144 IDENTITY OF THE PLANET LEVERRIER 



DIFFERENTIAL MEASURES. 



The place of the star seventh magnitude 7648 B. A. C. rests upon the following 

 authorities. Piazzi, Mayer, Taylor, Challis, six observations; Plantamour, four observa- 

 tions; Plana, one observation; Washington observatory, twenty-five observations. The 

 above are direct observations of 7648 B. A. C. There are also ten Berlin, and three 

 Washington equatorial comparisons of 7648 B. A. C. with Leverrier directly or through 

 * a, on nights when Leverrier was observed on the meridian, and its place was reduced 

 to a common date. 



The other star, Encke's * a, ninth magnitude, has for its place the following authori- 

 ties, Bessel's Zones, Encke and Galle, two nights' comparisons with 7648 B. A. C, Encke, 

 five nights' comparisons with Leverrier referred on these nights to fifteen meridian obser- 

 vations; Maury, six; Walker, ten nights' comparisons with 7648 B. A. C. 



I have adopted the mean place of the two stars from all these authorities for January 



1st, 1847, as follows: 



7648 B. A. C. 7th mag., R. A. 1847, 327°32'1G".79 December, 1847, — 13°23'39".17 

 ■fc a of Encke, 9th mag., " 327°57'42".81 " — 13°25'57".22 



I do not think that the error of either of these star's places much exceeds one second of 

 space. 



By means of my ephemeris I was able to compute the value of c, or the mean of the 

 second differences of the planet's daily places in R. A. and Dec. with a certainty of an 

 error not exceeding 0".02. The group of observations of any seven consecutive nights 

 were reduced to the corresponding value for the fourth night, by the following formula, 

 in which the difference»c of the daily motions, and not of the motions themselves, are 

 employed. 



I. Normal place (4th night,) a = _ . I h h ( a „ 1 



) 

 ) 

 )] 



Where n = the number of nights' works combined for single night. 



h = \/ n 



v V n — , + n + , / 

 /y<= W4, n -' x n + >) 



v V ' n — , + n -^ J 



