ON THE NEW PLANET CERES. 



4.9 



inted be-5 orrefpond . wkh 



its eccentricity- 



In this table the greateft difference between the arcs con- Remark con- 

 tained in the fame line of the two laft columns, is that in the JJ™J* mer " 

 line of Mercury ; but it may be worthy of remark, that half the 

 greateft equation of this planet, according to Dr. Halley's 

 tables, is 11° 5 V 18''; and alfo that Lalande himfelf made a 

 new determination of the elements of Mercury's orbit, as re- 

 lated in the " Memoires de Wnftitute Nationale " of Paris 

 for the '•* fourth year of the Republic ;" in which the grand 

 equation is given 23° 40' 45". 



Here, then, it appears, that the greateft equation of the Hence the great 

 new planet Ceres, which correfponds to the eccentricity af- Ceres^as "?- 

 figned by Gaufs, and copied into the different Journals, is figned, does not 

 about 3° 25', inftead of 9° 27' 41"; fo that, as I 

 fore, either the eccentricity is almoft two thirds too little, or 

 the greateft equation almoft two thirds too much. I mean not 

 at prefent to enter into a geometrical demonftration of the 

 analogy which I have ufed in procuring the above tabulated 

 refults ; but leave it to exercife the ingenuity of your mathe- 

 matical readers, fome of whom will probably be induced to 

 favour you and the public with a demonftration, as a feparate 

 article. I will, however, juft prove to the reader the accu- Proof of the *> 

 racy of the inference I have made with refpedt to Ceres, bySjELjf^!!* 

 means of the elliptic hypothefts of Ward, which is generally computation oa 

 allowed to be a convenient approximation to be ufed for the e,Ii P tic ^T* 

 finding the equation of a planet, inftead of either the direct orwari. 

 tentative methods, which are more accurate, but much more 

 intricate. 



Vol. II.— May, 1802. E By 





