316 



liaust the residual perturbations of Uranus, but are willing to leave 

 something to other still superior planets to be discovered hereafter. 



It was in the course of an examination of M. Leverrier's paper, by 

 Prof. Peirce, of Harvard University, in company with Mr. Walker, 

 for the purpose of explaining this discrepancy, that the suggestion 

 was made by the former, of the possibility of some neglected ine- 

 quality of long period being sufficient to account for it. To their 

 great surprise, on comparison it was found that 



For Uranus, i^! = 42.23312 Astr. Nachr.580. 



Walker's Elements II., Leverrier, (^ = 21.37881 

 2fc — [^'= 0.52450 



Here, then, if Mr. Walker's period is right, would be the most re- 

 markable inequality in the primary solar system. On a careful exa- 

 mination of Leverrier's paper, it does not appear that he took this into 

 account; but instead of it, that he used that of (3 /«. — jm.'), suited to 

 the first assumed mean motion for a = 38.37. When we consider 

 that this inequality, in its terms depending on the square of the time, 

 amounts to nearly one-twelfth of the entire perturbations of Uranus, 

 by Leverrier, in Flamsteed's time and at present, and that a similar 

 inequality of still greater power, if substituted in its place, might 

 amount to a much larger proportion, it would seem that the question 

 of a priori limits from residual perturbations depends much on a cir- 

 cumstance not noticed by M. Leverrier, viz. the possibility of a pow- 

 erful inequality of the order (2 jtt — ;«,'). If, then, it be probable that 

 Mr. Walker's period is correct, that period, by means of this new in- 

 equality, explains its departure from the limits assigned by M. Le- 

 verrier. 



Since, then, Mr. Walker's Elements II. are not necessarily incom- 

 patible with the limits of M. Leverrier and Adams, it was desirable 

 to see whether the indeterminate quantities e and 5r could be supplied 

 by finding some ancient observation. 



For this purpose, on the 2d of February he examined the principal 

 catalogues. 



I. Bradley seldom observed stars of 7lh and 8th magnitude. 

 II. Mayer. 



III. Lacaille. 



IV. Piazzi. There is no star among the list "not found in the Cata- 



logues," from 1792 to 1798, which could be supposed to be 

 Leverrier. The subsequent observations of Piazzi, under pro- 



