SECTION VII.

THE REPULSIVE FORCE A REAL PHYSICAL FORCE.

Theory of M. Faye-Rigorous definition of the repulsion inherent in the solar rays-Its intensity varies with the surfaces of the two bodies; it decreases inversely as the square of the distance-It is not propagated instantaneously-Discussion and accordance of the facts-Experiments in support of a repulsive force.

It was at the suggestion of M. Faye, as we have seen, that M. Roche introduced into his analytical researches upon cometary phenomena the hypothesis of a repulsive force which has, in fact, led to results more in conformity with what is observed. It should be remarked, however, that M. Roche has considered the matter rather from the point of view of a mathematician than of a physical astronomer; whilst, on the contrary, the physical bearing of the problem has more especially occupied the attention of M. Faye. This astronomer, This astronomer, after passing in review the different theories we have mentioned, and rigorously comparing their conclusions with the facts of recorded observations, in short, after the most exhaustive discussion, has finally decided in favour of an actual repulsive force inherent in the solar rays. This is the base of the theory known as Kepler's theory, and which has been distinguished by the adhesion of Euler and Laplace.

At the time when M. Faye made known his views, two great comets-that of Donati (1858) and that of 1861-had

recently appeared. Both comets had been subjected to careful telescopic scrutiny, and it was necessary to explain the physical phenomena which had been daily followed in their details by observers in Europe and America, and also to account for a phenomenon of another kind, but equally important, viz. the accelerated movement of the comets of Encke and Faye.

Encke, as we shall see, was in favour of the hypothesis of a resisting medium, and regarded it as the cause of the known acceleration of the above-mentioned comets. Newton likewise, as we have seen, attributed the formation of cometary tails to the existence of an interplanetary medium. Here, then, is a connexion between two very different classes of phenomena. M. Faye, on the hypothesis of a repulsive force, proceeds to examine the cause of the formation and development of aigrettes and tails, and the accelerated movement of the comets above referred to.

Let us see, in the first place, how M. Faye defines the repulsive force. This is an important point, concerning which the partisans of this theory had hitherto neglected to be explicit; there was supposed to be an impulsion of the solar rays, and that was all. M. Faye's words are:—

'A repulsive force having its origin in heat. By means of it heat produces mechanical effects. It depends upon the surface and not upon the mass of the incandescent body. The action upon a body is proportional to the surface of the body, and not to its mass. It is not propagated instantaneously, like the attractive force of Newton. Nor does it act through intervening matter, like attraction. It is provisionally assumed that its intensity decreases inversely as the square of the distance, and that its velocity of propagation is the same as that of rays of light or heat.'

Now, the existence of such a force being admitted, how does M. Faye deduce from it the theory of cometary pheno

mena? How does he explain by it the formation of tails, simple or multiple, their curvature, their direction, the development of luminous or dark sectors, the disengagement of envelopes more or less parabolic? Upon all these points M. Faye gives the following explanations, which he finds confirmed point by point by the observations of the most brilliant comets which have recently appeared:

'The action of the repulsive force upon a body in motion. about the sun does not coincide with the radius vector, but is always exerted in the plane of the orbit, so that the figure which it tends to impress upon a body originally spherical, such as that of a comet very remote from the sun, will be symmetrical with respect to this plane; nor can this result be changed either by the sun's attraction or by that of the nucleus, or by the progress of the deformation itself. In the second place, the action of this force being in proportion to the surface, the effects produced depend upon the density of the matter of which the comet is composed; it follows, then, that, except in the plainly exceptional event of these materials being completely homogeneous, it must give rise to the formation of several tails, resulting from a sort of purely mechanical selection on the part of the repulsive force. But the axes of these multiple tails, which are longer in proportion as their curvatures are less, will always be situated in the plane of the orbit, as in the case of a single tail.

'According to the mechanical generation of these appendages, the matter of which is in a state of division, tenuity, and molecular independence whereof it is difficult to form an idea, each tail, in its regular portion, exhibits a simple curvature behind the line of motion of the nucleus. At its origin each of these tails is tangential to the radius vector, or rather is inclined to it at a small angle.

'With respect to the special form of any particular tail, it

must be regarded as the envelope of matters of the same density which successively abandon the head of the comet, under the triple influence of the repulsive force, the power of solar attraction, and the general velocity, to which we must add, as Bessel has done, the small velocity of the nucleal emission. If we consider at a given moment the whole of the molecules thus driven from the narrow sphere of attraction of the comet, they will be found principally distributed over the circumference of a nearly circular section of the nebulosity; and if we follow the same series of particles for the next few moments, we shall see that, as a consequence of their motions in their independent trajectories, the nature of which can be assigned, they will occupy constantly increasing areas, the section continually lengthening in the plane of the orbit, while the transverse diameter increases in much less proportion. The tail of the comet, therefore, will be principally displayed in the plane of the orbit, more especially tails which are very much curved. But should they be viewed edgewise, they will appear straight, under the form of a narrow band, equally defined on the two edges, and more brilliant at the edges than in the middle. The two edges will be nearly parallel, or at all events but slightly divergent, unless the observer should be situated very near to a portion of the tail... Should there be several tails, they will appear projected one upon another, while the earth is crossing the plane of the comet's orbit, and as they are very far from being opaque, the narrowest of the tails will be seen defined in the midst of the largest, or that which is nearest to the observer. It is evident, therefore, that before they can be distinguished one from another the earth must have passed by a very considerable distance the plane of the comet's orbit.'

The above is M. Faye's explanation of the origin and development of tails, as well as of the varied appearances observable in cometary appendages. As a whole, this theory is

certainly satisfactory, but we cannot affirm, in presence of the numerous and complex facts which we have described, that it is quite complete or free from objection. For example, we do not see very clearly how M. Faye would explain the appearance of the multiple fan-shaped tail presented by the great comet of 1861, on June 30, the day when the earth was situated exactly in the plane of the orbit. In this situation the tails of the comet should have been seen projected upon each other, as described. But these are minor difficulties, arising, doubtless, from the real complexity of the phenomena, further enhanced by the effects of perspective.

As regards nucleal emissions, the sectors and luminous envelopes, &c., their formation is considered to be wholly attributable to the forces of attraction and the increasing influence of the solar calorific radiations. It is here that M. Faye refers to M. Roche, and considers the theoretical diagrams given by the latter as the most faithful representations possible of the real phenomena.

'Thus,' observes M. Faye, in conclusion, the figure of a comet, and the more extended portion of the tail, are the result of a purely mechanical action of two forces: the Newtonian attraction and the repulsion due to heat. The attraction is exercised by the respective masses of the sun and the comet, the repulsion by the incandescent surface of the sun; but it is further necessary to take into consideration the repulsive force which the heat belonging to the comet, or rather that which it receives in approaching the sun, develops amongst its molecules. From this cause arises an expansion more or less analogous to that of terrestrial bodies when brought to a gaseous state, an expansion which occurs in the phenomenon of the double nucleal emission. It is, thus, this expansion which enables the solar repulsion to take effect, and which, dilating the matter of the nucleus more and more, renders it of extreme tenuity, as