304. When the Moon is in the Equator, the Tides are equally high in both
parts of the lunar day, or time of the Moon’s revolving from the
Meridian to the Meridian again, which is 24 hours 48 minutes. But as the
Moon declines from the Equator towards either Pole, the Tides are
alternately higher and lower at places having north or south Latitude.
For one of the highest elevations, which is that under the Moon, follows
her towards the same Pole, and the other declines towards the opposite;
each describing parallels as far distant from the Equator, on opposite
sides, as the Moon declines from it to either side; and consequently,
the parallels described by these elevations of the water are twice as
many degrees from one another, as the Moon is from the Equator;
increasing their distance as the Moon increases her declination, till it
be at the greatest, when the said parallels are, at a mean state, 47
degrees from one another: and on that day, the Tides are most unequal in
their heights. As the Moon returns toward the Equator, the parallels
described by the opposite elevations approach towards each other, until
the Moon comes to the Equator, and then they coincide. As the Moon
declines toward the opposite Pole, at equal distances, each elevation
describes the same parallel in the other part of the lunar day, which
it’s opposite elevation described before. Whilst the Moon has north
declination, the greatest Tides in the northern Hemisphere are when she
is above the Horizon; and the reverse whilst her declination is south.
Let _NESQ_ be the Earth, _NCS_ it’s Axis, _EQ_ the Equator, _T_♋ the
Tropic of Cancer, _t_♑ the Tropic of Capricorn, _ab_ the arctic Circle,
_cd_ the Antarctic, _N_ the north Pole, _S_ the south Pole, _M_ the
Moon, _F_ and _G_ the two eminences of water, whose lowest parts are at
_a_ and _d_ (Fig. III.) at _N_ and _S_ (Fig. IV.) and at _b_ and _c_
(Fig. V.) always 90 degrees from the highest. Now when the Moon is in
her greatest north declination at _M_, the highest elevation _G_ under
her, is on the Tropic of Cancer _T_♋, and the opposite elevation _F_ on
the Tropic of Capricorn _t_♑; and these two elevations describe the
Tropics by the Earth’s diurnal rotation. All places in the northern
Hemisphere _ENQ_ have the highest Tides when they come into the position
_b_♋_Q_, under the Moon; and the lowest Tides when the Earth’s diurnal
rotation carries them into the position _aTE_, on the side opposite to
the Moon; the reverse happens at the same time in the southern
Hemisphere _ESQ_, as is evident to sight. The Axis of the Tides _aCd_
has now it’s Poles _a_ and _d_ (being always 90 degrees from the highest
elevations) in the arctic and antarctic Circles; and therefore ’tis
plain, that at these Circles there is but one Tide of Flood, and one of
Ebb, in the lunar day. For, when the point _a_ revolves half round to
_b_, in 12 lunar hours, it has a Tide of Flood; but when it comes to the
same point _a_ again in 12 hours more, it has the lowest ebb. In seven
days afterward, the Moon _M_ comes to the equinoctial Circle, and is
over the Equator _EQ_, when both Elevations describe the Equator; and in
both Hemispheres, at equal distances from the Equator, the Tides are
equally high in both parts of the lunar day. The whole Phenomena being
reversed when the Moon has south declination to what they were when her
declination was north, require no farther description.
[Sidenote: Fig. VI.
When both Tides are equally high in the same day, they arrive
at unequal intervals of Time; and _vice versa_.]
305. In the three last-mentioned Figures, the Earth is orthographically
projected on the plane of the Meridian; but in order to describe a
particular Phenomenon we now project it on the plane of the Ecliptic.
Let _HZON_ be the Earth and Sea, _FED_ the Equator, _T_ the Tropic of
Cancer, _C_ the arctic Circle, _P_ the north Pole, and the Curves _1_,
_2_, _3_, _&c._ 24 Meridians, or hour Circles, intersecting each other
in the Poles; _AGM_ is the Moon’s orbit, _S_ the Sun, _M_ the Moon, _Z_
the Water elevated under the Moon, and _N_ the opposite equal Elevation.
As the lowest parts of the Water are always 90 degrees from the highest,
when the Moon is in either of the Tropics (as at _M_) the Elevation _Z_
is on the Tropic of Capricorn, and the opposite Elevation _N_ on the
Tropic of Cancer, the low-water Circle _HCO_ touches the polar Circles
at _C_; and the high-water Circle _ETP6_ goes over the Poles at _P_, and
divides every parallel of Latitude into two equal segments. In this case
the Tides upon every parallel are alternately higher and lower; but they
return in equal times: the point _T_, for example, on the Tropic of
Cancer (where the depth of the Tide is represented by the breadth of the
dark shade) has a shallower Tide of Flood at _T_ than when it revolves
half round from thence to _6_, according to the order of the numeral
Figures; but it revolves as soon from _6_ to _T_ as it did from _T_ to
_6_. When the Moon is in the Equinoctial, the Elevations _Z_ and _N_ are
transferred to the Equator at _O_ and _H_, and the high and low-water
Circles are got into each other’s former places; in which case the Tides
return in unequal times, but are equally high in both parts of the lunar
day: for a place at _1_ (under _D_) revolving as formerly, goes sooner
from _1_ to _11_ (under _F_) than from _11_ to _1_, because the parallel
it describes is cut into unequal segments by the high-water Circle
_HCO_: but the points 1 and 11 being equidistant from the Pole of the
Tides at _C_, which is directly under the Pole of the Moon’s orbit
_MGA_, the Elevations are equally high in both parts of the day.
306. And thus it appears, that as the Tides are governed by the Moon,
they must turn on the Axis of the Moon’s orbit, which is inclined 23-1/2
degrees to the Earth’s Axis at a mean state: and therefore the Poles of
the Tides must be so many degrees from the Poles of the Earth, or in
opposite points of the polar Circles, going round these Circles in every
lunar day. ’Tis true that according to Fig. IV. when the Moon is
vertical to the Equator _ECQ_, the Poles of the Tides seem to fall in
with the Poles of the World _N_ and _S_: but when we consider that _FHG_
is under the Moon’s orbit, it will appear, that when the Moon is over
_H_, in the Tropic of Capricorn, the north Pole of the Tides, (which can
be no more than 90 degrees from under the Moon) must be at _c_ in the
arctic Circle, not at _N_; the north Pole of the Earth; and as the Moon
ascends from _H_ to _G_ in her orbit, the north Pole of the Tides must
shift from _c_ to _a_ in the arctic Circle; and the South Pole as much
in the antarctic.
It is not to be doubted, but that the Earth’s quick rotation brings the
poles of the Tides nearer to the Poles of the World, than they would be
if the Earth were at rest, and the Moon revolved about it only once a
month; for otherwise the Tides would be more unequal in their heights,
and times of their returns, than we find they are. But how near the
Earth’s rotation may bring the Poles of it’s Axis and those of the Tides
together, or how far the preceding Tides may affect those which follow,
so as to make them keep up nearly to the same heights, and times of
ebbing and flowing, is a problem more fit to be solved by observation
than by theory.
[Sidenote: To know at what times we may expect the greatest and least
Tides.]
307. Those who have opportunity to make observations, and choose to
satisfy themselves whether the Tides are really affected in the above
manner by the different positions of the Moon; especially as to the
unequal times of their returns, may take this general rule for knowing,
when they ought to be so affected. When the Earth’s Axis inclines to the
Moon, the northern Tides, if not retarded in their passage through
Shoals and Channels, nor affected by the Winds, ought to be greatest
when the Moon is above the Horizon, least when she is below it; and
quite the reverse when the Earth’s Axis declines from her: but in both
cases, at equal intervals of time. When the Earth’s Axis inclines
sidewise to the Moon, both Tides are equally high, but they happen at
unequal intervals of time. In every Lunation the Earth’s Axis inclines
once to the Moon, once from her, and twice sidewise to her, as it does
to the Sun every year; because the Moon goes round the Ecliptic every
month, and the Sun but once in a year. In Summer, the Earth’s Axis
inclines towards the Moon when New; and therefore the day-tides in the
north ought to be highest, and night-tides lowest about the Change: at
the Full the reverse. At the Quarters they ought to be equally high, but
unequal in their returns; because the Earth’s Axis then inclines
sidewise to the Moon. In winter the Phenomena are the same at Full-Moon
as in Summer at New. In Autumn the Earth’s Axis inclines sidewise to the
Moon when New and Full; therefore the Tides ought to be equally high,
and unequal in their returns at these times. At the first Quarter the
Tides of Flood should be least when the Moon is above the Horizon,
greatest when she is below it; and the reverse at her third Quarter. In
Spring, Phenomena of the first Quarter answer to those of the third
Quarter in Autumn; and _vice versa_. The nearer any time is to either of
these seasons, the more the Tides partake of the Phenomena of these
seasons; and in the middle between any two of them the Tides are at a
mean state between those of both.
[Sidenote: Why the Tides rise higher in Rivers than in the Sea.]
308. In open Seas, the Tides rise but to very small heights in
proportion to what they do in wide-mouthed rivers, opening in the
Direction of the Stream of Tide. For, in Channels growing narrower
gradually, the water is accumulated by the opposition of the contracting
Bank. Like a gentle wind, little felt on an open plain, but strong and
brisk in a street; especially if the wider end of the street be next the
plain, and in the way of the wind.
[Sidenote: The Tides happen at all distances of the Moon from the
Meridian at different places, and why.]
309. The Tides are so retarded in their passage through different Shoals
and Channels, and otherwise so variously affected by striking against
Capes and Headlands, that to different places they happen at all
distances of the Moon from the Meridian; consequently at all hours of
the lunar day. The Tide propagated by the Moon in the _German_ ocean,
when she is three hours past the Meridian, takes 12 hours to come from
thence to _London_ bridge; where it arrives by the time that a new Tide
is raised in the ocean. And therefore when the Moon has north
declination, and we should expect the Tide at _London_ to be greatest
when the Moon is above the Horizon, we find it is least; and the
contrary when she has south declination. At several places ’tis high
water three hours before the Moon comes to the Meridian; but that Tide
which the Moon pushes as it were before her, is only the Tide opposite
to that which was raised by her when she was nine hours past the
opposite Meridian.
[Sidenote: The Water never rises in Lakes.]
310. There are no Tides in Lakes, because they are generally so small
that when the Moon is vertical she attracts every part of them alike,
and therefore by rendering all the water equally light, no part of it
can be raised higher than another. The _Mediterranean_ and _Baltic_ Seas
suffer very small elevations, because the Inlets by which they
communicate with the ocean are so narrow, that they cannot, in so short
a time, receive or discharge enough to raise or sink their surfaces
sensibly.
[Sidenote: The Moon raises Tides in the Air.
Why the Mercury in the Barometer is not affected by the aerial
Tides.]
311. Air being lighter than Water, and the surface of the Atmosphere
being nearer to the Moon than the surface of the Sea, it cannot be
doubted that the Moon raises much higher Tides in the Air than in the
Sea. And therefore many have wondered why the Mercury does not sink in
the Barometer when the Moon’s action on the particles of Air makes them
lighter as she passes over the Meridian. But we must consider, that as
these particles are rendered lighter, a greater number of them is
accumulated, until the deficiency of gravity be made up by the height of
the column; and then there is an _equilibrium_, and consequently an
equal pressure upon the Mercury as before; so that it cannot be affected
by the aerial Tides.