of knowledge; and who possibly overrate them from disregarding the distinction between the degree of mathematical acquirement necessary for making discoveries, and that which is requisite for understanding what others have done. That the study of mathematics, and their application to astronomy, are full of interest, will be allowed by all who have devoted their time and attention to these pursuits; and they only can estimate the delight of arriving at the truths they disclose, whether it be in the discovery of a world or of a new property of numbers,'
After giving an account of the law of gravitation, and treating of the rules of Kepler, the figures of the heavenly bodies, and the inequalities in the motions of the planets, Mrs Somerville makes the following interesting observations on the stability of our system:—
'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
