294 



PROCEEDINGS OF THE AMERICAN ACADEMY 



" The terms A and B include the secular terms, and also those 

 of long period as well as those which acquire large coefficients by 

 the small divisors, which depend upon the near approach to commen- 

 surability in the mean motions of Neptune and Uranus. These coeffi- 

 cients will vary very sensibly by a change in the value of the mean 

 motion of Neptune arising from a more accurate determination of its 

 orbit. But the principal effect of these terms can for a limited period, 

 such as a century, for instance, be included in the ordinary forms of 

 elliptic motion, and the residual portion will assume a secular form, 

 which is no more liable to change, from a new correction of the mean 

 motion of Neptune, than the other small coefficients of the equations 

 of perturbation. The elliptic portions of A and B may therefore be 

 neglected until longer observation has given a more precise value of 

 Neptune's mean motion, and the residual portion is contained in the 

 following equation. 



A= 1.98 sin. (2 f + 221 46) " 



+ 0.36517 t sin. (f -f 20 58 12) 



4- 0.0002 t sin. (2 f 4- 322) 

 — 0.0020714 <2 



+ 0.0004027 t^ sin. (f -f 230° 3') 



B = — 0.00066 

 + .0.00134 

 -i- 0.0000115 t 

 -f 0.00002827 t 



COS. (f -f 38° 40') 

 sin. (f + 286 32 23) 



4- 0.0000000300 fi cos. (f + 125 1) 



" The following particular values of 5 u and 8 r, derived from the 

 preceding formulae, will be useful in computing the orbit of Neptune 

 from observation. 



May 9, 1795, 

 October 1, 1846, 

 January 1, 1847, 

 April 1, 

 July 1, " 



October 1, " 



8v 



II 



+ 47.80 

 -f 27.03 

 -f 27.13 

 -f 26.68 

 -}- 25.75 

 -j- 24.37 



dr 



+ 0.01283 

 4- 0.01793 

 + 0.01728 

 4- 0.01664 

 + 0.01602 

 -f 0.01544 



