THE ORBIT OF URANUS. 



121 



Applying the preceding corrections to the positions of the planet as originally 

 reduced and published, wc have a series of observed positions as nearly lionio- 

 gcneous as it is possible to make theni with the means now at our command. The 

 next step in order will be the computation of the geocentric place of the planet 

 from the provisional theory for the moment of every observation, to be compared 

 with the results of the hitter. The complete execution of this labor, ah initio, is, 

 however, at present impracticable, and it is proposed to diminish it by making use 

 of the published comparisons with the older tables. This can be done without 

 danger of serious error, and with all tlie more case that owing to the great distance 

 of Uranus the errors of the solar tables are, for the most part, without appreciable 

 effect upon the computed geocentric place of the planet. The method of making 

 the comparison is different with difl'erent series of observations, and each series 

 must therefore be described and discussed separately. The general plan, how- 

 ever, has been to replace observed and computed absolute positions by observed 

 and computed corrections to the geocentric positions deduced from Bouvard's 

 Tables. To carry out this plan it is necessary to liave at our disposal an ephcmeris 

 both of the heliocentric and geocentric positions derived from these tables. The 

 corrections to the latter given by the observations are then given by direct com- 

 parison. To obtain the corrections given by the provisional theory, the heliocentric 

 longitudes, latitudes, and radii vectores given by that theory are interpolated to 

 the dates of the heliocentric ephemeris from Bouvard's Tables, and compared with 

 that ephemeris. Tlic differences are then changed to differences of geocentric 

 place by the usual differential formuhr, and thus tlie corrections given by theory 

 are derived. The difl'ercnce between the two sets of corrections is the difference 



16 May, 1873. 



