

ON THE NEW PLANET CERES. [>j' 



the heliocentric place will be the place of the node, afcending 

 or defcending, as the cafe may be, which will appear by a 

 fubfequent obfervation ; but when the place of a planet, when 

 eroding the ecliptic, cannot be obferved, the middle point be- 

 tween two equal north and fouth latitudes, gained by obferva- 

 tion, will give the node. 



The heliocentric latitude, when a planet is juft 90° from 

 each node, is the meafure of the inclination of its orbit, and 

 is eafily obtained from the obferved geocentric latitude, taken 

 in that fituation, by the analogy already defcribed ; or, other- 

 wife, the greateft heliocentric latitude may be acquired from 

 an obfervation of a geocentric latitude and longitudinal dis- 

 tance from the node, thus : When the earth is in the line of 

 the nodes, the analogy will be, as the fine of the difference of 

 the longitudes of the fun and planet feen from the earth : radius :: 

 tangent of the geocentric latitude : tangent of the inclination. 



The two days on which the earth will be in the line of the Days when the 

 nodes of Ceres will be June 12. and December 13. this year, ^lin^of^he' 1 

 But it is beyond the propofed intention of this popular memoir nodes of Ceres. 

 to enter into all the minutiae of calculation, were the requifite 

 data before me ; but only to point out the methods of applying 

 obfervations for determining the fize, form, and pofition of a 

 planet's orbit : it may not, however, be unworthy of notice, 

 before I conclude, to remark, that the aftronomers on the The early deter, 

 continent, who availed themfelves of the earlieft obfervations foeain^ttaor- 

 only for determining an approximate fet of elements of Ceres, bit of Ceres wer* 

 were enabled to do this from noticing that this planet became ™ ac ! e from lt l 



J> ,.:.! itationary pofi* 



ftatwnary between the 10th and 11th of January, 1801, when tion. 

 its elongation was known by obfervations; for it has been 

 fhewn by writers on aflronomy, that, upon a fuppofition of 

 circular orbits, the tangent of the elongation is equal to the ferni- 

 diameter of the orbit, divided by the fquare root of that femU 

 diameter -j- l . 



Your's, &c. 



W. P. 



APPENDIX, 



