THE ORBIT OF URANUS. 99 



column. The secular and long period terms are here taken from columns (3) and 

 (4) of the tables on pages 89 to 93. 



The elliptic co ordinate's were then derived from the following elements, which 

 are a little diti'erent from those employed in the computation of the perturbations. 



Elements III. of Uranus. 

 7t, 168^ 15' 12".0 



Red. to Ecliptic, — 9". 37 sin 2 (v — 6) 



The longitudes thus found are corrected for lunar, but not for solar nutation, 

 and the results are given in the fifth column. 



The column "correction" arises in this way: after the comparison of the ephe- 

 meris with observations was nearly completed, it was found that some errors had 

 crept into the former, the most important of which was the employment of a mean 

 anomaly, (j, corrected for secular variation of the perihelion in the computation 

 of the perturbations from the preceding formuliB. As a large portion of the com- 

 putations on the provisional ephemeris had been made by assistants furnished by 

 tlie Smithsonian Institution and Nautical Almanac, I deemed it prudent to make 

 a careful recomputation of the perturbations for every sixth date during the entire 

 period of the modern observations. The longitudes actually printed in the fifth 

 column are the results of the original incorrect computation, while the numbers 

 in the next column show the several corrections to be applied to obtain the results 

 of my final revised computation. 



During tlie period of the modern observations the ephemeris is computed for 

 intervals of 120 days, and the selected dates are all exact multiples of that interval 

 before or after the fundamental epoch, 1850, Jan. 0, Greenwich mean noon. 

 For convenience of reference the dates are numbered from an epoch earlier by 212 

 intervals, and the number is given in the second column. 



Between 1796 and 1801 no observations worth using were made on Uranus, the 

 ephemeris has. therefore, not been extended over tliis interval. 



