312 



Sept. 26, Oct. 26, and Nov. 1, on the supposition of a constant ra- 

 dius vector, he computed the following table of the average true side- 

 rial daily motion n', n &, n^ for the first, vi'hole and last interval re- 

 spectively, for various radius vectors. Also the mean daily siderial 

 motion ;«, for r = a, or radius vector equal the mean distance. 



r n' n n^ Ia 



v-»v-^ V-'N/"^ V*V^ >.»-v-^ V,^v-W 



34 12.8 16.7 19.7 17.90 



33 14.6 17.7 20.3 18.71 



32 16.6 18.8 20.8 19.60 



31 19.4 20.1 21.2 20.56 



30 21.7 21.6 21.6 21.58 



29 24.1 23.4 22.0 22.67 



The most plausible value of r in this table is that in vv^hich (n — n'Y 

 + (ra -^ «,) 2 is a minimum. This gives nearly r = 30 , n' = 

 n = n^ = 1^. Hence the orbit comes out nearly a circle, unless we 

 suppose the planet to present, at this time, a value of r accidentally 

 equal to a, in a more eccentric ellipse with true anomaly nearly 90°. 



Accordingly, he selected for the next trial the circular hypothesis, 

 for which two places of the planet, Sept. 26th and Dec. 26th, sufficed. 

 The first was derived from the mean of nine European observations. 

 The last from his own observations with the Washington equatorial, 

 consisting of thirty-three comparisons in R. A. and eleven in Dec, 

 with the two stars first selected for comparison by Encke. In the 

 computations all the small corrections were taken into account. The 

 geocentric longitude x and latitude <Ji were referred to the mean equi- 

 nox and obliquity of Jan. 1st, 1847. The planet's place was corrected 

 for aberration as a fixed star, for planetary parallax, but not at first 

 (though subsequently so) corrected for planetary aberration. In this 

 manner, he obtained Elements I. and computed an ephemeris for the 

 six months following August 1st. He then reduced the entire col- 

 lection of European observations received, seventy nights' works in 

 all, and the forty-six nights' works of American observations at the 

 Washington Observatory, and compared them with the ephemeris. 

 The sixteen normal places indicated the following comparison be- 

 tween theory and observation. The dates are referred to mean time, 

 Greenwich. The places are reduced like those of Sept. 26th and 

 Dec. 26th, but are not corrected for planetary aberration. 



