But in order to ascertain the effects of declination and latitude on other tides, we mutt make a much more complicated conftruction, even tho' we fuppofe both luminaries in the ecliptic. For in this cafe the two depreffed poles of the watery fpheroid are not in the poles of the earth; and therefore the fections of the ocean, made by meridians, are by no means ellipfes.

In a neap tide, the moon is vertical at B (fig. 7. or 8.), and the fun at fome point of fF, 90° from B. If O be this point, the conftruction for the heights of the tides may be made by adding to both the fuperior and inferior tides for any point D, the quantity M+S DF or DKX fin. 2 Q fin.2d O, = M + S — tide × as is evident. cof. MQ' But if the fun be vertical at d, d will be the higheft part of the circle ƒ OF, and no correction is neceflary. But in this cafe the circle of high water will be inclined to the meridian in an angle equal to d BO (fig. 7.), and neither the times nor elevations of high water will be properly afcertained, and the error in time may be confiderable in high latitudes. The inaccuracies are not fo great in intermediate tides, and refpect chiefly the time of high water and the height of

low water.

ven.

The exact computation is very tedious and peculiar, fo that it is hardly poffible to give any account of a regular progrefs of phenomena; and all we can do is, to afcertain the precife heights of detached points. For which reafons, we must content ourselves with the conftruction already giIt is the exact geometrical expreffion of Bernoulli's analysis, and its confequences now related contain all that he has investigated. We may accommodate it very nearly to the real state of things, by fuppofing PC equal, not to CO of fig. 4. but to MS, exhibiting the whole compound tide. And the point B, inftead of reprefenting the moon's place, muft reprefent the place of high water,

Thus have we obtained a general, though not very accurate, view of the phenomena which muft take place in different latitudes and in different declinations of the fun and moon, provided that the phyfical theory which determines the form and pofition of the watery fpheroid be juft. We have only to compute, by a very fimple procefs of fpherical trigonometry, the place of the pole of this fpheroid. The fecond conftruction, in fig. 8. fhows us all the circumftances of the time and height of high water at any point. It will be recollected, that in computing this place of the pole, the anticipation of 20 degrees, ariling from the inertia of the

waters, must be attended to.

Were we to inftitute a comparifon of this theory with obfervation, without farther confideration, we should still find it unfavourable, partly in refpect of the heights of the tides, and more remarkably in refpect of the time of low water. We muft again confider the effects of the inertia of the waters, and recollect, that a regular theoretical tide differs very little in its progrefs from the motion of a wave. Even along the free ocean, its motion much refembles that of any other wave. All waves are propagated by an of cillatory motion of the waters, precifely fimilar to that of a pendulum. It is well known, that it a pendulum receive a fmall impulfe in the time of every defcent, its vibrations may be increased to infinity. Did the fucceffive actions of the fun or moon just keep time with the natural propagation of the tides, or the natural ofcillations of the waters, the tides would alfo augment to infinity: But there is an infinite odds against this exact adjustment. It is much more probable that the action of to-day interrupts or checks the ofcillation produced by yesterday's action, and that the motion which we perceive in this day's tide is what remaina, VOL. XVIII. Part II.

and is compounded with the action of to-day. This being Tide. the cafe, we fhould expect that the nature of any tide will depend much on the nature of the preceding tide. There fore we fhould expect that the fuperior and inferior tides of the fame day will be more nearly equal than the theory determines. The whole courfe of obfervation confirms this. In latitude 45°, the fuperior and interior tides of one day may differ in the proportion of 2 to 1, and the tides correfponding to the greatest and leaft declinations of the moon may differ nearly as much. But the diffesence of the fu perior and inferior tides, as they occur in the lift of Obfer. vations at Rochefort, is not the third part of this, and the changes made by the moon's declination is not above onehalf. Therefore we thall come much nearer the true mea.

fure of a spring tide, by taking the arithmetical mean, than by taking either the fuperior or inferior.

We should expect lefs deviation from the theory in the gradual diminution of the tides from fpring tide to neap tide, and in the gradual changes of the medium tide by the

declination of the moon; because the fucceffive changes are very fmall; and when they change in kind, that is, diminish after having for fome time augmented, the change is by infenfible degrees.

This is molt accurately confirmed by obfervation. The vast collection made by Caffini of the Obmedium of the two tides in one day being taken for the tide fervations at Breft being examined by Bernoulli, and the of that day, he found fuch an agreement between the pra、 greffion of these medium tides and the progreffion of the lines MS of fig. 4. that the one feemed to be calculated of the medium tides by the moon's declination. He found no lefs agreement in the changes

by the other.

ftances of the moon from the earth, were found abundantly In like manner, the changes produced by the different diother. This difference or inferiority is eafily accounted for: conformable to the theory, although not so exact as the When the moon changes in her mean distance, one of the cap tides is uncommonly fmall, and therefore the fucceffive diminutions are very great, and one tide fenfibly affects another. The fame circumftance operates when the changes in apogee, by reason of a very large fpring tide. And the changes correfponding both to the fun's diftance from the earth and his declination agreed almoft exactly. earth and his declination agreed almoft exactly. reafon to conclude, that not only the theory itself is just in All these things confidered together, we have abundant principle (a thing which no intelligent naturalift can doubt), but also that the data which are affumed in the application are properly chofen; that is, that the proportion of 2 to 5 is very nearly the true proportion of the mean folar and

lunar forces.

If we now compute the medium tide for any place in fucceffion, from tpring tide to neap tide, and still more, if we compute the series of times of their occurrence, but that there are many irregularities; but these are evi we fhall find as great an agreement as can be defired. Not dently fo anomalous, that we can afcribe them to nothing but circumstances which are purely local.

This general rule of computation muft be formed in the folowing manner:

and the neap tide B, recollect that the fpring tide, according The fpring tide, according to theory, being called A, to the regular theory, is meatured by MS. Recollect rior fpring tide is M × fin.2, ZM (fig. 8). alfo, that when the lunar tide only is confidered, the tupeBut when we confider the action of two adjoining tides on each other, we find it fafer to take the medium of the fupeior and inferior tides for the measure; and this is MX 1 + cof.2 2 ZQ × cof. 2 MQ

2

3 X

Let this be called m. This being

Tide, be conceived. Something like it is to be feen at Gibraltar. It is high water on the eat fide of the rock about 10 o'clock at full and change, and it is high water on the well fide, not a mile diftant, at 12. This difference is perhaps the chief cause of the fingular current which is obferved in the Straits mouth. There are three currents obferved at the fame time, which change their directions every 12 hours. The fmall tide of the Mediterranean proceeds along the Barbary fhore, which is very uniform all the way from Egypt, with tolerable regularity. But along the northern fide, where it is greatly obftructed by Italy, the islands, and the eaft coaft of Spain, it fets very irregularly; and the perceptible high water on the Spanish coatt differs four hours from that of the fouthern coaft. Thus it happens, that one tide ranges round Europa point, and another along the fhore near Ceuta, and there is a third current in the middle different from both. Its general direction is from the Atlantic Ocean into the Mediterranean Sea, but it fometimes comes out when the ebb tide in the Atlantic is confiderable.

Suppofe the moon over the middle of the Mediterranean. The furface of the fea will be level, and it will be half tide at both ends, and therefore within the Straits of Gibraltar. But without the Straits it is within half an hour of high water. Therefore there will be a current setting in from the Atlantic. About three and an half hours after, it is high water within and half ebb without. The cur rent now fets out from the Mediterranean. Three hours later, it is low water without the Straits and half ebb within; therefore the current has been setting out all this while. Three hours later, it is half flood without the Straits and low water within, and the current is again ietting in, &c.

Were the earth fluid to the centre, the only sensible motion of the waters would be up and down, like the waves on the open ocean, which are not brushed along by strong gales. But the fhallowness of the channel makes a horizontal motion neceffary, that water may be supplied to form the accumulation of the tide. When this is formed on a flat fhelving coaft, the water muft flow in and out, on the flats and fands, while it rifes and falls. These horizontal motions must be greatly modified by the channel or bed along which they move. When the channel contracts along the line of flowing water, the wave, as it moves up the channel, and is checked by the narrowing fhores, must be reflected back, and keep a-top of the waters ftill flowing in underneath. Thus it may rife higher in these narrow feas than in the open ocean. This may ferve to explain a little the great tides which happen on fome coafts, fuch as the coaft of Normandy. At St Malo the flood frequently rifes 50 feet. But we cannot give any thing like a full or fatisfactory account of thefe fingularities. In the Bay of Fundy, and particularly at Annapolis Royal, the water sometimes rises above 100 feet. This seems quite inexplicable by any force of the fun and moon, which cannot raife the waters of the free ocean more than eight feet. Thefe great floods are unquestionably owing to the proper timing of certain ofcillations or currents adjoining, by which they unite, and form one of great force. Such violent motions of water are frequently feen on a small scale in the motions of brooks and rivers; but we are too little acquainted with hydraulics to explain them with any precision.

We have seen that there is an ofcillation of waters formed under the fun and moon; and that in confequence of the rotation of the earth, the inertia and the want of perfect uidity of the waters, and obftructions in the channel, this accumulation never reaches the place where it would finally

fettle if the earth did not turn round its axis. The confe quence of this must be a general current of the waters from east to west. This may be feen in another way. The moon in her orbit round the earth has her gravity to the earth diminished by the fun's disturbing force, and therefore moves in an orbit lefs incurvated than the would defcribe independent of the fun's action. She therefore employs a longer time. If the moon were fo near the earth as almoft to touch it, the fame thing would happen. Therefore fuppofe the moon turning round the earth, almoft in contact with the equator, with her natural undiñurbed periodic time, and that the earth is revolving round its axis in the fame time, the moon would remain continually above the fame fpot of the earth's furface (fuppofe the city of Quito), and a spectator in another planet would fee the moon always covering the fame fpot. Now let the fun act. This will not affect the rotation of the earth, because the action on one part is exactly balanced by the action on another. But it will affect the moon. It will move more flowly round the earth's centre, and at a greater diftarce. It will be left behind by the city of Quito, which it formerly covered. And as the earth moves round from weft to caft, the moon, moving more flowly, will have a motion to the weft with refpect to Quito. In like manner, every particle of water has its gravity diminished, and its diurnal motion retarded; and hence arifes a general motion or current from east to west. This is very diftinctly perceived in the Atlantic and Pacific Oceans. It comes round the Cape of Good Hope, ranges along the coast of Africa, and then fets directly over to America, where it meets a fimilar stream which comes in by the north of Europe. Meeting the fhores of America, it is deflected both to the fouth along the coast of Brazil, and to the north along the North American fhores, where it forms what is called the Gulf Stream, because it comes from the Gulf of Mexico. This motion is indeed very flow, this being fufficient for the ac cumulation of feven or eight feet on the deep ocean; but it is not altogether infenfible.

We may expect differences in the appearances on the western fhores of Europe and Africa, and on the western fhore of America, from the appearances on the eastern coafts of America and of Afia, for the general current obftructs the waters from the western fhores, and fends them to the eastern fhores. Alfo when we compare the wide opening of the northern extremity of the Atlantic Ocean with the narrow opening between Kamtfchatka and America, we fhould expect differences between the appearances on the weft coafts of Europe and of America. The obfervations made during the circumnavigations of Captain Cook and others fhow a remarkable difference. All along the weft coaft of North America the inferior tide is very trifling, and frequently is not perceived.

In the very fame manner, the difturbing forces of the fun and moon form a tide in the fluid air which furrounds this globe, confifting of an elevation and depreffion, which move gradually from eaft to weit. Neither does this tide ever at tain that pofition with refpect to the difturbing planets which it would do were the earth at reft on its axis. Hence arifes a motion of the whole air from caft to weft; and this is the principal cause of the trade winds. They are a little accelerated by being heated, and therefore expanding. They expand more to the weftward than in the oppofite direction, because the air expands on that fide into air, which is now cooling and contracting. Thete winds very evidently fol low the fun's motion, tending more to the fouth or north as he goes fouth or north. Were this motion confiderably affected by the expansion of heated air, we fhould find the air rather coming northward and fouthward from the torrid 3 X 2

zone,

zone, in confequence of its expanfion in that climate. We repeat it, it is almoft folely produced by the aerial tide, and is neceffary for the very formation of this tide. We cannot perceive the accumulation. It cannot affect the barometer, as many think, because, though the air becomes deeper, it becomes deeper only because it is made lighter by the gravitation to the fun. Inftead of preffing more on the cistern of the barometer, we imagine that it preffes lefs; becaufe, like the ocean, it never attains the height to which it tends. It remains always too low for equilibrium, and therefore it fhould prefs with lefs force on the ciftern of a barometer.

There is an appearance precisely fimilar to this in the planet Jupiter. He is furrounded by an atmosphere which is arranged in zones or belts, probably owing to climate differences of the different latitudes, by which each seems to have a different kind of fky. Something like this will appear to a fpectator in the moon looking at this earth. The general weather and appearance of the fky is confiderably different in the torrid and temperate zones. Jupiter's belts are not of a conftant hape and colour; but there often appear large fpots or tracts of cloud, which retain their fhape during feveral revolutions of Jupiter round his axis. To judge of his rotation by one of thefe, we should say that he turns round in 9.55. There is alfo a brighter fpot which is frequently feen, occupying one certain fituation on the body of Jupiter. This is furely adherent to his body, and is either a bright coloured country, or perhaps a tract of clouds hovering over fome volcano. This fpot turns round in 9.51. And thus there is a general current in his atmofphere from east to west.

Both the motion of the air and of the water tend to diminish the rotation of the earth round its axis: for they move flower than the earth, because they are retarded by the luminaries. They muft communicate this retardation to the earth, and must take from it a quantity of motion precisely equal to what they want, in order to make up the equilibrated tide. In all probability this retardation is compenfated by other caufes; for no retardation can be obferved. This would have altered the length of the year fince the time of Hipparchus, giving it a smaller number of days. We fee caufes of compenfation. The continual wafhing down of foil from the elevated parts of the earth muft produce this effect, by communicating to the valley on which it is brought to reft the excess of diurnal velocity which it had on the mountain top.

While we were employed on this article, a book was put into our hands called Studies of Nature, by a Mr Saint Pierre. This author fcouts the Newtonian theory of the tides, as erroneous in principle, and as quite infufficient for explaining the phenomena; and he afcribes all pheno. mena of the tides to the liquefaction of the ices and fnows of the circumpolar regions, and the greater length of the polar than of the equatorial axis of the earth. He is a man of whom we wish to fpeak with refpect, for his conftant attention to final caufes, and the proof thence refulting of the wisdom and goodness of God. For this he is entitled to the greater praife, that it required no fmall degree of fortitude to refift the influence of national example, and to retain his piety in the midft of a people who have drunk the very dregs of the atheism of ancient Greece. This is a fpecies of merit rarely to be met with in a Frenchman of the prefent day; but as a philofopher, M. de St Pierre can lay claim to no other merit except that of having collected many important facts. The argument which he employs to prove that the earth is a prolate fpheroid, is a direct demon. ftration of the truth of the contrary opinion; and the melting of the ice and fnows at the poles cannot produce the

fmalleft motion in the waters. Were there even to times more ice and fnow floating on the northern fea than there is, and were it all to melt in one minute, there would be no flux from it; for it would only fill up the space which it formerly occupied in the water. Of this any person will be convinced, who fhall put a handful of fnow squeezed hard into a jar of water, and note the exact height of the water. Let the fnow melt, and he will find the water of the fame height as before.

TIDE-Waiters, or Tidefmen, are inferior officers belonging to the customhoufe, whofe employment is to watch or attend upon fhips until the cuftoms be paid: they get this name from their going on board fhips on their arrival in the mouth of the Thames or other ports, and fo come up with the tide.

TIEND, in Scots law. See TEIND.

TIERCE, or TEIRCE, a measure of liquid things, as wine, oil, &c. containing the third part of a pipe, or 42 gal. lons.

TIERCED, in heraldry, denotes the fhield to be divided by any part of the partition-lines, as party, coupy, tranchy, or tailly, into three equal parts of different colours or metals.

TIGER, in zoology. See FELIS.

TIGER Wolf, the name by which the hyena is called at the Cape of Good Hope. See HYÆNA.

TIGRIS, a river of Afia, which has its fource near that of the Euphrates in the mountain Tchildir in Turkomania: afterwards it feparates Diarbeck from Erzerum, and Khu. fiftan from Irac-Arabia; and uniting with the Euphrates at Gorno, it falls into the gulf of Baflorah, under the name of Schat el-Arab. This river pafles by Diarbekar, Gezira, Mouful, Bagdad, Gorno, and Bafforah.

TILIA, LIME or LINDEN TREE, in botany: A genus of plants belonging to the class of polyandria, and order of monogynia, and in the natural system ranging under the Columnifera. The calyx is quinquepartite; the corolla pentapetalous; the berry is dry, globofe, quinquelocular, quinque valve, and opening at the bafe. There are four fpecies; the europea and americana, pubefcens and alba.

Te

Til ca.

The europea, or common lime-tree, is generally fup: Coxe's Trapofed to be a native of Britain; but we are informed by Mrvels in Coxe, that Mr Pennant told him (on what authority is not Switzermentioned), that it was imported into England before the land, vol. ii. p. 64. year 1652.

The leaves are heart-fhaped, with the apex produced, and ferrated on the edges; the flowers grow in a thin umbel, from three to nine together, of a whitish colour and a fragrant fmell; very grateful to bees. The wood is light, fmooth, and of a spongy texture, ufed for making lafts and tables for fhoemakers, &c. Ropes and bandages are made of the bark, and mats and ruftic garments of the inner rind, in Carniola and fome other countries.-The lime-tree contains a gummy juice, which being repeatedly boiled and cla.. rified produces a fubitarice like fugar.

TILLEMONT' (Sebaftian le Nain de). See NAIN. TILLER of a SHIP, a strong piece of wood faftened in the head of the rudder, and in fmall fhips and boats called

the helm.

TILLA, in botany: A genus of plants belonging to the clafs of tetrandria, the order of tetragynia, and in the natural fyftem ranging under the 13th order, Succulenta. The calyx has three or four divifions; the petals are three or four, and equal; the capfules three or four, and polyfpermous. There are four fpecies; of which one only, the mufcofa, is a native of England, and is not mentioned among the Scotch plants.

The mufiofa, or procumbent tilla, has proftrate stems, almost

Barrow's works, and Dr Wilkins's Treatife of the Principles Timber and Duties of Natural Religion, and a volume of that divine's Sermons.

TIMBER, wood fit for building, &c. See TREE, and STRENGTH of Materials.

TIMBERS, the ribs of a fhip, or the incurvated pieces of wood, branching outward from the keel in a vertical direction, so as to give strength, figure, and folidity, to the whole fabric. See SHIP-BUILDING, book i. ch. ii.

TIME, a fucceffion of phenomena in the univerfe, or a mode of duration marked by certain periods or meafures, chiefly by the motion and revolution of the fun.

The general idea which time gives in every thing to which it is applied, is that of limited duration. Thus we cannot fay of the Deity, that he exifts in time; because eternity, which he inhabits, is abfolutely uniform, neither admitting limitation nor fucceffion. See METAPHYSICS, no 209.

TIME, in mufic, is an affection of found, by which it is faid to be long or fhort, with regard to its continuance in the fame tone or degree of tune.

Mufical time is diftinguished into common or duple time, and triple time.

Double, duple, or common time, is when the notes are in a duple duration of each other, viz. a femibreve equal to two mirims, a minim to two crotchets, a crotchet to two quavers, &c.

Common or double time is of two kinds. The first when every bar or measure is equal to a femibreve, or its value in any combination of notes of a lefs quantity. The fecond is where every bar is equal to a minim, or its value in lefs notes. The movements of this kind of measure are various, but there are three common diftinctions; the first flow, denoted at the beginning of the line by the mark C; the fecond brisk, marked thus ; and the third very

Tillotson. almoft ere&t, generally red, and grow longer after flowering. The parts of fructification are always three. The leaves grow in pairs, and are fiefhy. It is found on dry heaths in Norfolk and Suffolk, and flowers in May and June. TILLOTSON (John), a celebrated archbishop of Canterbury, was the fon of Robert Tillotfon of Sowerby, in the parish of Hallifax in Yorkshire, clothier; and was born there in the year 1630. He ftudied in Clare-hall, Cambridge; and in 1656 left this college, in order to become tutor to the fon of Edmund Prideaux, Efq; of Ford-abbey in Devonshire. He was afterwards curate to Dr Hacket vicar of Chefhunt, in Hertforde. In 1663, he was prefented by Sir Thomas Barnardiiton to the rectory of Ketton or Keddington in the county of Suffolk; but was the next year chofen preacher to Lincoln's Inn, when he procured Ketton to be bestowed on his curate. He was greatly admired in London for his fermons; and in the fame year was chofen Tuesday lecturer at St Lawrence's church, London, where his lectures were frequented by all the divines of the city, and by many perfons of quality and distinction. In1666, he took the degree of Doctor of Divinity at Cambridge; in 1669, was made prebendary of Canterbury; in 1672, was admitted dean of that cathedral; and three years after, was made a prebendary of St Paul's cathedral, London. In 1679, he became acquainted with Charles earl of Shrewf. bury, whom he converted from Popery; and the next year refused to fign the clergy of London's addrefs of thanks to king Charles II. for not agreeing to the bill of exclufion of the duke of York. In 1683, he vifited the unhappy Lord Ruffel when under condemnation; and attended him in his laft moments on the fcaffold. In 1689, he was inftalled dean of St Paul's; made clerk of the closet to King William and Queen Mary; and appointed one of the commiffioners to prepare matters to be laid before the convocation, in order to a comprehenfion of all Proteftants, as well diffenters as churchmen; but this attempt was fruftrated by the zeal of those members of that body, who refused to admit of any alteration in things confeffedly indifferent. In 1691, Dr Tillotson was, notwithstanding the warmeft remonftrances and intreaties on his part, consecrated archbifhop of Canterbury, and four days after was fworn one of the privy council; their majefties always repofing an entire confidence in his prudence, moderation, and integrity. In 1694, he was feized with a dead palfy, of which he died in the 65th year of his age. He was interred in the church of St Lawrence Jury, London, where a handfome monument is erected to his memory. This learned and pious divine, while living, was greatly inveighed against by the enemies of the revolution. After his death there was found a bundle of bitter libels which had been published against him, on which he had written with his own hand, "I forgive the authors of thefe books, and pray God that he may also forgive them." It is remarkable, that while this truly great man was in a private station, he always laid afide two-tenths of his income for charitable ufes. One volume in folio of Dr Tillotson's fermons was published in his life-time, and corrected by his own hand; thefe Barbeyrac tranflated into French. Thote which came abroad after his death, from his chaplain Dr Barker, made two volumes in folio, the copy of which was fold for 25001 and this was the only legacy he left to his family, his extenfive charity having confumed his yearly revenues as conftantly as they came to his hands. However, King William gave two grants to his widow; the firft of which was an annuity of 400 1. during the term of her natural life, and the fecond of 2001. as an addition to the former annuity. Dr Tillotson wrote fome other works befides his Sermons; and also published Dr

Triple time is when the durations of the notes are triple of each other, that is, when the femibreve is equal to three minims, the minim to three crotchets, &c. and it is marked T.

TIME-Keepers, or Inflruments for measuring Time. See CLOCK, DIAL, WATCH, &C.

Harrifon's TIME-Keeper. See HARRISON and LONGITUDE. TIMOLEON, a celebrated Corinthian general, who reftored the Syracufians to their liberty, and drove the Carthaginians out of Sicily. See SYRACUSE, no 50-54.

TIMON the Sceptic, who is not to be confounded with Timon the Mifanthrope, was a Phliafian, a difciple of Pyrrho, and lived in the time of Ptolemy Philadelphus. He took fo little pains to invite difciples to his school, that it has been faid of him, that as the Scythians fhot flying, Timon gained pupils by running from them. He was fond of rural retirement.; and was fo much addicted to wine, that he held a fuccessful contest with feveral celebrated champions in drinking. Like Lucian, he wrote with farcaftic humour against the whole body of philofophers. The fragments of his fatirical poem Silli, often quoted by the ancients, have been carefully collected by Henry Stephens in his Porfis Philofophica. Timon lived to the age of 90 years.

TIMON, furnamed Mifanthropos, or the Man-hater, a famous Athenian, who lived about 420 B. C. He was one day afked, why he loved the young Alcibiades while he de tefted all the reft of the human race? on which he replied,. "It is because I foresee that he will be the ruin of the Athe

nians."""

Timon.