, and the lowest Ebbe, the highest Tide; the
Tides from the _Quarter_ to the _highest Spring-tide_ increasing in a
certain proportion; and from the _Spring tide_ to the _Quarter-tide_
decreasing in like proportion, as is supposed: And also the _Ebbes_ rising
and falling constantly after the same manner: It is wished, that it may be
inquired, in what proportion these Increases and Decreases, Risings and
Fallings happen to be in regard of one another?

And 'tis supposed, upon some Observations, made in fit places, by the
above-mentioned Gentleman, though, (as himself acknowledges) not thoroughly
and exactly performed, that the Increase of the Tides is made in the
_Proportion_ of _Sines_; the first Increase exceeding the lowest in a small
proportion; the next in a greater; the third greater than that; and so on
to the mid-most, whereof the excess is greatest, diminishing again from
that, to the highest Spring-Tide; so as the proportions, before and after
the _Middle_, do greatly answer one another, or seem to do so. And
likewise, from the _highest Spring-tide_, to the _lowest Neap-tide_, the
_Decreases_ seem to keep the like proportions; the _Ebbes_ rising and
falling in like manner and in like proportions. All which is supposed to
fall out, when no Wind or other Accident causes an alteration. {299}

And whereas 'tis observed, that upon the main Sea-shore the Current of the
Ebbings and Flowings is sometimes swifter, and sometimes slacker, than at
others, so as in the beginning of the Floud the Tide moves faster but in a
small degree, increasing its swiftness constantly till towards the _Middle_
of the Floud; and then decreasing in velocity again from the _Middle_ till
to the top of the High water; it is supposed, that in Equal spaces of Time,
the Increase and Decrease of velocity, and consequently the degrees of the
Risings and Fallings of the same, in Equal spaces of time, are performed
according to the _Proportion_ of _Sines_.

But 'tis withall conceived, that the said _Proportion_ cannot hold
_exactly_ and _precisely_, in regard of the _Inequalities_, that fall out
in the _Periods_ of the _Tides_, which are commonly observed and believed
to follow certain _Positions_ of the _Moon_ in regard of the _Equinox_,
which are known not to keep a _precise_ and _constant_ Course: so that,
there not intervening equal portions of Time between one New Moon and
another, the Moons return to the same _Meridian_, cannot be alwaies
perf