THE ORBIT OF NEPTUNE. 



39 



The constants being so taken that the perturbations, and also the differential 

 coefficient of 81, shall all vanish at the epoch 1850.0. These perturbations are 

 given for the beginning of every tenth year, from 1GOO to 2000, in the following 

 table : 



SECULAR AND LONG-PERIOD PERTURBATIONS OF THE ELEMENTS OF NEPTUNE FROM 



1GOO TO 2000. 



ftp and $q refer to the fixed ecliptic of 1850.0, 5p'and V* tne movable ecliptic 

 of the date, the motion being that adopted in Hanson's " Tables du Soleil," and 

 concluded from the secular diminution of the obliquity there given. 



The corrections to the true longitude, latitude, and radius vector derived from 

 the pure elliptic elements require corrections for these perturbations as follows : 



