252 Prof. Encke on the Construction and Arrangement 



s* 



ness of the calculation. The places of Mercury might, should 

 it be wished, in future be given for every day of the year. 



The calculations for Venus, and the greater part of those for 

 Jupiter and Saturn, have been performed by Mr. Wolfers. For 

 Venus and Mars, the tables of M. Lindenau ; for Jupiter, Sa- 

 turn, and Uranus, the latest tables of Bouvard, — have been 

 used. 



The time of passage over the meridian is meant only ap- 

 proximately ; the astronomical use of it being supplied by the 

 right ascension in time, which is likewise given. Calling the 

 sidereal time at the moment for which the right ascension a 

 has been calculated, the time given in the column, headed 

 " Planet on the Meridian," is 



For the superior planets a— 



For the inferior planets 12 h + a— 



A corrective factor = -^^-— ar J ay ought to have been ap- 



planetary day ° r 



plied to a — ; but this factor would not have produced any 

 great change, and if required, its effect may easily be calcu- 

 lated. From the time of passage over the meridian and the 

 declination on that day, the times of rising and setting have 

 been calculated, which are therefore not to be considered as 

 rigorously correct. The times of rising and setting of the 

 heavenly bodies have in general been calculated with due re- 

 gard to refraction, for which purpose Bessel's horizontal re- 

 fraction of 36' has been adopted. For the moon the mean 

 parallax of 57' has besides been taken into account. The other 

 heavenly bodies are, therefore, in those moments 36' below, 

 and the moon 21', above the plane passing through the centre 

 of the earth, and parallel to the horizon. 



The four new planets make an exception; for there the 

 geocentric place only is given, together with the auxiliary co- 

 lumns. The form in which their perturbations are calculated, 

 is such that the accurate determination of their places would 

 require more extensive calculations than the possible use ren- 

 ders necessary. In the same manner the determination of 

 their heliocentric places would have caused a change in the 

 form of calculation, which is in no proportion to the possible 

 nse which might be made of them f For this reason the ele- 

 ments for the time of the opposition have been rigorously de- 

 duced, and then have been retained for the whole year. For 

 each planet, however, more accurate daily positions have been 

 given for the 28 days, within which the moment of opposition 

 is contained. 



The perturbations of Pallas, Juno, and Vesta, have been cal- 

 culated as far as the year 1830. For the first, the elements of 



Gauss 



