18 VARIATION IX INCLINATION. SECT. HI. 



That part of the disturbing force is now to be considered which 

 acts perpendicularly to the plane of the orbit, causing periodic 

 perturbations in latitude, secular variations in the inclination of 

 the orbit, 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 orbit, 

 according to the relative positions 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 coin- 

 cide 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 perpetually 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 dis- 

 turbing force, all its variations are compensated after a revo- 

 lution of the disturbed body, and are merely periodical perturba- 

 tions 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 com- 

 pensated by the revolution of the disturbing body, whose motion 

 has not hitherto been taken into the account, so that perturba- 

 tion compensates perturbation ; but still a comparatively per- 



