Another and smaller motion of a somewhat similar kind has been worked out since: it is due to the unsymmetrical attraction of the other planets for this same equatorial protuberance. It shows itself as a periodic change in the obliquity of the ecliptic, or so-called recession of the apses, rather than as a motion of the nodes.[21]
No. 15. The waters of the ocean are attracted towards the sun and moon on one side, and whirled a little farther away than the solid earth on the other side: hence Newton explained all the main phenomena of the tides.
And now comes another tremendous generalization. The tides had long been an utter mystery. Kepler likens the earth to an animal, and the tides to his breathings and inbreathings, and says they follow the moon.
Galileo chaffs him for this, and says that it is mere superstition to connect the moon with the tides.
Descartes said the moon pressed down upon the waters by the centrifugal force of its vortex, and so produced a low tide under it.
Everything was fog and darkness on the subject. The legend goes that an astronomer threw himself into the sea in despair of ever being able to explain the flux and reflux of its waters.
Newton now with consummate skill applied his theory to the effect of the moon upon the ocean, and all the main details of tidal action gradually revealed themselves to him.
He treated the water, rotating with the earth once a day, somewhat as if it were a satellite acted on by perturbing forces. The moon as it revolves round the earth is perturbed by the sun. The ocean as it revolves round the earth (being held on by gravitation just as the moon is) is perturbed by both sun and moon.
The perturbing effect of a body varies directly as its mass, and inversely as the cube of its distance. (The simple law of inverse square does not apply, because a perturbation is a differential effect: the satellite or ocean when nearer to the perturbing body than the rest of the earth, is attracted more, and when further off it is attracted less than is the main body of the earth; and it is these differences alone which constitute the perturbation.) The moon is the more powerful of the two perturbing bodies, hence the main tides are due to the moon; and its chief action is to cause a pair of low waves or oceanic humps, of gigantic area, to travel round the earth once in a lunar day, i.e. in about 24 hours and 50 minutes. The sun makes a similar but still lower pair of low elevations to travel round once in a solar day of 24 hours. And the combination of the two pairs of humps, thus periodically overtaking each other, accounts for the well-known spring and neap tides,—spring tides when their maxima agree, neap tides when the maximum of one coincides with the minimum of the other: each of which events happens regularly once a fortnight.