THE ORBIT OF URANUS. II5 



The correction to the reductions to apparent place given in the Tabiilte Re^io- 

 montanac on account of the correction to the constant of Nutation is; — 



In right ascension: 

 — 0".46 sin a — 0".18 sin Q, sin a tan ^ — 0".24 sin Q cos a tan 8. 



In dccHnation : 

 — 0"18 sin a cos a + 0.24 cos Q, sin a. 



The terms which contain tan 5 as a factor may be entirely neglected, as they are 

 small, periodic, and contain tan h as a factor which is sometimes positive and 

 sometimes negative. I shall also neglect the corrections in declination, as their 

 sum is sensibly 



0".21 sin (a — a) ' ■ 



the effect of which will generally be confounded with the accidental errors of 

 observation. 



The only correction we shall apply on account of nutation is, therefore, 



ha = — 0\030 sin Q. 



The values of this expression at the dates when it is zero, a maximum, or a 

 minimum, are as follows: — 



y. s. 



1778.5 —.03 

 1783.1 .00 

 1787.7 +.03 

 1792.4 .00 

 1797.0 —.03 

 1801.7 .00 

 1806.3 +.03 

 1811.0 .00 



1815.6 —.03 

 1820.3 .00 



Having adopted this system of standard positions, we may adopt two ways of 

 reducing the observations to it. One is to compare the positions of the stars 

 adopted in the published reductions with the standard, and apply the mean differ- 

 ence to the reduced place of the planet. Another is to make a similar com- 

 parison of the standard catalogue with the positions of the fundamental stars 

 which have been deduced from the observations by a system of reduction uniform 

 with that employed in reducing the observations of the planet, and to regard the 

 mean difference as a correction applicable to all the positions of the planet. If 

 the standard catalogue and the observations are both free from systematic eiTor, 

 the results obtained in these two ways should be substantially identical. These 

 are, however, conditions wliich we cannot expect to find fulfilled. In the follow- 

 ing discussions I liave sometimes used one, sometimes the other, and sometimes 



