146 PROCEEDINGS OF THE AMERICAN ACADEMY 



until the mass and orbit of this planet have been determined 

 with accuracy. Mr. Sears C. Walker, of Washington, is ac- 

 tively engaged in computing the orbit of Neptune, and has 

 sent an account of his results in a letter, from which the 

 following is an extract. 



''Washington, D. C, May 3d, 1847. 



" After computing my Elements IV. of the planet Neptune, I com- 

 pared with an ephemeris derived from them one hundred and thirteen 

 American and three hundred and sixty-six European observations, be- 

 ing the entire series extant to this date. 



" From this collection of observations I have derived thirteen nor- 

 mal places, which gave me thirteen conditional equations for correct- 

 ing Elements IV., which were a slight modification of Elements II. of 

 my former letter. 



" In computing the conditional equations I used the method sketched 

 out in my former letter. As this application of the method of me- 

 chanical quadratures to the formation of conditional equations for cor- 

 recting an approximate orbit is new, I will give a brief statement of it. 

 The conditional equation is, 



= ax-\-hy-{-cz-\-du-\-ev-}- &c. -f- n. 



Where a ■= {t — 1846 years, 340 days). 



J = 1. 



Numerical term ... n = (w, — a' j = (computed — observed) 

 true orbital longitude. 



Also, no = the assumed true daily sidereal angular motion for a =0. 

 C0(, = the assumed true orbital longitude for a ^ 0. 

 Tq = the assumed radius vector . . . for a =-. 0. 

 .T, y, and z =JnQ, Jo»o, and /jr^ = the required corrections for a = 0. 

 ft,'(") = value of w, from normal place, for date t, using r=^rQ. 

 w/«) = a)o + a Wq- 



r (") = r^ -j- 2 -j- au-\-a^v -\- &c. = corrected radius vector 

 for date t. 



