16 DISTURBING FORCES. [SECT. in. 



titles, in immense periods of time, and are therefore called 

 secular inequalities. 



The periodical perturbations are compensated when the 

 bodies return to the same relative positions with regard to 

 one another and to the sun : the secular inequalities are 

 compensated when the orbits return to the same positions 

 relatively to one another, and to the plane of the ecliptic. 



Planetary motion, including both these kinds of disturb- 

 ance, may be represented by a body revolving in an ellipse, 

 and making small and transient deviations, now on one side 

 of its path, and now on the other, whilst the ellipse itself is 

 slowly, but perpetually, changing both in form and position. 



The periodic inequalities are merely transient deviations 

 of a planet from its path, the most remarkable of which only 

 lasts about 918 years ; but, in consequence of the secular 

 disturbances, the apsides, or extremities of the major axes of 

 all the orbits, have a direct but variable motion in space, 

 excepting those of the orbit of Venus, which are retrograde 

 (N. 61), and the lines of the nodes move with a variable 

 velocity in a contrary direction. Besides these, the incli- 

 nation and excentricity of every- orbit are in a state of 

 perpetual but slow change. These effects result from the 

 disturbing action 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 in- 

 tensity, 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 dif- 

 ference 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. 



