THE RHYTHM OF MOTION. 265 



moving round common centres of gravity in periods some of 

 which are now ascertained, exhibit settled rhythmical ac- 

 tions in distant' parts of our siderial system. And another 

 fact which, though of a different order, has a like general 

 significance, is furnished by variable stars stars which 

 alternately brighten and fade. 



The periodicities of the planets, satellites, and comets, 

 are so familiar that it would be inexcusable to name them, 

 were it not needful here to point out that they are so many 

 grand illustrations of this general law of movement. But be- 

 sides the revolution of these bodies in their orbits (all more 

 or less excentric) and their rotations on their axes, the 

 Solar System presents us with various rhythms of a less 

 manifest and more complex kind. In each planet and satel- 

 lite there is the revolution of the nodes a slow change in 

 the position of the orbit-plane, which after completing itself 

 commences afresh. There is the gradual alteration in the 

 length of the axis major of the orbit; and also of its excen- 

 tricity: both of which are rhythmical alike in the sense 

 that they alternate between maxima and minima, and in the 

 sense that the progress from one extreme to the other is not 

 uniform, but is made with fluctuating velocity. Then, too, 

 there is the revolution of the line of apsides, which in course 

 of time moves round the heavens not regularly, but 

 through complex oscillations. And further we have varia- 

 tions in the directions of the planetary axes that known 

 as nutation, and that larger gyration which, in the 

 case of the Earth, causes the precession of the equi- 

 noxes. These rhythms, already more or less com- 

 pound, are compounded with each other. Such an instance 

 as the secular acceleration and retardation of the moon, 

 consequent on the varying excentricity of the Earth's 

 orbit, is one of the simplest. Another, having more impor- 

 tant consequences, results from the changing direction of 

 the axes of rotation in planets whose orbits are decidedly 



excentric. Every planet, during a certain long period, pre- 

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