124 



THE ORBIT OF URANUS. 



Paris, 1801-1827. 

 A complete reduction of tliis series is luund ih Le Verrier's Annales de VOhser- 

 vatoire Imperial tie Paris, Observations, tome I. No comparison with any ephemeris 

 is o-iven here, nor is tliere any complete ephemeris to compare them with. A 

 complete geocentric ephemeris was therefore computed from tlie provisional theory 

 for the principal groups of the Paris observations. The individual observations 

 being compared with it, the resulting mean corrections are given in the following 

 table : 



Jlean date. 



1801, March 24, 



1802, April 1, 



1805, April 22, 



1806, April 17, 



1807, April 28, 



1808, April 28, 



1809, May 5, 



1810, April 30, 



1811, Febr'y 18, 



1811, May 17, 



1812, Febr'y 16, 



1812, May 10, 



1813, Febr'y 25, 



Total number of observations in right ascension, 175, 



The observations in this series exhibit numbers of discordances of that class 

 which leave the astronomer in doubt whether the observation should be retained 

 or rejected. This remark applies more especially to the declinations. If we de- 

 termine the probable error of an observation in declination by the condition that 

 it is that amount which the error falls short of as often as it exceeds, it is fonnd 

 to be about 2". Then, if the errors followed the commonly assumed law of proba- 

 bility, only about one in six of the errors should exceed 4", and one in twenty- 

 three 6". But errors of these magnitudes arc much more numerous, the deviations 

 often amounting to six or eight seconds. I have rejected only a few in which tlie 

 discordances approached 10". 



BesscVs K(})ti(jsherg Observations, 1814-1835. 

 I have made a complete re-reduction of the right ascensions of this important 

 series, and of most of the declinations. In order to avoid the necessity of apply- 

 ing systematic corrections, Dr. Gould's riglit ascensions and Dr. Auwers' dechna- 

 tions were used throughout in these reductions. In this work a selection of 

 the fundamental stars observed by Besscl was made for each observation of the 

 planet, to be used for clock error. These Avere chosen so that the mean of their 

 right ascensions and declinations should be as near as practicable to those of 

 Uranus, a condition, however, which could not generally be fidfilled for the decli- 

 nations, owing to the southern position of the planet. Bessel's instrumental cor- 



