470 NOTES. 



NOTE 72, p. 21. This force tends to pull, $c. The force in question, acting in 

 the direction p rn, fig. 13, pulls the planet p towards the plane N mn, or pushes 

 it farther above it, giving the planet a tendency to move in an orbit above or 

 below its undisturbed orbit Npn, which alters the angle p N m, and makes the 

 node N and the line of nodes N n change their positions. 



NOTE 73, p. 21. Motion of the nodes. Let S, fig. 19, be the sun ; S N n the 

 plane of the ecliptic; P the disturbing body; and p a planet moving in its 

 orbit pn,of which p M is so small a part that it is represented as a straight line. 

 The plane S np of this orbit cuts the plane of the ecliptic in the straight line 

 S n. Suppose the disturbing force begins to act on p, so as to draw the planet 

 into the arc p p' ; then, instead of moving in the orbit p n, it will tend to move 

 in the orbit pp' n', whose plane cuts the ecliptic in the straight line S n. If the 

 disturbing force acts again upon the body when at p', so as to draw it into the 

 arcp'p", the planet will now tend to move in the orbit p' p" n", whose plane 

 cuts the ecliptic in the straight line S n". Th action of the disturbing force 

 on the planet when at p" will bring the node to n'", and so on. In this man- 

 ner the node goes backwards through the successive points n, n', n", n'", &c., 

 and the line of nodes S n has a perpetual retrograde motion about S, the centre 



Fig. 19. 



of the sun. The disturbing force has been represented as acting at intervals 

 for the sake of illustration : in nature it is continuous, so that the motion of 

 the node is continuous also ; though it is sometimes rapid and sometimes slow, 

 now retrograde and now direct; but, on the whole, the motion is slowly retro- 

 grade. 



NOTE 74, p. 21. When the disturbing planet is anywhere in the line S N, 

 fig. 19, or in its prolongation, it is in the same plane with the disturbed planet; 

 and, however much it may affect its motions in that plane, it can have no ten- 

 dency to draw it out of it. But when the disturbing planet is in P, at right 

 angles to the line S N, and not in the plane of the orbit, it has a powerful 

 effect on the motion of the nodes : between these two positions there is great 

 variety of action. 



NOTE 75, p. 22. The changes in the inclination are extremely minute when 



