SECTION II.

METHOD OF ESTIMATING THE MASSES OF COMETS BY

OPTICAL CONSIDERATIONS.

The masses of Encke's comet and the comet of Taurus determined by M. BabinetObjections to this method of determination.

We have thus a determination of cometary masses deduced from the reciprocal disturbances exercised by comets and the planets on one another. It shows that comets have extremely small masses, since, greatly disturbed themselves in their course when they approach a planet, they appear never to have exercised any disturbing influence upon the movements of the planet itself. But, from the value found for the mass of Lexell's comet-a value which, however, is only a maximum limit-it may be seen how far a comet is from being considered a visible nonentity (rien visible), to make use of the forcible expression of M. Babinet. The 5,000th part of the mass of the terrestrial globe is equivalent to the sixtieth part of the mass of the moon, a quantity, it will be agreed, far from negligible.

For the justification of his expression M. Babinet has relied upon the following optical considerations. He has called attention to the known fact that stars of exceedingly faint light may be seen through cometary nebulosities without their light losing any of its intensity. Considering, for

example, the comet of Encke, which in 1828 had the appearance of a globe-shaped nebulous mass of 311,000 miles in diameter, and through which Struve saw, without any apparent diminution of lustre, a star of the eleventh magnitude, M. Babinet reasons as follows:-The cometary nebulosity having in no respect altered the luminous intensity of the star, we may conclude that its intensity could not have been the sixtieth part of that of the star. Now, the atmosphere illuminated by the full moon obliterates all stars of less than the fourth magnitude, and yet the lunar light has, according to Wollaston, an illuminating power 800,000 times less than that of the sun. Lastly, taking into consideration the relative thicknesses of our atmosphere and of the comet, M. Babinet has arrived at this conclusion: that the substance of a coinet is of no greater density than that of our atmosphere divided by the enormous number forty-five thousand billions. According to this reckoning Encke's comet would hardly weigh twelve hundred tons.

The same method of estimating cometary masses by optical considerations has also been applied by M. Babinet to the comet of 1825, the so-called comet of Taurus. We have seen that the comet, when interposed before a star of the fifth magnitude, altered its brightness in no perceptible degree. The star in question had, therefore, not lost more than half a magnitude, or about a fifth of its light. It had consequently preserved at least four-fifths of its normal brightness. Now, its light was then traversing a stratum of about 5,000 miles in thickness; that is to say, a thousand times the thickness of the atmosphere, supposing it to be throughout of the density of the air at the surface of the earth. And as it is known that light in traversing perpendicularly our atmosphere loses more than a quarter of its intensity, it follows that the brightness of the star must have been reduced to the fraction (3)1,000 of its real brightness, if the density of the cometary nebulosity were

the same as that of the air. This density is, therefore, enormously less, and it is expressed by a fraction having unity for its numerator, and for its denominator a number consisting of 126 figures. When,' he says, in conclusion, 'Sir John Herschel, in his last work upon astronomy, spoke of a few ounces as the mass of a comet's tail, his statement was received with almost general incredulity. Nevertheless this estimate is quite exaggerated in comparison with the preceding.'

We will not seek to enquire if the calculations to which these ingenious methods lead are based upon data beyond all dispute, if the density is proportional to the absorption of light, and if the substance of which cometary nebulosities are formed is comparable to that of known gases, both in respect to their molecular composition and respective optical properties. But, granting the conclusion to be legitimate, it must be noticed that it is one which applies only to the comet of 1825 and to that of Encke, or at most to comets of no higher luminous intensity. The whole argument of M. Babinet depends upon the extremely feeble intensity of cometary light as compared with the illumination of the atmosphere by the sun, and the great extent of the nebulosity traversed by the stellar light. This reasoning, therefore, does not hold good in respect to very luminous comets-those, for example, which have been seen at noonday and in sunshine with the naked eye-such as that of the year B.C. 43, and those of the years 1006, 1402, 1532, 1577, 1618, 1744, and especially the great comet of 1843, which was observed at Florence at noonday, at 1° 23′ distance from the sun. The first comet of 1847 was visible at London in the vicinity of the sun. Even if we set aside these as exceptionally brilliant comets, we have seen that the obser vations of the 5th comet of 1857, on September 8, were in no respect obstructed by the light of the moon. Such comets are not to be compared with Encke's comet, a feeble

nebulosity, with hardly any central condensation.* Besides, it is not certain that the stars which have been seen through cometary nebulosities would not have been changed in their intensity, perhaps even eclipsed, if the occultation, instead of taking place behind some portion of the nebulosity, had occurred strictly behind the nucleus, the most luminous portion of the head of the comet. No occultation of this kind has yet, to our knowledge, been proved with certainty to have taken place. It would therefore be wrong to generalise upon the foregoing conclusion, for, whilst everything leads us to believe that cometary masses are in general greatly inferior to the planetary masses, there is nothing to prove that certain amongst them may not attain a value sufficiently great to produce, in the event of a rencontre with the earth, or with any other planet, a shock or some other kind of sensible perturbation.

* This condensation, however, has been sometimes much less feeble. M. Faye remarks: 'The relative density of Encke's comet must be pretty considerable, since it can appear to the naked eye as a star of the fourth magnitude.' + [See Chapter X. sec. ii. p. 294.--ED.]

SECTION III.

THIRD METHOD OF DETERMINING THE MASSES OF COMETS.

Theory of the formation and development of cometary atmospheres under the influence of gravitation and a repulsive force-Calculations of M. Edouard RocheMasses of the comets of Donati and Encke as determined by this method.

We are now about to see the same question, when investigated by another method, lead to results quite different to those of M. Babinet.* Between the opinions-entirely conjectural, be it observed of the savants of the eighteenth century who held that comets were bodies dense and massive as the planets, and those of some contemporary astronomers who regard them as visible nonentities, there is room for a determination which is removed from both extremes, and is moreover better justified.

For this method of determination we are indebted to M. Edouard Roche, professor in the Faculty of Sciences at Montpellier. In a series of very remarkable researches into the theory of cometary phenomena, which we shall analyse further on, M. Roche shows that there is a determinate relation

*The following is the passage from the Outlines of Astronomy, to which Babinet alludes (ante, p. 283): 'Newton has calculated (Princ., iii. p. 512) that a globe of air of ordinary density at the earth's surface of one inch in diameter, if reduced to the density due to the altitude above the surface of one radius of the earth, would occupy a sphere exceeding in radius the orbit of Saturn. The tail of a great comet, then, for aught we can tell, may consist of only a very few pounds or even ounces of matter.' But Herschel, it will be noted, speaks only of tails, not of atmospheres and nuclei.