As this subject is one of general interest, and as it holds a prominent place in 

 the history of astronomical science in America, I will make no apology for 

 entering here more fully into its consideration. 



The venerable and eminent astronomer and mathematician, Bernhard von 

 Lindenau, in a recent paper, entitled " Contribution to the history of the discov- 

 ery of Neptune," after stating the condition in which this very peculiar question 

 was left by the discoverers, Le Verrier and Adams, expresses his expectation 

 that it will soon be brought to a satisfactory conclusion by a new investigation 

 on the part of these geometers. 



" It is to be expected," he observes, " that the former results of the computa- 

 tions will undergo a material change ; for, if we apply to the perturbations of 

 Neptune by Uranus, computed by Peirce, the proposition of La Place, control- 

 hng the equations of the perturbations of long period, viz., that the reciprocal 

 perturbations of two planets are to each other as the products of the masses by 

 the square roots of the semi-axis major, (Mec. Cel., Vol. Ill, p. 147,) we shall 

 obtain for Uranus values very ditferent from those on vvhicii the investigations 

 of Le Verrier and Adams are based. If the question was in the beginning to 

 solve the inverse problem of perturbations, wc must now come back to the 

 direct problem, which is, to determine by means of the perturbations of Uranus 

 by Jupiter, Saturn, and Neptune, taken in connection with the observations of 

 Uranus from 1690 to 1848, an orbit of Uranus which will represent in the best 

 manner the whole of the observations."* 



After finishing his paper, however, and while wailing to see the subject 

 brought to a satisfactory termination by a new investigation on the part of Le 

 Verrier or Adams, Lindenau received the new and important work (such are 

 his words) on Neptune, contained in Vol. II. of the Smithsonian Contribu- 

 tions to Knowledge, by the American astronomer. Walker, whose first elliptic 

 elements he had previously communicated. 



He was thus led to append a supplement to the " Contribution," in which he 

 gives the more essential points of the further development of the theory of Nep- 

 tune and Uranus, and speaks of the labors of Mr. Walker in the following 

 terms: "By using all the observations made in the old and new world in the 

 years 1795, 1846-'47.- 48,t (amounting to more than a thousand,) and taking 

 into account the perturbations of Neptune by Jupiter, Saturn, and Uranus, com- 

 puted by Peirce, Mr. Walker obtained elements which represent not only the 

 two observations of Lalande, but also all the recent ones within the limits of 

 a few seconds. [Tenths of seconds of arc would have been more correct.] So 

 that the Ephemeris computed by him from those elements for the periods from 

 May 8 to 11, 1795, and from August, 1846, to January, 1850, is perfectly sufii- 

 cient as well for finding the planet as for the comparison of the observed place." 



* This and the following extracts from Lindenau 'a paper are taken from a translation made by Mr. Francois de Pour- 

 tnleB. The original is published by Prof. Schumacher in his supplement to the Astronomical Notices. 

 j This should be omitted, Mr. Walker having used only those of 1795, 1846, and 1847. 



