124 



THE ORBIT OF URANUS. 



Paris, 1801-1827. 



A complete reduction of this series is found in Le Verrier's Annules de I'Obser- 

 vatoire Imperial de Paris, Observations, tome 1. No comparison with any ephemeris 

 is given here, nor is there any complete ephemeris to compare them with. A 

 complete geocentric ephemeris was therefore computed from the 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 : 



Mean date. 



1813, May 20, 



1814, May 27, 



1815, May 24, 



1816, June 1, 



Mean 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, 



1817, June 5, 



1818, June 7, 



1819, June 18, 



1820, June 20, 



1821, June 22, 



1823, July 18, 



1824, July 13, 

 1827, July 25, 



Total number of observations in right ascension, 175. 



The observations in this scries 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 found 

 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 are much more numerous, the deviations 

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

 discordances approached 10". 



BesseTs Konigsberg 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 right ascensions and Dr. Auwers' declina- 

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

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

 planet, to be used for clock error. These were 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 fulfilled for the decli- 

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



