hold in store, it is certain that they affect in no respect either the cause of the cometary movements or their laws.

Lastly, there are unexplained facts, such as the nonreappearance of the comet of 300 years' period (that of 1264-1556), the non-return of some of the comets of short periods, and the division of Biela's comet into two distinct

comets.

But this last and very curious phenomenon may perhaps have been due to the action of external forces, and in this case it would belong to the second or physical category of problems involved in the question before us.

The mass, the density, the physical constitution of the luminous nucleus, of the atmosphere surrounding it, and of the matter which streams out from it as the comet draws near the sun; the variations of form and volume of the nucleus and the nebulosity; the singular transformations which are revealed to us by the telescope, more especially those relating to the origin, development, and disappearance of the tail, are all facts that have been well and carefully observed, as the preceding chapters testify, but which are nevertheless difficult to coordinate into a logical whole and to reduce to a single principle, from which all the observed facts could be deduced as so many particular consequences. The phenomena presented to us by these bodies indicate that they have a special constitution of their own, as has been justly remarked by M. Roche, the author of some researches of the highest interest that we shall shortly proceed to analyse. In the meanwhile we will give M. Roche's views on the subject before us :

'Comets are characterised less by the form and position of their orbits than by the changes they submit to during the times of their apparitions, and which sometimes succeed each other with wonderful rapidity. These changes denote a physical condition peculiar to comets, and mark important

distinctions between them and other celestial bodies. Whilst the centre of gravity of the comet is describing its trajectory around the sun, under the influence of the solar gravitation and the disturbing action of the planets it may happen to approach, the comet itself experiences important changes, in which it is impossible not to recognise the action of the sun; for it is chiefly in the neighbourhood of the perihelion that these modifications are developed upon the grandest scale.'

M. Roche divides the phenomena in question into two kinds—those relating to the tail, its appearance, its varied form, its brightness and extent; and those which have reference to the variations of form or luminous intensity of the parts which constitute the head. The latter, as we have seen, are phenomena which have only been observed in comparatively recent times, whilst the formation of the tail has been long studied. To the explanation of these appendages, considered as the principal characteristic element of cometary bodies, astronomers have devoted many efforts. The hypotheses arising from these attempts are numerous; but they may be distinguished into four principal hypotheses, which we will now proceed to describe successively.

SECTION II.

CARDAN'S HYPOTHESIS.

Cometary tails considered as effects of optical refraction-Objections made by Newton and Gregory-New theory of Gergonne : ideas of Saigey on the subject of planetary tails-Difficulties and lacunæ in this theory.

PANETIUS, a philosopher of antiquity, held the belief that comets did not really exist, but were false appearances. They are,' he says, 'images formed by the reflexion, in the heavenly expanse, of the rays of the sun.' In the opinion of Cardan and some astronomers and physicists, Apian, Tycho Brahé, in the Renaissance, and Gergonne and Saigey, in our time, the tails of comets are simple optical appearances.

The following is the passage in Cardan's work (De Subtilitate) which relates to this question: 'It is, therefore, evident that a comet is a globe situated in the heavens and rendered visible by the illumination of the sun; the rays which pass through it form the appearance of a beard or tail.'* The Milanese doctor has entered into no particulars respecting the manner in which these appearances are formed, which, in his opinion, were doubtless analogous to the effects of refraction produced by the convergence of luminous rays passing

* Quo fit ut clarè pateat cometem globum esse in cælo constitutum, qui a sole illuminatus videtur, et dum radii transeunt; barbæ aut caudæ effigiem formant.' (De Subtilitate, lib. iv. 118; edition 1554.)

through a lenticular glass or globe filled with water; such as were formerly employed by artisans for concentrating the light upon their work.

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But, as Newton and Gregory have remarked,' justly objects M. Roche, 'the light is only visible in proportion as it reaches the eye; it would be necessary, therefore, that the solar rays, refracted by the head of the comet and collected behind in one convergent beam, should be sent towards the earth by material particles. Thus, sometimes when the sun is near the horizon and hidden by clouds, its rays, reflected by particles of air or vapour, are seen clearly defined against the sky like luminous jets.'

The fundamental idea upon which this explanation rests, and which still bears the name of Cardan, has since been several times taken up and modified. Following in the same order of ideas, we shall mention only a memoir by Gergonne, entitled Essai analytique sur la nature des queues des comètes. The origin of the phenomenon is there considered as purely optical, tails being only an appearance due to the most illuminated portion of the cometary atmosphere, or, more correctly speaking, to the caustic surface which is the envelope of the solar rays that are refracted whilst traversing the nucleus or its surrounding layers. These rays become visible when reflected upon the particles which compose the atmosphere of the comet. But, according to this theory, the atmosphere should have a radius at least equal to the length of the tail; and this constitutes an almost insurmountable objection, which the author himself does not conceal. We must not forget that certain comets have had tails many millions of miles in length. The atmospheres of comets being certainly much more limited, the reflexion, we must suppose, takes place upon the particles of an interplanetary medium, independent of the comet itself, and extending to distances

far beyond the limits of the zodiacal light. Saigey, in his Physique du Globe, admits this explanation of cometary tails, and, according to him, planets have virtual tails, which would become real if the interplanetary spaces were filled with a matter similar to that which accompanies these last-mentioned bodies.' Saigey, it is evident by this last line, believes in the indefinite extension of cometary atmospheres, and the objection made above exists in full force. As regards the form of tails, their curvature, their multiplicity, and their oscillations, he explains them as follows: the curvature, by an effect of aberration due to the finite velocity of the propagation of light, the multiplicity by irregularities in the form of the nucleus, the oscillations by a movement of rotation, which causes these irregularities to be periodic.*

According to this system, now almost entirely abandoned, it is difficult to explain the phenomena of which we have already given an account, and which are seen by the telescope to vary from hour to hour; we mean the development of luminous jets in front of the nucleus, together with the envelopes and the lateral reflux of the luminous matter to form the edges of the tail. Nor is it less difficult to explain the formation of tails, which have sometimes been projected towards the sun, unless, not content with comparing comets to transparent and refracting globes, we are willing to make them perform at the same time the part of concave mirrors.

We have seen that the observations of occultations of stars by cometary atmospheres do not furnish proof of any refracting power whatever in the nebulosity of the head. It must,

* Speaking of the tail of the earth, he observes: 'The axis of the luminous sheaf ought to have, mathematically, the form of a spiral of Archimedes, the generating circle of which is 64,000 times greater than the terrestrial orbit; so that the most brilliant portion of this sheaf is slightly curved in the rear of the earth's movement of translation.'