sponding periods of rotation are 3·1 and 8·81 years. They both revolve, therefore, on either hand, outside of the limit, 2·8, assigned by Bode's law. If we take account of the eccentricities, 131 comes within the distance 1·31 from the sun, and 175 goes as far as 4·73 from it. The asteroids, therefore, perform their movements within a very extended zone, and the ensemble of their positions forms a kind of ring, the breadth of which is more than three times the distance of the earth from the sun. A comparison of the eccentricities shows a mean of 0·15, much higher than the corresponding mean, 0·86, of the older planets. This, too, indicates that there are notable differences in the conditions of their formation. The difference is still more striking in the inclinations of their orbits. The mean of the inclinations is 8°, a little higher than that of Mercury and that of the equator of the sun. But of two hundred and ninety-three asteroids, there are seventeen that have inclinations higher than 20°. When their mean distances are also considered, these seventeen seem to arrange themselves in two groups, around the distances 2·75 and 3·15 respectively; but this appears to be only because asteroids are more numerous in those two regions. It is also noteworthy that the much inclined orbits are usually also very eccentric, but the converse does not hold. A great eccentricity does not seem to involve of necessity a great inclination.
The question may arise whether the asteroids may not all at first have been placed in orbits of slight eccentricity and slightly inclined to the plane of the ecliptic, and their eccentricities and inclinations then have increased considerably—at least those of some of them—under the influence of perturbations. The researches of Lagrange and Laplace have shown that the eccentricities and inclinations of the old planets could vary under the influence of their mutual attractions only within narrow limits. But this result is established only for determined distances of the planets from the sun. Is it sure in advance for other intermediate positions, and particularly for the space in which the asteroids move? Leverrier asked this question, and made the curious remark on the subject that there exists, between Jupiter and the sun, a region in which, if we place a small mass, in an orbit but little inclined to that of Jupiter, that mass will leave its primary orbit and attain large inclinations to the plane of the orbit of Jupiter and to that of Saturn. It is remarkable that this position is at nearly twice the distance of the earth from the sun—that is, near the interior edge of the zone in which the minor planets are found. This fact, interesting as it is in itself, does not explain the large inclinations that have been determined at the distances 2·15 and 3·15, which are very different from those indicated by Leverrier as those at which a certain amount of in-
