elusions. Gauss, communicating to Bessel in 1812 the discovery of the ratio of 718 between the mean motions of Pallas and of Jupiter, said that that value ought to be realized more and more exactly under the influence of the attraction of Jupiter, in the same way as the motions of translation and rotation of the moon are equalized. Newcomb has expressed the same opinion, to which he was led by his studies of the system of Saturn, saying that while one would think that, in the case of movements absolutely commensurable, perturbations would not fail to grow beyond limits to the point of compromising the stability of the system, the consequence is not a necessary one; there would probably be only oscillations more or less irregular, but equilibrium would be re-established incessantly. The labors of M. Gyldén and my own personal researches tend to the same conclusion.
It is therefore probable that, if the voids had not existed in the beginning, further perturbations by Jupiter would not have been sufficient to produce them; they without doubt already existed, immediately on the formation of the asteroids, and give another reason for considering the question they present as of primary interest from a cosmogonical point of view. It is of no less interest in the matter of the celestial mechanism, for it corresponds, as we have said, to a case in which the old methods default, and which has instigated the most interesting studies of the period. Laplace has already considered it in his theory of the satellites of Jupiter, but the asteroids present it to us under conditions which make its solution still more difficult.
The minor planets situated at the outer limit of the ring are interesting from several points of view. Some of them furnish a kind of transition between the asteroids and some of the periodical comets. Thus, the orbit of 175 is very like that of Tempel's periodical comet. The distinction between planets and comets, founded on the dissimilarity of their orbits, vanishes here. We have nothing left to distinguish them but their physical aspect. The asteroids of which we are speaking, being near Jupiter, are always very distant from the earth. They must, therefore, appear small in proportion to their dimensions. It is possible that, by seeking with a strong enough glass, we shall find others; and some of these may come in to corroborate the resemblances with the periodical comets. Planet 279, discovered two years ago by M. Palisa, is one of the most remarkable of the group of which we have just spoken. In 1912 it will come with the distance 1 of Jupiter, and will continue there for a considerable time. The attraction of Jupiter will then be more than one fiftieth as great as that of the sun. The calculation of the perturbations promises to be interesting and difficult,
