the Planet exterior to Uranus, 531* 



errors given by the observations of 1781, 1782, and 1783, and 

 those of 1769 and 1771. The differences between the results 

 of the two hypotheses are exceedingly small till we come to 

 the last years of the series, and become sensible precisely at 

 the point where both sets of results begin to diverge from the 

 observations ; the errors corresponding to the second hypo- 

 thesis being, however, uniformly smaller. The errors given 

 by the Greenwich Observations of 1843 are very sensible, 

 being for the first hypothesis 4- 6"'84, and for the second 

 + 5"*50. By comparing these errors, it may be inferred that 

 the agreement of theory and observation would be rendered 



very close by assuming — = 0*57, and the corresponding mean 



longitude on the 1st of October, 1846, would be about 315° 

 20', which I am inclined to think is not far from the truth. 

 It is plain also that the excentricity corresponding to this value 



of —j would be very small. In consequence of the divergence 



of the results of the two hypotheses, still later observations 

 would be most valuable for correcting the distances, and I 

 should feel exceedingly obliged if you would kindly commu- 

 nicate to me two normal places near the oppositions of 1844 

 and 1845. 



"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 se- 

 cond hypothesis than for the first, the errors being + 44"* 5 and 

 4- 50"'0 respectively. If the error be supposed to change in 

 proportion to the change of mean distance, its value corre- 

 sponding to — j-=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 de- 

 sirable 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 : — 



"The correction for 1834 is very nearly the same as that 

 which you have deduced from observation, in the Astrono- 

 mische Nachrichten ; but the increase in later years is more 



