16 



SECULAR VARIATIONS OF THE ELEMENTS OF 



/ D3 /) / 



I ^ | ^_ 





f [HO 



I HTTl 



I EH]/) / Ci3n / I . J EZ] 



= s |^=-^3/3 p^M.A r ~=~ 1 jYYi 



J EZ 



- rHE 



1 



f -* 



/En] 



1 pj n 



moi M- 



T71 I 

 Z11 



m I 



\r' 



A'N+f 



- (57) 



' 



" Lly ; (58) 



" 



(55) 



( 56 ) 



^RTU"Z>" |2,i||o, : ,M' 



; (60) 





- 



; (61) 





N r "=, 



'1/4 rripr?i 



3 Z? 3 |4,V||0,S| 





. (64) 



11. Equations (53) to (64) are entirely rigorous. They are, moreover, under a 

 very simple and convenient form for the computation of JV, N", N'", &c. and, as 

 there are duplicate and independent formulae for all these quantities, any error that 

 may accidentally creep into the computation of one formula is at once detected by 

 computation of the other. They have also this additional advantage : sometimes 

 one of the formula? for N, N", N", &c., gives value for these quantities of the form 



