of the New Berlin Astronomical Ephemeris. 255 



taken in such a manner as if they were visible ; and the semi- 

 duration is added in order to reduce to the same form the mo- 

 ments in which no eclipse takes place. The calculation has been 

 executed by M. Wolfers from Delambre's latest tables of the 

 satellites. However well founded M. Hansen's remark re- 

 specting the incorrectness of the table of equation C for the 

 first satellite may be, yet it was preferred to retain this* table 

 unchanged, partly because some other corrections in the pre- 

 face likewise require amendments, partly because it is doubtful 

 whether Delambre has not compared the observations with 

 tables which contained the same small deviations. At any 

 rate the difference will seldom amount to 1" for the first satel- 

 lite, and for all the others it will always be within this limit. 

 The last page of this section contains the elements for the geo- 

 centric form of the ring of Saturn, with the explanation of the 

 notation. For the node and inclination, Bessel's paper in the 

 Astron. Jahrbuch for 1829, and for the dimensions of Saturn's 

 ring, the measurements of Struve in the Astron, Nachr. v. 

 No. 97, have been used. 



The following section contains the places of the pole star, 

 8 Urs. Min. and of Bessel's 45 stars, after the model of the 

 excellent auxiliary tables of Prof. Schumacher, with this only 

 difference, that the inferior culminations of the two polar stars 

 have not been given. The apparent places refer to the time 

 of culmination at Berlin, and the asterisk denotes that in that 

 place not ten, as everywhere else, but eleven sidereal days are 

 to be taken. 



The mean places on which these positions are founded are 

 enumerated together in the beginning. Their comparison with 

 the corresponding numbers in the auxiliary tables for 1827, 

 has shown that there is a small deviation in some of those stars 

 only, which Bessel has not introduced into his fundamental 

 catalogue, probably owing to a differently assumed proper 

 motion. They are all founded on M. Bessel's latest determi- 

 nations. The calculation has been performed with great care 

 by M. Dannemann. 



The daily aberrations for the polar stars are given below 

 for the culminations. Its values for the other stars are to be 

 found by the side of the last of them, u Andromeda. For the 

 reduction of other stars from their mean places in the begin- 

 ning of the year to the apparent ones at any other time, two 

 tables have been added, whose construction will be evident 

 from the formulae * at the beginning of this section. The first, 



* The tables here described, together with the formulae alluded to, we 

 hope to be enabled to publish in a future Number of the Phil. Mag. and An- 

 nals.— Edit. 



the 



