2 ELEMENTS OF AN EXTERIOR PLANET, [l 



the Cambridge and Greenwich observations, and those given in the Astro- 

 nomische Nachrichten, have been made use of. The following are the 

 remaining errors of mean longitude : 



OBSERVATION THEORY. 



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 Lemon- 

 nier's observations in 1769 and 1771. 



For the ancient observations, the following are the remaining errors : 



OBSERVATION THEORY. 



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. 



II. 



In the investigation, the results of which I communicated to you last 

 October, the mean distance of the supposed disturbing planet is assumed 

 to be twice that of Uranus. Some assumption is necessary in the first 

 instance, and Bode's law renders it probable that the above distance is 

 not very remote from the truth : but the investigation could scarcely be 

 considered satisfactory while based on anything arbitrary ; and I therefore 



