physical constitution, they have become, through the medium of exact calculation, unexpected instruments of inquiry into points connected with the planetary system itself, of no small importance. We have seen that the movements of the comet of Encke, thus minutely and perseveringly traced by the eminent astronomer whose name is used to distinguish it, has afforded ground for believing in the presence of a resisting medium filling the whole of our system. Similar inquiries, prosecuted in the cases of other periodical comets, will extend, confirm, or modify our conclusions on this head. The perturbations, too, which comets experience in passing near any of the planets, may afford, and have afforded, information as to the magnitude of the disturbing masses, which could not well be otherwise obtained. Thus the approach of this comet to the planet Mercury in 1838 afforded an estimation of the mass of that planet, the more precious, by reason of the great uncertainty under which all previous determinations of that element laboured. Its approach to the same planet in the present year (1848) will be still nearer. On the 22d of November their mutual distance will be only fifteen times the moon's distance from the earth. (599.) It is, however, in a physical point of view that these bodies offer the greatest stimulus to our curiosity. There is, beyond question, some profound secret and mystery of nature concerned in the phænomenon of their tails. Perhaps it is not too much to hope that future observation, borrowing every aid from rational speculation, grounded on the progress of physical science generally, (especially those branches of it which relate to the æthereal or imponderable elements), may ere long enable us to penetrate this mystery, and to declare whether it is really matter, in the ordinary acceptation of the term, which is projected from their heads with such extravagant velocity, and if not impelled, at least directed in its course by a reference to the sun, as its point of avoidance. In no respect is the question as to the materiality of the tail more forcibly pressed on us for consideration, than in that of the enormous sweep which it makes round the sun in perihelio, in the manner of a straight and rigid rod, in defiance of the law of gravitation, nay, even of the received laws of motion, extending (as we have seen in the comets of 1680 and 1843) from near the sun's surface to the earth's orbit, yet whirled round unbroken; in the latter case through an angle of 180° in little more than two hours. It seems utterly incredible that in such a case it is one and the same material object which is thus brandished. If there could be conceived such a thing as a negative shadow, a momentary impression made upon the luminiferous æther behind the comet, this would represent in some degree the conception such a phænomenon irresistibly calls up. But this is not all. Even such an extraordinary excitement of the æther, conceive it as we will, will afford no account of the projection of lateral streamers; of the effusion of light from the nucleus of a comet towards the sun; and its subsequent rejection; of the irregular and capricious mode in which that effusion has been seen to take place; none of the clear indications of alternate evaporation and condensation going on in the immense regions of space occupied by the tail and coma,-none, in short, of innumerable other facts which link themselves with almost equally irresistible cogency to our ordinary notions of matter and force. (600.) The great number of comets which appear to move in parabolic orbits, or orbits at least undistinguishable from parabolas during their description of that comparatively small part within the range of their visi bility to us, has given rise to an impression that they are bodies extraneous to our system, wandering through space, and merely yielding a local and temporary obedience to its laws during their sojourn. What truth there may be in this view, we may never have satisfactory grounds for deciding. On such an hypothesis, our elliptic comets owe their permanent denizenship within the sphere of the sun's predominant attraction to the action of one or other of the planets near which they may have passed, in such a manner as to diminish their velocity, and render it compatible with elliptic motion.1 A similar cause acting the other way, might with equal probability, give rise to a hyperbolic motion. But whereas in the former case, the comet would remain in the system, and might make an indefinite number of revolutions, in the latter it would return no more. This may possibly be the cause of the exceedingly rare occurrence of a hyperbolic comet as compared with elliptic ones. (601.) All the planets without exception, and almost all the satellites, circulate in one direction. Retrograde comets, however, are of very common occurrence, which certainly would go to assign them an exterior or at least an independent origin. Laplace, from a consideration of all the cometary orbits known in the earlier part of the present century, concluded that the mean or average situation of the planes of all the cometary orbits, with respect to the ecliptic, was so nearly that of perpendicularity, as to afford no presumption of any cause biassing their directions in this respect. Yet we think it worth noticing, that among the comets which are as yet known to describe elliptic orbits, not one whose inclination is under 17° is retrograde; and that out of thirty-six comets which have. had elliptic elements assigned to them, whether of great or small excentricities, and without any limit of inclination, only five are retrograded, 1 The velocity in an ellipse is always less than in a parabola, at equal distances from the sun; in an hyperbola always greater. and of these only two, viz. Halley's and the great comet of 1843, can be regarded as satisfactorily made out. Finally, of the 125 comets whose elements are given in the collection of Schumacher and Olbers, up to 1823, the number of retrograde comets under 10° of inclination is only 2 out of 9, and under 20°, 7 out of 23. A plane of motion, therefore, nearly coincident with the ecliptic, and a periodical return, are circumstances eminently favourable to direct revolution in the cometary as they are decisive among the planetary orbits. [Here also we may notice a very curious remark of Mr. Hind, (Ast. Nachr. No. 724,) respecting periodic comets, viz., that, so far as at present known, they divide themselves for the most part into two families, the one having periods of about 75 years, corresponding to a mean distance about that of Uranus; the other corresponding more nearly with those of the asteroids, and with a mean distance between those small planets and Jupiter. The former group consists of four members, Halley's comet revolving in 76 years, one discovered by Olbers in 74, De Vico's 4th comet in 73, and Brorsen's 3d in 75, respectively. Examples of the latter group are to be seen in the table, p. 552, at the end of this volume. It may be added, also, that one or two of the asteroids are described as having a faint nebulous envelope about them, indicating somewhat of a cometic nature.] PART II. OF THE LUNAR AND PLANETARY PERTURBATIONS. "Magnus ab integro sæclorum nascitur ordo."-VIRG. Pollio. CHAPTER XII. SUBJECT PROPOUNDED.-PROBLEM OF THREE BODIES.-SUPERPOSITION (602.) IN the progress of this work, we have more than once called the reader's attention to the existence of inequalities in the lunar and planetary motions not included in the expression of Kepler's laws, but in some sort supplementary to them, and of an order so far subordinate to those leading features of the celestial movements, as to require, for their detection, nicer observations, and longer continued comparison between facts and theories, than suffice for the establishment and verification of the elliptic theory. These inequalities are known, in physical astronomy, by the name of perturbations. They arise, in the case of the primary planets, from the mutual gravitations of these planets towards each other, which derange their elliptic motions round the sun; and in that of the secondaries, partly from the mutual gravitation of the secondaries of the same system similarly deranging their elliptic motions round their common primary, and partly from the unequal attraction of the sun and planets on them and on their primary. These perturbations, although small, and, in most instances, insensible in short intervals of time, yet, when accumulated, as some of them may become, in the lapse of ages, alter very greatly the original elliptic relations, so as to render the same elements of the planetary orbits, which at one epoch represented perfectly well their movements, inadequate and unsatisfactory after long intervals of time. (603.) When Newton first reasoned his way from the broad features of the celestial motions, up to the law of universal gravitation, as affecting all matter, and rendering every particle in the universe subject to the influence of every other, he was not unaware of the modifications which this generalization would induce upon the results of a more partial and limited application of the same law to the revolutions of the planets about the sun, and the satellites about their primaries, as their only centres of attraction. So far from it, his extraordinary sagacity enabled him to perceive very distinctly how several of the most important of the lunar inequalities take their origin, in this more general way of conceiving the agency of the attractive power, especially the retrograde motion of the nodes, and the direct revolution of the apsides of her orbit. And if he did not extend his investigations to the mutual perturbations of the planets, it was not for want of perceiving that such perturbations must exist, and might go the length of producing great derangements from the actual state of the system, but was owing to the then undeveloped state of the practical part of astronomy, which had not yet attained the precision requisite to make such an attempt inviting, or indeed feasible. What Newton left undone, however, his successors have accomplished; and, at this day, it is hardly too much to assert that there is not a single perturbation, great or small, which observation has become precise enough clearly to detect and place in evidence, which has not been traced up to its origin in the mutual gravitation of the parts of our system, and minutely accounted for, in its numerical amount and value, by strict calculation on Newton's principles. (604.) Calculations of this nature require a very high analysis for their successful performance, such as is far beyond the scope and object of this |