122 



THE ORBIT OF URANUS. 



between the provisional theory and observation. A condensed summary of the 

 results for each of the principal series of observations is here presented. 



Greenwich, 1781-1830. 



In Airy's reductions, already referred to, we have given for the moment of each 

 individual observation a heliocentric place computed from Bouvard's Tables, and 

 the geocentric longitudes and latitudes thence deduced. The observed right 

 ascensions and declinations are then changed to longitudes and latitudes, and the 

 apparent error of the tables thence deduced. The means of these errors are taken 

 for groups of observations, and expressed in terms of the errors of heliocentric 

 longitude, radius vector, and latitude. The mode in which these means have been 

 treated is fully shown in the following table. The first column gives the mean 

 date of each individual group of observations. The next three give the mean 

 excesses of the co-ordinates interpolated from the heliocentric ephemeris, p. 100, 

 and corrected for solar nutation, over those printed in the " Computations of tabular 

 place, etc.," in the Greenwich reductions. In the fifth column these corrections 

 are changed to corrections of geocentric longitude. In the next two columns we 

 have the mean corrections to Bouvard's geocentric places given by observation. It 

 is the negative of the mean error of tabular place printed in the " Reductions," 

 corrected by the numbers already given to reduce the star places to a uniform 

 system. Then we have the difference between these two sets of corrections, or, 

 the mean correction to the geocentric place of the provisional theory as given by 

 observation. Lastly, we have the differential coefficients for expressing the errors 

 of geocentric in terms of the errors of heliocentric co-ordinates taken without 

 change from the Greenwich volume. 



