state of perpetual but slow change. At the present time the inclinations of all the orbits are decreasing, but so slowly that the inclination of Jupiter's orbit is only about six minutes less now than it was in the age of Ptolemy. The terrestrial eccentricity is decreasing at the rate of about 41'44 miles annually; and, if it were to decrease equably, it would be 37527 years before the earth's orbit became a circle. But, in the midst of all these vicissitudes, the major axes and mean motions of the planets remain permanently independent of secular changes; they are so connected by Kepler's law of the squares of the periodic times being proportional to the cubes of the mean distances of the planets from the sun, that one cannot vary without affecting the other.

With the exception of these two elements, it appears that all the bodies are in motion, and every orbit in a state of perpetual change. Minute as these changes are, they might be supposed to accumulate in the course of ages sufficiently to derange the whole order of nature, to alter the relative positions of the planets, to put an end to the vicissitudes of the seasons, and to bring about collisions which would involve our whole system, now so harmonious, in chaotic confusion. It is natural to inquire what proof exists that nature will be preserved from such a catastrophe? Nothing

can be known from observation, since the existence of the human race has occupied comparatively but a point in duration, while these vicissitudes embrace myriads of ages. The proof is simple and convincing. All the variations of the solar system, secular as well as periodic, are expressed analytically by the sines and cosines of circular arcs, which increase with the time; and, as a sine or cosine can never exceed the radius, but must oscillate between zero and unity, however much the time may increase, it follows that when the variations have, by slow changes, accumulated, in however long a time, to a maximum, they decrease, by the same slow degrees, till they arrive at their smallest value, and again begin a new course, thus for ever oscillating about a mean value. This, however, would not be the case if the planets moved in a resisting medium, for then both the eccentricity and the major axes of the orbits would vary with the time, so that the stability of the system would be ultimately destroyed. The existence of such a fluid is now clearly proved; and although it is so extremely rare that hitherto its effects on the motions of the planets have been altogether insensible, there can be no doubt that, in the immensity of time, it will modify the forms of the planetary orbits, and may at last even cause the destruction

of our system, which in itself contains no principle of decay.

Three circumstances have generally been supposed necessary to prove the stability of the system: the small eccentricities of the planetary orbits, their small inclinations, and the revolutions of all the bodies, as well planets as satellites, in the same direction. These, however, though sufficient, are not necessary conditions; the periodicity of the terms in which the inequalities are expressed is enough to assure us that, though we do not know the extent of the limits, nor the period of that grand cycle which probably embraces millions of years, yet they never will exceed what is requisite for the stability and harmony of the whole, for the preservation of which every circumstance is so beautifully and wonderfully adapted.

The plane of the ecliptic itself, though assumed to be fixed at a given epoch for the convenience of astronomical computation, is subject to a minute secular variation of 45"7, occasioned by the reciprocal action of the planets; but, as this is also periodical, and cannot exceed 3°, the terrestrial equator, which is inclined to it at an angle of about 23° 27′ 34′′-5, will never coincide with the plane of the ecliptic: so there never can be perpetual spring. The rotation of the earth is uniform;

therefore day and night, summer and winter, will continue their vicissitudes while the system endures, or is undisturbed by foreign causes.

Yonder starry sphere

Of planets, and of fixed, in all her wheels
Resembles nearest mazes intricate,

Eccentric, intervolved, yet regular,

Then most, when most irregular they seem.

The stability of our system was established by La Grange: a discovery,' says Professor Playfair, that must render the name for ever memorable in science, and revered by those who delight in the contemplation of whatever is excellent and sublime.' After Newton's discovery of the mechanical laws of the elliptical orbits of the planets, La Grange's discovery of their periodical inequalities is, without doubt, the noblest truth in physical astronomy; and, in respect of the doctrine of final causes, it may be regarded as the greatest of all.

Notwithstanding the permanency of our system, the secular variations in the planetary orbits would have been extremely embarrassing to astronomers when it became necessary to compare observations separated by long periods. The difficulty was in part obviated, and the principle for accomplishing it established, by La Place; but it has since been extended by M. Poinsot; it appears that there exists an invariable plane passing through

the centre of gravity of the system, about which the whole oscillates within very narrow limits, and that this plane will always remain parallel to itself, whatever changes time may induce in the orbits of the planets, in the plane of the ecliptic, or even in the law of gravitation; provided only that our system remains unconnected with any other. The position of the plane is determined by this property -that if each particle in the system be multiplied by the area described upon this plane in a given time, by the projection of its radius vector about the common centre of gravity of the whole, the sum of all these products will be a maximum. La Place found that the plane in question is inclined to the ecliptic at an angle of nearly 1° 35' 31", and that, in passing through the sun, and about midway between the orbits of Jupiter and Saturn, it may be regarded as the equator of the solar system, dividing it into two parts, which balance one another in all their motions. This plane of greatest inertia, by no means peculiar to the solar system, but existing in every system of bodies submitted to their mutual attractions only, always maintains a fixed position, whence the oscillations of the system may be estimated through unlimited time. Future astronomers will know, from its immutability or variation, whether the sun and his attendants are connected or not with.