated a portion of their momentum to the molecules emitted by the comet, to those which by the action of heat had been previously reduced to a sufficiently small tenuity, and hence the formation of the tail. But it is less easy to conceive of this repulsive force in the wave-theory of light, now universally adopted. Undulations are propagated with enormous velocity in the ether, but the matter is not transported forward.* It is difficult to see how the force that gives rise to the successive waves can produce the rectilinear movement of the molecules of the cometary atmosphere. Moreover, before assuming the existence of an actual repulsive force, it should, if possible, be demonstrated by experiment. Arago, when citing the experiments of Homberg, opposes to them the negative verifications of Bennet, and concludes thus: The fundamental idea of an impulsion due to the solar rays is, therefore, only an hypothesis, without real value.' The question, however, is not yet settled, as we shall see.

* M. Roche cites the following comparison, due to Euler, and by which that great mathematician, a partisan of the theory of luminous waves, justifies his adhesion to the hypothesis of the impulsion of the solar rays:

As a violent sound excites not only a vibratory movement in the particles of air, but also causes a real and perceptible movement in the light dust floating in the atmosphere, we cannot doubt that in the same way the vibratory motion caused by light produces a similar effect.'

This very vague comparison is not conclusive. Sonorous waves have an amplitude sufficient to produce visible agitation; the fact that we have to prove is the existence of a progressive rectilinear movement, not the existence of oscillation.