On the Comtruction r/Prof. Encke's Ephemerisfor 1831, 173 



stars, and as they may, perhaps, still be used for observations 

 of the moon in general. 



I have now availed myself, in the calculations for Mercury, of 

 the corrections of Lindenau's tables, which Prof. Schumacher 

 had already published some time since. I deem it not super- 

 fluous again to observe, that the examination of the places cal- 

 culated for every second day by their diflFerences, is not suffi- 

 cient to discover all possible errors of the calculation. 



There is an error of 10" in the heliocentric place of Venus 

 on the 31st of December in the preceding Ephemeris, caused 

 by an error in the calculation, which extends likewise to the 

 geocentric place ; this error has however no influence on the 

 data for other days, as the place on that day had been calcu- 

 lated directly and could not be examined by differences. 



Mr. Hansen has kindly informed me that the longitude of the 

 node of Venus, used in the calculations for this year and the 

 preceding one, differs from the value assigned to it in Lin- 

 denau's tables. I have thought proper to make an alteration 

 in this element, because the value derived for 1808, in the 

 preface of the tables, from the latest epoch, is smaller by 1' 15" 

 than the value afterwards adopted. The calculation is founded 

 on the epoch of 1750, and from that date forward an annual 

 motion of 3l"-2 has been applied, contrary to what the author 

 himself declares to have been formerly adopted. As the cal- 

 culations of the transits of Venus likewise give a smaller longi- 

 tude of the node, and a motion of the node smaller than 31"-2, 

 I have thought that I might assume the longitude of the node 

 of Venus £3 = 74° 33' 48" + 30-66 (^-1765). 



Elence we have for 1808, S =74° 55' 46"; while, accordmg 

 to the preface, the observations have given 8 = 74° 56' 37"; 

 and the tables have £3 = 74° 57' 52". The values adopted by 

 me give therefore a result more nearly approximating to the 

 latest observations, than that of the tables, and agree at the 

 same time with those transits which must give the longitude of 

 the node with greater accuracy than any other observation. 

 If, however, later observations should prove the longitude of the 

 tables to be more accurate, I shall adopt their values in future. 

 Of all heavenly bodies whose places were given in the last 

 Ephemeris, Ceres was the one whose places were likely to de- 

 viate most from the truth. For the present year, 1 have there- 

 fore derived new elements from the last oppositions, taking into 

 calculation the perturbations of Jupiter only, respecting which 

 a more detailed explanation will be found below*. Ahhough 

 it cannot be expected lliat these preliminary determinations will 

 very accurately represent the places of Ceres, yet they will give 



♦ To 1)C ^ivcn ill ii tiiturc Number f)f tlie Piiil. Mag. & Annuls. 



them 



