1 806. ] Literari/ and Philojophical Intelligence^ 



481 



The clafs of mathematical and phy- 

 fical iciences of tlie National Inftitute 

 of France, at its meeting on the 7th of 

 July laft, prorioled a prize, to confiil of 

 a gold medal of the value of GOOO francs 

 (250/. Iterling), for the beft theory of 

 the pertmbations of the planet Pallas 

 difcovered by Dr. Olbers. Ti;c motives 

 for propoiing this fubjett, and tiie plan 

 of operation recommended to the com- 

 petitors, arc explained in the folJowing 

 obfervations : " Geometricians have giv- 

 en the theory of perturbations with fuf- 

 Hcient extent and accuracy for all the 

 planets formerly known, and fur all fuch 

 as may ftill be difcovcred, as long as 

 they are contained in the fame zodiac, 

 and have only an inconlidcrable eccen- 

 tricity. iMercury was till our time the 

 molt eccentric of planets, and had alio 

 the greatell inclination : but its fmall 

 iize, and its fituation at one of the li- 

 mits of the planetary iyllem, render it 

 incapable of cauling any very great al- 

 terations in the motions of the other 

 ])ianets. The G eorgimii Sidus, difcover- 

 ed twenty-five years f^o by Dr. Her- 

 fchell, is at the extremity of the fyftem. 

 With a diminutive mafs and a moderate 

 eccentricity, it has the finalleft of all 

 known inclinations : fo that the formula 

 jvhicli had I'crved for Jupiter and Saturn 

 were more than futticient for this modern 

 planet. Ceres, difcovered live years 

 fiDce by M, Piazzi, having, with an ec- 

 centricity as coniidcrablc, an inclination 

 of 10° 38', ought to be fubje"!'! to greater 

 and more numerous inequalities. It ne- 

 verthelefs appears, that all the aftrono- 

 mcrs "iio iiave endeavoured to deter- 

 mine them, liave been fatisfied with 

 known formul?e, the development of 

 i\ Inch does not exceed the produce of 

 three diracnlions of the eccentricities 

 and incliuati(;ns. Thofc of five dimen- 

 Jions liave been employd in the Mc- 

 pinitp/e Ccli'Jh', after a form of JVI. 

 Burekhardt. 'J'he fame altronomer has 

 fmce prefcnted to the Inftitute the ge- 

 neral and eoiiipletc develoijenient of the 

 third, fourth, and lifth orders ; but this 

 flegrec of precifion would not be. fuffi- 

 cient for Pallas, whr)re eccentricity is 

 greater than even that of iNIcrcury, and 

 the inclination ."4° 38', that is five times 

 as great as thatof any of the old planets. 

 Nay, it is dillieult to conjecture what 

 I'owers and wiiut dimenfions of the pro- 

 ducts it might be allowable to neglec^l ; 

 the calculations, therefore, might be of 

 j^'ucli iengthj and ihc fonaulu; fu conipl<'x, 



as to deter the geometricians and aftro- 

 nomers wlio are bell able to execute 

 fuqh an undertaking. This confideratioiji 

 induced the clafs, two years ago, to pro- 

 pofe this lubjcft f>r the prize to be ad- 

 judged in Auguft 1306 : but the time 

 appearing too Ihort, and the number of 

 planets having been encreafed by the 

 difcove-ry of Juno by M. Ilarding, whofe 

 eccentricity Icems to be uill greater than 

 that of Pallas, and whole inclination of 

 13° exceeds that of all the other planets, 

 excepting Pallas; the clais thought fic 

 to renew the fubiett with certain modi- 

 lications, and a double premium. Ac- 

 cordingly, it invites geometricians and 

 aftronomeis to a complete dilcultion of 

 all the points of this theory, fo as not to 

 omit any inequality that can polfibly be 

 of any confequence ; and as thefe in- 

 equalities cannot be accurately deter- 

 mined unlefs the elliptical elements are 

 perfectly well known, it is iiidifpenlably 

 necelVary that the competitors Ihould uot 

 confine themfelves to a tlatcment of the 

 numerical co-efticients of the equations : 

 it is the analytical formulas which it is of 

 the moil importance to know, that the 

 more exact amounts of the mean dif- 

 tance of the eccentricity, of the peri- 

 piielion, and of the inclination, may be 

 fucceliively fubftituted in their llead, in 

 proportion as thole elements Ihall be 

 perfected. The competitors may even 

 difpenfe with giving any numerical 

 amount, provide'! the analytical expref- 

 fions be prefented in a manner futiici- 

 ently detailed to enable an intelligent 

 calculator to follow their development, 

 and to reduce them into tables. From 

 thefe general formula; will rcfult anf)tlier 

 advantasrc ; namely, that the planets 

 Ceres, Pallas, and ,Tuno, being at dif- 

 taiices from the fun fo nearly alike, that 

 it cannot yet be decided with any cer- 

 tainty which of the three is the fartheft 

 or the neareft, the formula given for 

 Pallas may likewife ferve for the two 

 others, as well as for any other planet 

 that may hereafter be difcovered, and 

 whofe eccentricity and inclination may 

 be contained within the fame limits. 

 The memoirs intended for the compe- 

 tition muft be written in French or 

 Latin, and will not be received after 

 the Ki; of Ottober, 1808. The prize 

 will be adjudged on the hrft Monday in 

 January 1809. 



A difcovcry has been made at Lyons 

 of a highly interefting jiieee of moiaic- 

 woik, reprcfciiting chariot and horfe 



races 



