ON THE NEW PLANET CERES. 



this fuppofition, have been at that time 3 S. 21° 8' 56", fo 

 that it had patted the place of mean motion about either 19° 

 or 15°, accordingly as we make the greateft equation 3° 25' 

 or 9° 27' 41" : therefore the daily motion was nearer a mean 

 motion than it has been ever iince ; and it will be yet fome 

 months before it arrives at its place of mean motion in the op- 

 pofite half of its orbit ; which place is either 2° or 6° ftiort of 

 the ninth iign of anomaly, accordingly as we take the eccen- 

 tricity. Let us fuppofe now the whole period to be upwards 

 of 1681 days, as has been, perhaps prematurely, determined; 

 one fourth of this time had elapfed on the 24th of February 

 laft ; on which fuppofition, the mean anomaly muft then have 

 been advanced juft three ftgns from the original fituation ; 

 namely, it muft have been upwards of 6S. 21°, at which rate 

 the planet had palled the perihelion by a fpace of time aniwer- 

 ing to 21° of mean motion, which is about 98 days: therefore 

 the 18th of November, 1801, muft have been the day on 

 which it was at the perihelion, or place of greateft velocity ; 

 but at that time the planet xvas loft, and we are not in pof- 

 feflion of any obfervation of it nearer that time than the 

 7 th of December following, when Baron Von Zach re-dif- 

 covered it. 



The continuance of any planet in the firft quadrant from 

 aphelion is longer than in the fecond quadrant, by a fpace of 

 time which correfponds to the whole equation, taken at three 

 iigns of mean anomaly; in which fituation, it has been already 

 obferved, that the equated or apparent motion is alfo, as nearly 

 as may be, a mean motion ; if therefore the equation at three 

 iigns be divided by the mean daily rate of motion, we mail 

 have a fpace of time, which, added to one fourth of the whole 

 period, and fubtracled from another fourth, will give nearly 

 the refpedtive times of continuance in the firft and fecond 

 quadrants of anomaly : Hence arifes this rule for finding the 

 two femicircles, refpeclively bife&ed by the perihelion and 

 aphelion points, viz. divide four times the equation at three 

 iigns of anomaly, (which may be the greateft equation where 

 the eccentricity is fmall), by the mean daily motion, and the 

 quotient will be the number of days that the planet continues 

 longer in the femicircle from nine to three iigns of anomaly 

 than from three to nine. For inftance, if we take the equa- 

 tion 



53 





