168 SECULAR VARIATIONS OF THE ELEMENTS OF 



Equations (408) and (409) will also become 



na 



na 



(539) 



no, 



a 



cos 



If we substitute in these equations the values of 

 by equations (537), they will become 



(540) 



,po, &c., g , g ', &c., given 



(541) 



-a 

 ( 



na 



w a 



(542) 



Now according to equations (410), the coefficient of N t in this equation is equal 

 to nothing; and if we substitute the values of the coefficients of a cos /? 4 , and a sin /3 4 , 

 which are given by equations (408) and (409), both members of equations (541) 

 and (542) will be divisible by the coefficients of a sin (gt-}-(3 m ), and a cos 

 and we shall find 



Whence we get 

 Therefore 



sn (#/-=a sn 

 cos (gt+ppj=a cos 



tan 



>); > 



>). J 



ft^tan (7<+ 1 3 (0) ) 



>=3-?, and =1. 



(543) 



(544) 



It therefore follows that in order to apply our numbers to the invariable plane, 

 we have only to diminish the constants /?, p^ /? 2 , &c., by the longitude of the 

 ascending node of that plane, on the fixed ecliptic of 1850, and neglect the con- 

 stant term. 



