[Sidenote: Adams' announcement of the new planet.] "'According to my calculations, the observed irregularities in the motion of _Uranus_ may be accounted for by supposing the existence of an exterior planet, the mass and orbit of which are as follows:-- Mean distance (assumed nearly in accordance with Bode's Law) 38.4 Mean sidereal motion in 365.25 days 1°30'.9 Mean longitude, 1st October 1845 323 34 Longitude of 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."]