Part 20

_J. Ferguson delin._ _J. Mynde Sculp._] [Illustration: Plate IX.

_J. Ferguson delin._ _J. Mynde Sculp._]

CHAP. XVII.

_Of the ebbing and flowing of the Sea._

[Sidenote: The cause of the Tides discovered by KEPLER.

PLATE IX.

Their Theory improved by Sir ISAAC NEWTON.]

295. The cause of the Tides was discovered by KEPLER, who, in his _Introduction to the Physics of the Heavens_, thus explains it: “The Orb of the attracting power, which is in the Moon, is extended as far as the Earth; and draws the waters under the torrid Zone, acting upon places where it is vertical, insensibly on confined seas and bays, but sensibly on the ocean whose beds are large, and the waters have the liberty of reciprocation; that is, of rising and falling.” And in the 70th page of his _Lunar Astronomy_——“But the cause of the Tides of the Sea appears to be the bodies of the Sun and Moon drawing the waters of the Sea.” This hint being given, the immortal Sir ISAAC NEWTON improved it, and wrote so amply on the subject, as to make the Theory of the Tides in a manner quite his own; by discovering the cause of their rising on the side of the Earth opposite to the Moon. For KEPLER believed that the presence of the Moon occasioned an impulse which caused another in her absence.

[Sidenote: Explained on the Newtonian principles.

Fig. I.

Fig. I.]

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.

Fig. I.]

300. On this Theory so far as we have explained it, the Tides ought to be highest directly under and opposite to the Moon; that is, when the Moon is due north and south. But we find, that in open Seas, where the water flows freely, the Moon _M_ is generally past the north and south Meridian as at _p_ when it is high water at _Z_ and at _n_. The reason is obvious; for though the Moon’s attraction was to cease altogether when she was past the Meridian, yet the motion of ascent communicated to the water before that time would make it continue to rise for some time after; much more must it do so when the attraction is only diminished: as a little impulse given to a moving ball will cause it still move farther than otherwise it could have done. And as experience shews, that the day is hotter about three in the afternoon, than when the Sun is on the Meridian, because of the increment made to the heat already imparted.

[Sidenote: Nor always answer to her being at the same distance from it.]

301. The Tides answer not always to the same distance of the Moon from the Meridian at the same places; but are variously affected by the action of the Sun, which brings them on sooner when the Moon is in her first and third Quarters, and keeps them back later when she is in her second and fourth: because, in the former case, the Tide raised by the Sun alone would be earlier than the Tide raised by the Moon; and in the latter case later.

[Sidenote: 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.

[Sidenote: 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.

[Sidenote: 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.

[Sidenote: 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.

[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.

CHAP. XVIII.

_Of Eclipses: Their Number and Periods. A large Catalogue of Ancient and Modern Eclipses._

[Sidenote: A shadow, what.]

312. Every Planet and Satellite is illuminated by the Sun; and casts a shadow towards that point of the Heavens which is opposite to the Sun. This shadow is nothing but a privation of light in the space hid from the Sun by the opake body that intercepts his rays.

[Sidenote: Eclipses of the Sun and Moon, what.]