116 THE ORBIT OF URANUS. 



combined both, the choice being determined by circumstances. We shall con- 

 sider the different series of observations in succession. 



Greenwich Observations from 1781 to 1830. 



These observations are completely reduced by Airy and compared with Bou- 

 vard's Tables, in the work lieduction of the Observations of Planets made at the 

 Royal Observatory, Greenwich, from 1750 to 1830. London, 1845. The con- 

 cluded positions given in this work depend mainly on the star places of tlie 

 Tabulae Regiomontanje, both in right ascension and declination. If we consider 

 the first four oppositions — 17S1-1785— as forming a single group of which the 

 mean epoch is 1783, we find that the general correction to the Tabulae Regio- 

 montanae for this epoch is 



In right ascension, — 0\030 ; 



In declination, -|-0".08. 



If, on the other hand, we consider only the particular stars compared with Uranus, 

 the result will be a little diff'erent. The number of times each of the fundamental 

 stars has been compared with Uranus, and the correction in right ascension cor- 

 responding to each star, are nearly as follows: — 



The mean correction from these data comes out — 0'.008, difi"ering by 0\022 from 

 the general mean correction. Our choice between the two corrections depends 

 on whether we are to consider the relative positions of the Tabula? Ilegiomontana>, 

 or those of the standard catalogue, as nearest the truth at the epocli 1783, and 

 particularly upon whether we are to consider the large correction to the proper 

 motion of (3 Tauri as real. In the absence of exact data for settling this ques- 

 tion, the mean of the two results, or — 0'.020, has been adopted. 



A similar anomaly is exhibited by the declinations. It is probable that the 

 declinations of Uranus during this period mainly depend on stars in the first 

 twelve hours in right ascension, for which the mean correction is about — 0".30 

 instead of +0".08. I have adopted — 0".16. Changing these corrections to lon- 

 gitude and latitude, we have, during the period 1781-1786: — 



Correction to observed longitude, = — 0".30 ; 

 Correction to observed latitude, —0 .19. 



