402 



NOTES. 



NOTE 71, pp. 18, 19. The ecliptic is the apparent path of the sun in 

 the heavens. See Note 46. 



NOTE 72, p. 18. This force tends to pull, <$-c. The force in question 

 acting in the direction pm, fig. 13, pulls the planet p toward the plane 

 N m M, or pushes it farther above it, giving the planet a tendency to move 

 in an orbit above or below its undisturbed orbit N^n, which alters the 

 angle p N m, and makes the node N and tbe line of nodes N n change 

 their positions. 



NOTE 73, p. 18. 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 p n, of which p n is so small a part that it is represented as a 

 straight line. The plane Snp of this orbit cuts the plane of the ecliptic 

 in the straight line S M. Suppose the disturbing force begins to act on p 

 so as to draw the planet into the arc pp' ; 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 arcy 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". The 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 backward through the successive points, n,n',n",n"\ 

 &c., and the line of nodes S n has a perpetual retrograde motion about 



S, the center 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 retrograde. 



NOTE 74, p. 18. When the disturbing planet is anywhere in the line 

 SN, fig. 19, or in its prolongation, it is in the same plane with the dis- 

 turbed planet; and however much it may affect its motions in that 

 plane, it can have no tendency 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. 19. The changes in the inclination are extremely minute 

 when compared with the motion of the node, ns evidently appears front 

 fig. 19, where the angles npn', n' p' n", &c. are much smaller than the 

 corresponding angles n S n', S n", &c. 



NOTE 76, p. 20. Sines and cosines. Figure 4 is a circle ; n.p K the 

 sine, and Cp is the cosine of an arc mn. Suppose the radius Cm to 

 begin to revolve at m, in the direction mna; then at the point m the 

 sign is zero, and the cosine is equal to the radius Cm. As the line C m 



