400 



NOTES. 



Let S, fig. 13, be the sun, 

 Fig. 13. 



brium when it is so balanced as to remain at rest. But there are two 

 kinds of equilibrium, stable and unstable. If a body balanced in stable 

 equilibrium be slightly disturbed, it will endeavor to return to rest by a 

 number of movements to and fro, which will continually decrease till 

 they cease altogether, and then the body will be restored to its original 

 state of repose. But if the equilibrium be unstable, these movements to 

 and fro, or oscillations, will become greater and greater till the equili- 

 brium is destroyed. 



NOTE 61, p. 13. Retrograde. Going backward, as from east to west, 

 contrary to the motion of the planets. 



NOTE 62, p. 14. Parallel directions. Such as never meet, though 

 prolonged ever so far: 



NOTE 63, pp. 14, 16. The whole force, be. 

 Nmw the plane of the ecliptic,^ the dis- 

 turbed planet moving in its orbit 7ipN, and 

 d the disturbing planet. Now, d attracts the 

 sun and the planet^ with different intensities 

 in the directions d S, dp : the difference only 

 of these forces disturbs the motion of p ; it 

 is, therefore, called the disturbing force. But 

 this whole disturbing force may be regarded 

 as equivalent to three forces, acting in the 

 directions p S, p T, and p m. The force act- 

 ing in the radius vector p S, joining the cen- 

 ters of the sun and planet, is called the 

 radial force. It sometimes draws the dis- 

 turbed planet p from the sun, and sometimes 

 brings it nearer to him. The force which 

 acts in the direction of the tangent, p T, 

 is called the tangential force. It disturbs 

 the motion of p in longitude, that is, it accel- 

 erates its motion in some parts of its orbit 

 and retards it 

 in others, so 

 that the ra- 

 dius vector 

 S p does not 

 move over 

 equal areas 



in equal times. (See Note 26.) Forexam- 

 ~ pie, in the position of the bodies in fig. 14, 

 it is evident that, in consequence of the 

 attraction of d, the planet P will have its 

 motion accelerated from Q, to C, retarded 

 from C to D, again accelerated from D to 

 O, and, lastly, retarded from O to Q,. The 

 disturbing body is here supposed to be at 

 rest, and the orbit circular ; but as both 

 bodies are perpetually moving with dif- 

 ferent velocities in ellipses, the perturba- 

 tions or changes in the motions of P are 

 very numerous. Lastly, that part of the 

 disturbing force which acts in the direc- 

 tion of a line p m, fig. 13, at right angles 

 to the plane of the orbit N pn, may be 

 called the perpendicular force. It some- 

 times causes the body to approach nearer, 

 nnd aornptimp-- to rfredp fnrthf>r from, the 





