66 THE ORBIT OF URANUS. 



I have submitted these perturbations to such duplicate computations and other 

 checks as lead me to believe that none of the terms can be in error by more than 

 a small fraction of a second, but, as they are not intended to form the basis of a 

 definitive theory of Saturn, I do not vouch for their absolute precision. 



In this provisional correction of the orbit of Saturn only heliocentric longitudes 

 have been employed. These were derived for a series of dates from Airy's reduc- 

 tion of the Greenwich observations, the modern Greenwich observations, and the 

 Washington observations. 



For these dates the value of n*z for Saturn was computed from the formula? 

 found on pages 189 and 190 of the work of Hanson, already quoted, omitting all 

 terms less than 1", and including only tenths of seconds in the results. The dates, 

 the resulting values of n*z, of the factor e l cos (g + \ nl.z) + 2e. 2 cos 2 (</ + | ?tz), 

 and of the concluded lv are as follows. The formula? for tv is 



lv = 1.0216 nz \\ + e L cos (g + | Y> + 2e, cos 2 (g + \ nlz) \ . 



Date T-, 



rt j.r XT v&z Factor. lv 



Gr. Mean Noon. 



* n 



1751 May 31 -1947.7 -.0900 1792.7 



1757 Aug. 7 -2134.2 -.0652 -2038.2 



1758 Aug. 27 -2212.5 -.0474 -2153.2 

 1761 Oct. 6 -2546.2 +.0244 -2664.5 

 1763 Nov. 1 -2880.3 +.0729 3157.1 

 1765 Nov. 23 -3095.1 +.1082 3504.0 

 1773 Feb. 26 -3342.0 +.0419 -3557.2 

 1780 May 24 2858.2 -.0956 2640.7 

 1794 Nov. 16 -3321.1 +.1017 3737.9 

 1802 Feb. 23 -3184.7 +.0529 -3425.5 

 1823 Nov. 13 -2716.3 +.0944 3036.8 

 1831 Feb. 18 -3378.5 +.0639 -3671.7 

 1838 May 19 -2976.7 -.0866 -2777.9 

 1845 Aug. 17 -2342.7 -.0721 -2220.9 

 1852 Nov. 15 -2847.0 +.0863 -3159.3 

 1860 Feb. 14 -3161.4 +.0740 -3468.3 

 1867 May 15 -2373.1 -.0812 -2227.6 



The perturbations by Uranus and Neptune were computed from the values of 

 their terms just given. The principal terms, the sum of which make up the helio- 

 centric longitude resulting from the adopted elements, are shown in the first of the 

 following tables. 



In the next table we have after the date the heliocentric longitude from Bouvard's 

 Tables, as deduced from the longitudes given in Airy's reductions of the Green- 

 wich Observations, from the AstronomiscJies JahrbucJi for 1831, and from the 

 Nautical Almanac. Then follow the corrections, roughly deduced from observa- 

 tions made near the opposition. Adding these columns, we have the longitude 



