1] ELEMENTS OF AN EXTERIOR PLANET. 5 



As Flamsteed's first observation of Uranus (in 1690) is a single one, 

 and the interval between it and the rest is so large, I thought it unsafe to 

 employ this observation in forming the equations of condition. On comparing 

 it with the theory, I find the difference to be rather large, and greater for 

 the second hypothesis than for the first, the errors being + 44"-5 and + 50"'0 

 respectively. If the error be supposed to change in proportion to the change 



of mean distance, its value corresponding to = 0-57, will be about +70", 



and the error in the time of transit will be between 4 s and 5 s . It would 

 be desirable to ascertain whether Flamsteed's manuscripts throw any light 

 on this point. 



The corrections of the tabular radius vector of Uranus, given by the 

 theory for some late years, are as follows : 



Date. Hypotli. I. Hypoth. II. 



1834 +0-005051 +0-004923 



1840 +0-007219 +0-006962 



1846 +0-008676 +0-008250 



The correction for 1834 is very nearly the same as that which you 

 have deduced from observation, in the Astronomische Nachrichten ; but the 

 increase in later years is more rapid than the observations appear to give 

 it : the second hypothesis, however, still having the advantage. 



I am at present employed in discussing the errors in latitude, with 

 the view of obtaining an approximate value of the inclination and position 

 of the node of the new planet's orbit ; but the perturbations in latitude 

 are so very small that I am afraid the result will not have great weight. 

 According to a rough calculation made some time since, the inclination 

 appeared to be rather large, and the longitude of the ascending node to 

 be about 300; but I am now treating the subject much more completely, 

 and hope to obtain the result in a few days. 



I have been thinking of drawing up a brief account of my investigation 

 to present to the British Association. 



NOTE. The mass was found to be three times that of Uranus, and 

 it was thence inferred and stated to Professor Challis that the brightness 

 would not be below that of a star of the ninth magnitude. 



