4 RESULTS OF CALCULATIONS OF THE [l 



MODERN OBSERVATIONS. 



(Obs.- Theory.) n t (Obs. -Theory.) 



Date - Hypoth. I. Hypoth. II. Hypoth. I. Hypoth. II. 



1780 +6-27 +0-54 1813 -6-94 -l"-00 



i; 8 3 -0-23 -0-21 1816 -0'31 -0'46 



1786 -0-96 -I'lO 1819 -2-00 -2-19 



1789 +1'82 +1-63 1822 +0-30 +0-14 



1792 -0-91 -1-06 1825 +1-92 +1-87 



1795 +0'09 +0-04 1828 +2'25 + 2'35 



1798 -0-99 -0-93 1831 -T06 -0-82 



1801 -0-04 +0-11 1834 -1-44 -1-17 



1804 +176 +T94 1837 -T62 -1-53 



1807 -0-21 -0-08 1840 +173 +1-31 



1810 +0-56 +0-61 



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

 deduced from a single observation, whereas the difference immediately 

 preceding, which is deduced from the mean of several observations, is much 

 smaller. The error of the tables for 1780 is found by interpolating between 

 the errors given by the observations of 1781, 1782, and 1783, and those 

 of 1769 and 1771. The differences between the results of the two hypo- 

 theses are exceedingly small till we come to the last years of the series, 

 and become sensible precisely at the point where both sets of results 

 begin to diverge from the observations ; the errors corresponding to the 

 second hypothesis being, however, uniformly smaller. The errors given by 

 the Greenwich Observations of 1843 are very sensible, being for the first 

 hypothesis +6"'84, and for the second +5" - 50. By comparing these errors, 

 it may be inferred that the agreement of theory and observation, would 



be rendered very close by assuming = 0'57, and the corresponding mean 



ct 



longitude on the 1st October, 1846, would be about 3 15 20', which I am 

 inclined to think is not far from the truth. It is plain also that the 



eccentricity corresponding to this value of , would be very small. In 



Ct 



consequence of the divergence of the results of the two hypotheses, still 

 later observations would be most valuable for correcting the distances, and 

 I should feel exceedingly obliged if you would kindly communicate to me 

 two normal places near the oppositions of 1844 and 1845. 



