QUESTIONS CONCERNING THE MINOR PLANETS. 199 



elusions. Gauss, communicating to Bessel in 1812 the discovery 

 of the ratio of ^ 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 ab- 

 solutely commensurable, perturbations would not fail to grow be- 

 yond 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 equi- 

 librium would be re-established incessantly. The labors of M. 

 Gylde'n and my own personal researches tend to the same con- 

 clusion. 



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 ex- 

 isted, 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 cor- 

 responds, as we have said, to a case in which the old methods de- 

 fault, 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 peri- 

 odical comets. Thus, the orbit of 175 is very like that of Tem- 

 pers 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 phys- 

 ical 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, discov- 

 ered 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 calcula- 

 tion of the perturbations promises to be interesting and difficult, 



