206 REMARKS ON THE SMALL PLANETS. 



would be for referring Mars, the Earth, Venus, and Mercury to a sim- 

 ilar origin. It would be in vain to rely on the great eccentricities of 

 the orbits with the view of instituting an inquiry, whether, notwith- 

 standing the differences in their great axes, those orbits did not pre- 

 sent some points sufficiently adjacent to lend a degree of probability 

 to the hypothesis of Olbers. We should find twenty-five millions of 

 leagues to be the least distance for the orbits of Harmonia and Doris, 

 thirty millions for Mnemosyne and Flora, forty-five millions for Maxi- 

 miliana and Ariana. It is true that the nodes and apsides change 

 their places, and, notwithstanding the slowness of those displace- 

 ments, it is possible that, some thousands of ages before the present 

 era, the orbits in other relative situations may have presented points 

 more approximate than at present. But in vain should we ascend the 

 course of ages, or even arbitrarily modify the position of the planes in 

 which the asteroids revolve ; we shall still have to dispose of minimum 

 distances of at least fifteen millions of leagues, since the aphelion of 

 Nemausa, for instance, is but at 2.52 units of distance from the sun, 

 while the perihelion distance of Mnemosyne is indicated by 2.82, and 

 that of Maximiliana by 2.96. It cannot be admitted that the pertur- 

 bations of the planetary system could have produced such difference, 

 and the hypothesis of Olbers is thus shown to be absolutely irrecon- 

 cileable with the data which we now possess with regard to the aste- 

 roids. Is it necessary on that account to renounce the idea of a com- 

 mon origin ? Not so ; for, if we admit, with Laplace, that the planets 

 have been formed by the condensation of rings of vapor successively 

 abandoned by the sun in cooling, it suffices, in order to explain the 

 coexistence of all the asteroids between Mars and Jupiter, to suppose 

 that there existed in one of the rings many simultaneous centres of 

 attraction, and we must acknowledge, with M. Le Verrier, that the 

 difficulty is not to account for the exception, but, on the contrary, to 

 comprehend why it did not become the rule. 



VI. 



If science shall ever succeed in resolving these delicate questions, 

 it will doubtless be by adopting as a basis the relations of form and 

 position of the different planetary orbits. What we should propose at 

 present is less to mark out the work than to inquire in what direction 

 the future seems likely to hold a discovery in reserve for astronomers. 

 For that purpose we must see if the comparison of analogous elements 

 reveals the existence of any remarkable law. 



DISTANCES FROM THE SUN AND THE EARTH. 



Let US add to what has been just said on this subject in discussing 

 the hypothesis of Olbers, that the mean of all the distances of the 

 seventy asteroids from the sun is 2.645 radii of the earth's orbit, 

 or about 105 millions of leagues ; which is almost exactly the distance 

 of Fides, and less than that of Ceres and Pallas which best corre- 

 sponds with the law of Bode. Of the seventy orbits, thirty-eight 

 have their greater axes below the mean, and thirty-two above — an 



