THE Oil BIT OP URANUS. 191 



applied in tliis table. Tin- numbers at the bottom of this table, in the line A|JJ, 

 shoxv the variation of the corresponding ( |uantity in 1'JO days, lor the epoch 1850.0. 

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

 A ( ,ii is the second difference tor intervals of 120 days. By means of these num- 

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

 at intervals of l.'O days may lie found by successive addition. 



Table 111 gives the motion of the several arguments between the epochs of the 

 preceding table and the zero day of earli month 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 

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

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

 ff of this table, therefore, Drives the correction which must be applied to the motion 

 of at the end of a century (1950) in order that, being applied to alone, o -f- 

 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 jr, as 

 all the others can be readily enough 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 



iJ 0.535 sin (110 21' + 40 45' 20' T) 



The corrections to the several arguments are 



lg = II 



3arg. 1= W U 



3 arg. 2 = II 



Sarg. 3= II IN =1.755? 



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 2160". 



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 the 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.c.O) in Tables VIII, IX, 

 X and XVII. 



