APPENDIX. 



Reducing the observed places of the planet from the equator to the ecliptic, 

 we find 



And also, 



The method of article 72 gives 



The reduction of time is merely added to show that it is wholly insensible. 



All the longitudes, both of the planet and of the earth, are to be reduced to 

 the mean vernal equinox for the beginning of the year 1845, which is taken as 

 the t poch ; the nutation, therefore, being applied, we are still to subtract the 

 precession, which for the three observations is 28&quot;.99, 34&quot;.20, and 39&quot;.41, re 

 spectively ; so that for the first observation it is necessary to add 43&quot;.98, for 

 the second, 48&quot;.26, and for the third, 51&quot;.57. 



Finally, the latitudes and longitudes of Ceres are to be freed from the aber 

 ration of the fixed stars, by subtracting from the longitudes 18&quot;.76, 19&quot;.69,.and 

 10&quot;.40, respectively, and adding to the latitudes 2.02, +1.72, and +4.02, 

 numbers which are obtained from the following formulas of Prof. PEIRCE : 



d a = m cos ( O ) sec ft 



d ft =^ m sin ( O ) sin a ; 



where O = sun s longitude, and m = aberration of Q. 



