TbeGEORGIUMSIDUS. 325 



given, will enable us to diminim them as much again. When 

 it is confidered, that in th'ofe elements no attention has been paid 

 to the gravitation of the Planet to the other fix, it will ftill more 

 clearly appear how abundantly accurate they are for the pur- 

 pofes of aftronomical computation. 



I TOOK another method of obtaining elements, by means of 

 the ratio of three diftances from the Sun ; namely, by interpo- 

 lating heliocentric places of the Planet, for the times of its vici- 

 nity to its ftations, and comparing thefe with its geocentric 

 places. It is eafy to fee, that this method alfo is fufceptible of 

 great accuracy, after having obferved five oppofitions, which 

 give us fecond and third differences of the heliocentric places, 

 and therefore afford a proper application of the methods of in- 

 terpolation. Elements deduced in this way, almofl perfectly 

 coincided with the above. I alfo obtained, in January 1784, a fet 

 of elements very nearly the fame, by means of the three oppo- 

 fitions which had then been obferved, and by the help of a 

 theorem which I make ufe of in my elements of phyfical aftro- 

 nomy, viz. That the velocity of a body, in any point of the 

 path which it defcribes by the adlion of a centripetal force, is 

 that which it would acquire if uniformly impelled by the cen- 

 tripetal force along \ of that chord of the ofculating circle 

 which pafTes through the centre of forces. 



I SHALL here fubjoin tables for computing the motion of 

 this Planet. 



TABLE I. contains the Radical Mean Longitudes of the Planet, 

 Aphelion, and Node ; for the Mean Time of noon at Green- 

 wich, at the beginning of the Aftronomical Year, that is, for 

 the Mean Noon of the 3 1 ft of December immediately preceding., 

 It alfo contains the Mean Sydereal Motions of the Planet for 

 months, days, and hours, and the preceflion of the Equinoxes 

 at the beginning of each month. The fydereal motions are 

 chofen in preference to the tropical, becaufe the motions of the 

 aphelion and node are not yet known. One application of the 



preceffion of the equinoctial points, is therefore fufficient. 



TABLE 



