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. These are the main effects, but besides these there are the effects of varying distances and obliquity to be taken into account; and so we have a whole series of minor disturbances, very like those discussed in No. 7, under the lunar theory, but more complex still, because there are two perturbing bodies instead of only one. The subject of the tides is, therefore, very recondite; and though one may give some elementary account of its main features, it will be best to defer this to a separate lecture (Lecture XVII). I had better, however, here say that Newton did not limit himself to the consideration of the primary oceanic humps: he pursued the subject into geographical detail. He pointed out that, although the rise and fall of the tide at mid-ocean islands would be but small, yet on stretches of coast the wave would fling itself, and by its momentum would propel the waters, to a much greater height--for instance, 20 or 30 feet; especially in some funnel-shaped openings like the Bristol Channel and the Bay of Fundy, where the concentrated impetus of the water is enormous.