TIDES

, two periodical motions of the waters of the sea; called also the flux and reflux, or the ebb and flow.

The Tides are found to follow periodically the course of the sun and moon, both as to time and quantity And hence it has been suspected, in all ages, that the Tides were somehow produced by the influence of these luminaries. Thus, several of the ancients, and among others, Pliny, Ptolomy, and Macrobius, were acquainted with the influence of the sun and moon upon the Tides; and Pliny says expressly, that the cause of the ebb and flow is in the sun, which attracts the waters of the ocean; and adds, that the waters rise in proportion to the proximity of the moon to the earth. It is indeed now well known, from the discoveries of Sir Isaac Newton, that the Tides are caused by the gravitation of the earth towards the sun and moon. Indeed the sagacious Kepler, long ago, conjectured this to be the cause of the Tides: “If, says he, the earth ceased to attract its waters towards itself, all the water in the ocean would rise and flow into the moon: the sphere of the moon's attraction extends to our earth, and draws up the water.” Thus thought Kepler, in his Introd. ad Theor. Mart. This surmise, for it was then no more, is now abundantly verified in the theory laid down by Newton, and by Halley, from his principles.

As to the Phenomena of the Tides: 1. The sea is observed to flow, for about 6 hours, from south towards north; the sea gradually swelling; so that, entering the mouths of rivers, it drives back the river-waters towards their heads, or springs. After a continual flux of 6 hours, the sea seems to rest for about a quarter of an hour; after which it begins to ebb, or retire back again, from north to south, for 6 hours more; in which time, the water sinking, the rivers resume their natural course. Then, after a seeming pause of a quarter of an hour, the sea again begins to flow, as before: and so on alternately.

2. Hence, the sea ebbs and flows twice a day, but falling every day gradually later and later, by about 48 minutes, the period of a flux and reflux being on an average about 12 hours 24 minutes, and the double of each 24 hours 48 minutes; which is the period of a lunar day, or the time between the moon's passing a meridian, and coming to it again. So that the sea flows as often as the moon passes the meridian, both the arch above the horizon, and that below it; and ebbs as often as she passes the horizon, both on the eastern and western side.

Other phenomena of the Tides are as below; and the reasons of them will be noticed in the Theory of the Tides that follows.

3. The elevation towards the moon a little exceeds the opposite one. And the quantity of the ascent of the water is diminished from the equator towards the poles.

4. From the sun, every natural day, the sea is twice elevated, and twice depressed, the same as for the moon. But the solar Times are much less than the lunar ones, on account of the immense distance of the sun; yet they are both subject to the same laws.

5. The Tides which depend upon the actions of the sun and moon, are not distinguished, but compounded, and so forming as to sense one united Tide, increasing and decreasing, and thus making neap and spring Tides: for, by the action of the sun, the | lunar Tide is only changed; which change varies every day, by reason of the inequality between the natural and lunar day.

6. In the syzygies the elevations from the action of both luminaries concur, and the sea is more elevated. But the sea ascends less in the quadratures; for where the water is elevated by the action of the moon, it is depressed by the action of the sun; and vice versa. Therefore, while the moon passes from the syzygy to the quadrature, the daily elevations are continually diminished: on the contrary, they are increased while the moon moves from the quadrature to the syzygy. At a new moon also, cæteris paribus, the elevations are greater; and those that follow one another the same day, are more different than at full moon.

7. The greatest elevations and depressions are not observed till the 2d or 3d day after the new or full moon. And if we consider the luminaries receding from the plane of the equator, we shall perceive that the agitation is diminished, and becomes less, according as the declination of the luminaries becomes greater.

8. In the syzygies, and near the equinoxes, the Tides are observed to be the greatest, both luminaries being in or near the equator.

9. The actions of the sun and moon are greater, the nearer those bodies are to the earth; and the less, as they are farther off. Also the greatest Tides happen near the equinoxes, or rather when the sun is a little to the south of the equator, that is, a little before the vernal, and after the autumnal equinox. But yet this does not happen regularly every year, because some variation may arise from the situation of the moon's orbit, and the distance of the syzygy from the equinox.

10. All these phenomena obtain, as described, in the open sea, where the ocean is extended enough to be subject to these motions. But the particular situations of places, as to shores, capes, straits, &c, disturb these general rules. Yet it is plain, from the most common and universal observations, that the Tides follow the laws above laid down.

11. The mean force of the moon to move the sea, is to that of the sun, nearly as 4 1/2 to 1. And therefore, if the action of the sun alone produce a Tide of 2 feet, which it has been stated to do, that of the moon will be 9 feet; from which it follows, that the spring Tides will be 11 feet, and the neap Tides 7 feet high. But as to such elevations as far exceed these, they happen from the motion of the waters against some obstacles, and from the sea violently entering into straits or gulphs where the force is not broken till the water rises higher.

1. If the earth were entirely fluid, and quiescent, it is evident that its particles, by their mutual gravity towards each other, would form the whole mass into the figure of an exact sphere. Then suppose some power to act on all the particles of this sphere with an equal force, and in parallel directions; by such a power the whole mass will be moved together, but its figure will suffer no alteration by it, being still the same perfect sphere, whose centre will have the same motion as each particle.

Upon this supposition, if the motion of the earth round the common centre of gravity of the earth and moon were destroyed, and the earth left to the influence of its gravitation towards the moon, as the acting power above mentioned; then the earth would fall or move straight towards the moon, but still retaining its true spherical figure.

But the fact is, that the effects of the moon's action, as well as the action itself, on different parts of the earth, are not equal: those parts, by the general law of gravity, being most attracted that are nearest the moon, and those being least attracted that are farthest from her, while the parts that are at a middle distance are attracted by a mean degree of force: besides, all the parts are not acted on in parallel lines, but in lines directed towards the centre of the moon: on both which accounts the spherical figure of the fluid earth must suffer some change from the action of the moon. So that, in falling, as above, the nearer parts, being most attracted, would fall quickest; the farther parts, being least attracted, would fall slowest; and the fluid mass would be lengthened out, and take a kind of spheroidical form.

Hence it appears, and what must be carefully observed, that it is not the action of the moon itself, but the inequalities in that action, that cause any variation from the spherical figure; and that, if this action were the same in all the particles as in the central parts, and operating in the same direction, no such change would ensue.

Let us now admit the parts of the earth to gravitate toward its centre: then, as this gravitation far exceeds the action of the moon, and much more exceeds the differences of her actions on different parts of the earth, the effect that results from the inequalities of these actions of the moon, will be only a small diminution of the gravity of those parts of the earth which it endeavoured in the former supposition to separate from its centre; that is, those parts of the earth which are nearest to the moon, and those that are farthest from her, will have their gravity toward the earth somewhat abated; to say nothing of the lateral parts. So that supposing the earth fluid, the columns from the centre to the nearest, and to the farthest parts, must rise, till by their greater height they be able to balance the other columns, whose gravity is less altered by the inequalities of the moon's action. And thus the figure of the earth must still be an oblong spheroid.

Let us now consider the earth, instead of falling toward the moon by its gravity, as projected in any direction, so as to move round the centre of gravity of the earth and moon: it is evident that in this case, the several parts of the fluid earth will still preserve their relative positions; and the figure of the earth will remain the same as if it fell freely toward the moon; that is, the earth will still assume a spheroidal form, having its longest diameter directed toward the moon. |

From the above reasoning it appears, that the parts of the earth directly under the moon, as at H, and also the opposite parts at D, will have the flood or highwater at the same time; while the parts, at B and F, at 90° distance, or where the moon appears in the horizon, will have the ebbs or lowest waters at that time.

Hence, as the earth turns round its axis from the moon to the moon again in 24 hours 48 minutes, this oval of water must shift with it; and thus there will be two Tides of flood and two of ebb in that time.

But it is further evident that, by the motion of the earth on her axis, the most elevated part of the water is carried beyond the moon in the direction of the rotation. So that the water continues to rise after it has passed directly under the moon, though the immediate action of the moon there begins to decrease, and comes not to its greatest elevation till it has got about half a quadrant farther. It continues also to descend after it has passed at 90° distance from the point below the moon, to a like distance of about half a quadrant. The greatest elevation therefore is not in the line drawn through the centres of the earth and moon, nor the lowest points where the moon appears in the horizon, but all these about half a quadrant removed eastward from these points, in the direction of the motion of rotation. Thus in open seas, where the water flows freely, the moon M is generally past the north and south meridian, as at p, when the high water is at Z and at n: the reason of which is plain, because the moon acts with the same force after she has passed the meridian, and thus adds to the libratory or waving motion, which the water acquired when she was in the meridian; and therefore the time of high water is not precisely at the time of her coming to the meridian, but some time after, &c.

Besides, 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 2d and 4th; 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.

2. We have hitherto adverted only to the action of the moon in producing Tides; but it is manifest that, for the same reasons, the inequality of the sun's action on different parts of the earth, would produce a like effect, and a like variation from the exact spherical figure of a fluid earth. So that in reality there are two Tides every natural day from the action of the sun, as there are in the lunar day from that of the moon, subject to the same laws; and the lunar Tide, as we have observed, is somewhat changed by the action of the sun, and the change varies every day on account of the inequality between the natural and the lunar day. Indeed the effect of the sun in producing Tides, because of his immense distance, must be considerably less than that of the moon, though the gravity toward the sun be much greater: for it is not the action of the sun or moon itself, but the inequalities in that action, that have any effect: the sun's distance is so great, that the diameter of the earth is but as a point in comparison with it, and therefore the difference between the sun's actions on the nearest and farthest parts, becomes vastly less than it would be if the sun were as near as the moon. However the immense bulk of the sun makes the effect still sensible, even at so great a distance; and therefore, though the action of the moon has the greatest share in producing the Tides, the action of the sun adds sensibly to it when they conspire together, as in the full and change of the moon, when they are nearly in the same line with the centre of the earth, and therefore unite their forces: consequently, in the syzygies, or at new and full moon, the Tides are the greatest, being what are called the Spring-Tides. But the action of the sun diminishes the effect of the moon's action in the quarters, because the one raises the water in that case where the other depresses it; therefore the Tides are the least in the quadratures, and are called Neap-Tides.

Newton has calculated the effects of the sun and moon respectively upon the Tides, from their attractive powers. The former he finds to be to the force of gravity, as 1 to 12868200, and to the centrifugal force at the equator as 1 to 44527. The elevation of the waters by this force is considered by Newton as an effect similar to the elevation of the equatorial parts above the polar parts of the earth, arising from the centrifugal force at the equator; and as it is 44527 times less, he finds it to be 24 1/2 inches, or 2 feet and 1/2 an inch.

To find the force of the moon upon the water, Newton compares the spring-tides at the mouth of the river Avon, below Bristol, with the neap-tides there, and finds the proportion as 9 to 5; whence, after several necessary corrections, he concludes that the force of the moon to that of the sun, in raising the waters of the ocean, is as 4.4815 to 1; so that the force of the moon is able of itself to produce an elevation of 9 feet 1 3/4 inch, and the sun and moon together may produce an elevation of about 11 feet 2 inches, when at their mean distances from the earth, or an elevation of about 12 3/4 feet, when the moon is nearest the earth. The height to which the water is found to rise, upon coasts of the open and deep ocean, is agreeable enough to this computation.

Dr. Horsley estimates the force of the moon to that of the sun, as 5.0469 to 1, in his edit. of Newton's Princip. See the Princip. lib. 3, sect. 3, pr. 36 and 37; also Maclaurin's Dissert. de Causa Physica Fluxus et Refluxus Maris apud Phil. Nat. Princ. Math. Com- | ment. le Seur & Jacquier, tom. 3, p. 272. And other calculators make the proportion still more different.

3. It must be observed, that the spring-tides do not happen precisely at new and full moon, nor the neaptides at the quarters, but a day or two after; because, as in other cases, so in this, the effect is not greatest or least when the immediate influence of the cause is greatest or least. As, for example, the greatest heat is not on the day of the solstice, when the immediate action of the sun is greatest, but some time after; so likewise, if the actions of the sun and moon should suddenly cease, yet the Tides would continue to have their course for some time; and like also as the waves of the sea continue aster a storm.

4. The different distances of the moon from the earth produce a sensible variation in the Tides. When the moon approaches toward the earth, her action on every part increases, and the differences of that action, on which the Tides depend, also increase; and as the moon approaches, her action on the nearest parts increases more quickly than that on the remote parts, so that the Tides increase in a higher proportion as the moon's distances decrease. In fact, it is shewn by Newton, that the Tides increase in proportion as the cubes of the distances decrease; so that the moon at half her distance would produce a Tide 8 times greater.

The moon describes an oval about the earth, and at her nearest distance produces a Tide sensibly greater than at her greatest distance from the earth: and hence it is that two great spring-tides never succeed each other immediately; for if the moon be at her least distance from the earth at the change, she must be at her greatest distance at the full, having made half a revolution in the intervening time, and therefore the spring-tide then will be much less than that at the last change was; and for the same reason, if a great spring-tide happen at the time of full moon, the Tide at the ensuing change will be less.

5. The spring-tides are highest, and the neap-tides lowest, about the time of the equinoxes, or the latter end of March and September; and, on the contrary, the spring-tides are the lowest, and the neap-tides the highest, at the solstices, or about the latter end of June and December: so that the difference between the spring and neap Tides, is much more considerable about the equinoctial than the solstitial seasons of the year. To illustrate and evince the truth of this observation, let us consider the effect of the luminaries upon the Tides, when in and out of the plane of the equator. Now it is manifest, that if either the sun or moon were in the pole, they could not have any effect on the Tides; for their action would raise all the water at the equator, or at any parallel, quite around, to a uniform height; and therefore any place of the earth, in describing its parallel to the equator, would not meet, in its course, with any part of the water more elevated than another; so that there could be no Tide in any place, that is, no alteration in the height of the waters.

On the other hand, the effect of the sun or moon is greatest when in the equinoctial; for then the axis of the spheroidal figure, arising from their action, moves in the greatest circle, and the water is put into the greatest agitation; and hence it is that the spring-tides produced when the sun and moon are both in the equinoctial, are the greatest of any, and the neaptides the least of any about that time. And when the luminary is any where between the equinoctial and the pole, the Tides are the smaller.

6. The highest spring tides are after the autumnal and before the vernal equinox: the reason of which is, because the sun is nearer the earth in winter than in summer.

7. Since the greatest of the two Tides happening in every diurnal revolution of the moon, is that in which the moon is nearest the zenith, or nadyr: for this reason, while the sun is in the northern signs, the greater of the two diurnal Tides in our climates, is that arising from the moon above the horizon; when the sun is in the southern signs, the greatest is that arising from the moon below the horizon. Thus it is found by observation that the evening Tides in the summer exceed the morning Tides, and in winter the morning Tides exceed the evening Tides. The difference is found at Bristol to amount to 15 inches, and at Plymouth to 12. It would be still greater, but that a fluid always retains an impressed motion for some time; so that the preceding Tides affect always those that follow them. Upon the whole, while the moon has a north declination, the greatest Tides in the northern hemisphere are when she is above the horizon, and the reverse while her declination is south.

8. Such would the Tides regularly be, if the earth were all over covered with the sea very deep, so that the water might freely follow the influence of the sun and moon; but, by reason of the shoalness of some places, and the narrowness of the straits in others, through which the Tides are propagated, there arises a great diversity in the effect according to the various circumstances of the places. Thus, a very slow and imperceptible motion of the whole body of water, where it is very deep, as 2 miles for instance, will suffice to raise its surface 10 or 12 feet in a Tide's time: whereas, if the same quantity of water were to be conveyed through a channel of 40 fathoms deep, it would require a very rapid stream to effect it in so large inlets as are the English channel, and the German ocean; whence the Tide is found to set strongest in those places where the sea grows narrowest, the same quantity of water being in that case to pass through a smaller passage. This is particularly observable in the straits between Portland and Cape la Hogue in Normandy, where the Tide runs like a sluice: and would be yet more so between Dover and Calais, if the Tide coming round the island did not check it.

This force, when once impressed, continues to carry the water above the ordinary height in the ocean, especially where the water meets a direct obstacle, as it does in St. Maloes; and where it enters into a long channel which, running far into the land, grows very strait at its extremity, as it does into the Severn sea at Chepstow and Bristol.

This shoalness of the sea, and the intercurrent continents, are the reasons that in the open ocean the Tides rise but to very small heights in proportion to what they do in wide-mouthed rivers, opening in the direc- | tion of the stream of the Tide; and that high water is not soon aster the moon's appulse to the meridian, but some hours after it, as it is observed upon all the western coast of Europe and Africa, from Ireland to the Cape of Good Hope; in all which a south-west moon makes high water; and the same it is said is the case on the western side of America. So that Tides happen to different places at all distances of the moon from the meridian, and consequently at all hours of the day.

To allow the Tides their full motion, the ocean in which they are produced, ought to be extended from east to west 90 degrees at least; because that is the distance between the places where the water is most raised and depressed by the moon. Hence it appears that it is only in the great oceans that such Tides can be produced, and why in the larger Pacific ocean they exceed those in the Atlantic ocean. Hence also it is obvious, why the Tides are not so great in the torrid zone, between Africa and America, where the ocean is narrower, as in the temperate zones on either side; and hence we may also understand why the Tides are so small in islands that are very far distant from the shores. It is farther manifest that, in the Atlantic ocean, the water cannot rise on one shore but by descending on the other; so that at the intermediate islands it must continue at a mean height between its elevations on those two shores. But when Tides pass over shoals, and through straits into bays of the sea, their motion becomes more various, and their height depends on many circumstances.

To be more particular. The Tide that is produced on the western coasts of Europe, in the Atlantic, corresponds to the situation of the moon already described. Thus it is high water on the western coasts of Ireland, Portugal and Spain, about the 3d hour after the moon has passed the meridian: from thence it flows into the adjacent channels, as it finds the easiest passage. One current from it, for instance, runs up by the south of England, and another comes in by the north of Scotland; they take a considerable time to move all this way, making always high water sooner in the places to which they first come; and it begins to fall at these places while the currents are still going on to others that are farther distant in their course. As they return, they are not able to raise the Tide, because the water runs faster off than it returns, till, by a new Tide propagated from the open ocean, the return of the current is stopped, and the water begins to rise again. The Tide propagated by the moon in the German ocean, when she is 3 hours past the meridian, takes 12 hours to come from thence to London bridge; so that when it is high water there, a new Tide is already come to its height in the ocean; and in some intermediate place it must be low water at the same time. Consequently when the moon has north declination, and we should expect the Tide at London to be the greatest when the moon is above the horizon, we find it is least; and the contrary when she has south declination.

At several places it is high water 3 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 9 hours past the opposite meridian.

It would be endless to recount all the particular solutions, which are easy consequences from this doctrine: as, why the lakes and seas, such as the Caspian sea and the Mediterranean sea, the Black sea and the Baltic, have little or no sensible Tides: for lakes are usually so small, that when the moon is vertical she attracts every part of them alike, so that no part of the water can be raised higher than another: and having no communication with the ocean, it can neither increase nor diminish their water, to make it rise and fall; and seas that communicate by such narrow inlets, and are of so immense an extent, cannot speedily receive and empty water enough to raise or sink their surface any thing sensibly.

In general; when the time of high water at any place is mentioned, it is to be understood on the days of new and full moons.—Among pilots, it is customary to reckon the time of flood, or high water, by the point of the compass the moon bears on, at that time, allowing 3/4 of an hour for each point. Thus, on the full and change days, in places where it is flood at noon, the Tide is said to flow north and south, or at 12 o'clock: in other places, on the same days, where the moon bears 1, 2, 3, 4, or more points to the east or west of the meridian, when it is high water, the Tide is said to flow on such point; thus, if the moon bears SE, at flood, it is said to flow SE and NW, or 3 hours before the meridian, that is, at 9 o'clock; if it bears SW, it flows SW and NE, or at 3 hours after the meridian; and in like manner for the other points of the moon's bearing.

The times of high water in any place fall about the same hours after a period of about 15 days, or between one spring Tide and another; but during that period, the times of high water fall each day later by about 48 minutes.

On the subject of this article, see Newton Princ. Math. lib. 3, prop. 24, and De System. Mundi sect. 38, &c. Apud Opera edit. Horsley, tom. 3, pa. 52 &c. p. 203 &c. Maclaurin's Account of Newton's Discoveries, book 4, ch. 7. Ferguson's Astron. ch. 17. Robertson's Navig. book 6, sect. 7, 8, 9. Lalande's Astron. vol. 4.

Tide Dial, an instrument contrived by Mr. Ferguson, for exhibiting and determining the state of the Tides. For the construction and use of which see his Astron. p. 297.

Tide Tables, are tables commonly exhibiting the times of high water at sundry places, as they fall on the days of the full and change of the moon, and sometimes the height of them also. These are common in most books on Navigation, particularly Robertson's, and the 2d ed. of Tables requisite to be used with the Nautical Almanac. See one at High- water.