20 



turbed Elements III, of Neptune, upon the hypothesis that Lalande had observed 

 it upon the 10th of May, 1795. These elements were completed February 6. 

 They were only approximate ; yet they were such as, in my opinion, confirmed 

 the period of the Disturbed Elements II, and estabhshed the smallness of the 

 *eccentricity of Neptune, viz., 0.0088407. 



I subjoin the Disturbed Elements III, as they were published in the Union, 

 on the 9th of February, 1847. 



DISTURBED ELEMENTS III, OF NEPTUNE, COMPUTED ON HYPOTHESIS OF IDENTITY WITH THE LALANDE 



STAR OF MAY 10, 1795. 



rt = 0° 12' 25".51 

 Q, = 131 17 35 .80 



f = 1 54 53 .83 



6=0.0088407 

 1^ = 21".3260 

 f = 328° 7' 56". 641 

 Radius vector r = 30.02596 j- 1847, September 28, m. noon, Greenwich. 



V = 21". 64553 

 T = 166>. 38134 



I 



In order to present the question of identity or non-identity in a more 

 conclusive form, I reviewed my computations of the loci for the 10th of May, 

 making them functions of the increasing values of the eccentricity «, from the 

 minimum e =. 0.006457, viz., ?? = 0, to e = 0.06 for « = ± 87°.'2. 



The computations were made by the equation, 



a (\ — e e) 



t*r\a If . — _^ ' ... 



For w =. 0, e is 0.006474. For w = ± 90°, e is 1. Hence the limit v < ± 90° 

 for the true anomaly, January 1, 1847. When we consider that between + 90° 

 and — 90°, all values of v for completion of Elements II, are a priori equally 

 plausible, the following table is readily formed: 



*My most recent value of this element, for Elliptic Elements 11, is 0.00871946, being a diminution of 0. 0001213. The 

 remarks of M. Leverrier, in noticing these elements, Comptes Rendus, for March 29, 1847, that this smallness of my 

 concluded eccentricity was " incompatible with the nature of the residual perturbations of Uranus ;" but " perhaps it was 

 not a necessary consequence of the representation of the Lalande observation," cannot be sustained. Prof. Peirce has 

 demonstrated its perfect compatibility with the anomalies of Uranus. Adams has confirmed the necessity of this smallness 

 for the representation of the Lalande observation. See Proceedings R. Ast. Soc, Vol. VII, p. 269, May 14, 1847 ; also 

 Aatronomische Nachrichten, No. 600. Adams' value is even smaller than that of Elements IH, by 0.000457. 



