SECT. III. PERTURBATIONS. 13 



tions with regard to each other, begins from zero, in- 

 creases to a maximum, decreases, and becomes zero 

 again, when the planets return to the same relative 

 positions. In consequence of these, the disturbed planet 

 is sometimes drawn away from the sun, sometimes 

 brought nearer to him : sometimes it is accelerated in 

 its motion, and sometimes retarded. At one time it is 

 drawn above the plane of its orbit, at another time below 

 it, according to the position of the disturbing body. All 

 such changes, being accomplished in short periods, some 

 in a few months, others in years, or in hundreds of 

 years, are denominated periodic inequalities. The in- 

 equalities of the other kind, though occasioned likewise 

 by the disturbing energy of the planets, are entirely in- 

 dependent of their relative positions. They depend 

 upon the relative positions of the orbits alone, whose 

 forms and places in space are altered by very minute 

 quantities, in immense periods of time, and are, there- 

 fore, 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 ine- 

 qualities 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 dis- 

 turbance, 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, while the 

 ellipse itself is slowly, but perpetually, changing both in 

 form and position. 



The periodic inequalities are merely transient devi- 

 ations 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 eccen- 

 tricity of every orbit are in a state of perpetual- but slow 

 change. These effects result from the disturbing action 

 B 



