of the New Berlin Astronomical Ephemeris. 253 



Gauss have been used ; for the second, those of Nicolai ; for the 

 third, mine; which will appear in another place. For these 

 three planets the errors will hardly amount to a minute. The 

 planet Ceres, however, w r hose elements have not been further 

 investigated since M. Gauss last corrected his Elements in the 

 year 1809 (Elements, xiii.), and whose perturbations have not 

 been completely developed, may deviate more considerably. 

 In accordance with the last oppositions, the epoch of mean 

 longitude has for the present been diminished by 14' for the year 

 1 830. It is to be hoped that this correction will likewise have 

 nearly approximated it to its true position. 



All data for the planets have been given, without any re- 

 gard to aberration and parallax. On account of the former, the 

 given places do hot belong, with respect to the actual obser- 

 vations, to the moments h and 12 h , but (calling the geocen- 

 tric distance of any planet A ) to those moments (viz. h or 

 12 h ) + 493"*2. A (time). 



With regard to the satellites of Jupiter, which then follow, 

 it was customary to give, besides the eclipses which supply the 

 place of the heliocentric place, a graphical representation of 

 their geocentric position with respect to Jupiter for a certain 

 definite moment. But as their position is thus only obtained 

 for a single moment of time, it has appeared to me that the 

 advantage of an ocular graphical representation is overba- 

 lanced by the concomitant want of being deprived of the means 

 of deducing the geocentric position for any other given time. 

 I have therefore preferred giving the time of the superior 

 geocentric conjunction, together with the corresponding ratio 

 of the axes of the apparent ellipsis of the orbit of the satellite, 

 accompanied by the tables of reduction ; by means of which, 

 from the time elapsed since the last preceding conjunction, the 

 geocentric coordinates of the satellite, with respect to the 

 centre of Jupiter, may be derived. 



It is to be observed that these results have been founded, both 

 as regards the derivation of the superior geocentric conjunction 

 from the heliocentric conjunction and the time of revolution, 

 on which the tables of reduction are founded, on the hypo- 

 theses of the mean heliocentric synodic time of revolution of 

 the satellite, and of the perfectly circular form of their orbits, 

 while the true synodic geocentric revolution ought to have been 

 taken. They may, however, should more accurate measure- 

 ments render it necessary, be corrected without any great 

 trouble. The difference will always be small, and quite insig- 

 nificant as to inspection. 



By this arrangement the observer of eclipses is, at the same 

 time, enabled accurately to determine the place of emersion, 



on 



