106 THE ORBIT OF URANUS. 



CHAPTER VI. 



REDUCTION OF THE OBSERVATIONS OF URANUS, AND THEIR COMPARISON 



WITH THE PRECEDING THEORY. 



THE observations of Uranus naturally divide themselves into two distinct 

 classes. (1) The purely accidental ones, made previous to the recognition of the 

 planet by Herschel in 1781, and therefore without any suspicion on the part of the 

 observers that the object was not a fixed star, and (2) the systematic observations 

 made since. 



The first class are nearly all so uncertain in comparison with the second that I 

 have hesitated over the question of employing them at all. If nothing but a 

 determination of the elements of Uranus were called for, they would certainly not 

 be worth using, since these elements may be determined with entire certainty 

 from the observations which have been made during the entire revolution of the 

 planet since 1781. But the mass of Neptune is also to be determined, and it is 

 at least possible that these observations, uncertain though they are, may add 

 materially to the weight of this determination. I have, therefore, determined to 

 include them all, re-reducing them when there seemed to be good reason so to do. 



The earliest observations are those of Flamstead, published in the Historic 

 Ccelestis. The observations themselves, as printed, together with the principal 

 elements for reduction, are given in the following tables. 



The first column of the table gives the name of the star. The second gives 

 the clock time of transit over the wire of the quadrant as given by Flamstead. 

 The time, it will be seen, is only given to entire seconds. We must, therefore, 

 expect to find a probable error, of which the mathematical minimum is O s .25, 

 and of which the minimum we can reasonably expect is much greater. 



Next we have the apparent right ascensions of the stars as computed. For 

 these data I am indebted to Prof. Coffin, Superintendent of the American 

 Ephemeris. The mean places are mostly derived from the " Star Tables of the 

 American Ephemeris," and from the two Greenwich Seven Year Catalogues, while 

 the reduction to apparent place is made with the modern constants. 



The fourth column gives the apparent clock correction for sidereal time, in which 

 is included the effect of deviation of the instrument from the meridian. 



The clock keeping mean time, the errors are in the next column reduced to 

 those of sidereal time at the moment of the transit of Uranus. 



The next two columns give the corrections for clock rate, and for deviation of 

 the instrument from the meridian, as inferred from the observations themselves, 

 both being referred to the time and position of the transit of Uranus. 



