ded within a globe through the orbit of Mercury, when at its least distance, there will be a hundred and seventeen thousand, six hundred, and forty-nine comets, similarly included, within the globe through the orbit of Herschel. But as there are thirty ascertained to be within the former globe, there will therefore be three millions, five hundred and twenty-nine thousand, four hundred and seventy within the orbit of Herschel.

Thus it appears that, supposing no comet ranging within the limits of Mercury has escaped observation, that portion of space enclosed within the globe through Herschel, must be swept by at least three millions and a half of comets. But there can be no doubt that much more than thirty comets pass within the globe through Mercury; for it would be contrary to all probability to assume that, notwithstanding the many causes obstructing the discovery of comets, and the short period during which we have possessed instruments adequate to such an enquiry, we should have discovered all the comets ranging within that limit. It is, therefore, more probable that seven millions of comets are enclosed within the known limits of the system, than the lesser number! Such is the astounding conclusion to which M. Arago's reasoning leads.

The light of comets is an effect of which astronomers have hitherto given no satisfactory account. If any of these bodies had been observed to have exhibited phases like those of the moon and the inferior planets, the fact of their being opaque bodies, illuminated by the sun, would be at once established. But the existence of such phases must necessarily depend upon the comet itself being a solid mass. A mere mass of cloud or vapour, though not itself luminous, but rendered visible by borrowed light, would still exhibit no effect of this kind its imperfect opacity would allow the solar light to affect its constituent parts throughout its entire depth-so that, like a thin fleecy cloud, it would appear not superficially illuminated, but receiving and reflecting light through all its dimensions. With respect to comets, therefore, the doubt which has existed is, whether the light which proceeds from them, and by which they become visible, is a light of their own, or is the light of the sun shining upon them, and reflected to our eyes like light from a cloud. For a long period this question was sought to be determined by the discovery of phases. M. Arago then proceeded to apply to the question a very elegant mode of investigation, depending on a property by which reflected light may be distin

* Polarisation.

guished from direct light, and the existence of which property there are sufficient optical means of detecting. He has, however, within the last year, furnished, as we conceive, much more simple and satisfactory means of putting the question finally at rest; if, indeed, it be not already decided.

It is an established property of self-shining bodies, that at all distances from the eye they have the same apparent splendour. Thus the sun, as seen from the planet Herschel, seems as bright as when seen from the earth. It is true that he is much smaller, but still equally bright. The smallest brilliant may be as bright as the largest diamond. We must not here be understood to imply that he affords the same light; that is quite another effect. What is intended to be conveyed, will perhaps be best understood by considering the effect of viewing the sun through a pin hole made in a card. The card being placed at a small distance from the eye, it is evident that the eye will view only a small portion of the sun's disc, limited by the magnitude of the pin hole; but that portion, so far as it goes, will be as bright as it would be were the card removed. Now, the effect here produced, by limiting the portion of the sun's disc which the eye is permitted to see, is precisely the same as if the eye were carried to so great a distance from the sun, that its apparent magnitude would be reduced to equality with that portion of its disc which is seen through the hole in the card.*

Now, applying this principle to the question of cometary light, it will follow that, if a comet shines by light of its own, and not by light received from the sun, it will, like all other self-luminous bodies, have the same apparent brightness at all distances. It will therefore cease to be visible, not from want of sufficient apparent brightness, but from want of sufficient visual magnitude. Now, it may be shown that the limit of visual magnitude which would cause the disappearance of a selfluminous body is so extreme, that it would be wholly inapplicable to this case. By varying the magnitude of the objectglass of a telescope (which may be easily done), with which such a body is viewed, in proportion to the magnifying power of the eye-glass, it is always possible to make the image of the same apparent brightness; that is, supposing the object itself to maintain. a uniform splendour. Consequently, if a body, submitted to this species of observation, cease to be visible even by a telescope, it will follow, that it must disappear either by a very extreme diminution of visual magnitude, or by the loss of its own intrinsic

This property is demonstrable by mathematical reasoning.

splendour. Now, to apply this test to the question of comets. Let us ask in what manner they disappear? Is their disappearance the consequence of an excessive diminution of visual magnitude? Or is it to be attributed to the diminished quantity of light which they transmit? Every astronomer will immediately reply that the latter only can cause the disappearance. The greater number of comets, including the most brilliant and remarkable one of 1680 more especially, have obviously disappeared by the gradual enfeeblement of their light. They were, as it were, extinguished. At the very time they ceased to be visible, they possessed considerable visual magnitude. But such a mode of disappearance is incompatible with the character of a self-luminous body, unless we suppose that, from some physical cause, it gradually loses its luminosity.

But, in answer to this is adduced the observed fact, that the dimensions of comets are enlarged as they recede from the sun; that the luminous matter, thus existing in a less condensed state, will shine with a proportionally enfeebled splendour; and that at length, by the dilatation of the body, the light becomes so dilute, that it is incapable of affecting the retina so as to produce

sensation.

In answer to this objection, M. Arago has submitted to examination the rate at which comets increase their dimensions as they recede from the sun, according to Valz; and calculates the corresponding diminution of intrinsic splendour which would arise from such a cause. The question then is, whether, by such a diminution of splendour, the brightest comets would be invisible beyond the orbit of Jupiter? This question he proposes to decide by the following experimental test, to be applied to some future comet.

Let a telescope be selected having a large opening and low magnifying power, by the aid of which the comet may be observed in every part of its visible course. Let the body be observed with this instrument, at some determinate distance from the sun, such as, for example, the distance of Venus. M. Arago shows how, by applying different magnifying powers to the telescope under these circumstances, the image of the comet may be made to assume different degrees of brightness. He shows also how the magnifying power may be regulated, so as to exhibit the image of the comet with just that degree of brightness with which it would appear at any given increased distance to the lowest magnifying power; on the supposition of its being a self-shining body, losing brightness by reason of the enlargement of its dimensions. In this way, he shows that the actual brightness which the comet ought to have at any given distance

from the sun, when looked at with any given magnifying power, may be predicted. He proposes, then, that, this observation being previously made, the comet should be observed subsequently at the proposed distances. If it appear with that degree of brightness which it ought to have in correspondence with such previous observations, then there will be a presumption that it shines with its own light. But if, as is probable, and perhaps nearly certain, the splendour of the comet at increased distances will be greatly less than it ought to be, and that it will be wholly invisible at distances at which it ought to be seen, then there will be conclusive proof that it is a body not self-luminous, but one which derives its light from the sun; and that its disappearance, when removed to any considerable distance from that luminary, arises from the extreme faintness of the light which its attenuated matter reflects.

It will, of course, be perceived, that the enlargement of the volume of the comet will produce a diluting effect upon its reflected light, as much as it would if it shone with direct light; and this furnishes an additional reason for its rapid disappearance as it recedes from the sun.

It will doubtless excite surprise, that the dimensions of a comet should be enlarged as it recedes from the source of heat. It has been often observed in astronomical enquiries, that the effects, which at first view seem most improbable, are nevertheless those which frequently prove to be true; and so it is in this case. It was long believed that comets enlarged as they approached the sun; and this supposed effect was naturally and probably ascribed to the heat of the sun expanding their dimensions. But more recent and exact observations have shown the very reverse to be the fact. Comets increase their volume as they recede from the sun; and this is a law to which there appears to be no well-ascertained exception. This singular and unexpected phenomenon has been attempted to be accounted for in several ways. Valz ascribed it to the pressure of the solar atmosphere acting upon the comet; that atmosphere, being more dense near the sun, compressed the comet and diminished its dimensions; and, at a greater distance, being relieved from this coercion, the body swelled to its natural bulk, A very ingenious train of reasoning was produced in support of this theory. The density of the solar atmosphere and the elasticity of the comet being assumed to be such as they might naturally be supposed, the variations of the comet's bulk were deduced by strict reasoning, and showed a surprising coincidence with the observed change in the dimensions. But this theory is tainted by a fatal error. It proceeds upon the supposition that the comet, on the one

hand, is formed of an elastic gas or vapour; and, on the other, that it is impervious to the solar atmosphere through which it moves. To establish the theory, it would be necessary to suppose that the elastic fluid composing the comet should be surrounded by a nappe or envelope as elastic as the fluid composing the comet, and yet wholly impenetrable by the solar atmosphere. Several solutions of this phenomenon have been proposed by Sir John Herschel: one is, that the comet consists of a cloud of particles, which either have no mutual cohesion, or none capable of resisting their solar gravitation; that, therefore, these particles move round the sun as separate and independent planets, each describing an ellipse or parabola, as the case may be. If this be admitted, it is demonstrable on geometrical principles, and indeed it follows as a necessary consequence of the principle of gravitation, that the particles thus independently moving, must converge as they approach the sun, so as to occupy a more limited space and to become condensed; and that on receding from the sun, they will again diverge and occupy increased dimensions.

Herschel insists upon this the more, because he conceives it has the character of a vera causa. The fact is, the hypothetical part of it consists, not in the assumed effect of the gravitation of the particles of the comet, but in the assumption that the mutual cohesion or mutual gravitation of these particles is a quantity evanescent in comparison with their separate gravitation towards the sun. This can scarcely be ranked as any thing but a supposition assumed to account for the phenomena.

Another theory proposed by Sir John Herschel, which indeed is not altogether incompatible with the simultaneous operation of the former cause, is, that the nebulous portion of the comet, or that portion which reflects the sun's rays, is of the nature of a fog, or a collection of discrete particles of a vaporisable fluid floating in a transparent medium;-similar, for example, to the cloud of vapour which appears at some distance from the spout of a boiling kettle. Now, since these molecules, during the comet's approach to the sun, absorb its rays and become heated, a portion of them will be constantly passing from the liquid to the gaseous or invisible As this change must commence from without, and must be propagated inwards, the effect will be a diminution of the comet's visible bulk. On the other hand, as it retreats from the sun, it will lose by radiation the heat thus acquired; which, in conformity with the general analogy of radiant heat, will escape chiefly from the unevaporated or nebulous mass within. The

state.

*Memoirs Royal Astron. Soc. Vol. VI. P. 104.