compose it having the same polarisation, tend also to approach the sun. But these particles are moving in a space filled with matter having an opposite polarisation, and which is constantly being replaced. Thus the two polarisations neutralise each other, and the particles which compose the aigrette will acquire the opposite property to that which they had previously, in proportion as they recede from the comet.'

SECTION VI.

THEORY OF COMETARY PHENOMENA.

Researches of M. E. Roche upon the form and equilibrium of the atmospheres of celestial bodies under the combined influence of gravitation, solar heat, and a repulsive force-Figure of equilibrium of a solid mass submitted to gravitation and the heat of the sun-Comets should have two opposite tails-Completion of the theory of cometary tides by the admission of a repulsive force, real or apparent-Accordance of the theory so completed with observation.

M. EDOUARD ROCHE has devoted a series of highly interesting memoirs to the discussion of the figure assumed by the atmosphere of celestial bodies under the action of the forces of the solar system. He has more particularly given his attention to the study of cometary atmospheres, and to all the phenomena which take place in and around cometary masses.

M. Roche begins by reducing the question to its simplest form. He assimilates a comet to an entirely fluid mass, sensibly homogeneous, and having no movement of rotation.' The forces which act upon it are the mutual attraction of its own particles and gravitation towards the sun. For such a mass to be in equilibrium under the action of these forces it must have the figure of a prolate spheroid with its centre at the centre of gravity, and its axis of revolution coincident with the radius vector from the sun.

Introducing then the motion of the comet towards the sun, M. Roche examines the modifications that would be occasioned

in the figure of the atmosphere by a diminution of the distance between itself and the sun, only taking into account the mutual attraction of the two bodies. At first spherical when the comet is far off, its figure becomes ellipsoidal, and gradually lengthens as it draws near the sun.' But there is a limit to the amount of lengthening, a limit which depends upon the density of the fluid of which the cometary atmosphere is formed.

Although, according to M. Roche, there may not exist amongst the numerous comets of the solar system any one whose physical constitution accords exactly with the above hypothesis, nevertheless it is more natural to consider the general question of a central nucleus surrounded by an atmosphere of much greater rarity. In all the atmospheres of the celestial bodies the gaseous envelope is retained by gravitation towards the nucleus. Let us see what theory gives on this new hypothesis:

'On following with care,' says M. Roche, 'the phenomena developed by a comet during its approach to the sun, we clearly see that they result, at least in part, from the increasing action of the solar gravity. The difference of the attractions exerted by the sun upon the nearest and the furthest portions of the cometary atmosphere must needs have the effect of lengthening the comet in the direction of the sun, and more and more in proportion as the distance of the comet from the latter continues to decrease. In a word, the cause that produces the terrestrial tides will here manifest itself in a similar manner, but on a much grander scale, in the neighbourhood of the perihelion. This has been confirmed by my mathematical investigations.' In fact, the surfaces of equilibrium,* originally spherical, lengthen more and more towards

* [A surface of equilibrium, or, as it is often called, a level surface, is a surface such that if a particle were placed at any point on it, the resultant of the action

the sun, as by the diminution of the distance from the sun its action increases; the comet also lengthens not only towards the sun, but also to an equal extent in the opposite direction. But the atmosphere cannot extend further than to the points where the attractions of the sun and the nucleus exactly balance one another. Any particle that escapes beyond this limiting surface of equilibrium, which is called the free surface, is then subject to the preponderating influence of the sun, and as it were abandons the comet. The exterior surfaces of equilibrium have no longer a spheroidal form: they open themselves as it were at the two poles, A and A', and consist of sheets that extend to infinity. (Fig. 63.)

Fig. 63.-M. Roche's theory of cometary phenomena. Limiting atmospheric surface of equilibrium.

'If, from any cause, the cometary fluid should pass beyond the free surface, it will spread itself in all directions over the surfaces of equilibrium that are immediately exterior; and, as they are infinite in extent, the fluid in excess will stream off through the two conical summits or poles as through two openings and lose itself in space.' (Fig. 64.) So far gravitation is the only force whose action we have

of the external forces upon the particle would act in a direction perpendicular to the surface at the point. Thus, at any point within the free, or bounding, surface of the atmosphere the resultant of the external forces acting upon the particle of the atmosphere that is situated there is perpendicular to the surface of equilibrium passing through it, and this resultant is balanced by the pressure of the atmospheric layers underneath.-ED.]

taken into account, and we have deduced from it the figure of equilibrium of a comet, regarded as a homogeneous fluid mass, or as a nucleus, either liquid or solid, surrounded by a ponderable atmosphere. We may go further still without the intervention of another force; for M. Roche finds that, as regards the free surface, its dimensions vary with the distance of the sun this surface, as it were, contracts as the comet approaches perihelion, and the fluid layer that is thus left outside it flows away at the two poles, thus forming two opposite jets along the radius vector of the sun. If the fluid is elastic and behaves like a gas, the outflow will continue so long as molecules continue to come from the interior to re

Fig. 64.-Flow of cometary matter beyond the free surface of the atmosphere. No repulsive force.

place those which escape. This is

the comet is drawing near the sun.'

what must happen whilst When the perhelion has

passed this state of things no longer continues.

But another cause will have been contributing, and doubtless in a much more powerful degree, to produce this outflow of cometary fluids from the two extremities of the axis of the comets, as represented in fig. 64. This cause is the calorific action of the solar rays upon the nucleus, an action which continues rapidly to increase in the neighbourhood of the perihelion. The accumulated heat then gradually dilates and volatilises the cometary substance which rises by the diminution of its specific weight, attains the free surface, and, passing beyond it, flows off into space, as we have just said.