' 87 



From these elements, the following co-ordinates of the comet have been 

 computed with reference to the equator, the mean equinox of 1841, Jan, 0, and 

 Bessel's mean obliquity of the ecliptic, 23°27'36".06. 



x = r [9.7865707] sin (v + 97° 36 53.34) 

 y = r [9.9989828] sin (v + 12 41 53.70) 

 z=r [9.8998221] sin (v + 105 42 19.84) 



And for the reduction of these co-ordinates to the actual apparent equator, 

 I have used the following differential formulse. 



dx = r [9.97884] sin (v + 212° 3' 22) d Jl 

 d y = x cos i d Jl — ■ z d s 

 d z = x sin i d e/l-^ y d e 



where d efl'is the reduction of the mean to the apparent equinox, and d s is the 

 difference of the apparent from the mean obliquity of the ecliptic. 



With these formulsB, and with the assistance of the excellent tables given 

 by Bessel in the 12th volume of the Monatliche Correspondenz, the comet's 

 co-ordinates have been carefully computed with reference to the apparent 

 equator; and by the aid of the sun's co-ordinates in the Berlin Jahrbuch for 

 1841, the corresponding geocentric places of the comet have been obtained 

 free from aberration. Whence the following ephemeris for mean noon, Ber- 

 lin, has been prepared, with the hundredths of a second, as correct as they 

 -can be obtained from the solar tables with seven placed logarithms. 



