286 PROCEEDINGS OF THE AMERICAN ACADEMY 



" Mr. Walker has applied to the elh'ptic values of v and r the per- 

 turbations d V and d r, which Professor Peirce communicated to him, 

 and has compared the instantaneous values with the normal right 

 ascensions and declinations, as follows : — 



" Mr. Walker has omitted the comparison of place II. because it is 

 not the result of direct observation, like the rest. A closer represen- 

 tation might be obtained by least squares ; but Mr. Walker prefers to 

 wait for Mr. Peirce's new values of the perturbations." 



Professor Peirce communicated his formulas for the pertur- 

 bations of Neptune's longitude and radius vector, resulting 

 from his second approximation to the theory of Neptune. In 

 his first approximation, Neptime's mean time of revolution 

 was assumed to be just twice that of Uranus, and the eccen- 

 tricity of Neptune's orbit was neglected. But the present 

 approximation is based upon Mr. Walker's orbit, which has 

 been presented to the Academy this evening, and includes all 

 sensible terms as high as the cubes of the eccentricities. 



" The masses of the disturbing planets, and the elements of their 

 orbits, which are adopted in this theory, are the same with those 

 adopted by Leverrier, in his theories of Mercury and Uranus, with 

 the exception of the mass of Uranus, which is taken from Lament's 

 determination by observations of the satellites. 



" The following notation is adopted in these formulse : — 



'■^ t = the time in Julian years from Jan. 1, 1850. 



" The mean longitude of each planet is denoted by the appropriate 

 symbol of that planet. 



" The Longitude of the perihelion of each planet is denoted by n 

 with the symbol of the planet subjacent. 



" The coefficient for correction of the mass of each planet is given 

 in the usual form with the symbol of the planet subjacent. 



" The formulsB are as follows : — 



