SECT, nr.] DISTURBING FOECES. 17 



Although both the sun and planet are under the influence of 

 the disturbing force, the motion of the disturbed planet is 

 referred to the centre of the sun as a fixed point, for con- 

 venience. 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. Another acts upon the same body 

 in the direction of its radius vector, that is, in the line join- 

 ing the centres 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 lati- 

 tude, 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 in- 

 dependent 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 centre of the 

 sun. Hence the tangential force, not being directed to the 

 centre, occasions an unequable description of areas, or, what 

 is the same thing, it disturbs the motion of the planet in 

 longitude. The tangential force sometimes accelerates the 

 planet's motion, sometimes retards it, and occasionally has 

 no effect at all. Were the orbits of both planets circular, a 

 complete compensation would take place at each revolution 

 of the two planets, because the arcs in which the accelera- 

 tions and retardations take place would be symmetrical on 

 each side of the disturbing force. For it is clear, that if 

 the motion be accelerated through a certain space, and then 



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