14 DISTURBING FORCES. SECT. III. 



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 disturbance, 

 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 per- 

 petually, 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 inclination 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 intensity, 

 and in parallel directions (.N. 62), it would have no effect in 

 disturbing the elliptical motion. The inequality of this attrac- 

 tion 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 posi- 

 tions 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 centre 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. Another acts upon the same body in the direction 

 of its radius vector, that is, in the line joining the centres of 



