QUESTIONS CONCERNING THE MINOR PLANETS. 197 



sponding periods of rotation are 3"11 and 8*81 years. They both 

 revolve, therefore, on either hand, outside of the limit, 2'8, as- 

 signed "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 move- 

 ments 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, 0'8G, of the older planets. This, too, indicates 

 that there are notable differences in the conditions of their forma- 

 tion. 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 re- 

 searches of Lagrange and Laplace have shown that the eccen- 

 tricities 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 inter- 

 mediate 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 in- 

 dicated by Leverrier as those at which a certain amount of in- 



