142 IDENTITY OF THE PLANET LEVERRIER 



Nine European observations combined, furnished me one place of Leverrier, September 

 26, 18 16. Three Washington observations, October 21th, and three more, November 21st, 

 completed the three observed places. I commenced with the trial of radii vectores 33 

 and 34, which include Leverrier's and Adams's hypothetical values. I found that 33 was 

 too great, and extended the scale downwards to 32, 31, 30, and 29. 



I subjoin the table of computed daily sidereal orbital motions for the three intervals, of 

 thirty days from September 26; fifty-eight days from September 26; and twenty-eight 

 days from October 24, for this scale of assumed constant radii vectores. They are the 

 results of an approximate computation only, r is the radius vector, ri is the daily sidereal 

 orbital motion for the first thirty days, n for the whole term of fifty-eight days, and », for 

 the last twenty-eight days, p is the mean daily sidereal motion for r — a = the semi- 

 axis major. 



The same analogies that led to the assumption of the constancy of the radius vector 

 for fifty-eight days, also lead to the conclusion that n must be nearly constant. 

 Accordingly, the true radius vector, to be interpolated from this table, was that in which 

 [(/?. — n') a -+- (n — ?f,) 2 ] should be a minimum. 



A slight inspection of the table shows that this value of r is very nearly 30.0, and that 

 since for this value n = f.t, n = /.i, and n, = ft, very nearly, therefore a = r very nearly. 

 In other words, the orbit approaches very nearly to the circular form, and that which 

 was at first inferred from the analogies of the solar system (viz., the smallness of the 

 eccentricity,) is now established as a deduction from actual observation.* 



I was now prepared to commence a rigorous computation of the circular elements, on 

 the hypothesis of a uniform radius vector, r = a. For this computation two observed 

 places arc sufficient. I chose the above place of the 26th of September, and a place 

 deduced from my own observations with the Washington Equatorial, December 26th. 

 On this night I compared Leverrier in right ascension by transits, thirty-three times, with 

 each of the two Enckian stars which have been used for comparison with Leverrier from 

 its discovery by Galle, to the middle of January last. I also compared it eleven times in 

 declination with the same stars, with the filar micrometer. 



A test of the precision of a night's work with the equatorial is furnished by the fact 

 that the observed relative position of the two fixed stars should be constant on all the 

 nights. In this way I found the probable error of one night's woi'k to be about 0".6 of 

 space in Dill'. R, A., and 0".5 in Dill". Dec. I mention this to show the precision of the 

 measured path when many nights' works are combined, and the comparisons are .through- 

 out made with the same stars. After correcting the observed places for parallax, and 



1 The possible accidental case off = a in a very eccentric ellipse, was rejected from its improbability. 



