rise of the tides. We have therefore no immediate and practical reason to regret the imperfection of our cometary theories. Perturbations Passing from the perturbations proper to of rotation. motions of translation, we must notice those belonging to rotation. on the surface of a planet, that we might The ellipsoid bodies of our system must, whether they began or not, have ended, sooner or later, with turning round one of their axes, and that one the most stable,that of their smallest diameter: for, as we have seen, it is their rotation that has produced their deviation from a perfectly spherical form, and determined the direction favourable to stability. The regularity of this rotation is evidently so indispensable to the existence of living bodies The planets. à priori assert this stability wherever life is possible, from the time when it became possible. But, stable as each planet is in itself, its mutual gravitation with others must introduce certain secondary modifications, the bearing of which must be upon the direction of its axis in space. It is only with regard to the earth that these modifications concern us; for however great they might be in any other body, they could in no way affect us. If the planets were perfect spheres, the total gravitation of their particles must pass through their centres of gravity; and thus, it is only through their slight failure in sphericity that they can act at all upon one another's rotation; that failure being caused by the rotation itself. We see here how the same necessity which secures the stability of the rotations, with regard to their duration and their poles, determines, from another point of view, the inevitable alteration of the parallelism of their axes.-In our own planet the precession of the equinoxes, modified by the nutation, results from the action of the other bodies of our system,-especially of the sun and moon,-upon our equatorial protuberance. The power of each body is, as in the case of the tides, in the direct ratio of its mass, and inversely to the cube of its distance; so that the sun and moon are the only bodies whose influence need be considered. Further, the extent of the deviation depends on PERTURBATIONS OF ROTATION. 219 the mass and magnitude of the earth, on the time of its rotation, on its degree of flattening, and on the obliquity of the ecliptic. The intensity of the influence must vary, as in the case of the tides, with the variable distance of the sun from the earth, and yet more of the moon; but the want of uniformity is too slight to be perceptible to direct observation. These are the general causes which determine the small changes which the rotation of our globe undergoes, in regard to the direction of its axis in space. The case of the other planets bears a general likeness to that of the earth, varied according to the different inclinations of their axes to their orbits, their position, their mass, their size, the duration of their rotation, and the degree of their flattening at the poles. On all these grounds, the perturbations of Mars are the most remarkable. The rotation of the satellites presents one The satellites. consideration of the highest interest,-that remarkable equality between the duration of this rotation and that of their circuit round their planet, by which they present always the same hemisphere, except from those very small oscillations called librations, whose law is well understood. The fact is absolutely certain only with regard to the moon; but our mechanical principles justify our erecting it into a general law of all the satellites. Lagrange has shown that it results from the preponderance that, by the action of the planet, the nearer hemisphere must acquire at the outset, whence arises a natural tendency in the satellite to return perpetually to the same position. If it is thus with the moon, there is every reason to suppose the same fact with regard to satellites belonging to heavier planets, to which they are proportionally nearer. Such are the various kinds of perturbations produced in the movements of the bodies of our system, by their mutual action. This study may be simplified and rendered much more exact, by the device of referring all these movements to a plane whose position must necessarily be independent of all their variations. -Among several planes which have been proposed, differing in their degrees of variableness, M. Poinsot has discovered one which is the only truly invariable one, but which is extremely difficult to deter Device of an invariable plane. mine, since it requires not only an estimate of the planetary masses, but data dependent on the mathematical law of the interior density of the heavenly bodies, a law which is still very hypothetical. The theory is complete; but its precise application is at present impossible. Whatever may be the practical difficulties, we cannot but feel a deep interest in seeing how Celestial Mechanics has accomplished the fixing of an invariable plane in the midst of all the interior perturbations of our system, as Newton had first recognized an inalterable velocity,-that of the centre of general gravity. These are the only two elements in our system which are rigorously independent of all the events that can occur in its interior;-of even the vastest commotions that our imagination can suggest. Such variations as they can be conceived to have could relate only to the most general phenomena of the universe, produced by the mutual action of different suns, of which they would afford us the clearest manifestation, if such knowledge were within our reach. Stability of our system. We end this study of perturbations with a recognition of the stability of our own system, in regard to all its most important constituent bodies. Setting aside the comets, all the variations whatever of any perceptible value are periodical; and their period is usually very long, while their extent is very small; so that the whole of our planetary system can only oscillate with extreme slowness round a mean state, from which it deviates very little. Through all starry changes the translations of our planets present the almost rigorous invariableness of the great axes of their elliptical orbits, and of the duration of their sidereal revolutions : and their rotation shows a regularity even more perfect, in its duration, in its poles, and even, though in a somewhat smaller degree, in the inclination of its axis to the corresponding orbit. We know, for instance, that from the time of Hipparchus, the length of the day has not varied the hundredth part of a second. Amidst all this general regularity, we perceive a special and most marked stability with regard to the elements which are concerned in the continued existence of living beings. Such are the sublime theorems of natural philosophy for which humanity is STABILITY OF THE SOLAR SYSTEM. 221 indebted to the sum of the great works executed in the last century by the successors of Newton. The general cause of these important results lies in the small eccentricity of all the principal orbits, and the small divergence of their planes. If the planets had had cometary orbits and planes, there would have been no regularity -no periodicity, and, we may add, no life upon their surface. No planets can be habitable but such as have their oscillations restricted within very narrow limits. : Resistance of a Medium. The Mathematical theory of celestial mechanics has taken no notice, thus far, of the resistance of any general medium, in which these motions are proceeding. The conformity of our mathematical tables with observed facts shows that the resistance is imperceptible in degree; yet, as it is manifestly impossible that it should be null, the geometers have endeavoured to prepare beforehand a general analysis of it. Considered apart from its intensity, this action is of a totally different nature from that of perturbations, though gradual like them for it cannot be periodical, and must always be exercised in the same direction, so as continually to diminish all velocities, and the more the greater they are. It cannot alter the positions of the orbits, but can by possibility affect only their dimensions, and periodic times, and the duration of rotations: that is, it affects the elements which are spared by the perturbations. Thus, the rotations must become slower, the orbits must grow smaller and rounder, and their periodic times shorter; because, as velocity diminishes, the solar action must become more powerful, and these effects are not only continuous, but always increasing in rapidity. So, in a future too remote to be assigned, all the bodies of our system must be united to the solar mass, from which it is probable that they proceeded: and thus the stability of the system is simply in relation to the perturbations properly so called. These are among the incontestable indications of Celestial Mechanics. As yet, we practically fail to recognize the effect of a resisting medium. We neither trace its operations, nor should know how to calculate it if we could trace it. Whenever we do, it will be by the study of comets; for their small mass, and the great surface which they present to the action of the medium when their atmospheres are widely diffused, must render its resistance much more appreciable than in the case of planets,-their velocity being besides naturally at its maximum at the moment of this expansion. Some contemporary astronomers believe that they have established the effect of this resistance in regard to one or two comets. Hitherto the study of these bodies seems to be only negatively useful, to prevent the return of the absurd terrors which they formerly occasioned. We now see that there is no body in our system, however insignificant, whose theory may not offer to us a direct and positive interest, since we may owe to comets the knowledge of one of the most important general laws of the system to which we belong, and that which, in a remote future, must chiefly rule its destinies.1 Independence of the solar system. In our geometrical review we saw, by the agreement of astronomical tables with direct observation, that our system is independent of all that lies outside. This incontestable truth is confirmed by the mechanical view. If our system gravitated towards any of the suns outside, the action of other suns would nearly neutralize the tendency. Again, it would be only by an unequal action of those suns upon our plantets that any change could be occasioned. Again, the vast distances would, according to our law of gravitation, make the action of remote suns imperceptible. The nearest body, if a million times heavier than our system, would produce an effect incalculably smaller than the action which occasions our tides. We may therefore pronounce the independence of our system to be perfectly certain. I notice this because we seem to find here the only exception to the great encyclopedical law which is the basis of this work,that the most general phenomena rule the most particular, without being in any degree reciprocally influenced. Thus our astronomical phenomena regulate those of our own globe, whether physical, chemical, physiological, or social. Yet here we find that the phenomena of the universe have no influence over those of the solar system. There is no difficulty about this to persons who, like myself, admit 1 M. Comte estimates too lightly the indications of a medium given by Encke's comet.-J. P. N. |