A secondary conclusion must not be omitted. In the last chapter we sawthat motion is never absolutely rectilinear; and here it remains to add that,as a consequence, rhythm is necessarily incomplete. A truly rectilinear rhythmcan arise only when the opposing forces are in exactly the same line, andthe probabilities against this are infinitely great. To generate a perfectlycircular rhythm, the two forces concerned must be exactly at right anglesto each other, and must have exactly a certain ratio; and against this theprobabilities are likewise infinitely great. All other proportions and directionsof the two forces (omitting such as produce parabolas or hyperbolas) willproduce an ellipse of greater or less eccentricity. And when, as always happens,above two forces are engaged, the curve described must be more complex, andcannot exactly repeat itself. So that throughout nature, this action andreaction of forces never brings about a complete return to a previous state.
Where the movement is that of some aggregate whose units are partially independent,regularity is no longer traceable. And on the completion of any periodicchange, the degree in which the state arrived at differs from the state departedfrom, is marked in proportion as the influences at work are numerous. §83. That spiral arrangement common among the more structured nebulae,shows us the progressive establishment of revolution, and therefore of rhythm,in those remote spaces which the nebulae occupy. Double stars, moving inmore or less eccentric orbits round common centres of gravity in periodssome of which are now ascertained, exhibit settled rhythmical actions indistant parts of our Sidereal System.
The periodicities of the planets, satellites, and comets, familiar thoughthey are, must be named as so many grand illustrations of this general lawof movement. But besides the revolutions of these bodies in their orbits(all more or less eccentric), the Solar System presents us with rhythms ofa less manifest and more complex kind. In each planet and satellite thereis 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 alterationin the length of the axis major of the orbit, and also of its eccentricity: both of which are rhythmical alike in the sense that they alternate betweenmaxima and minima, and in the sense that the progress from one extreme tothe other is not uniform, but is made with fluctuating velocity. Then, too,there is the revolution of the line of apsides round the heavens -- not regularly,but through complex oscillations. And, further, we have changes in the directionsof the planetary axes -- that known as nutation, and that larger gyrationwhich, in the case of the Earth, causes the precession of the equinoxes.
These rhythms, already more or less compound, are compounded with one another.
One of the simplest re-compoundings is seen in the secular acceleration andretardation of the moon, consequent on the varying eccentricity of the Earth'sorbit. Another, having more important consequences, results from the changingdirection of the axis of rotation in a planet having a decidedly eccentricorbit. The Earth furnishes the best example. During a certain long periodit presents more of its northern than of its southern hemisphere to the Sunat the time of nearest approach to him; and then again, during a like period,presents more of its southern hemisphere than of its northern: a recurringcoincidence which involves an epoch of 21,000 years, during which each hemispheregoes through a cycle of temperate seasons and seasons that are extreme intheir heat and cold. Nor is this all. There is even a variation of this variation.
For the summers and winters of the whole Earth become more or less stronglycontrasted, as the eccentricity of its orbit increases or decreases. Henceduring the increase of the eccentricity, the epochs of moderately contrastedseasons and epochs of strongly contrasted seasons, through which alternatelyeach hemisphere passes, must grow more and more different in the degreesof their contrasts; and contrariwise during decrease of the eccentricity.
