296. It has been already shewn § 106, that the power of gravity
diminishes as the square of the distance increases; and therefore the
waters at _Z_ on the side of the Earth _ABCDEFGH_ next the Moon _M_ are
more attracted than the central parts of the Earth _O_ by the Moon, and
the central parts are more attracted by her than the waters on the
opposite side of the Earth at _n_: and therefore the distance between
the Earth’s center and the waters on it’s surface under and opposite to
the Moon will be increased. For, let there be three bodies at _H_, _O_,
and _D_: if they are all equally attracted by the body _M_, they will
all move equally fast toward it, their mutual distances from each other
continuing the same. If the attraction of _M_ is unequal, then that body
which is most strongly attracted will move fastest, and this will
increase it’s distance from the other body. Therefore, by the law of
gravitation, _M_ will attract _H_ more strongly than it does _O_, by
which, the distance between _H_ and _O_ will be increased: and a
spectator on _O_ will perceive _H_ rising higher toward _Z_. In like
manner, _O_ being more strongly attracted than _D_, it will move farther
towards _M_ than _D_ does: consequently, the distance between _O_ and
_D_ will be increased; and a spectator on _O_, not perceiving his own
motion, will see _D_ receding farther from him towards _n_: all effects
and appearances being the same whether _D_ recedes from _O_ or _O_ from
_D_.
[Sidenote: PLATE IX.]
297. Suppose now there is a number of bodies, as _A_, _B_, _C_, _D_,
_E_, _F_, _G_, _H_ placed round _O_, so as to form a flexible or fluid
ring: then, as the whole is attracted towards _M_, the parts at _H_ and
_D_ will have their distance from _O_ increased; whilst the parts at _B_
and _F_, being nearly at the same distance from _M_ as _O_ is, these
parts will not recede from one another; but rather, by the oblique
attraction of _M_, they will approach nearer to _O_. Hence, the fluid
ring will form itself into an ellipse _ZIBLnKFNZ_, whose longer Axis
_nOZ_ produced will pass through _M_, and it’s shorter Axis _BOF_ will
terminate in _B_ and _F_. Let the ring be filled with bodies, so as to
form a flexible or fluid sphere round _O_; then, as the whole moves
toward _M_, the fluid sphere being lengthned at _Z_ and _n_, will assume
an oblong or oval form. If _M_ is the Moon, _O_ the Earth’s center,
_ABCDEFGH_ the Sea covering the Earth’s surface, ’tis evident by the
above reasoning, that whilst the Earth by it’s gravity falls toward the
Moon, the Water directly below her at _B_ will swell and rise gradually
towards her: also, the Water at _D_ will recede from the center
[strictly speaking, the center recedes from _D_] and rise on the
opposite side of the Earth: whilst the Water at _B_ and _F_ is
depressed, and falls below the former level. Hence, as the Earth turns
round it’s Axis from the Moon to the Moon again in 24-3/4 hours, there
will be two tides of flood and two of ebb in that time, as we find by
experience.
[Sidenote: Fig. II.]
298. As this explanation of the ebbing and flowing of the Sea is deduced
from the Earth’s constantly falling toward the Moon by the power of
gravity, some may find a difficulty in conceiving how this is possible
when the Moon is Full, or in opposition to the Sun; since the Earth
revolves about the Sun, and must continually fall towards it, and
therefore cannot fall contrary ways at the same time: or if the Earth is
constantly falling towards the Moon, they must come together at last. To
remove this difficulty, let it be considered, that it is not the center
of the Earth that describes the annual orbit round the Sun; but the
[63]common center of gravity of the Earth and Moon together: and that
whilst the Earth is moving round the Sun, it also describes a Circle
round that centre of gravity; going as many times round it in one
revolution about the Sun as there are Lunations or courses of the Moon
round the Earth in a year: and therefore, the Earth is constantly
falling towards the Moon from a tangent to the Circle it describes round
the said common center of gravity. Let _M_ be the Moon, _TW_ part of the
Moon’s Orbit, and _C_ the center of gravity of the Earth and Moon:
whilst the Moon goes round her Orbit, the center of the Earth describes
the Circle _ged_ round _C_, to which Circle _gak_ is a tangent: and
therefore, when the Moon has gone from _M_ to a little past _W_, the
Earth has moved from _g_ to _e_; and in that time has fallen towards the
Moon, from the tangent at _a_ to _e_; and so round the whole Circle.
[Sidenote: PLATE IX.]
299. The Sun’s influence in raising the Tides is but small in comparison
of the Moon’s: For though the Earth’s diameter bears a considerable
proportion to it’s distance from the Moon, it is next to nothing when
compared with the distance of the Sun. And therefore, the difference of
the Sun’s attraction on the sides of the Earth under and opposite to
him, is much less than the difference of the Moon’s attraction on the
sides of the Earth under and opposite to her: and therefore the Moon
must raise the Tides much higher than they can be raised by the Sun.
[Sidenote: Why the Tides are not highest when the Moon is on the Meridian.