38 



ON THE PERTURBATIONS OF URANUS. 



ANCIENT OBSERVATIONS. 



Observation - Theory. 

 Year. Hypoth. I. Hypoth. II. 



MODERN OBSERVATIONS. 



1712 + 67 



1715 6-8 



1750 IT) 



1753 + 57 



1756 4-1 



1764 5'1 



1769 + 0'6 



1771 +11-8 



+ 6-3 



- 6-6 



- 2-6 

 + 5-2 



4-0 



4-1 



+ 1-8 



+ 12'8 



Observation - Theory. 



Tear. Hypoth. I. Hypoth. II. 



1780 +6-27 + o'-54 



1783 -0-23 -0-21 



1786 -0-96 -1-10 



1789 +1-82 +1-63 



1792 -0-91 -1-06 



1795 +0-09 +0'04 



1798 -0-99 -0-93 



1801 -0-04 +0-11 



1804 +176 +1-94 



1807 -0-21 -0-08 



1810 +0-56 +0-61 



Observation - Theory. 



Year. Hypoth. I. Hypoth. II. 



1813 -0-94 -l"-00 



1816 -0-31 -0-46 



1819 -2-00 -2-19 



1822 +0-30 +0-14 



1825 +1-92 +T87 



1828 +2'25 +2'35 



1831 -1-06 -0-82 



1834 -1-44 -1-17 



1837 -1-62 -1-53 



1840 +173 +1-31 



The largest difference in the above table, viz. that for 1771, is deduced 

 from a single observation ; whereas the difference immediately preceding it, 

 which is deduced from the mean of several, is very small. 



53. The results of the two theories agree very closely with each other, 

 and with observation, till we come to the later years of the series ; and it 

 is to be observed, that the difference between the theories becomes sensible 

 at precisely the point where they both shew symptoms of diverging from 

 the observations, the errors of the second hypothesis, however, being less 

 than those of the other. 



Recent observations shew that the errors of the theory soon become 

 very sensible, though decidedly less for the second hypothesis than for the 

 first. The following are the differences of mean longitude, as deduced from 

 theory and observation, for the oppositions of 1843, 1844, and 1845 : 



Year. 



1843 

 1844 



1845 



Observation - Theory. 

 Hypoth. I. Hypoth. II. 



+ 7-11 



+ 879 



+ 12-40 



+ 577 

 + 7-05 

 + 10-18 



