SECT, in.] VARIATION IN THE INCLINATION. 21 



clination 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 coincide with the plane of the ecliptic, 

 and sometimes increases its inclination to that plane. In con- 

 sequence of which, its nodes alternately recede or advance en 

 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 ad- 

 vancing or receding with unequal velocity ; but, as a com- 

 pensation is not effected, their motion is, on the whole, re- 

 trograde. 



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 per- 

 turbations in the planet's latitude ; and no secular change is 

 induced in the inclination of the orbit. When, on the con- 

 trary, that orbit is not symmetrical on each side of the dis- 

 turbing 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 



