OF ARTS AND SCIENCES. 



147 



K^ = (rQ 4" ^Y (% ~h ^) = Neptune's daily area. 

 71 ("^ = K^ (r("^)~'^= value of n for date t for conserva- 

 tion of areas. 

 ^(0, 5(0, &c. = the part of the coefficients of u, u, introduced by the 

 quadratures. 

 " These coefficients were computed from Laplace's formula ( Mec. 

 Cel, Vol. v.), viz. : — 



J a = 



_J.9 (J3„(.-3,_^3^(0)J 



— - rf^CJ^m"'-^^ — J^m<°>) 



— &c. 



" The solution of the thirteen equations of condition by least squares 

 gave for Elements V., — 

 Longitude of the Perihelion, n= 1° 45' 32".90 m. eq. Jan. 1, 184L 



Ascending Node, . 

 Inclination, . . . 

 Eccentricity, . . 

 Mean distance, 



9> = 129° 51' 13".53 



t= 1° 45' 38". 10 



e = 0.00505292 

 a = 30.145119 



M= 326° 2' 1".34 for mean noon at 



[Greenwich. 



Epoch, Jan. 1st, 1847, 



Mean daily sidereal motion,// = 21". 437843 



Period in tropical years, T= 165.51330. 



" The ephemeris from Elements V. in order to agree with the thir- 

 teen normal places requires the following corrections of the geocentric 

 longitude and latitude. 



