Chapter XI: Part 11

This Table was not computed, but only estimated as near as could be done from a common Globe, on which the Moon’s Orbit was delineated with a black lead pencil. It may at first sight appear erroneous; since as we have supposed the Moon to be full in either Node at the autumnal Equinox, she ought by the Table to rise just at six o’clock, or at Sun-set, on the 15th day of her age; being in the Ecliptic at that time. But it must be considered, that the Moon is only 14-1/4 days old when she is Full; and therefore in both cases she is a little past the Node on the 15th day, being above it at one time, and below it at the other.

[Sidenote: The period of the Harvest Moons.]

292. As there is a compleat revolution of the Nodes in 18-2/3 years, there must be a regular period of all the Varieties which can happen in the rising and setting of the Moon during that time. But this shifting of the Nodes never affects the Moon’s rising so much, even in her quickest descending Latitude, as not to allow us still the benefit of her rising nearer the time of Sun-set for a few days together about the Full in Harvest, than when she is Full at any other time of the year. The following Table shews in what years the Harvest-Moons are least beneficial as to the times of their rising, and in what years most, from 1751 to 1861. The column of years under the letter _L_ are those in which the Harvest-Moons are least of all beneficial, because they fall about the Descending Node: and those under _M_ are the most of all beneficial, because they fall about the Ascending Node. In all the columns from _N_ to _S_ the Harvest-Moons descend gradually in the Lunar Orbit, and rise to less heights above the Horizon. From _S_ to _N_ they ascend in the same proportion, and rise to greater heights above the Horizon. In both the columns under _S_ the Harvest-Moons are in the lowest part of the Moon’s Orbit, that is, farthest South of the Ecliptic; and therefore stay shortest of all above the Horizon: in the columns under _N_ just the reverse. And in both cases, their rising, though not at the same times, are nearly the same with regard to difference of time, as if the Moon’s Orbit were coincident with the Ecliptic.

+------------------------------------------------------------+ | | | _Years in which the Harvest-Moons are least beneficial._ | | | | N L S | | 1751 1752 1753 1754 1755 1756 1757 1758 1759 | | 1770 1771 1772 1773 1774 1775 1776 1777 1778 | | 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 | | 1807 1808 1809 1810 1811 1812 1813 1814 1815 | | 1826 1827 1828 1829 1830 1831 1832 1833 1834 | | 1844 1845 1846 1847 1848 1849 1850 1851 1852 | | | | _Years in which they are most beneficial._ | | | | S M N | | 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 | | 1779 1780 1781 1782 1783 1784 1785 1786 1787 | | 1798 1799 1800 1801 1802 1803 1804 1805 1806 | | 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 | | 1835 1836 1837 1838 1839 1840 1841 1842 1843 | | 1853 1854 1855 1856 1857 1858 1859 1860 1861 | +------------------------------------------------------------+

[Sidenote: PL. VIII.]

293. At the Polar Circles, when the Sun touches the Summer Tropic, he continues 24 hours above the Horizon; and 24 hours below it when he touches the Winter Tropic. For the same reason the Full Moon neither rises in Summer, nor sets in Winter, considering her as moving in the Ecliptic. For the Winter Full Moon being as high in the Ecliptic as the Summer Sun, must therefore continue as long above the Horizon; and the Summer Full Moon being as low in the Ecliptic as the Winter Sun, can no more rise than he does. But these are only the two Full Moons which happen about the Tropics, for all the others rise and set. In Summer the Full Moons are low, and their stay is short above the Horizon, when the nights are short, and we have least occasion for Moon-light: in Winter they go high, and stay long, above the Horizon when the nights are long, and we want the greatest quantity of Moon-light.

[Sidenote: The long continuance of Moon-light at the Poles.

Fig. V.]

294. At the Poles, one half of the Ecliptic never sets, and the other half never rises: and therefore, as the Sun is always half a year in describing one half of the Ecliptic, and as long in going through the other half, ’tis natural to imagine that the Sun continues half a year together above the Horizon of each Pole in it’s turn, and as long below it; rising to one Pole when he sets to the other. This would be exactly the case if there were no refraction: but by the Atmosphere’s refracting the Sun’s rays, he becomes visible some days sooner § 183, and continues some days longer in sight than he would otherwise do: so that he appears above the Horizon of either Pole before he has got below the Horizon of the other. And, as he never goes more than 23-1/2 degrees below the Horizon of the Poles, they have very little dark night: it being twilight there as well as at all other places till the Sun be 18 degrees below the Horizon, § 177. The Full Moon being always opposite to the Sun, can never be seen while the Sun is above the Horizon, except when the Moon falls in the northern half of her Orbit; for whenever any point of the Ecliptic rises the opposite point sets. Therefore, as the Sun is above the Horizon of the north Pole from the 20th of _March_ till the 23d of _September_, it is plain that the Moon, when Full, being opposite to the Sun, must be below the Horizon during that half of the year. But when the Sun is in the southern half of the Ecliptic he never rises to the north Pole, during which half of the year, every Full Moon happens in some part of the northern half of the Ecliptic, which never sets. Consequently, as the polar Inhabitants never see the Full Moon in Summer, they have her always in the Winter, before, at, and after the Full, shining for 14 of our days and nights. And when the Sun is at his greatest depression below the Horizon, being then in Capricorn, the Moon is at her First Quarter in Aries, Full in Cancer, and at her Third Quarter in Libra. And as the beginning of Aries is the rising point of the Ecliptic, Cancer the highest, and Libra the setting point, the Moon rises at her First Quarter in Aries, is most elevated above the Horizon, and Full in Cancer, and sets at the beginning of Libra in her Third Quarter, having continued visible for 14 diurnal rotations of the Earth. Thus the Poles are supplied one half of the winter time with constant Moon-light in the Sun’s absence; and only lose sight of the Moon from her Third to her First Quarter, while she gives but very little light; and could be but of little, and sometimes of no service to them. A bare view of the Figure will make this plain; in which let _S_ be the Sun, _e_ the Earth in Summer when it’s north Pole _n_ inclines toward the Sun, and _E_ the Earth in Winter, when it’s north Pole declines from him. _SEN_ and _NWS_ is the Horizon of the north Pole, which is coincident with the Equator; and, in both these positions of the Earth, ♈♋♎♑ is the Moon’s Orbit, in which she goes round the Earth, according to the order of the letters _abcd_, _ABCD_. When the Moon is at _a_ she is in her Third Quarter to the Earth at _e_, and just rising to the north Pole _n_; at _b_ she changes, and is at the greatest height above the Horizon, as the Sun likewise is; at _c_ she is in her First Quarter, setting below the Horizon; and is lowest of all under it at _d_, when opposite to the Sun, and her enlightened side toward the Earth. But then she is full in view to the south Pole _p_; which is as much turned from the Sun as the north Pole inclines towards him. Thus in our Summer, the Moon is above the Horizon of the north Pole whilst she describes the northern half of the Ecliptic ♈♋♎, or from her Third Quarter to her First; and below the Horizon during the progress through the southern half ♎♑♈; highest at the Change, most depressed at the Full. But in winter, when the Earth is at _E_, and it’s north Pole declines from the Sun, the New Moon at _D_ is at her greatest depression below the Horizon _NWS_, and the Full Moon at _B_ at her greatest height above it; rising at her First Quarter _A_, and keeping above the Horizon till she comes to her Third Quarter _C_. At a mean state she is 23-1/2 degrees above the Horizon at _B_ and _b_, and as much below it at _D_ and _d_, equal to the inclination of the Earth’s Axis _F_. _S_♋ and _S_♑ are, as it were, a ray of light proceeding from the Sun to the Earth; and shews that when the Earth is at _e_, the Sun is above the Horizon, vertical to the Tropic of Cancer; and when the Earth is at _E_, he is below the Horizon, vertical to the Tropic of Capricorn.

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

_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.]

313. When the Sun’s light is so intercepted by the Moon, that to any place of the Earth the Sun appears partly or wholly covered, he is said to undergo an Eclipse; though properly speaking, ’tis only an Eclipse of that part of the Earth where the Moon’s shadow or [64]Penumbra falls. When the Earth comes between the Sun and Moon, the Moon falls into the Earth’s shadow; and having no light of her own, she suffers a real Eclipse from the interception of the Sun’s rays. When the Sun is eclipsed to us, the Moon’s Inhabitants on the side next the Earth (if any such there be) see her shadow like a dark spot travelling over the Earth, about twice as fast as its equatoreal parts move, and the same way as they move. When the Moon is in an Eclipse, the Sun appears eclipsed to her, total to all those parts on which the Earth’s shadow falls, and of as long continuance as they are in the shadow.

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

[Sidenote: A proof that the Earth and Moon are globular bodies.]

314. That the Earth is spherical (for the hills take off no more from the roundness of the Earth, than grains of dust do from the roundness of a common Globe) is evident from the figure of its shadow on the Moon; which is always bounded by a circular line, although the Earth is incessantly turning its different sides to the Moon, and very seldom shews the same side to her in different Eclipses, because they seldom happen at the same hours. Were the Earth shaped like a round flat plate, its shadow would only be circular when either of its sides directly faced the Moon; and more or less elliptical as the Earth happened to be turned more or less obliquely towards the Moon when she is eclipsed. The Moon’s different Phases prove her to be round § 254; for, as she keeps still the same side towards the earth, if that side were flat, as it appears to be, she would never be visible from the third Quarter to the first; and from the first Quarter to the third, she would appear as round as when we say she is Full: because at the end of her first Quarter the Sun’s light would come as suddenly on all her side next the Earth, as it does on a flat wall, and go off as abruptly at the end of her third Quarter.

[Sidenote: And that the Sun is much bigger than the Earth, and the Moon
much less.]

315. If the Earth and Sun were equally big, the Earth’s shadow would be infinitely extended, and all of the same breadth; and the Planet Mars, in either of its nodes and opposite to the Sun, would be eclipsed in the Earth’s shadow. Were the Earth bigger than the Sun, it’s shadow would increase in breadth the farther it was extended, and would eclipse the great Planets Jupiter and Saturn, with all their Moons, when they were opposite to the Sun. But as Mars in opposition never falls into the Earth’s shadow, although he is not then above 42 millions of miles from the Earth, ’tis plain that the Earth is much less than the Sun; for otherwise it’s shadow could not end in a point at so small a distance. If the Sun and Moon were equally big, the Moon’s shadow would go on to the Earth with an equal breadth, and cover a portion of the Earth’s surface more than 2000 miles broad, even if it fell directly against the Earth’s center, as seen from the Moon: and much more if it fell obliquely on the Earth: but the Moon’s shadow is seldom 150 miles broad at the Earth, unless when it falls very obliquely on the Earth, in total Eclipses of the Sun. In annular Eclipses, the Moon’s real shadow ends in a point at some distance from the Earth. The Moon’s small distance from the Earth, and the shortness of her shadow, prove her to be less than the Sun. And, as the Earth’s shadow is large enough to cover the Moon, if her diameter was three times as large as it is (which is evident from her long continuance in the shadow when she goes through it’s center) ’tis plain, that the Earth is much bigger than the Moon.

[Sidenote: The primary Planets never eclipse one another.

PLATE X.]

316. Though all opake bodies on which the Sun shines have their shadows, yet such is the bulk of the Sun, and the distances of the Planets, that the primary Planets can never eclipse one another. A Primary can eclipse only it’s secondary, or be eclipsed by it; and never but when in opposition or conjunction with the Sun. The primary Planets are very seldom in these positions, but the Sun and Moon are so every month: whence one may imagine that these two Luminaries should be eclipsed every month. But there are few Eclipses in respect of the number of New and Full Moons; the reason of which we shall now explain.

[Sidenote: Why there are so few Eclipses.

The Moon’s Nodes.

Limits of Eclipses.]

317. If the Moon’s Orbit were coincident with the Plane of the Ecliptic, in which the Earth always moves and the Sun appears to move, the Moon’s shadow would fall upon the Earth at every Change, and eclipse the Sun to some parts of the Earth. In like manner the Moon would go through the middle of the Earth’s shadow, and be eclipsed at every Full; but with this difference, that she would be totally darkened for above an hour and half; whereas the Sun never was above four minutes totally eclipsed by the interposition of the Moon. But one half of the Moon’s Orbit, is elevated 5-1/3 degrees above the Ecliptic, and the other half as much depressed below it: consequently, the Moon’s Orbit intersects the Ecliptic in two opposite points called _the Moon’s Nodes_, as has been already taken notice of § 288. When these points are in a right line with the center of the Sun at New or Full Moon, the Sun, Moon, and Earth are all in a right line; and if the Moon be then New, her shadow falls upon the Earth; if Full the Earth’s shadow falls upon her. When the Sun and Moon are more than 17 degrees from either of the Nodes at the time of Conjunction, the Moon is then too high or too low in her Orbit to cast any part of her shadow upon the Earth. And when the Sun is more than 12 degrees from either of the Nodes at the time of Full Moon, the Moon is too high or too low in her Orbit to go through any part of the Earth’s shadow: and in both these cases there will be no Eclipse. But when the Moon is less than 17 degrees from either Node at the time of Conjunction, her shadow or Penumbra falls more or less upon the Earth, as she is more or less within this limit. And when she is less than 12 degrees from either Node at the time of opposition, she goes through a greater or less portion of the Earth’s shadow, as she is more or less within this limit. Her Orbit contains 360 degrees; of which 17, the limit of solar Eclipses on either side of the Nodes, and 12 the limit of lunar Eclipses, are but small portions: and as the Sun commonly passes by the Nodes but twice in a year, it is no wonder that we have so many New and Full Moons without Eclipses.

[Sidenote: Fig. I.

PLATE X.

Line of the Nodes.]

To illustrate this, let _ABCD_ be the _Ecliptic_, _RSTU_ a Circle lying in the same Plane with the Ecliptic, and _VWXY_ the _Moon’s Orbit_, all thrown into an oblique view, which gives them an elliptical shape to the eye. One half of the Moon’s Orbit, as _VWX_, is always below the Ecliptic, and the other half _XYV_ above it. The points _V_ and _X_, where the Moon’s Orbit intersects the Circle _RSTU_, which lies even with the Ecliptic, are the _Moon’s Nodes_; and a right line as _XEV_ drawn from one to the other, through the Earth’s center, is the _Line of the Nodes_, which is carried almost parallel to itself round the Sun in a year.

If the Moon moved round the Earth in the Orbit _RSTU_, which is coincident with the Plane of the Ecliptic, her shadow would fall upon the Earth every time she is in conjunction with the Sun; and at every opposition she would go through the Earth’s shadow. Were this the case, the Sun would be eclipsed at every Change, and the Moon at every Full, as already mentioned.

But although the Moon’s shadow _N_ must fall upon the Earth at _a_, when the Earth is at _E_, and the Moon in conjunction with the Sun at _i_, because she is then very near one of her Nodes; and at her opposition _n_ she must go through the Earth’s shadow _I_, because she is then near the other Node; yet, in the time that she goes round the Earth to her next Change, according to the order of the letters _XYVW_, the Earth advances from _E_ to _e_, according to the order of the letters _EFGH_, and the line of the Nodes _VEX_ being carried nearly parallel to itself, brings the point _f_ of the Moon’s Orbit in conjunction with the Sun at that next Change; and then the Moon being at _f_ is too high above the Ecliptic to cast her shadow on the Earth: and as the Earth is still moving forward, the Moon at her next opposition will be at _g_, too far below the Ecliptic to go through any part of the Earth’s shadow; for by that time the point _g_ will be at a considerable distance from the Earth as seen from the Sun.

[Sidenote: Fig. I and II.]

When the Earth comes to _F_, the Moon in conjunction with the Sun _Z_ is not at _k_, in a Plane coincident with the Ecliptic, but above it at _Y_ in the highest part of her Orbit: and then the point _b_ of her shadow _O_ goes far above the Earth (as in Fig. II, which is an edge view of Fig. I.) The Moon at her next opposition is not at _o_ (Fig I) but at _W_ where the Earth’s shadow goes far above her, (as in Fig. II.) In both these cases the line of the Nodes _VFX_ (Fig. I.) is about 90 degrees from the Sun, and both Luminaries as far as possible from the limits of Eclipses.

[Sidenote: PLATE X.]

When the Earth has gone half round the Ecliptic from _E_ to _G_, the line of the Nodes _VGX_ is nearly, if not exactly, directed towards the Sun at _Z_; and then the New Moon _l_ casts her shadow _P_ on the Earth _G_; and the Full Moon _p_ goes through the Earth’s shadow _L_; which brings on Eclipses again, as when the Earth was at _E_.

When the Earth comes to _H_ the New Moon falls not at _m_ in a plane coincident with the Ecliptic _CD_, but at _W_ in her Orbit below it: and then her shadow _Q_ (see Fig. II) goes far below the Earth. At the next Full she is not at _q_ (Fig. I) but at _Y_ in her orbit 5-1/3 degrees above _q_, and at her greatest height above the Ecliptic _CD_; being then as far as possible, at any opposition, from the Earth’s shadow _M_ (as in Fig. II.)

So, when the Earth is at _E_ and _G_, the Moon is about her Nodes at New and Full; and in her greatest _North_ and _South Declination_, (or Latitude as it is generally called) from the Ecliptic at her Quarters: but when the Earth is at _F_ or _H_, the Moon is in her greatest _North_ and _South Declination_ from the Ecliptic at New and Full, and in the _Nodes_ about her Quarters.

[Sidenote: The Moon’s ascending and descending Node.

Her North and South Latitude.]

318. The point _X_ where the Moon’s Orbit crosses the Ecliptic is called _the Ascending Node_, because the Moon ascends from it above the Ecliptic: and the opposite point of intersection _V_ is called _the Descending Node_, because the Moon descends from it below the Ecliptic. When the Moon is at _Y_ in the highest point of her Orbit, she is in her greatest _North Latitude_; and when she is at _W_ in the lowest point of her Orbit, she is in her greatest _South Latitude_.

[Sidenote: The Nodes have a retrograde motion.

Fig. I.

Which brings on the Eclipses sooner every year than they would
be if the Nodes had not such a motion.]

319. If the line of the Nodes, like the Earth’s Axis, was carried parallel to itself round the Sun, there would be just half a year between the conjunctions of the Sun and Nodes. But the Nodes shift backward, or contrary to the Earth’s annual motion, 19-1/3 degrees every year; and therefore the same Node comes round to the Sun 19 days sooner every year than on the year before. Consequently, from the time that the ascending Node _X_ (when the Earth is at _E_) passes by the Sun as seen from the Earth, it is only 173 days (not half a year) till the descending Node _V_ passes by him. Therefore, in whatever time of the year we have Eclipses of the Luminaries about either Node, we may be sure that in 173 days afterward we shall have Eclipses about the other Node. And when at any time of the year the line of the Nodes is in the situation _VGX_, at the same time next year it will be in the situation _rGs_; the ascending Node having gone backward, that is, contrary to the order of Signs from _X_ to _s_, and the descending Node from _V_ to _r_; each 19-1/3 degrees. At this rate the Nodes shift through all the Signs and degrees of the Ecliptic in 18 years and 225 days; in which time there would always be a regular period of Eclipses, if any compleat number of Lunations were finished without a fraction. But this never happens, for if the Sun and Moon should start from a conjunction with either of the Nodes in any point of the Ecliptic, whilst the same Node is going round to that point again the Earth performs 18 annual revolutions about the Sun and 222 Degrees (or 7 Signs 12 Degrees) over; and the Moon 230 Lunations or Courses from Change to Change and 85 Degrees (or 2 Signs 25 Degrees) over; so that the Sun will be 138 Degrees from the same Node when it comes round, and the Moon 85 Degrees from the Sun. Hence, the period of Eclipses and revolution of the Nodes are completed in different times.

[Sidenote: A period of Eclipses.

The defects of it.]

320. In 18 years 10 days 7 hours 43 minutes after the Sun Moon and Nodes have been in a line of conjunction, they come very near to a conjunction again: only, if the conjunction from which you reckon falls in a leap-year, the return of the conjunction will be one day later. Therefore, if to the [65]mean time of any Eclipse of the Sun or Moon in leap-year, you add 18 years 11 days 7 hours 43 minutes; or in a common year a day less, you will have the mean time of that Eclipse returned again for some ages; though not always visible, because the 7 hours 43 minutes may shift a solar Eclipse into the night, and a lunar Eclipse into the day. In this period there are just 223 Lunations, and the Sun is again within half a degree of the same Node, but short of it. Therefore, although this period will serve tolerably well for some ages to examine Eclipses by, it cannot hold long; because half a degree from the Node sets the Moon 2-1/2 minutes of a degree from the Ecliptic. And as the Moon’s mean distance from the Earth is equal to 60 Semidiameters of the Earth, every minute of a degree at that distance is equal to 60 geographical miles, or one degree on the Earth; consequently 2-1/2 minutes of declination from the Ecliptic in the Moon’s Orbit, is equal to 150 such miles, or 2-1/2 degrees on the Earth. Consequently, if the Moon be passing by her ascending Node at the end of this period, her shadow will go 150 miles more southward on the Earth than it did at the beginning thereof. If the Moon be passing by her descending Node, her shadow will go 150 miles more northward: and in either case, in 500 years the shadow will have too great a Latitude to touch the Earth. So that any Eclipse of the Sun, which begins (for example) to touch the Earth at the south Pole (and that must be when the Moon is 17 degrees past her descending Node) will advance gradually northward in every return for about a thousand years, and then go off at the north Pole; and cannot take such another course again in less than 11,683 years.