PHYSICAL ASTRONOMY* 



which the motions both of P and P' may be de- 

 termined. 



This is the problem of the Three Bodies, as far as 

 the principles of Dynamics are concerned. The 

 rest depends on the integral calculus, and involves 

 a multitude of investigations which do not belong 

 to this place. See Memoir of LA PLACE, sur tes 

 Inegalites de Jupiter et Saturn. Acad. des Sciences, 

 1785. Also Mecanique Celeste, liv. vi. 



What is given above, is merely an elementary expo- 

 sition of the dynamical principles employed in 

 these investigations ; a sketch follows of some 

 of the most important conclusions deduced from 

 them. 



267. The place of every planet in its orbit, 

 is changed by the action of the other planets, 

 and the orbit itself is changed in all its elements 

 but two, the mean distance from the Sun and 

 the mean motion of the Planet. 



a. In the orbit of a planet, the line of the nodes, the 

 inclination to the plane of the ecliptic, the line of 

 the apsides, and the eccentricity, all vary. The 

 lines of the nodes and of the apsides revolve conti- 

 nually ; but the inclination of the orbit and its ec- 

 centricity are only subject to small periodical va- 

 riations on each side of a mean, front which they 

 never depart far. 



*. The 



