Instances of the alternation, either total or approximative, of these principles are many and familiar.  They may be seen in the systole and diastole of the heart; in the alternate activity and passivity of the lungs; in the feet of the pedestrian, one pausing while the other proceeds; in the waving wings of birds; in the undulation of the sea; in the creation and propagation of sound, and the propagation, at least, of light; in the alternate acceleration and retardation of the earth’s motion in its orbit, and in the waving of its poles.  In all vibrations and undulations there is a going and returning, between which must exist minute periods of repose; but in many instances the return is simply a relaxation or a subsidence, and belongs, therefore, to the department of rest.  Discourse itself, it will be observed, has its pauses, seasons of repose thickly interspersed in the action of speech; and besides these has its accented and unaccented syllables, emphatic and unemphatic words,—­illustrating thus in itself the law which it here affirms.  History is full of the same thing; the tides of faith and feeling now ascend and now subside, through all the ages, in the soul of humanity; each new affirmation prepares the way for new doubt, each honest doubt in the end furthers and enlarges belief; the pendulum of destiny swings to and fro forever, and earth’s minutest life and heaven’s remotest star swing with it, rising but to fall, and falling that they may rise again.  So does rhythm go to the very bottom of the world:  the heart of Nature pulses, and the echoing shore and all music and the throbbing heart and swaying destinies of man but follow and proclaim the law of her inward life.

The universality and mutual relationship of these primal principles have, perhaps, been sufficiently set forth; and this may be the place to emphasize the second chief point,—­that the perfection of this mutuality measures the degree of excellence in all objects and actions.  It will everywhere appear, that, the more regular and symmetrical their relationship, the more beautiful and acceptable are its results.  For example, sounds proceeding from vibrations wherein the strokes and pauses are in invariable relation are such sounds as we denominate musical. Accordingly all sounds are musical at a sufficient distance, since the most irregular undulations are, in a long journey through the air, wrought to an equality, and made subject to exact law,—­as in this universe all irregularities are sure to be in the end.  Thus, the thunder, which near at hand is a wild crash, or nearer yet a crazy crackle, is by distance deepened and refined into that marvellous bass which we all know.  And doubtless the jars, the discords, and moral contradictions of time, however harsh and crazy at the outset, flow into exact undulation along the ether of eternity, and only as a pure proclamation of law attain to the ear of Heaven.  Nay, whoso among men is able to plant his ear high enough above this rude clangor may, in like manner, so hear it, that it shall be to him melody, solace, fruition, a perpetual harvest of the heart’s dearest wishes, a perpetual corroboration of that which faith affirms.