but straggling, and has a spacious and handsome church. It gives name to a jurisdiction of very great extent, and to which many manors owe suit and service. About half a mile from the town is Possington Well, a medicinal bath, now of little repute. To the east is a large piece of water, curiously diversified with rocks and ruins; under one of the rocks is the mouth of a cavern, said to have had communication with a monastery that stood near. Market on Friday. TICKLE, v. a., v. n., & adj. Lat. titillo. To TICK'LISH, adj. titillate; to affect with a prurient sensation by slight touches; please slightly to feel titillation: as an adjective, tottering; unfixed; unstable: ticklish is easily tickled; tottering; uncertain; nice;, fastidious.

Dametas, that of all manners of stile could best conceive of golden eloquence, being withal tickled by Musidorus's praise, had his brain so turned that he became slave to that which he that sued to be his Sidney. servant offered to give him.

He with secret joy therefore Did tickle inwardly in every vein, And his false heart, fraught with all treason's store, Was filled with hope his purpose to obtain.

Spenser.

When the last O'Neal began to stand upon some tickle terms, this fellow, called baron of Dungannon, Id. on Ireland. was set up to beard him.

The state of Normandy

Stands on a tickle point now they are gone.

Shakspeare.

Expectation tickling skittish spirits,

Sets all on hazard.

Id.

Id. Coriolanus.

Dissembling courtesy! How fine this tyrant

Can tickle where she wounds.

Id. Cymbeline.

The mind is moved in great vehemency only by tickling some parts of the body.

Bacon.

Ireland was a ticklish and unsettled state, more easy to receive distempers and mutations than England was.

Id.

It is a good thing to laugh at any rate; and, if a straw can tickle a man, it is an instrument of happiDryden.

ness.

I cannot rule my spleen;

Id.

Locke.

New York. It is famous in the history of the American wars, and situated on an eminence on the west shore of Lake Champlain, just north of the entrance of the outlet from Lake George into Lake Champlain. Fifteen miles south of Crown Point, and twenty-four north of Whitehall. Long. 73° 62′ W., lat. 43° 50′ N. It is now in ruins. TIDE, n. s., v. A., & I Sax. ty; Belg. and TIDEWAITER. [v. n. Isl. tijd. Time; season; while; alternate ebb and flow of the sea; stream; course; concurrence; commotion: to tide is, to drive with the stream: as a verb neuter to pour a flood: a tide-waiter, a custom-house officer, who watches the landing of goods.

There they alight, in hope themselves to hide From the fierce heat, and rest their weary limbs a Spenser.

Flows from the exhilarating fount. When from his dint the foe still backward shrunk, Wading within the Ouse, he dealt his blows, And sent them, rolling, to the tiding Humber. Id. Employments will be in the hands of Englishmen ; nothing left for Irishmen but vicarages and tidewaiters' places. Swift.

TIDES. On the shores of the ocean, and in bays, creeks, and harbours, which communicate freely with the ocean, the waters rise up above this mean height twice a day, and as often sink below it, forming what is called a flood and an ebb, a high and a low water. The whole interval between high and low water is called a tide; the water is said to flow and to ebb, and the rising is called the flood tide, and the falling is called the ebb tide. This rise and fall of the waters is variable in quantity. At Plymouth, for instance, it is sometimes twenty-one feet between the greatest and least depth of the water in one day, and These different sometimes only twelve feet. heights of tide succeed each other in a regular series, diminishing from the greatest to the least, and then increasing from the least to the greatest. The greatest is called a spring tide, and the least is called a neap tide. This series is completed in about fifteen days. More careful observation shows that two series are completed in the ex

act time of a lunation. For the spring tide in any place is observed to happen precisely at a certain interval of time (generally between two and three days) after new or full moon, and the neap tide at a certain interval after half moon; or, to be more accurate, the spring tide always happens when the moon has got a certain number of degrees east of the line of conjunction and opposition, and the neap tide happens when she is a certain number of degrees from her first or last quadrature. Thus the whole series of tides appear to be regulated by the moon. High water happens at new and full moon when the moon has a certain determined position with respect to the meridian of the place of observation, preceding or following the moon's southing a certain interval of time; which is constant with respect to that place, but very different in different places. The time of high water in any place appears to be regulated by the moon; for the interval between the time of high water and the moon's southing never changes above threequarters of an hour, whereas the interval between the time of high water and noon changes six hours in the course of a fortnight. The interval between two succeeding high waters is variable. It is least of all about new and full moon, and greatest when the moon is in her quadratures. As two high waters happen every day, we may call the double of their interval a tide day, as we call the diurnal revolution of the moon a lunar day. The tide day is shortest about new and full moon, being then about 24h. 37'; about the time of the moon's quadratures it is 25h. 27'. These values are taken from a mean of many observations made at Barbadoes by Dr. Maskelyne. The tides in similar circumstances are greatest when the moon is at her smallest distance from the earth, or in her perigee, and, gradually diminishing, are smallest when she is in her apogee. The same, remark is made with respect to the sun's distance; and the greatest tides are observed during the winter months of Europe. The tides in any part of the ocean increase as the moon, by changing her declination, approaches the zenith of that place. The tides which happen while the moon is above the horizon, are greater than the tides of the same day when the moon is below the horizon. There is also a kind of rest or cessation of about half an hour between the flux and reflux; during which time the water is at its greatest height, called high water. The flux is made by the motion of the water of the sea from the equator towards the poles: which, in its progress, striking against the coasts in its way, and meeting with opposition from them, swells, and where it can find passage, as in flats, rivers, &c., rises up and runs into the land. This motion follows, in some measure, the course of the moon; as it loses or comes later every day by about three-quarters of an hour, or, more precisely, by forty-eight minutes; and by so much is the motion of the moon slower than that of the sun. It is always highest and greatest in full moons, particularly those of the equinoxes. In some parts, as at Mount St. Michael, it rises tighty or ninety feet, though in the open sea it never rises above a foot or two; and in some places, as about the Morea, there is no flux at

all. It runs up some rivers above 120 miles. Up the river Thames it only goes eighty, viz., near to Kingston in Surrey. Above London bridge the water flows four hours and ebbs eight; and, below the bridge, flows five hours and ebbs seven.

Homer is the earliest profane author who speaks of the tides; but (in the twelfth book of the Odyssey) only takes notice of the tides of Charybdis, which rise and retire thrice in every day. Herodotus and Diodorus Siculus speak more distinctly of the tides in the Red Sea. Pytheas of Marseilles is the first who says any thing of their cause. According to Strabo he had been in Britain, where he must have observed the tides of the ocean. Plutarch says expressly that Pytheas ascribed them to the moon. It is surprising that Aristotle says so little about the tides. The army of Alexander, his pupil, were startled at their first appearance to them near the Persian Gulph: and we should have thought that Aristotle would be well informed of all that had been observed there. But there are only three passages concerning them in all Aristotle's writings, and they are very trivial. In one place he speaks of great tides observed in the north of Europe; in another, he mentions their having been ascribed by some to the moon; and in a third, he says that the tide in a great sea exceeds that in a small one.

The conquest and the commerce of the Romans gave them more acquaintance with tides. Cæsar speaks of them in the fourth book of his Gallic War. Strabo, after Posidonius, classes the phenomena into daily, monthly, and annual. He observes that the sea rises as the moon gets near the meridian, whether above or below the horizon, and falls again as she rises or falls; also, that the tides increase at the time of new and full moon, and are greatest at the summer solstice. Pliny explains the phenomena at some length: and says that both the sun and moon are their cause, dragging the waters along with them (book ii., c. 97). Seneca (Nat. Quest. iii. 28) speaks of the tides with correctness; and Macrobius (Somn. Scip. i. 6) gives a very accurate description of their motions. Such phenomena, however, could not but exercise human curiosity as to their cause. Plutarch (Plaut. Phil. iii. 17), Galileo (Syst. Mund. Dial. 4), Riccioli in his Almogest, ii. p. 374, and Gassendi, ii. p. 27, have collected most of the notions of their predecessors on the subject; but they are of so little importance that they do not deserve our notice. Kepler speaks more like a philosopher.-De Stella Martis, and Epit. Astron. p. 555. He says that all bodies attract each other, and that the waters of the ocean would all go to the moon were they not retained by the attraction of the earth; and then goes on to explain their elevation under the moon and on the opposite side, because the earth is less attracted by the moon than the nearer waters, but more than the waters which are more remote.

The honor of a complete explanation of the tides was reserved to Sir Isaac Newton. He laid hold of this class of phenomena as the most incontestible proof of universal gravitation, and has given a most beautiful and synoptical view of the

whole subject; contenting himself, however, with merely exhibiting the chief consequences of the general principle, and applying it to the phenomena with singular address. But the wide steps taken by this great philosopher, in his investigation, leave ordinary readers frequently at fault: many of his assumptions require the greatest mathematical knowledge to satisfy us of their truth. The academy of Paris, therefore, proposed to illustrate this among other parts of the principles of natural philosophy, and published the theory of the tides as a prize problem. This produced three excellent dissertations by M'Laurin, Dan. Bernoulli, and Euler. Aided by these, and chiefly by the second, we shall here give a physical theory, and accommodate it to the purposes of navigation, by giving the rules of calculation. It is an unexpected fact that every particle of matter in the solar system is actually deflected toward every other particle; and that the deflection of a particle of matter toward any distant sphere is proportional to the quantity of matter in that sphere directly, and to the square of the distance of the particle from the centre of that sphere inversely; and, having found that the heaviness of a piece of terrestrial matter is nothing but the supposed opponent to the force which we exert in carrying this piece of matter, we conceive it as possessing a property, or distinguishing quality, manifested by its being gravis or heavy. This is heaviness or gravity; and the manifestation of this quality, or the event in which it is seen, whether it be directly falling, or deflecting in a parabolic curve, or stretching a coiled spring, or breaking a rope, or simply pressing on its support, is gravitatio, gravitation; and the body is said to gravitate. When all obstacles are removed from the body, as when we cut the string by which a stone is hung, it moves directly downwards, tendit ad terram. By some metaphysical process, this nisus ad motum has been called a tendency in our language, and is used to signify the energy of any active quality in those cases where its simplest and most immediate manifestation is prevented by some obstacle. The stretching the string in a direction perpendicular to the horizon, is a full manifestation of this tendency. This tendency, this energy of its heaviness, is therefore named by the word which distinguishes the quality called gravitation. But Sir Isaac Newton discovered that this deflection of a heavy body differs in no respect from that general deflection observed in all the bodies of the solar system. For sixteen feet, which is the deflection of a stone in one second, has the very same proportion to one-tenth of an inch, which is the simultaneous deflection of the moon, that the square of the moon's distance from the centre of the earth has to the square of the stone's distance from it, namely, that of 3600 to one. Thus we are enabled to compare all the effects of the mutual tendencies of the heavenly bodies with the tendency of gravity, whose effects and measures are familiar to us. If the earth were a sphere, covered to a great depth with water, the water would form a concentric spherical shell; for the gravitation of every particle of its surface would then be directed to the centre, and would be equal. The curvature of its surface, VOL. XXII.

therefore, would be every where the same, that is, it would be the uniform curvature of a sphere.

The waters of the ocean have their equilibrium disturbed by the unequal gravitation of their different particles to the sun or to the moon; and this equilibrium cannot be restored till the waters come in from all parts, and rise up around the line joining the centres of the earth and of the luminary. The spherical ocean must acquire the form of a prolate spheroid generated by the revolution of an ellipse round its transverse axis. The waters will be highest in that place which has the luminary in its zenith, and in the antipodes to that place; and they will be most depressed in all those places which have the luminary in their horizon. Mr. Ferguson, in his Astronomy, assigns another cause of this arrangement, viz. the difference of the centrifugal forces of the different particles of water, while the earth is turning round the common centre of gravity of the earth and moon. This, however, is a mistake. It would be just if the earth and moon were attached to the ends of a rod, and the earth kept always the same face toward the moon. It is evident that its absolute quantity may be discovered by our knowledge of the proportion of the disturbing force to the force of gravity. Now this proportion is known; for the proportion of the gravitation of the earth's centre to the sun or moon, to the force of gravity at the earth's surface, is known; and the proportion of the gravitation of the earth's centre to the luminary, to the difference of the gravitations of the centre and of the surface, is also known, being very nearly in the proportion of the distance of the luminary to twice the radius of the earth. We must therefore take the subject more generally, and show the proportion and directions of gravity in every point of the spheroid. We need not, however, again demonstrate that the gravitation of a particle placed any where without a perfect spherical shell, or a sphere consisting of concentric spherical shells, either of uniform density or of densities varying according to some function of the radius, is the same as if the whole matter of the shell or sphere were collected in the centre. We need only remind the reader of some consequences of this theorem which are of continual use in the present investigation. 1. The gravitation to a sphere is proportional to its quantity of matter directly, and to the square of the distance of its centre from the gravitating particle inversely. 2. If the spheres be homogeneous, and of the same density, the gravitations of particles placed on their surfaces, or at distances which are proportional to their diameters, are as the radii; for the quantities of matter are as the cubes of the radii, and the attractions are inversely as the squares of the radii; and therefore the whole gravitations are as 72 or as 7. 3. A particle placed within a sphere has no tendency to the matter of the shell which lies without it, because its tendency to any part is balanced by an opposite tendency to the opposite part. Therefore, 4. A particle placed any where within a homogeneous sphere gravitates to its centre with a force proportional to its distance from it. It is a much more difficult

H

38604600

problem to determine the gravitation of particles to a spheroid. To do this in general terms, and for every situation of the particle, would require a train of propositions which our limits will by no means adınit. The ratio of the axes may be obtained and ascertained by knowing the ratio of the gravitation at the pole to that of the equator. See SPHERE, SPHEROID, and PROJECTION OF THE SPHERE. The gravitation of the moon to the earth is to the disturbing force of the sun as 178,725 to 1 very nearly. The lunar gravitation is increased as she approaches the earth in the reciprocal duplicate ratio of the distances. The disturbing force of the sun diminishes in the simple ratio of the distances; therefore the weight of a body on the surface of the earth is to the disturbing force of the sun on the same body, in a ratio compounded of the ratio of 178,725 to 1, the ratio of 3600 to 1, and the ratio of 60 to 1; that is, in the ratio of 38,604,600 to 1. If the mean radius of the earth be 20934500 feet, the difference of the axis, or the elevation of the pole of the watery spheroid produced by the gravitation to the sun, will be 4500 feet, or very nearly twenty-four inches and a half. This is the tide produced by the sun on a homogeneous fluid sphere. It needs no proof that if the earth consists of a solid nucleus of the same density with the water, the form of the solar tide will be the same. But, if the density of the nucleus be different, the form of the tide will be different, and will depend both on the density and on the figure of the nucleus. If the nucleus be of the same form as the surrounding fluid, the whole will still maintain its form with the same propor. tion of the axis. If the nucleus be spherical, its action on the surrounding fluid will be the same as if all the matter of the nucleus, by which it exceeds an equal bulk of the fluid, were collected at the centre. In this case the ocean cannot maintain the same form; for the action of this central body, being proportional to the square of the distance inversely, will augment the gravity of the equatorial fluid more than it augments that of the circumpolar fluid; and the ocean, which was in equilibrio, by supposition, must now become more protuberant at the poles. It may, however, be again balanced in an elliptical form when it has acquired a just proportion of the axes. The process for determining this is tedious, but precisely similar to the preceding. In the dissertations by Clairault and Boscovich on the Figure of the Earth, this curious problem is treated in the most complete manner. The earth is not a sphere, but swelled out at the equator by the diurnal rotation. But the change of form is so very small, in proportion to the whole bulk, that it cannot sensibly affect the change of form afterwards induced by the sun on the waters of the ocean. For the disturbing force of the sun would produce a certain protuberance on a fluid sphere; and this protuberance depends on the ratio of the disturbing force to the force of gravity at the surface of this sphere. If the gravity be changed in any proportion, the protuberance will change in the same proportion. Therefore, if the body be a spheroid, the protuberance produced at any point by the sun will increase or diminish in the

It

same proportion that the gravity at this point has been changed by the change of form. Now the change of gravity, even at the pole of the terrestrial spheroid, is extremely small in comparison with the whole gravity. Therefore the change produced on the spheroid will not sensibly differ from that produced on the sphere; and the elevations of the waters above the surface, which they would have assumed independent of the sun's action, will be the same on the spheroid as on the sphere. For the same reason, the moon will change the surface already changed by the sun in the same manner as she would have changed the surface of the undisturbed ocean. Therefore the change produced by both these luminaries in any place will be the same when acting together as when acting separately; and it will be equal to the sum, or the difference of their separate changes, according as these would have been in the same or in opposite directions. The difference between a solar day and a tide day is called the priming or the retardation of the tides. This is evidently equal to the time of the earth's describing in its rotation an angle equal to the motion of the high water in a day from the sun. The smallest of these retardations is to the greatest as the difference of the disturbing forces to their sum. Of all the phenomena of the tides, this seems liable to the fewest and most inconsiderable derangements from local and accidental circumstances. therefore affords the best means for determining the proportion of the disturbing forces. By a comparison of a great number of observations made by Dr. Maskelyne at St. Helena and at Barbadoes, places situated in the open sea, it appears that the shortest tide-day is 24h. 37', and the longest is 25h. 27'. This gives M-S: M+S 37: 87, and S: M = 2: 4·96; which differs only 1 part in 124 from the proportion of 2 to 5, which Daniel Bernoulli collected from a variety of different observations. We shall therefore adopt the proportion of 2 to 5 as abundantly exact. It also agrees exactly with the phenomena of the nutation of the earth's axis and the precession of the equinoxes. It follows that while the moon moves uniformly from 56° 47′ W. elongation to 56° 47′ E., or from 123° 13′ E. to 123° 13′ W., the tide-day is shorter than the lunar-day; and, while she moves from 56° 47′ E. to 123° 13', or from 123° 13′ W. to 56° 47', the tide-day is longer than the lunar-day. The time of high-water, when the sun and moon are in the equator, is never more than fortyseven minutes different from that of the moon's southing (+ or a certain fixed quantity, to be determined once for all by observation). There is now no difficulty in determining the hour of high-water corresponding to any position of the sun and moon in the equator. The following table of Bernoulli's exhibits these times for every tenth degree of the moon's elongation from the

The tide is the height of high-water above lowwater. This is the interesting circumstance in practice. Many circumstances render it almost impossible to say what is the elevation of highwater above the natural surface of the ocean. In many places the surface at low water is above the natural surface of the ocean. This is the case in rivers at a great distance from their mouths. This may appear absurd, and is certainly very paradoxical; but a little attention to the motion of running waters will explain this completely. Whatever checks the, motion of water in a canal must raise its surface. Water in a canal runs only in consequence of the declivity of this surface; therefore a flood tide coming to the mouth of a river checks the current of its waters, and they accumulate at the mouth. This checks the current farther up, and therefore the waters accumulate there also; and this checking of the stream, and consequent rising of the waters, is gradually communicated up the river to a great distance. The water rises every where, though its surface still has a slope. In the mean time the flood tide at the mouth passes by, and an ebb succeeds. This must accelerate even the ordinary course of the river. It will more remarkably accelerate the river now raised above its ordinary level, because the declivity at the mouth will be so much greater. Therefore the waters near the mouth by accelerating will sink in their channel, and increase the declivity of the canal beyond them. This will accelerate the waters beyond them and thus a stream more rapid than ordinary will be produced along the whole river, and the waters will sink below their ordinary level. Thus there will be an ebb below the ordinary surface as well as a flood above it, however

sloping that surface may be. Hence we cannot tell what is the natural surface of the ocean by any observations made in a river, even though near its mouth. Yet even in rivers we have regular tides, subjected to all the varieties deduced from this theory. But the geometrical construction of this problem not only explains all the interesting circumstances of the tides, but also points them out, almost without employing the judgment, and exhibits to the eye the gradual progress of each phenomenon. But on these we cannot enlarge. On the whole, the solar force does not vary much, and may be retained as constant without any great error. But the change of the moon's force has great effects on the tides both as to their time and their quantity. I. As to their time. 1. The tide day following a spring tide is 24h. 27′ when the moon is in perigee, but 24h. 33′ when she is in apogee. See APOGEE and PERIGEE. 2. The tide day following neap tide is 25h. 15', and 25h. 40′ in these two situations of the moon. 3. The greatest interval of time between high water and the moon's southing is 39' and 61'; the angle y being 9° 45′ in the first case, and 15° 15′ in the second. II. As to their heights. 1. If the moon is in perigee when new or full, the spring tide will be eight feet instead of seven, which corresponds to her mean distance. The very next spring tide happens when she is near her apogee, and will be six feet instead of seven. The neap tides happen when she is at her mean distance, and will therefore be three feet. But, if the moon be at her mean distance when new or full, the two succeeding spring tides will be regular, or seven feet, and one of the neap tides will be four feet and the other only two feet.

Mr. Bernoulli gives the following table of the time of high water for the chief situations of the moon, viz. her perigee, mean distance, and apogee :-It may be had by interpolation for all intermediate positions with as great accuracy as can be hoped for in phenomena which are subject to such a complication of disturbances.

> and O P. M.

A.

20

30

50

60

70

80

90