These eccentricities, however, continually change, though very slowly, in the progress of time, but in such a manner that none of them can ever become very great. They may vanish, or become nothing, when the orbit will be exactly circular; in which state, however, it will not continue, but change in the course of time, into an ellipsis, of an eccentricity that will vary as before, so as never to exceed a certain limit. What this limit is for each individual planet, would be difficult to determine, the expression of the variable eccentricities being necessarily very complex. But, notwithstanding of this, a general theorem, which shows that none of them can ever become great, is the result of one of Laplace's investigations. It is this-If the mass of each planet be multiplied into the square of the eccentricity of its orbit, and this product into the square root of the axis of the same orbit, the sum of all these quantities, when they are added together, will remain for ever the same. This sum is a constant magnitude, which the mutual action of the planets cannot change, and which nature preserves free from alteration. Hence no one of the eccentricities can ever increase to a great magnitude; for as the mass of each planet is given, and also its axis, the square of the eccentricity in each, is multiplied into a given coefficient, and the sum of all the products so formed, is incapable of change. Here, therefore, we have again another

general property, by which the stability of our system is maintained; by which every great alteration is excluded; and the whole made to oscillate, as it were, about a certain mean quantity, from which it can never greatly depart.

If it be asked, Is this quantity necessarily and unavoidably permanent in all systems that can be imagined, or under every possible constitution of the planetary orbits? We answer, By no means: if the planets did not all move one way,—if their orbits were not all nearly circular, and if their eccentricities were not small, the permanence of the preceding quantity would not take place. It is a permanence, then, which depends on conditions that are not necessary in themselves; and therefore we are authorized to consider such permanence as an argument of design in the construction of the universe.

When we thus obtain a limit, beyond which all the changes that can ever happen in our system shall never pass, we may be said to penetrate, not merely into the remotest ages of futurity, but to look beyond them, and to perceive an object, situated, if we may use the expression, on the other side of infinite duration.

Though, in the detail into which we have now entered, we have anticipated many things that may be thought to belong to another place, we think that the leading facts are in this way least separat

ed from one another. Laplace, after treating of the problems of the Three Bodies generally in the Second Book, to which the observations made above chiefly refer, resumes the consideration of the same problem, and the application of it to the tables of the planets in the Sixth and Seventh. These we shall be able to pass over slightly, as much of what might be said concerning them is contained in the preceding remarks. We go on now to the Second Volume, which treats of the Figure of the Planets, and of the Tides.

In the First Book, a foundation was laid for this research by the general theorems that were investigated concerning the equilibrium of fluids and the rotation of bodies. These are applied here; first, to the figure of the planets in general; and afterwards particularly to the figure of the earth.

The first inquiry into the physical causes which determine the figure of the earth and of the other planets, was the work of Newton, who showed, that a fluid mass revolving on its axis, and its particles gravitating to one another with forces inversely as the squares of their distances, must assume the figure of an oblate spheroid; and that, in the case of a homogeneous body, where the centrifugal force bore the same ratio to the force of gravity that obtains at the surface of the earth, the equatorial diameter of the spheroid must be to the polar axis as 231 to 230. The method by which this conclusion

was deduced was, however, by no means unexcep tionable, as it took for granted, that the spheroid must be elliptical. The defects of the investigation were first supplied by Maclaurin, who treated the subject of the Figure of the Earth in a manner alike estimable for its accuracy and its elegance. His demonstration had the imperfection, at least in a eertain degree, of being synthetical; and this was remedied by Clairaut; who, in a book on the Figure of the Earth, treated the subject still more fully; simplified the view of the equilibrium that determines the figure; and showed the true connection between the compression at the poles and the diminution of gravity on going from the poles to the equator, whatever be the internal structure of the spheroid. Several mathematicians considered the same subject afterwards; and, in particular, Legendre proved, that, for every fluid mass given in magnitude, and revolving on its axis in a given time, there are two elliptic spheroids that answer the conditions of equilibrium: in the instance of the Earth, one of these has its eccentricity in the ratio of 231 to 230; the other, in the ratio of 680 to 1.

The results of those investigations, with the addition of several quite new, are brought together in the work before us, and deduced according to the peculiar methods of the author. These theoretical conclusions are next applied to the experiments and

observations that have been actually made, whether by determining the length of the seconds pendu lum in different latitudes, or by the measurement of degrees. After a very full discussion, and a comparison of several different arches, on each of which an error is allowed, and this condition superadded, that the sum of the positive and negative errors shall be equal, and, at the same time, the sum of all the errors, supposing them positive, shall be minimum, Laplace finds that the result is not reconcileable with the hypothesis of an elliptic spheroid, unless a greater error be admitted in some of the degrees than is consistent with probability. In this determination, however, the Lapland degree is taken as measured by Maupertuis, and the other academicians who assisted him. The correction by the Swedish mathematicians was not made when this part of Laplace's work was published. If that correction is attended to, the result will come out more favourable to the elliptic theory than he supposes. There are, however, even after that correction is admitted, considerable deviations from the elliptic figure, such as the attraction of mountains is hardly sufficient to explain. The degrees that have been lately measured in France with so much exactness, compared with one another, give an ellipticity of about, and the same ellipticity corresponds well to the degrees measured in the trigonometrical survey of England, whether of the meridi