SCIENTIFIC NEWS, 261 



cated as to discourage geometers and astronomers the best 

 qualified to execute a work of this kind. 



Two years ago the Class of Physical and Mathematical 

 Sciences of the Institute determined, from this considera- 

 tion, to propose the subject for the prize to be distri- 

 buted at the public sitting on the first Monday in Messi- 

 dor of the year XIV. But the term having appeared too 

 short, and the number of the planets being again in- 

 creased by the discovery of Juno by M. Harding, of 

 which the eccentricity appears to be still greater thart 

 that of Pallas, and the inclination of 13 degrees greatly 

 exceeds that of all the other planets except Pallas; the 

 Class has thought proper to propose the same subject 

 again, with some modifications and a double prize. They 

 accordingly invite astronomers and geometers to discuss 

 completely all the points of this theory, with the omission 

 of none of the inequalities which may become sensible ; 

 and as these inequalities cannot be well determined if the 

 elliptical elements be not perfectly known, it is indis- 

 pensible that the concurrents should not confine them- 

 selves to give the numerical coefficients of the equations. 

 It is more particularly important to exhibit analytical 

 formulas, in order that substitution may be successively 

 made of more exact values of the mean distance, the 

 eccentricity, the perihelium, and the inclination, accord- 

 ingly as the elements shall become better known. The 

 concurrents may even dispense with giving any numerical 

 faluc, provided the analytical expressions be presented 

 sufficiently in detail to enable an intelligent calculator to 

 follow the developement and reduce them into tables. 



Another advantage will result from these general for- 

 mulas j namely, that the planets Ceres, Pallas, and Juno 

 being at distances from the sun so little difterent that it 

 can scarcely at present be with certainty decided which 

 of the three is the nearest or the most remote : the for- 

 mula given for Pallas may serve equally for the two 

 others, as well as for every planet which may hereafter be 

 discovered which shall have its eccentricity and inclina- 

 tion within the same limits. 



The Class entertains the hope that this question will 



appear of sufficient interest to geometers to induce them 



Vol. XV.-— Nov. 1806. Mm to 



