18 VARIATION IN THE INCLINATION. SECT. III. 



variations in the inclination of the oibit, and a retrograde 

 motion to its nodes on the true plane of the ecliptic 

 (N. 71). This force tends to pull the disturbed body 

 above, or push (N. 72) it below, the plane of its orb.t, 

 according to the relative pos.tions of the two planets with 

 regard to the sun, considered to be fixed. By this 

 action, it sometimes makes the plane of the orbit of the 

 disturbed body tend to coincide with the plane of the 

 ecliptic, and sometimes increases its inclination to that 

 plane. In consequence of which, its nodes alternately 

 recede or advance on the ecliptic (N. 73). When the 

 disturbing planet is in the line of the disturbed planet's 

 nodes (N. 74), it neither affects these points, the latitude, 

 nor the inclination, because both planets are then in the 

 same plane. When it is at right angles to the line of 

 the nodes, and the orbit symmetrical on each side of the 

 disturbing force, the average motion of these points, 

 after a revolution of the disturbed body, is retrograde, 

 and comparatively rapid ; but when the disturbing planet 

 is so situated that the orbit of the disturbed planet is not 

 symmetrical on each side of the disturbing force, which 

 is most frequently the case, every possible variety of 

 action takes place. Consequently, the nodes are per- 

 petually advancing or receding with unequal velocity ; 

 but, as a compensation is not effected, their motion is, 

 on the whole, retrograde. 



With regard to the variations in the inclination, it is 

 clear, that, when the orbit is symmetrical on each side 

 of the disturbing force, all its variations are compensated 

 after a revolution of the disturbed body, and are merely 

 periodical perturbations in the planet's latitude ; and no 

 secular change is induced in the inclination of the orbit. 

 When, on the contrary, that orbit is not symmetrical on 

 each side of the disturbing force, although many of the 

 variations in latitude are transient or periodical, still, 

 after a complete revolution of the disturbed body, a 

 portion remains uncompensated, which forms a secular 

 change in the inclination of the orbit to the plane of the 

 ecliptic. It is true, part of this secular change in the 

 inclination is compensated by the revolution of the dis- 

 turbing body, whose motion has not hitherto been taken 

 into the account, so that perturbation compensates per- 



