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.

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 h