THE ORBIT OF URANUS. 191 



applied in tliis table. Tlie numbers at the bottom of this tabic, in the Hue A|.!i, 

 show the variation of the corresponding quantity in 1'20 days, for the epoch 1850.0. 

 In the line "Factor 7"' is given the change of this variation in a century, while 

 AS20 is the second difference for intervals of 120 days. By means of these num- 

 bers, when the arguments are computed for any date, their values for other dates 

 at intervals of 120 days may be found by successive addition. 



Table III gives the motion of the several arguments between the epochs of the 

 preceding table and the zero day of each montli in the course of a four-year cycle. 

 The variable motions, u and 0, correspond to the epoch 1850, and rigorously they 

 each require a correction for any other four-year cycle than that between 1848 and 

 1852. But, owing to the small inclination of the orbit of Uranus it is not neces- 

 sary that either w or should be exact, if only their sum is exact. The column 

 0' of this table, therefore, gives tlie correction which must be applied to the motion 

 of d at the end of a century (1950) in order that, being applied to alone, u -{- 

 may be exact. This correction is, in fact, that for the secular variation of the 

 precession. 



Tables IV and V give the motion of the arguments for days and hours. The 

 motion for hours is, however, not necessary in the case of any argument but g, as 

 all the others can be readily enougli interpolated to fractions of a day. 



Table VI gives the corrections to the arguments on account of the terms of long 

 period from 1000 to 2200. The terms in question are, in the case of Jupiter, the 

 great inequality produced by the action of Saturn, in the case of Neptune the 

 great inequality produced by Uranus, and, in the case of Uranus, the inequalities 

 in the mean longitude tabulated in the preceding chapter. The numerical expres- 

 sions are 



<V= 0.5:55 sin (11G° 21' -f 40° 45' 20" T) 



hU=ll 



hN= —0.75 U. 



The corrections to the several arguments are ' * 



b 



No correction to the mean longitude of Saturn is applied, all its inequalities being 

 taken account of in the terms of the second order. 



'The corrections, expressed in seconds, have been reduced to units of the argu- 

 ment by dividing them by 21 GO". 



Outside the limits of the table these corrections must be computed from their 

 formula;. 



Table VII gives the equation of the centre, and the elliptic part of tlio logarithm 

 of the radius vector. No constant is applied to the former, but the latter is dimi- 

 nished by .0003400, the sum of the constants added to (p.^.O) in Tables VIIT, IX, 

 X and XVII. 



