Spring and neap Tides.
[PLATE IX].
Fig. VI.
302. The Moon goes round the Earth in an elliptic Orbit, and therefore she approaches nearer to the Earth than her mean distance, and recedes farther from it, in every Lunar Month. When she is nearest: she attracts strongest, and so rises the Tides most; the contrary happens when she is farthest, because of her weaker attraction. When both Luminaries are in the Equator, and the Moon in Perigeo, or at her least distance from the Earth, she raises the Tides highest of all, especially at her Conjunction and opposition; both because the equatoreal parts have the greatest centrifugal force from their describing the largest Circle, and from the concurring actions of the Sun and Moon. At the Change, the attractive forces of the Sun and Moon being united, they diminish the gravity of the waters under the Moon, which is also diminished on the other side, by means of a greater centrifugal force. At the full, whilst the Moon raises the Tide under and opposite to her, the Sun acting in the same line, raises the Tide under and opposite to him; whence their conjoint effect is the same as at the Change; and in both cases, occasion what we call the Spring Tides. But at the Quarters the Sun’s action on the waters at O and H diminishes the Moon’s action on the waters at Z and N; so that they rise a little under and opposite to the Sun at O and H, and fall as much under and opposite to the Moon at Z and N; making what we call the Neap Tides, because the Sun and Moon then act cross-wise to each other. But, strictly speaking, these Tides happen not till some time after; because in this, as in other cases, § [300], the actions do not produce the greatest effect when they are at the strongest, but some time afterward.
Not greatest at the Equinoxes, and why.
303. The Sun being nearer the Earth in Winter than in Summer, § [205], is of course nearer to it in February and October than in March and September: and therefore the greatest Tides happen not till some time after the autumnal Equinox, and return a little before the vernal.
The Tides would not immediately cease upon the annihilation of the Sun and Moon.
The Sea being thus put in motion, would continue to ebb and flow for several times, even though the Sun and Moon were annihilated, or their influence should cease: as if a bason of water were agitated, the water would continue to move for some time after the bason was left to stand still. Or like a Pendulum, which having been put in motion by the hand, continues to make several vibrations without any new impulse.
The lunar day, what.
The Tides rise to unequal heights in the same day, and why.
[PLATE IX].
Fig. III, IV, V.
Fig. III.
Fig. IV.
Fig. V.
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.
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.