530 Prof. G. B. Airy on the History of the Discovery of 



this distance to be less than the former value by about 7 \,th 

 part of the whole. The result is very satisfactory, and appears 

 to show that, by still further diminishing the distance, the 

 agreement between the theory and the later observations may 

 be rendered complete, and the excentricity reduced at the 

 same time to a very small quantity. The mass and the ele- 

 ments of the orbit of the supposed planet, which result from 

 the two hypotheses, are as follows : — 



Hypothesis I. Hypothesis II. 



(S= M ) G= ' 515 ) 



Mean longitude of planet, 1st Oct. 1846 325° 8' 323° 2' 



Longitude of perihelion 315-57 299'11 



Excentricity 016103 0*12062 



Mass (that of sun being 1) 000016563 0-00015003 



" The investigation has been conducted in the same manner 

 in both cases, so that the differences between the two sets of 

 elements may be considered as wholly due to the variation of 

 the fundamental hypothesis. The following table exhibits the 

 differences between the theory and the observations which 

 were used as the basis of calculation. The quantities given 

 are the errors of mean longitude, which I found it more con- 

 venient to employ in my investigations than those of the true 

 longitude. 



Ancient Observations. 



DatP (Obg.— Theory.) „ . (Obs.-Theory.) 



uale - Hypoth. I. Hypoth. II. ^ ate - Hypoth. I. Hypoth. II. 



1712 +67 +6"3 1756 — 4 : — 4-0 



1715 —6-8 —6-6 1764 — 5-1 — 4-1 



1750 —1-6 —2-6 1769 + 0-6 + 1-8 



1753 +5-7 +5-2 1771 +H-8 +12-8 



Modern Observations. 



1780 +027 + 054 1810 + 0-56 +0-61 



1783 —0-23 —0-21 1813 —0-94 -1-00 



1786 —096 —1-10 1816 —031 —046 



1789 +1-82 +1-63 1819 —200 —2-19 



1792 —0-91 —1-06 1822 +0-30 +0-14 



1795 +0 09 +004 1825 +1-92 +1-87 



1798 —0-99 —0-93 1828 +225 +2-35 



1801 —0 04 +0-11 1831 —1-06 —0-82 



1804 +1-76 +1-94 1834 —1-44 —1-17 



1807 -0 21 —0 08 1837 —1-62 —1-53 



1810 +0-56 +0-61 1840 +1-73 +1-31 



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

 1771, is deduced from a single observation, whereas the dif- 

 ference 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 



