1 76 On the Constructioti and A>ra7igement 



Ceres. 



Mean longitude 307° 3' 25"-6 



Mean anomaly 159 



Longitude of the perihelion 147 



Longitude of the node 80 



Inclination 10 



Angle of eccentricity 4 



Mean daily sidereal motion 769*26059 



Log. of the semi-axis major 0"442622 



With these elements the places of the planets may be deter- 

 mined almost the whole 3'ear to a few minutes. If the planets 

 were to be arranged by the length of the great axis, Pallas and 

 Ceres ought properly to exchange places. As, however, by 

 this manner of applying the perturbations, Ceres may and will 

 have at times, in consequence of the periodical changes of the 

 great axis, a greater mean distance, it will not be necessary to 

 deviate from the ari'angement usually followed. 



With regard to Jupiter and Saturn, it had been overlooked, 

 when preparing the preceding volume, that the data of the 

 tables of epochs were to be corrected, on account of the in- 

 equality of the precession. Without regarding the changes 

 of the longitudes of the perihelion and of the node, as well as 

 the greatest equation of the centre, all which will have but an 

 exceedingly small influence, the heliocentric longitudes of Ju- 

 piter and Saturn, as given for the year 1830, must, for the 

 reason above assigned, be augmented throughout by 2"*2 de- 

 cimal seconds, or 0"*7 sexagesimal seconds. The influence of 

 this correction on the geocentric places will not be of any con- 

 sequence for the declinations of the two planets, as it may be 



assumed with sufficient accuracy = 0"*3 . cos A, where r 



and K designate the heliocentric distance and longitude, A and 

 S the geocentric distance and declination. In like manner, the 

 principal part of the influence of the geocentric right ascension 

 may be applied by increasing the right ascensions in time by 

 0"-05. 



The ratioof the axesof the orbitsof all thesatellitesof Jupiter, 

 given in the preceding volume, deviates considerably from the 

 truth. This ratio was obtained b^'the reduction of the positions 

 of the orbits of the satellites to the ecliptic, for which purpose 

 Gauss's formulae were applied. In calculating them, however, 

 it was overlooked, that these formulae do not give the inclination 

 itself, butonlyone half of it; so that the ratio of the axes given in 

 the preceding year's Ephemeris refers to an inclination of the 

 orbits, which is only one half ofwhat it ought to be. This error 

 may for the greatest part be remedied by substituting for the 



given 



