perihelion 315 55
Eccentricity 0.1610.
Mass (that of the sun being unity) 0.0001656.

For the modern observations I have used the method of normal places,
taking the mean of the tabular errors, as given by observations near
three consecutive oppositions, to correspond with the mean of the
times; and the Greenwich observations have been used down to 1830:
since which, the Cambridge and Greenwich observations, and those
given in the _Astronomische Nachrichten_, have been made use of. The
following are the remaining errors of mean longitude:--

_Observation--Theory._

"
1780 +0.27
1783 -0.23
1786 -0.96
1789 +1.82
1792 -0.91
1795 +0.09
1798 -0.99
1801 -0.04
1804 +1.76
1807 -0.21
1810 +0.56
1813 -0.94
1816 -0.31
1819 -2.00
1822 +0.30
1825 +1.92
1828 +2.25
1831 -1.06
1834 -1.44
1837 -1.62
1840 +1.73

The error for 1780 is concluded from that for 1781 given by
observation, compared with those of four or five following years, and
also with Lemonnier's observations in 1769 and 1771.

"'For the ancient observations, the following are the remaining
errors:--

_Observation--Theory._

"
1690 +44.4
1712 + 6.7
1715 - 6.8
1750 - 1.6
1753 + 5.7
1756 - 4.0
1763 - 5.1
1769 + 0.6
1771 +11.8

The errors are small, except for Flamsteed's observation of 1690.
This being an isolated observation, very distant from the rest, I
thought it best not to use it in forming the equations of condition.
It is not improbable, however, that this error might be destroyed by
a small change in the assumed mean motion of the planet.'

"I acknowledged the receipt of this paper in the following terms:--

NO. 12.--G. B. AIRY _to_ J. C. ADAMS, Esq.

"'ROYAL OBSERVATORY, GREENWICH, _1845, Nov. 5_.

[Sidenote: Airy's inquiry about the "radius vector."]

"'I am very much obliged by the paper of results which you left here
a few days since, showing the perturbations on the place of _Uranus_
produced by a planet with certain as