14 D1STUKBING FORCES. SJBCT. III. 



of all the planets on each. But as it is only necessary 

 to estimate the disturbing influence of one body at a 

 time, what follows may convey some idea of the manner 

 in which one planet disturbs the elliptical motion of 

 another. 



Suppose two planets moving in ellipses round the sun ; 

 if one of them attracted the other and the sun with 

 equal intensity, and in parallel directions (N. 62), it 

 would have no effect in disturbing the elliptical motion. 

 The inequality of this attraction is the sole cause of 

 perturbation, and the difference between the disturbing 

 planet's action on the sun and on the disturbed planet 

 constitutes the disturbing force, which consequently 

 varies in intensity and direction with every change in 

 the relative positions of the three bodies. Although 

 both the sun and planet are under the influence of the 

 disturbing force, the motion of the disturbed planet is 

 referred to the center of the sun as a fixed point, for 

 convenience. The whole force (N. 63) which disturbs 

 a planet is equivalent to three partial forces. One of 

 these acts on the disturbed planet, in the direction of a 

 tangent to its orbit, and is called the tangential force : it 

 occasions secular inequalities in the form and position of 

 the orbit in its own plane, and is the sole cause of the 

 periodical perturbations in the planet's longitude. An- 

 other acts upon the same body in the direction of its 

 radius vector, that is, in the line joining the centers of 

 the sun and planet, and is called the radial force : it 

 produces periodical changes in the distance of the planet 

 from the sun, and affects the form and position of the 

 orbit in its own plane. The third, which may be called 

 the perpendicular force, acts at right angles to the plane 

 of the orbit, occasions the periodic inequalities in the 

 planet's latitude, and affects the position of the orbit 

 with regard to the plane of the ecliptic. 



It has been observed, that the radius vector of a 

 planet moving in a perfectly elliptical orbit, passes over 

 equal spaces or areas in equal times; a circumstance 

 which is independent of the law of the force, and would 

 be the same whether it varied /inversely as the square 

 of the distance, or not, provided only that it be directed 

 to the center of the sun. Hence the tangential force. 



