n EEMAEKS ON THE SMALL PLANETS. 206 



ters, in three families. The four superior planets, Neptune, Uranus, 

 Saturn, and Jupiter, are distinguished by considerable volume and 

 slight density ; the time of rotation about their axes is about ten 

 hours, and from this there results in these bodies considerable flatten- 

 ing ; moreover, of the twenty-two satellites of the solar system, 

 twenty-one pertain to this group. The four inferior planets. Mars, 

 :the Earth, Venus, and Mercury, have, on the contrary, much smaller 

 volumes and much greater density : they revolve on themselves in 

 'nearly twenty-four hours, are but little flattened, and possess, among 

 ■all the four, but one satellite, the Moon. 



[ It is between these two groups so distinct, that the singular family 



I of the asteroids revolves. Their orbits, in general more eccentric 



land more inclined to the ecliptic than those of the ancient planets, 



their volumes much inferior to those of the smallest satellites, and 



■ above all their mean distances from the sun constantly interme- 

 diate between those of Mars and Jupiter, evidently make of these 

 small bodies a planetary family very diflerent from the two others, 



• and seem, indeed, rightly to consign them to a common origin. Such, 



I as has been said, was the first idea of Olbers, from the time of his 

 observing Pallas, and though his hypothesis must needs have ap- 



■ peared less probable after the discovery of Yesta, the geometers 



• judged it sufiiciently worthy of attention to be submitted to calcula- 

 ' tion. We find in the Connaissance des Temps for 1814 a curious me- 

 moir, in which Lagrange determines that, taking into account the 

 velocity of translation of the primitive planet, and considering the 

 thirty-four degrees of inclination of the orbit of Pallas as the maximum 

 inclination of the new orbits of each fragment, a force capable of 

 communicating to these fragments a velocity equal to twenty times 

 that of a 24-pound cannon ball would have sufficed, in order that each 

 of them should pursue an elliptical orbit around the sun, the common 

 intersection of the new planes passing at the point where the explo- 

 sion had taken place. A geometer would not nowadays undertake 

 this calculation ; for an examination, however rapid, of the mean dis- 

 tances of the 70 [three] asteroids at present known, permits us no longer 

 to believe that their orbits could ever have passed at the same point. 

 These mean distances, in effect, which will be found expressed in radii of 

 the earth's orbit in one of the columns of our tables, vary between the 

 numbers 2.20 for Flora or Harmouia, and 3.45 for Maximiliana, one of 

 the planets most recently discovered. This important difference cor- 

 responds to about fifty millions of leagues of four kilometers. What 

 would it be if we should compare the extreme distances ? We should 

 see Phocoea and Melpomene approach the sun as near as 1.79 radii of 

 the earth's orbit, while Euphrosyne and Maximiliana vrithdraw from 

 that luminary to distances marked respectively by 3.83 and 3.93. 

 What is usually called the zone of the small planets extends, there- 

 fore, over a width of ninety millions of leagues, that is, over a space 

 greater than the distance of the sun from the inferior border of that 

 zone. The zone of the interior planets is twice as narrow, and there 

 is consequently no more reason for regarding the asteroids as frag- 

 ments resulting from the explosion of a single planet, than there 



