Not greatest at the equinox. es, and why. The tides immedi 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 greastet effect when they are at the strongest, but some time afterward. 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 sea being thus put in motion, would contiwould not nue to ebb and flow for several times, even though atelycease the Sun and Moon were annihilated, or their influupon the ence should cease: as if a bason of water were agition of the tated, the water would continue to move for some Sun and time after the bason was left to stand still. Or like Moon. annihila The lunar The tides the same day, and why. a pendulum, which, having been put in motion by the hand, continues to make several vibrations without any new impulse. 304. When the Moon is in the equator, the tides day, what are equally high in both parts of the lunar day, or rise to time of the Moon's revolving from the meridian to unequal the meridian again, which is 24 hours 50 minutes. heights in But as the Moon declines from the equator toward 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 toward the pole to which she is nearest, and the other declines toward the opposite pole; each elevation 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 PLATE IX. 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 toward each other, until the Moon comes to the equator, and then they coincide. As the Moon declines towards the opposite pole, at equal distances, each elevation describes the same parallel in the other part of the lunar day, which its opposite elevation described before.While the Moon has north declination, the greatest tides in the northern hemisphere are when she is above the horizon, and the reverse while her declination is south. Let NE SQ be the Earth, NC SFig. III. its axis, E Q the equator, To the tropic of Can. IV. V. cer, tv the tropic of Capricorn, a b the arctic cir cle, 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 Nand 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 Fig. III. tropic of Capricorn, t vs; and these two elevations describe the tropics by the Earth's diurnal rotation. All places in the northern hemisphere E N Q have the highest tides when they come into the position bQ, under the Moon; and the lowest tides when the Earth's diurnal rotation carries them into the position a TE, on the side opposite to the Moon; the reverse happens at the same time in the southern hemisphere ES Q, as is evident to sight. The axis of the tides a Cd has now its poles a and d (being always 90 degrees from the highest elevations) in the arctic and antarctic circles; and therefore it is plain, that at these circles there is but one tide Kk PLATE IX. 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 Fig. IV. 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 E Q, 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 Fig. V. the Moon has south declination, to what they were when her declination was north, require no farther description. 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. Fig. VI. Let HZ ON be the earth and sea, FED the equator, T the tropic of Cancer, C the arctic circle, P both tides day, they intervals the north pole, and the curves 1, 2, 3, &c. 24 meridians, or hour-circles, intersecting each other in the When poles; A G M is the Moon's orbit, S the Sun, M are equal- the Moon, Z the water elevated under the Moon, and ly high in N the opposite equal elevation. As the lowest parts the same of the water are always 90 degrees from the highest, arrive at when the Moon is in either of the tropics (as at M) unequal the elevation Z is on the tropic of Capricorn, and the of time; opposite elevation N on the tropic of Cancer; the and vice low-water circle HC O touches the polar circles at C, and the high-water circle E TP 6 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 verså. revolves as soon from When the Moon is of the numeral figures; but it 6 to Tas it did from T to 6. 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 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 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. It is 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 FGH 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 P, 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 To know at what times we may ex pect the greatest and least tides. 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 its 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. 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 toward 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 side |