468 



NOTES. 



Fig. 13. 



NOTE 63, pp. 17, 19. The whole Jorce, #c. 

 Let S, fig. 13, be the sun, N m n the plane of 

 the ecliptic, p the disturbed planet moving in 

 its orbit npN, and d the disturbing planet. 

 Now, d attracts the sun and the planet p 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 dis- 

 turbing 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 acting in the radius vector 

 p S, joining the centres of the sun and planet, 

 is called the radial force. It sometimes draws 

 the disturbed planet p from the sun, and 

 sometimes brings it nearer to him. The 

 force which acts in the direction of the tan- 

 gent p T is called the tangential force. It 

 disturbs the motion of p in longitude, that 

 is, it accelerates its motion in some parts of 

 its orbit and retards it in others, so that the 

 radius vector Sp does not move over equal 

 areas in equal times. (See Note 26.) For ex- 

 ample, 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 dis- 

 turbing body is here supposed to be at rest, 

 and theorbit circular; but, as both bodies are 

 perpetually moving with different velocities 

 in ellipses, the perturbations or changes in 

 the motions of p are very numerous. Lastly, 

 that part of the disturbing force which acts 

 in the direction of a line p m, fig. 13, at right 

 angles to the plane of the orbit N p M, may 

 be called the perpendicular force. It some- 

 times causes the body to approach nearer, 

 and sometimes to recede farther from, the 

 plane of the ecliptic N m n, than it would 

 otherwise do. The action of the disturbing 

 forces is admirably explained in a work on 

 gravitation, by Professor Airy, of Cam- 

 bridge. 



NOTE 64, pp. 18, 84. Perihelion. Fig. 10, P, the point of an orbit nearest 

 the sun. 



NOTE 65, p. 18. Aphelion. Fig. 10, A, the point of an orbit farthest from 

 the sun. 



