260 SiJreNTIFIC NEWS. 



The subject oi' the mathematical prize, and the pro- 

 spective remarks upon the same, were as follow : 

 Prize question. U is required to establish a theorij of (he perturbaitQns^ 



of the planet Pallav^ discovered bi/ Mr.Olbers. 

 On the com- Geometers have given the theory of perturbations suf- 

 putations for ficiently extensive and accurate for all the planets formerly 

 the respective ^^i^^wn, and for all those which might be discovered, 

 places of the provided they were confined to the same zodiac and had 



Mercury until our time was the i?iost eccentric of ^11 

 the planets, and at the same time that which had the 

 greatest inclination ; but its small mass, and^ its situation 

 at one of the iim'its of the planetary system, render it of 

 little effect to produce any sensible alteratior^s in the 

 motions of the other planets ; Uranus, discovered twenty- 

 fire years ago by Dr. Herschell, is placed at the other 

 limit of the system. With a small mass and moderate 

 eccentricity it has also the smallest of all the known in- 

 clinations ; so that the formulas which had served for 

 Jupiter and Saturn have been more than sufficient for this 

 modern planet. 



Ceres, discovered five years ago by Mr. Piazzi, having 

 with a considerable eccentricity an inclination 10° 38', 

 must be subject to great and numerous inequalities. It 

 appears, nevertheless, that all the astronomers who have 

 laboured to determine them have been content vrith thoN 

 known formulas, of which the developemcnt docs not ex- 

 ceed the products of three dimensions of the eccentricir. 

 ties and inclinations. Those of five dimensions have been 

 used in the Mecaniq '^ Celeste according to a formula of 

 Mr. Burckhardt. l*he same astronomer has since pre- 

 sented the general and complete developemcnt of the 

 tliird, fourth, and fifth orders; but this degree of pre- 

 cision is hot sufficient for PaHas, of which the eccentri- 

 city is greater than even that of Mercury, and the incliM 

 nation 34° 38' is five times as much as that of any 

 anticnt planet. It is even difficult to conjecture what 

 'may be the powers and what may be the dimensions of 

 the products which admit of being neglected ; so that the 

 calculations may be so long, and the formulas so compU- 



i)ated 



