372 ANNUAL OF SCIENTIFIC DISCO VERY. 



which approach most nearly to one, and live in their aphelia and perihelia 

 respectively. 



The two independent results were as follows : 



( f5,094 ) L, 

 Equatorial diameter -j 53345 f miles. 



The polar diameter must have been very small, as it was independent of 

 the density. With a density equal to that of the earth, it would be only from 

 about 8 to 11| mil eg. No less than eleven facts were stated, which this 

 hypothesis would reconcile. The recently discovered asteroids had the posi- 

 tion of their orbits represented, and the inclination of the orbit of the original 

 planet was deduced anew, and found to be about 4 deg. 20 min. 



THE ASTEROIDS. 



The following paper has been communicated by Daniel Vaughan, Esq., of 

 Cincinnati : Of the planets already discovered between Mars and Jupiter, 

 none move in orbits having an eccentricity greater than y^, nor less than y 1 ^, 

 of their mean distance from the sun. In the orbits of the eight large planets 

 of the solar system, the ratio between the least and greatest eccentricities is a 

 little over thirty. If we leave out the orbits of Mercury and Venus, the ratio 

 will be nearly eleven. In the Saturnian system, the ratio of the least and 

 greatest eccentricities exceeds 20, while in the asteroids, which comprise five 

 times as many members, the ratio is less than four. 



The total absence of orbits of small eccentricities in the asteroidal region, is 

 fatal to the idea, that these small bodies originated in the destruction of a pri- 

 mitive planet by centrifugal force ; and neither this, nor the hypothesis of 

 Olbers, can account for the great inclination to the ecliptic of the orbits of 

 Pallas, Euphrosyne, Phocea, Hebe, and Egeria. An impulse capable of 

 deflecting any of the fragments of a shattered world 25 degrees from the 

 plane in which it previously moved, should have imparted a hyperbolic orbit 

 to those fragments which were projected in the direction of its motion at the 

 time of the supposed catastrophe. The fragments thrown in an opposite 

 direction, with the same force, should, at their perihelia, approach as close to 

 the sun as the planet Mercury. Had the asteroids been produced by the 

 destruction of a single world, the ellipses which they describe should exhibit 

 the greatest discrepancy in size and eccentricity, and should intersect the 

 orbits of the nearest and most distant members of the solar system. 



These difficulties can be only removed by supposing a collusion of two 

 planets once occupying the region beyond Mars. In such an event, it is evi- 

 dent that the fragments of both worlds should fly into space, in a plane perpen- 

 dicular to the line in which both moved, when the terrible encounter was at 

 hand. The fragments should, accordingly, have the magnitude and eccen- 

 tricity of their new orbits confined to a very limited range, but would be per- 

 mitted to deviate, to the greatest degree, from the ecliptic, or from the plane 

 of their primitive motion. It is probable, that so violent a mechanical action 

 would produce heat enough to bring the fragments into a molten condition. 



There is reason to suspect the existence of two groups of asteroids in the 

 Satumian system. Judging from the mean ratio which subsists between the 



