Note N. 63 — SECTION III.

Note 63, pp. 14, 16. The whole force, &c. Let S, fig. 13, be the sun, N m n the plane of the ecliptic, p the disturbed planet moving in its orbit n p N, and d the disturbing planet. Now, d attracts the sun and the planet p with different intensities in the directions d S, d p: 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 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 440the direction of the tangent 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 S p does not move over equal areas in equal times. (See note 26.) For example, 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 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 n, may be called the perpendicular force. It sometimes 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 Mr. Airy, the Astronomer Royal.