29 



E, = 2.445 ; log q — 0.8582—9 ; 



dF ' - ö./ 



- = — [0. 340 1 — 7] - ; 0= 74°22' (1900.0), J= 7°15'; 

 d o 



therefore 



— = — [0.9836—1] ; ~ = — [0.4305-1] ; 

 O/) 05' 



therefore 



^V dF 



— = + [0.3237 — 7] ; — = 4- [0.7706—8] ; 



from which, taking as unit of time the centurj^ I get : 



dp dq 



-^ = 4- 0".125 ; -^ =: — 0".447. 

 dt dt 



Therefore the perturbation caused bv both elH|jsoids together is: 



^^= + 0"..190; ^ = _0".501. 

 dt dt 



Let f be the obliquity of the ecliptic for the time t, 8„ the same 



for the time t^, I and £l inclination and longitude of the node of 



the ecliptic for t with reference to the ecliptic for Z^, Ihen: 



cos e ■==■ cos i cos e^ — sin i sin e^ cos Sh, 



from which, differen Hating, we get: 



de . . di . (i . . 



— sin 8 — = — sin i cos f ,, sin f ,, — (sin i cos S}^) 



dt dt dt 



therefore for t^= t^ : 



c/g dq 



dt ~ dt' 



ch 

 The perturbation of the obliquity of the ecliptic thus is — = — 0".50J . 



dt 



The difference between observation and theory given by J^ewcomb 

 is — 0".22 ±0.18 (probable error); this thus becomes -f 0".28. The 

 addition to the planetary precession a is given by ; 

 da 1 dp 



dt sin e dt 



+ 0".478. 



It. Perturhatiom of the motion of the moon. 



We siiall now proceed to the formulae for the C0ml»tltatioli ol' 

 the perturbation of the motion of the moon. As the perturbative 

 force in the motion of tlie moon we have to take the difference 

 between the attractions of the ellipsoid on the moon and on the 

 earth. Suppose a system of coordinates, the sun at the origin, the 

 axis of z perpendicular to the eliptic; let x,y,z be the coordinates 



