50 0X TUE NEW PLANET CERES. 



By the elliptic hj pothefis, the analogy for converting mean 

 into equated anomaly is fimply this : ^.y the aphelion diftance : 

 is to the perihelion diftance :: fo is the tangent of half the mean 

 anotnaly : to the tangent of half the equated anomaly ; and the 

 difference between thefe two anomalies conftitutes the equa- 

 tion itfetf". Now, it is well known to all who are converfant 

 in the theory of planetary motion, that in the projection of 

 any elliptic orbit, a circle, defcribed from the focus in which 

 the fun is fuppofed to be, with a radius that is a mean pro- 

 portional between the major and minor femi-axes, will cut the 

 ellipfe in two points, which (hall be the points of mean difiance ; 

 or, which is the fame thing, the points where the equation 

 becomes Jlationary, and confequently where it is a maximum. 

 It is alfo equally well known to practical aftronomers, and 

 calculators of an ephemeris, that the equation varies very 

 flowly for many degrees both before and after the points of 

 mean anomaly correfponding to the greateft equation ; and 

 likewife that thefe points fall a little beyond the firft quadrant 

 from the aphelion, or three degrees of mean anomaly, by a 

 quantity which depends upon the eccentricity of the orbit. 

 In the orbit of Mercury the point of mean anomaly, when 

 the equation is greateft, is nearly at 105° from the aphelion ; 

 in that of Venus it is between 90° and 91* ; in that of the 

 Earth about 91° : in that of Mars about 97° ; in that of Jupi- 

 ter and Georgian between 93° and 94°; and in that of 

 Saturn about 94°. Hence it may be inferred, that if the 

 greateft equation of Ceres be S Q 25', the faid point of mean 

 anomaly will be about 92° : but that if the equation be 9° 

 27' 41", it will be about 96° ; namely, fomewhat fhort of that 

 of Mars, the greateft equation of which is 10° 40' 40''. 



Let us try now what the greateft equation will be upon both 

 fuppofitions iucceflively, according to the fimple elliptic hypo- 

 thefts. 



Log. 

 As the aphelion diftance (27673+825) 28498 4,45481 

 Is to the perihelion dift. (27673—825) 26848 4,42891 

 So is the tangent of 46 ° ( $£ •) £ mean anom . 1 0,0 1 5 1 6 



14,44407 

 4,45481 



To the tangent of i eq. anom. 44° 17' nearly 9,98926 



Then 92°— -88° 34'=3° 26' is the greateft equation. 



Agaia, 



