& X-J - +4—' XT * / ' Edinburgh, March 6, 1810. THE FOLLOWING NEW WORKS WILL SPEEDILY BE PUBLISHED, BY ARCHIBALD CONSTABLE & CO. EDINBURGH, AND CONSTABLE, HUNTER, PARK, & HUNTER, LONDON. I. CALEDONIA: or an Account, Historical and Topographical, of North Bri¬ tain, from the most antient to the present times. By George Chalmers, Esq. F. R. S. Vol. II. Quarto. *** The firet Tulrnne of the above work published (1807), contains the Antient History of North Britain, •ihe second volume, wfilcir appear in March 1810, will detail, after an introduc ory chapier ot 26 sections, the Local History or tio «.Uf!rai sliiies ; beginning with Roxburgh, the most southern snire, and pioceediug, successively, to Berwick, Haouiiuituii, i^a.nhurgh, Linlithgow Reeblesi Selkirk. Dumfries, Kirkcudbright, Wigton, and perhaps Ayrshire: and the Local History of each shire will be given in eight distinct sections1. Of its Name ; 2. Of its Situation anfl Extent - 3. Of its Natural Objects ; 4. Of its Antiquities; 5. Of its Establishment as a Shire ; 6. Of its Civil History; 7. Of its Agriculture, Manufactures, Trade; 8. Of its Ecclesiastical History; the account of each shire concluding with a Supplemental State, which contains, in a Tabular form, the Names of the several parishes, and the number of their Ministers; their Extent and Population in 1756 1791 and 1801; with the Ministers’ Stipends in 1755 and 1798, and their Patrons; forming, what Scotland does not now possess, a sort of Liber Regis. This most interesting work will be completed by the publication of two other volumes. The third will contain the Local History and description of the remaining counties, on ihe plan stated above. The fourth volume will consist of a Topographical Dictionary, containing whatever is interestin'*- re¬ lative to all places and objects of any importance in this part of the United Kingdom. This volume will be preceded by an Historical View of the different Languages spoken in Scotland. II. The GENEALOGY of the EARLS of SUTHERLAND, from the origin of that illustrious House to the year 1630, with the History of the Northern parts of Scotland during that period, by Sir Robert Gordon of Gordonstone, Baronet, continued to the year 1651, by Gilbert Gordon of Sallagh. Published from the Original Manuscript in the possession of the Marchioness of Stafford. Handsomely printed in Folio. *** The public is here presented not only with an accurate genealogical history of the antient house of Sutherland, hut also with a minute detail of the principal transactions which occurred tim ing a pe¬ riod of nearly-600 years, particularly in the counties of Sutherland and Caithness, and the Highlands of Scotland in general. Tne history of these parts, it is presumed, will receive more elucidation from this work than from any which the public is at present possessed oft The whole has been carefully transcribed by the kind permission of the Marchioness of Stafford, from the original manuscript pre¬ served at Dunfobin Castle. An Appendix will he added, containing an inventory of writs of the Earldom, and the work will be illustrated by several Engravings. III. The PEERAGE of SCOTLAND; containing an fl Historical and Genealogi¬ cal Account of the Nobility of that Kingdom, from their Origin to the present Gene¬ ration.^ Collected from the Public Records, and Antient Chartularies of this Nation, the Charters an(i other Writings of the Nobility, and the Works of our best Histo¬ rians. By Sir iAouticr Gf Glenbervie, Baronet. Continued to the present time by J. P. VY ood, Esq. Handsomely Printed in Two Volumes Folio, with the Arms of each Family beautifully Engraven. *** A few Copies arc printed on Large Paper, forming Two Superb Volumes with First Impressions of the Plates; and as the Number printed is very limited, No¬ blemen and Gentlemen who wish to secure copies, are respectfully requested to leave their Names, either with Archibald Constable and Company, Edinburgh, or with Constable, Hunter, Parr, and Hunter, 10, Ludgate Street, London, where Spe¬ cimens of the Work may now be seen. Ihe Plan of the Work is fully detailed in the following Advertisement from ihe Editor.—The Peers of Scotland, the Repre¬ sentatives of dormant, attainted, and extinct titles, and persons connected with them are respectfully informed, that this edition is now in the press. 2 The 2 Works speedily to be Published The first edition was published in 1764. In the introduction, Sir Robert Douglas thus expresses himself: a The necessity of publishing a New Peerage of Scotland, and u the utility of it, is acknowledged by all. The Compiler of the present Work has attempted it on a more regular and accurate plan than has hitherto appeared. How far he has succeeded, the world must judge. But if the most assiduous application 6i for many jears; if a painful inquiry into the public records and antient chartularies; if an unwearied search after every degree of knowledge necessary for carrying on so tc arduous a task,—if these have any merit, or deserve the favour of the public, the Au- <4 thor Hatters himself this Work, on perusal, will not be found deficient. The chief and principal point the Author had in view, and the great object of his attention 44 [was], in a plain and distinct manner, to deduce the history of each family, from Wih ‘^encouragement, which the importance of this species of composition in the history its fi«rfted^ie8Saap;i5SSt,OD> comprising those excluded from this selection, on account VUI TheH^TORY and CHRONICLES at SCOTLAND, by Robert Lind, say of I itscottie. Edited from Antient and Authentic Manuscripts, by John Graham Dal yell. Esq. One Volume Quarto, handsomely printed, with a Portrait of King James V. from an Original Picture. fnAdT DISASTERS at SEA, according to the most An then, -ic Accounts, An tieu t and Modern. Ihrce Volumes Octavo. N. The 4 Works speedily to be Published, &Y« X. The DRAMATIC WORKS of JoHNFoun; with an Introduction and Ex¬ planatory Notes. By Henry Weber,, Esq. In Two Volumes Octavo. *** Tliis author was coeval with Fletcher and Massinger, and others who succeeded Shakespeare. He imitated the latter with a success sufficient to provoke the envy of Ben Johnson, and to excite great admiration from his contemporaries. Notwithstanding their great merit, Ins plays have never, with the exception of two, been reprinted, and are now, for the first time, collected in a uniform edi¬ tion, XI. HISTORY of the REFORMATION in SCOTLAND. By George Cook, D. D. Minister of Laurencekirk, Author of u An Illustration of the General Evidence establishing the Reality of Christ’s Resurrection.” Three Volumes Octavo. XII. RESEARCHES into the ORIGIN and AFFINITY of the GREEK and TEUTONIC LANGUAGES. By A. Murray, F. A.S.E. and Secretary for Foreign Correspondence. One Volume Quarto. *** The immediate object of this work is, to illustrate the early state and connexion of these lan¬ guages, on accurate and philosophical principles. The light which i- 57 -f 0.79 0.00 — 0.80 — 1.62 ~ 2-45 — 3*31 — 4.16 — 5-°4 Difference. 0.78 O.79 0.80 0.82 0.82 c.85 0.86 0.88 . x7 Sir George Shuck- burgh’s ob- fervations compared with De Lee’s rules. The numbers in the firfi: column of this table e.vprefs heights of the quickhiver in the barometer in Engliih inches and decimal parts: the fecond column (hows the equation to be applied, according to the fign prefixed, to 212° of Bird’s Fahrenheit, to find the true boiling point for every fuch Hate of the barometer. The boil¬ ing point for all intermediate flares of the barometer may be had with fufficient accuracy, by taking propor¬ tional parts, by means of the third column of differences of the equations. See Philofophical Tranfadfions, vol. Ixiv. art. 30. j alfo Dr Mafkelyne’s Paper, vol. Ixiv. art. 20. In the following table we have the refult of fif¬ teen different obfervations made by Sir George Shuck- burgh compared with the refult of M. de Luc’s rules. Height of the Baro¬ meter redu¬ ced to the fame tem¬ perature of 50°. Mean Boiling Point by Obferva- Boiling 1 TT . , Point by ^ht De Luc’ of Bal 0~ Rules. meter. Inch. 26.498 27.241 27-954 28.377 28.699 28.898 28.999 29.447 29.805 207, 208, 209, 210, 21 X. 21 I. 21 I, 212, 212, ,07 ,64 87 50 27 50 60 551 95| 208.54 208.84 2I0.03‘ 210.81! 211.34 21 I.67 211.8 i; 212.74 213.!5 Boiling Boiling Point by Point by Obferva-iDe Luc’s Rules Inch. 30.008 30.207 30.489 3°-76.3 30.847 30-957 213.22 213.47 213.58 213.79 214.15: 214.23 214.37! 214.66 214.83: 214.79 214.96 214.96 Sir George Shuckburgh has alfo fubjoined the follotv- ing general table for the ufe of artifls in conftrudting the thermometer, both according to his own oblerva- tions and thofe of M. de Luc. Height of the Barometer 26.0 26.5 27.O 27-5 28.0 28.5 29.0 29-5 30.0 3^-5 31.0 Cor re (ft. of the Boiling Point. — 7.O9 — 6.18 — 5-27 — 4-37 — 348 — 2.59 — 1.72 — c.85 0.00 + 0.85 -f 1.69 Differ¬ ence. .91 •91 .90 .89 .89 .87 .87 .85 .85 .84 Correct, ac¬ cording to M de Luc. -6.83 — 5-93 — 5.04 — 4.16 — 3-31 — 2.45 — 1.62 — 0.80 0.00 + 0.79 + I-57 Differ¬ ence. .90 .89 .88 .87 .86 .83 .82 .80 •79 .78 18 The Royal Society, fully apprifed of the importance Obferva- of adjufting the fixed points of thermometers, appointedtions 1T:a'Je a committee of feven gentlemen to confider of the heft ^ a com‘ method for this purpole ; and their report is publilhed j-he ^oyd in the Phil. Tranf. vol. Ixvii. part ii. art. 37. Society for They obferved, that though the boiling point be pla- adjufting ced fo much higher on fome of the thermometers nowtlle fixect made than on others, yet this does not produce any con-1X)iritS’ fiderable error in the obfervations of the weather, at leal! in this climate 5 for an error of i-J0 in the pofition of the boiling point, will make an error only of half a degree in the pofuion of 920, and of not more than a quarter of a degree in the point of 62°. It is only in nice experiments, or in trying the heat of hot liquors, that this error in the boiling point can be of much im¬ portance. In adjufting the freezing as well as the boiling point, the quickfilver in the tube ought to be kept of the fame heat as that in the ball. When the freezing point is placed at a confiderable diftance from the ball, the pounded ice fhould be piled to fuch a height above the ball, that the error which can arife from the quickfilver in the remaining part of the tube not being heated equally with that in the ball, {hall be very fmall, or the obferved point muft be corredled on that account ac¬ cording to the following table : Heat of the Air. 42u 52 62 72 82 Corre&ion. .00087 .00174 .00261 .00348 •0°435 I9 Table for cor edhng the freezing point. The corre&ion in this table is expreffed in 1 oooth parts of the diftance between the freezing point and the furface of the ice : e. gr. if the freezing point Hands leven inches above the furface of the ice, and the heat of the room is 62, the point of 320 (hould be placed 7X00261, or .or8 of an inch lower than the obfer¬ ved point. A diagonal fcale will facilitate this correc¬ tion. 3E Vol. XX. Part II. The 20 'the qukk- filver in the tube ought to be heated to the fame degree as that in the ball. 21 The tubes ought to be cylindri¬ cal and ca¬ pillary. * L.eco??sde Phyf. Exp. tom. iv. P 37<>- •22 The num¬ ber of de¬ grees into which the feale ought to be divi¬ ded. T H E [ 402 ] THE that in trying the heat of feelings, for it is what few can ever experience. There would be feveral great advantages gained, we allow, by adopting the freezing point of mercury. It is the low- eft degree of cold to which mercury can be applied as a and it would render unneceffary the ufe of the 23 At what po'nt the fcale ought to com¬ mence. The committee obferv , „ ^ liquors, care Pnould be > iken that the quickfilver in the tube of the thermometer be heated to the fame degree as that in the ball •, or if this cannot be done conveniently, the obferved heat flrould be co:reeled on that account ; for the manner of doing which, and a table calculated for this purpofe, we mull refer to their excellent report in the Phil. Trank vol. Ixvii. part ii. art. 37. With regard to the choice of tubes, they ought to be exactly cylindrical. But though the diameter ftiould vary a little, it is eafy to manage that matter in the manner propofed by the Abbe Nollet *, by making a {mall portion of the quickfilver, e. gr. as much as fills up an inch or half an inch, Hide backward and forward in the tube j and thus to find'the proportions of all its inequalities, and from thence to adjuft the divifions to a fcale of the moft perfefl equality. 'The capillary tubes are preferable to others, becaide they require fmaller bulbs, and they are alfo more fenfible, and lefs brittle. The moft convenient fize for common experiments has the internal diameter about the 40th or 50th of an inch, about nine inches long, and made of thin glafs, that the rife and fall of the mercury may be better feen. _ indicate the various gravity of the atmo- rometer. fphere, or the height of the barometer. But as he does not fay that the inlfrument has been tried with the de- fired fuccefs, we forbear to delcribe it. Thole who wilh to know his ideas refpeCting it may confult the Philofo- plucal TranfaClions, vol. Ixxi. p. 524. The thermometers hitherto delcribed are very limited in their extent; they indeed point out to us the lowell degrees of heat which are commonly obferved even in cold climates, but they by no means reach to thole de¬ grees of heat which are very familiar to us. 'I he mer¬ curial thermometer extends no farther than to 6co of Fahrenheit’s fcale, the heat of boiling mercury } but we are lure that the heat of folid bodies, when heated to ignition, or till they emit light, far exceeds the heat of boiling mercury. In order to remedy this defeCl, Sir Ifaac Newton, whofe genius overcame thofe oblfacles which ordinary „ m:n(is could not approach, attempted by an ingenious the fcale of experiment to extend the kale to any degree required, the thermo-Having heated a mafs of iron red hot, and expoled it to the cold air, he ooferved the time which elapfed till it became cold, or of the fame temperature with the air ; and w1'en the heat fo far decreafed that he could apply fome known meafure (as a thermometer) to it, he obferved the degrees of heat loft in given times •, and thence drew the general conclufion, that the quantities of heat loft in given fmall fpaces are always proportional to the heat remaining in the body, reckoning the heat to be the excefs by which it is warmer than the ambient air. So that taking the number of minutes which it took to cool after it came to a determined point in an arithmetical progreffion, the decrements of the heat of the iron would be continually proportional. Having by this proportion found out the decrements of heat in a given time after it came to a- known point, it was eafy, by carrying upwards the fame proportion to the begin¬ ning' of its cooling, to determine the greateft heat which the body had acquired. This proportion of Sir Ilaac’s was found by Dr Martine to be fomewhat inaccurate. The heat of a cooling body does not decreafe exafUy in proportion to that which the body retains. As the re- fult of many obfervations, he found that two kinds of proportion took place, an arithmetical as well as the geometrical proportion which Sir Ifaac Newton had 33 Sir liaac Newton’s method of sneter. Mi’tine’i EJJuys. Thermo¬ meter, Thermopy- Ise 34 adopted ; namely, that the decrements of heat were partly proportional to the times (that is, that quantities of heat are loft in equal times), as well as partly in proportion to the remaining heat ; and that if thefe two are added together the rule will be lufficiently accurate. By the geometrical proportion which Sir liaac Newton adopted he difeovered the heat of metals red hot or in fufton. This method, fo fuccefsfully purfued by Sir Ifaac, Mr Wedg- was lufticient to form a fcale of high degrees of heat, wood’sther- but was not convenient for pvadtical purpofes. ^_c_ mometer tor cordingly the ingenious Mr Jofiah Wedgwood, who isj.*^ well known for his great improvement m the art of pot- gibes of tery, apphed himfelf in order to difeover a thermometer heat which might be eafily managed. After many experi¬ ments recorded in the Phiioiophical Tranfadfions, but which it is unneceflary to detail in this place, he has in¬ vented a thermometer which marks with much precifion the diffe'rent degrees of ignition from a dull red heat vi- fible in the dark to the beat of an air-lurnace. This thermometer is extremely fimple. It confifts of two rulers fixed upon a fmooth flat plate, a little farther afunder at the one end than at the other, leaving an open longitudinal fpace between them. Small pieces of alum and clay mixed together are made of fuch a lize as juft to enter at the wide end ; they are then heated in the fire along with the body whole heat we with to determine. The fire, according to the degree of heat it contains, diminiflies or contracts the earthy body, fo that when applied to the wide end of the gage, it will Hide on towards the narrow end, lefs or more according to the degree of heat to which it has been expofed. That this inftrument may be perfectly undeiflood, vve have given a reprefentation of it in fig. 9. ABCD is a ^ ^ fmooth flat plate •, and EF and GH tw© rulers or fiat b pieces, a quarter of an inch thick, fixed fiat upon the plate, with the fides that are towards one another made perfecfly true, a little farther afunder at one end EG than at the other end FH : thus they include be¬ tween them a long converging canal, which is divided on one fide into a number of fmall equal parts, and which may be confidered as performing the offices both of the tube and fcale of the common thermometer. \\. PhllofopM- is obvious, that if a body, fo adjufted as to fit exa6fly ca^ 1 ranf- at the wider end of this canal, be afterwards diminifhed in its bulk bv fire, as the thermometer pieces are, it will then pafs further in the canal, and more and more fo according as the diminution is greater j and converfe- ly, that if a body, fo adjufted as to pafs on to the nar¬ row' end, be afterwards expanded by fire, as is the cafe with metals, and applied in that expanded ftate to the fcale, it will not pafs fo far j and that the divifions on the fide will be the meafures of the expanfions of the one, as of the contraftions of the other, reckoning in both cafes from that point to which the body was adjuft¬ ed at firft. I is the body whofe alteration of bulk is thus to be meafured. This is to be gently pufhed or flid along to¬ wards the end FH, till it is flopped bv the converging fides of the canal. See CHEMISTRY, N° 141 2. THERMOPYLAE, in Ancient Geography, a nar¬ row pafs or defile, between the wafh of the Sinus Mali- acus on the eaft, and fteep mountains, reaching to Oeta, made dreadful by unpaflable woods, on the weft \ lead¬ ing from Theffuly to Locris and Boeotia. Thefe moun¬ tains THE [ 405 ] . T .H E Thcr«i tains divide Greece in the middle, in the fame manner troop from village to village in a waggon, from which Thelklian 11 as the A pennine does Italy j forming one continued they pertormed their pieces. Alceltis was the hr it Theurgy> ThelPis- j-idge from Leucale on the welt to the i'ea on the eait, tragedy they performed at Athens, 536 iJ. U bee * ' with thicket* and rocks interfperfed 5 that perfons even Theatre. . prepared for travelling, much lefs an army encumbered THESSALIAN CHAIR, To ca.led from Ineiiilyr with barrcxaae, cannot eafily find a c immodious palfage. where chairs of this figure were moil in ufe j it is re- In the valley verging towards the Sinus Maliacus, the commended by Hippocrates * in place ot a machine tor dc road is only fixty paces broad ; the only military way reducing a recent luxation of the ihoulder bone. *he' 7 • for an army to pals, if not obftruaed by an enemy; and back of this chair is perpendicular to the feat, as Galen therefore the place is called Py/.e, and by others, on ac- tells us; by which conitruftion it is diftmguiihed and count of its hot water, Thermopylce Ennobled by the accommodated to the operation. brave (land made by Leonidas and 300 Spartans againft 1HESSALY, a country of Greece, \shofe ooun a~ the whole army of Perfia ; and by the bold refolution ries have been different at different periods. Properly of blind Euthycus, choofing rather to fall there in fpeaking, Iheffaly was bounded on the iouth by the fiyht, than return to Sparta, and efcape the common louthern parts of Greece, or Grtecia Propria ; call, by danger. Famous alfo for the Amphiayones, the com- the iEgean ; north, by Macedonia and Mygdonia; and nion council or dates general of Greece, affembling well, by Illyricum and Epirus. It was generally di- there tivice a-year, fpring and autumn. For an account vided into four feparate provinces, I heffiliotis, Pehtfgi- of the battle of Thermopylae at which Leonidas with otis, Idiaeotis, and Phthiotis, to which lome add M^j* a handful of men engaged the Perfian army, fee nefia. It has been feverally called JEmonia, Pe/cfgi- Sparta. cum-> Argos, Hellas, Argeia, Dryopis, Pelafgia, Pyr- THESE A, in antiquity, feads celebrated by the A- rhcea, &c. The name of Theffaly is derived from L»mpri- thenians in honour of 1'hefeus, confiding of fports and Theffalus, one of its monarchs.^ Theffdy is famous for games, with mirth and banquets. Such as were poor a deluge which happened there in the age of Deucalion. and unable to contribute to them were entertained at Its mountains and cities are alfo celebrated, fuch as the public expence. Olympus, Pelion, Offa, Lariffa, &c* _ Argonauts THESEUS, a famous hero of antiquity, ranked were partly natives of Theffaly. The inhabitants of the among the demigods, whofe hidory is fabulous. He country palled for a treacherous nation, fo that fake mo- was the reputed fon of ASgeus king of Athens. He ney was called Thejfalian coin, arid a perfidious aftion a threw Sciron, a cruel robber, down a precipice ; faden- Ihejfalian deceit. 1 heflaly was originally governed by ed Procrudes tyrant of Attica to a bending pine, which kings, till it became fubjeft to the Macedonian mo- being let loofe tore him afunder ; killed the Minotaur narchs. The cavalry was univerfally edeemed, and the kept in the labyrinth by King Minos, in Crete ; and people were fuperditious and addifted to the dudy of by the aflidance of that prince’s daughter, Ariadne, magic and incantations. See Lucan, lib. vi. ver. 438* who gave him a clue, efcaped out of that labyrinth, &c. ; Dionyf 219 ; Curt. lib. iii. cap. 2. •, JElian, Var. and failed with his deliverer to the ide of Naxos, where Hi/l. lib. iii. cap. 1.; Pauf. lib. iv. cap. 36. lib. x. cap. 1.; he had the ingratitude to leave her. Meta, lib. ii. cap. 3.; Jujhn, lib. vii. cap.6.; Diod. iv. Thefeus afterwards overcame the Centaurs, fubdued l heffaly is now called Janna, a province o( Euiopean the Thebans, and defeated the Amazons. He affided Turkey, bounded by Macedonia on the north, by the his friend Pirithous in his expedition to the infernal re- Archipelago on the ead, by Achaia or Livadia on the gions to carry off Proferpine ; but was imprifoned by fouth, and by Epirus on the wed. Pluto, till he was releafed by Hercules. He is alfo faid IHE1 IS, in Pagan mythology, the \vife of Ocea-» to have edablifhed the Idhmean games, in honour of nus, and the mother of Nereus ami Doris, who were Neptune ; to have united the twelve cities of Attica ; married to eacli other ; and from this marriage fprung and to have founded a republic there, 1236B. C. Some the nymphs of the earth and foa.. Among the fea time after, taking a voyage into Epirus, he was feized nymphs there w’as one named Thetis the Younger, who by Aidonius king of the Molodians ; meanwhile Me- excelled all the red in beauty, and for whom Jupiter nedheus rendered himfelf mader of Athens. But at conceived luch a padion, that he relolved to efpoule length Thefeus being releafed from prifon, retired to her : but being informed by the Dedinies that die Scyros, where King Lycomedes eaufed him to be would bring forth a fon who would rife above his 'atlur, thrown from the top of a rock. Thefeus had feveral he married her to Pe’eus. To their nuptials all die wives ; the fird of whom was Helena the daughter of gods and goddeffes were invited except D-fcord, who, Tyndarus ; the fecond, Hypolita queen of the Ama- to be revenged for this contempt, threw a golden apple zons ; and the lad, Phedra dder to Ariadne, who pu- into the affembly, on which was engraven, For the fair~ nifhed him for his infidelity to her filler, by her incedu- cjl. Juno, Pallas, and Venus, difpuied for this apple ; ous paffion for his fon Hippolitus. but Paris being chofen to decide the difference, adjudged THESIS, a general pofition which a perfon advan- it to \enus. From this marriage of Thetis and Peleus ces, and offers to maintain. In taking- degrees in uni- fprung Achilles. verfities, the candidates are generally obliged to write a THEURGY, a name which the ancients thefis, which they mud afterwards defend. gave to that facred part of magid which we fometimes THESIUM, Base Fluellin ; a genus of plants call white magic, or the white art. belonging to the clafs of pentandria, and order of mo- The word is formed from ©soj, “ God,” and egyovf nogynia. See Botany Index. “ work q. d. the art of doing divine things, or \\ru s THESPIS, a famous Greek tragic poet, and the which God alone can do: or the power of workj >g ex* fird renrefenter of tragedy at Athens. He carried his traordinary and fupernatural things, by invokin ' tee names- T H I [ 4o6 Theurgy names of God, faints, angels, $t'c. Accordingly, thofe Ti !ije W^° ^ave w“tten ot niagic in general, divide it into - -,-i- -- ' »three parts: the firrt whereo is called theurgy, as ope¬ rating by divine or celeftial means; the fecond, natural magic, performed by the powers of nature ; and the third, comprehending necromancy, forcery, and witch¬ craft or magic, performed by the affiftance of demons or departed men. See Magic. THIBET. See Tibet. THIGH. See x^lnatomy, N° 58. THINKING, a general name for any aft or opera¬ tion of the mind. See Metaphysics. THIRLAGE. See Law, N°clxx. 12—18. THIRST, an uneafy fenfation arifing from a defici¬ ency of the faliva to moiflen the inward parts of the mouth. Hence arifes a Tlrong defire for drink; and third; is a fymptom generally attending fevers of all kinds.—Third is bed allayed by acids •, water kept a while in the mouth, then fpit out, and repeated as re¬ quired ; a bit of bread chewed with a little water, which latter may be gradually fwallowed ; if the perfon is very hot, brandy is the bed for holding in the mouth, but diould be fpit out again : except in fevers, large draughts of cold water are hurtful. Prefervation againjl Hunger and THIEST. See Hunger. THISTLE, a name applied to different genera and fuecies of plants belonging chiefly to the fyngenefia clafs. See Carduus, Onopordum, Serratula, Son- CHUS, and alfo Dipsacus, Botany Index. Order of the THISTLE, or of St Andrew, a military order of knighthood in Scotland, the rife and inditution of which is varioufly related by different authors. Lef- ley bifliop of Rofs reports, that the night before the battle between Athelflan king of Northumberland and Hungus king of the Pifts, a bright crofs, in form of that whereon St Andrew (the tutelar faint of Scotland) fuffered martyrdom, appeared to Hungus •, who having gained the viftory, ever after bore the figure of that crofs on his banners. Others aflert, that Achaius king of Scotland fird indituted this order, after having made the famous league offenfive and defenfive with Charle¬ magne king of France. But although the thiflle had been acknowledged as the fymbol of the kingdom of Scotland from the reign of Achaius, yet fome refer the beginning of this order to Charles VII. of France. Others place the foundation of it as low as the year 15°°. The chief and principal enfign is a gold collar com- pofed of thidles and fprigs of rue interlinked with amu¬ lets of gold, having pendent thereto the image of St Andrew with his crofs, and the motto, Nemo me im- pune lacesset. “ No body fliall provoke me writh impunity.” The ordinary or common enfign worn by the knights is a dar of four filver points, and over them a green cir¬ cle, bordered and lettered with gold, containing the faid motto, and in the centre is a thidle ; all which is embroidered on their, left bread, and worn with the col¬ lar, with a green ribband over the left flioulder, and brought under the right arm ; pendent thereto is the image of St Andrewq with his crofs, in a purple robe, within an oval of gold enamelled vert, with the former motto •, but fometimes they wear, encircled in the fame manner, a thidle crowned. Thifde , II Thomas. ] T H O About the time of the Reformation, this order was dropped, till James II. of Great Britain refumed it, by creating eight knights. The Revolution unfettled it , _ again ; and it lay neglefted, till Queen Anne, in 1703, redored it to the primitive defign, of twelve knights of St Andrew. I HL APSI, Bastard-cress, or mithridate-mufard; a genus ol plants belonging to the clafs of tetradynamia. See Botany Index. THOLOUSE. See Toulouse. THOM ALANS, Thomists. See Christians of St Thomas. IHOMAS Aquinas. See Aquinas. St Thomas's Day, * feflival of the Chridian church, obferved on December 21. in commemoration of St Tho¬ mas the apoflle. St THOMAS of Canterbury's Day, a feflival of the Romifli church, obferved on December 29. in memory of 1 homas Becket archbifliop of Canterbury, who was murdered, or, as the Romanifls lay, martyred, in the reign of King Henry II. THOMAS the Reymour, called alfo Thomas Lermont, and Thomas of Erceldon, was born at Erceldon, a vil¬ lage near Melrole in LVeedale, in what year is uncer¬ tain ; but he w'as an old man when Edward I. was car¬ rying on war in Scotland. The charafter of Lermont as a prophet, and which wTas common to him with Linus, Orpheus, and other early poets in many countries, arofe, if we may believe Mackenyie in his Lives of Scottilh Writers, from his having conferences with Eliza, a nun and prophetefs at Haddington. Lermont put her prediftions into verfe, and thus came in for his lhare of the prophetic fpirit. None of thefe ancient prophecies now remain ; but the Pinker tort's following, which pretends to be one of them, is given Account of from a manufeript of the time of Edward I. or II. The seottiJh countefs of Dunbar is the lady famous for the defence o{^oets- her cafile againd the Englidi. Her proper title was Countefs of March ; but it was common in thefe times to Ryle a nobleman from his chief refidence. Thus Gil¬ bert Strongbow, earl of Pembroke, is called Earl of Striguil, from his refidence at Striguil-caflle, near Chep- dow, Monmouthlhire, &c. La Counteffe de Donbar demande a Thomas de Effe- doune, quant la guere d'Efcoce prendreit fyn. E yl la repoundy, et dyt. When man as mad a kyng of a capped mon. When mon is levere other mons thyng than is owen. When londe thouys forefl, and fored ys felde. Wrhen hares kendles othe herflon. When Wyt and WTille werres togedere. Wrhen mon makes flables of kyrkes: and deles caflles wyth dyes. When Rokefbourh nys no burgh ; ant market is at Forwyleye. Wrhen the aide is gan, and the newx is come that doue noht. WTen Bambomme ys donged with dede men, WThen men ledes men in ropes to buyen ant to fellen. When a quarter of vvhaty whete is chaunged for a colt of ten markes. WThen prude prikes, ant pees is leyd in prifoun. WThen a Scot ne may hym hude afe hare in forme, that the Englydi ne dial hym fynde. When / Thomas II Thomfon. T H O [ When ryht ant wrong aftente the togeJere. When laddcs weddeth lovedie'. When Scottes flen fo fade, that for faute of fhip, by drouneth hemfelve. When fhal this be ? Nouther in thyne tyrae, ne in myne. Ah comen, ant gone, Withinne twenty wynter ant on. In fact, the prophecies of Lermont appear to have been merely traditional ; nay, it feeins doubtful if he ever pretended to fuch folly, notwithdanding Mac- kenyie’s dory of Eliza. The reverence of the people for a learned and refpectable charafter feems to have been the foie foundation of Thomas’s claim to prophecy. But, in the 16th century, prophecies were made, and afcribed to him, as well as others given to Bede, Mer¬ lin, Stc. (a). They were printed at Edinburgh, 1615 j reprinted 1680, and 1742. THOMISM. See Aquinas. THOMSON, James, an excellent Britifh poet, the fon of a . Scotch divine, was born in the diire of Rox¬ burgh in 1700, and was educated in the univerfity of Edinburgh with a view to > the minidry. But his ge¬ nius inclining him to the dudy of poetry, which he foon found would be incompatible with that of theology, or at lead might prevent his being provided for in that way in his own country, he relinquiihed his views of engaging in the facred fundtion, and repaired to London in confequence of fome encouragement which he had received from a lady of quality there, a friend of his mother. The reception he met with wherever he was intro¬ duced, emboldened him to rilk the publication of his excellent poem on Winter.—This piece was publidied in 1726 ; and from the univerfal applaufe it met with, Mr Thomfon’s acquaintance was courted by people of the fird tade and fafhion. But the chief advantage which it procured him was the acquaintance of Dr Bundle, afterward bilhop of Derry, who introduced him to the late lord chancellor Talbot; and fome years after, when the elded fon of that nobleman was to make his tour on the continent, Mr Thomfon was chofen as a proper companion for him. The expectations which his Winter had raifed, were fully fatisfied by the fuc- cedive publications of the other feafons •, of Summer, in the year 1727 •, of Spring, in the following year.*, and of Autumn, in a quarto edition of his works, in 1730. Bebde the Seafons, and his tragedy of Sophonilba, written and aCted with applaufe in the year 1729, he had, in 1727, publidied his poem to the memory of Sir Ifaac Newton, with an account of his chief dif- coveries; in which he was adided by his friend Mr Gray, a gentleman well verfed in the Newtonian philo- fophy. That fame year the refentment of our merchants, for the interruption of their trade by the Spaniards in America, running very high, Mr Thomfon zealoufly took part in it, and wrote his Bwtannia, to roufe the nation to revenge. 407 ] T H O With the honourable Charles Talbot, our author vi- Thomfon. dted mod of the courts in Europe, and returned with v— his views greatly enlarged j not only of exterior nature and the works of art, but of human life and manners, and of the conditution and policy of the feveral dates, their connexions, and their religious inditutions. How particular and judicious his obfervations were, we fee in his poem on Liberty, begun foon after his return to England. We lee at the lame time to what a high pitch his care of bis country was raifed, by the com¬ panions he had all along been making of our happy go¬ vernment with thofe of other nations. To infpire his fellow-fubje61s with the like fentiments, and fhow them by what means the precious freedom we enjoy may be preferved, and how it may be abufed or lod, he employ¬ ed two years in compofing that noble wrork, upon which he valued himfelf more than upon all his other writings. On his return to England with Mr Talbot (who loon after died), the chancellor made him his fecretary of briefs j a place of little attendance, fuiting his retired indolent w'ay of life, and equal to all his wants. From this office he w7as removed, when death, not long after, deprived him of his noble patron. He then found him¬ felf reduced to a ftate of a precarious dependence. In this fituation, having created fome few debts, and his cre¬ ditors finding that he had no longer any certain fuppoit, became inexorable; and imagined by confinement to force that from his friends, which his inodeffy would not permit him to alk. One of thefe occafions furniffi- ed Quin, the celebrated aXor, with an opportunity of difplaying the natural goodnefs of his heart, and the dff- intereffednefs of his friendffiip. Hearing that Thom¬ fon was confined in a fpunging houfe for a debt of about 70I. he repaired to the place 5 and, having inquir¬ ed for him, was introduced to the bard. Thomfon was a good deal difconcerted at feeing Quin, as he had al¬ ways taken pains to conceal his wants j and the more fo, as Quin told him he was come to fup with him. His anxiety upon this head was however removed, upon Quin’s informing him, that, as he fuppofed it would have been inconvenient to have had the fupper drefl'ed in the place they were in, he had ordered it from an adjacent tavern ; and, as a prelude, half a dozen of claret was introduced. Supper being over, and the bottle circulating pretty brifkly, Quin laid, “ It is time now7 we ftiould balance accounts.” This aftonilhed Thomfon, w'ho imagined he had fome demand upon him j but Quin perceiving it, continued, “ Mr Themfon, the pleafure I have had in perufing your works I cannot effimate at lefs than a hundred pounds, and I infill upon now acquitting the debt.” On faying this, he put down a note of that value, and took his leave, without wailing for a reply. The profits arifing from his works were not inconfider- able ; his tragedy of Agamemnon, aXed in 1738, yield¬ ed a good fum. But his chief dependence was upon the prince of Wales, who fettled on him a handfome allowance, and honoured him with many marks of par¬ ticular favour. Notwithftanding, this, however, he was (a) Sibilla and Baniffer Anglicus are mentioned in the time of Edward IV. (MSS. Cot. Dom. A. IX.) A long Latin prophecy of Bridlington is there given. Waldhave and Eltraine feem alfo Englilh prophets. In the whole colleXion, therefore, Thomas is the only Scottilh one. T HO [ 408 ] T H O iTliomfon. was refufed a licence for his tragedy of Edward and Eleanora, which he had prepared for the itage in the year 1736, for fome political reafons. Mr Thomfon’s next performance was the Malque of Alfred, written in the year 1740 jointly with Mr Mallet, by the com¬ mand of the prince of Wales, for the entertainment of his royal highnefs’s court at Clifden, his fummer refi- dence. Mr Thomfon’s poem, entitled the Caftle of Indo¬ lence, was his laft work publiihed by himfelf; his tragedy of Coriolanus being only prepared for the theatre, when a fatal accident robbed the world of one of the bell of men and bed of poets. He would commonly w7alk the diftance between London and Richmond (where lie lived) with any acquaintance that offered, with whom he might chat and red himfelf, or perhaps dine by the way. One fummer evening being alone in his walk from town to Hammerfmith, he had over-heated him¬ felf, and in that condition imprudently took a boat to carry him to Kew; apprehending no bad confequence from the chill air on the river, which his w^alk to his houfe, towards the upper end of Kew-lane, had always hitherto prevented. But now the cold had fo feized him, that the next day he was in a high fever. This, however, by the ufe of proper medicines, was removed, fo that he was thought out of danger •, till the fine wTealher having tempted him to expofe himfelf once more to the evening dews, his fever returned with violence, and with fuch fymptoms as left no hopes of a cure. His death happened on the 27 th of Augufl I743' • Mr Thomfon had improved his tafte upon the fined originals, ancient and modern. The autumn was his favourite feafon for poetical compofition, and the deep filence of the night he commonly chofe for his fludics. The amufement of his leifure hours wTere civil and natu¬ ral hiflory, voyages, and the bed relations of travellers. Though he performed on no indrument, he was paffion- ately fond of mufic, and would fometimes liden a full hour at his window to the nightingales in Richmond gardens 5 nor w7as his tade lefs exquifite in the arts of painting, fculpture, and architecture. As for the more didinguidung qualities of his mind and heart, they bed appear in his waitings. There his devotion to the Su¬ preme Being, his love of mankind, of his country, and friends, diine out in every page j his tendernefs of heart was fo unbounded, that it took in even the brute crea¬ tion. It is not knowm, that through his whole life he ever gave any perfon a moment’s pain, either by his writings or otherwife. He took no part in the political fquabbles of his time, and was therefore refpeCted and left undidurbed by both fides. Thefe amiable virtues did not fail of their due reward ; the applaufe of the public attended all his produdions, and his friends loved him w ith an enthufiadic ardour. “ As a writer (fays D> Johnfon), he is entitled to one praife of the highed kind j his mode of thinking, and of expreffing his thoughts, is original. His! lank verfe is no more the blank verfe of Milton, or of any other poet, than the rhymes of Prior are the rhymes of Cowley. His numbers, his paufes, his diCfion, are of his own growth, without tranfcription, without imita¬ tion. He thinks in a pecubar trail , ai d thinks always as a man of genius j he looks round on Nature and on life with the eye which Nature beftows only on a poet j jfobnf'jn's Lives of t,bg_ Loots. the eye that didinguiffies, in every thing reprefented to Thomfon its view, whatever there is on which imaginat’on can de¬ light to be detained, and with a mind that at once com- ^10rnliu!,f prebends the vad, and attends to the minute. The reader of the Seafons wonders that he never faw before what Thomfon (hews him, and that he never yet has felt wffiat Thomfon impreffes.” His tedamentary executors were the lord Lyttelton, whofe care of our poet’s fortune and fame ceaied not w’ith his life; and Mr Mitchell, a gentleman equally noted for1 the truth and condancy of his private friend- drip, and for his addrefs and ipint as a public miniller. By their united interelis, the orphan play of Coriolanus was brought on the dage to the bed advantage ; from the profits of which, and the fale of manufcripts and other effeCts, a handfonre fum was remitted to his fiders. His remains wTere depofited in the church of Richmond, under a plain done, without any inlcription. A hand- feme monument was ereCted to him in Wedminder abbey in the year 1762, the charge of which was de¬ frayed by the profits arifing from a fplendid edition of all his w'orks in qto; Mr Millar the bookfeller, wTho had purchaled all Mr Thornton’s copies, giving up his property on this grateful occafion. A monument has alfo been ereCted to him at the place of his birth. THOR, the elded and braved of the fons of Odin and Frea, was, after his parents, the greated god of the Saxons and Danes while they continued heathens. They Henry's believed, that Thor reigned overall the aerial regions, Hiftory of which compofed his immenfe palace, confiding of 54° ^ Fir halls; that he launched the thunder, pointed the light-part’4. ! ning, and direCted the meteors, winds, and dorms. To him they addreffed their prayers for favourable winds, refrediing rains, and fruitful feafons ; and to him the fifth day of the week, wffiich dill bears his name, was confecrated. THORAX. See Anatomy. White 01 Haw THORN. See Crategus, Bcr- TANY Index. Thorn, a torvn of Poland, in Regal Pruffia, and in the palatinate of Culm. It wras formerly a Hanfeatic tow'n, and dill enjoys great privileges ; is large and w^ell fortified ; but part of the fortifications, and a great number of houfes, were ruined by the Swedes, in 1703. It is feated on the Vidula, and contains 10,000 inhabi¬ tants. E. Long. 18. 42. N. Lat. 53. 6. THORNBACK. See Raia, Ichthyology Index. THORNHILL, Sir James, an eminent Englidi TyiEiLnary painter, was born in Dorfetdiire in 1676, of an ancient of Painters. family ; but was condrained to apply to fome profeffion by the didreffes of his father, who had been reduced to the neceffity of felling his family edate. His inclina¬ tion direCted him to the art of painting; and on his arrival at London he applied to his uncle, the famous Dr Sydenham, who enabled him to proceed in the dudy of the art under the direction of a painter who was not very eminent. However, the genius of Thornhill made ample amends for the inlufficiency of his initruCtor, and by a happy application of his talents he made fo great a progrefs, that he gradually rofe to the highed reputa¬ tion. His genius was well adapted to hidorical and allego- ncal compofitions; he pollened a fertile and fine inven¬ tion ; and he Iketched his thoughts with great eafe, freedom, and fpirit. He excelled alfo equally in por¬ trait, T H R r 409 ] T H R Tliornliill trait, peifpective, and architedure j Jliewed an excel- Thrnce ^Cnt ta^e ^°r ^e^gn» an<^ a ^ree an^ ^rm Penc^* 1 ‘Had he been fo fortunate as to have ftudied at Rome and Venice, to acquire greater correftnefs at the one, and a more exact knowledge of the perfedlion of colour¬ ing at the other, no arlift among the moderns might perhaps have been his fuperior. Neverthelefs, he was fo eminent in many parts of his proteflion, that he mult for ever be ranked among the belt painters of his time j and his performances in the dome of St Paul’s church at London, in the hofpital at Greenwich, and at Hamp- ton-court, are fuch public proofs of his merit as will con¬ vey his name to pofterity with great honour. This painter lived in general efteem ; he enriched himfelf by the excellence of his works 5 was appointed flate-painter to Oueen Anne, from whom he received the honour of knighthood ; had the Angular fatisfadtion to repurchafe his family eftate j and was fo much di- ftinguilhed as to be eledted one of the members of par¬ liament. He died in 1732. THOROUGH-wax, in Botany. See Bupleurum. THOTH, or Theut, (called by the Phoenicians Taaut, by the Greeks Hermes, and by the Romans Mer- cunj'), was a Phoenician of very fuperior talents, and one of the civilizers of mankind. He was prime mini- fter to Ofiris, whom, after his death, he deified 5 and he was himfelf deified by his countrymen the Egyptians, for the benefits that he had rendered to the human race. See Mercury, Mythology, N° 34. and Polythe¬ ism, N° 18. TPIOUGHT, a general name for all the ideas con- fequent on the operations of the mind, and even on the operations themfelves. See Metaphysics. Thought, in compofition. See Oratory, Part I. and II. THOUINIA, a genus of plants belonging to the clafs of diandria, and order of monogynia. See Botany Index. THRACE, a country very frequently mentioned by the Greek and Latin writers, deriving its name, ac¬ cording to Jofephus, from Tiras one of the fons of Ja- phet. It was bounded on the north by Mount Haem us j on the fouth, by the .ffigean fea j on the weft, by Ma- cedon and the river Strymon \ and on the eaft, by the Euxine fea, the Hellefpont, and the Propontis.—The Thracian Cherfonefus is a peninfula inclofed on the foulh by the iEgean lea, on the weft by the gulf of Melas, and on the eaft by the Hellefpont; being join¬ ed on the north to the continent by a neck of land about 37 furlongs broad. The inland parts of Thrace are very cold and barren, the fnow lying on the moun¬ tains the greateft part of the year ; but the maritime provinces are produflive of all forls of grain and necef- faries for life 5 and withal fo pleafant, that Mela com¬ pares them to the moft fruitful and agreeable countries of Alia. The ancient Thracians were deemed a brave and warlike nation, but of a cruel and favage temper ; be¬ ing, according to the Greek writers, ftrangers to all hu¬ manity and good nature. It was to the Thracians, however, that the Greeks were chiefly indebted for the polite arts that flouriftied among them j for Orphaeus, Lmus, Mufaeus, Thamyris, and Eumolpus, all Thra- ci-ijis, were the firft, as Euftathius informs us, who charmed the inhabitants of Greece with their eloquence Vol, XX. Part II. and melody, and perfuaded them to exchange their Thrace, fiercenefs for a focfable life and peaceful manners j nay, lina.l-mg., great part of Greece was anciently peopled by Thra- v cians. Tereus, a Thracian, governed at Daulis in Pho-> cis, where the tragical ftory of Philomela and Progne w;as adled. From thence a body of Thracians piffled over to Euboea, and pofleflfed themfelves of that illand. Of the lame nation were the Aoncs, Tembices, and Hyanthians, who made themfelves mailers of Boe. tia : and great part of Attica itfelf was inhabited by Thra¬ cians, under the command of the celebrated Eumolpus. It is not therefore without the utmoft ingratitude and injuftice that the Greeks ftyle them Bariarians, fince to them chiefly they were indebted both for the peo¬ pling and polilhing ol their country. Thrace was anciently divided into a number of petty ftates, which wrere firft fubdued by Philip of Macedon. On the decline of the Macedonian empire, the country fell under die pow'er of the Romans. It continued under fubjedlion to them till the inuption of the Turks, in whofe hands it ftill remains. THRASHING, in Agriculture, the operation by which corn is feparated from the ftraw. This opera¬ tion is performed in a variety of w'ays, fometimes by the feet of animals, fometimes by a flail, and fometimes by a machine. The moft ancient method of feparating the corn from the ftraw w^as by the hoofs of cattle or horfes. This was pradlifed by the Ifraelites, as we find from the books of Mofes; it wras alfo common among the Greeks and Romans*. Flails and thrafhing machines were al-* Pliny, fo not uncommon among thefe nations f. The flail xv“‘*.^c" which was ufed by the Romans, called bcculus, fujlis,;;; or pertica, was probably nothing more than a cudgel or^. Col. ii. pole. The thralhing machine, which was called tribula 21 • Tibull. or tribulum, and fometimes traha, was a kind of fledge’; 5; made of boards joined together, and loaded with ftone iron. Horfes were yoked to this machine, and a man W'as//S,,.er> ii., feated upon it to drive them over the Iheaves of corn. xx. 495. Different methods are employed in different countries for feparating the corn from the ftalk. In the greateft: part of France the flail is ufed ; but in the foutheru diitridts it is generally performed by the feet of animals. Animals are alfo ufed for the fame purpofe in Spain, in Italy, in the Morea, in the Canaries, in China, and in the vicinity of Canton, where the flail is alfo fometimes ufed. It appears that in hot climates the grains do not adhere lo firmly to the ftalk as in cold countries, and therefore may be more eafily feparated. This will explain the reafon why animals are fo frequently employed in hot countries for treading out the corn *, whereas in cold climates we know they are feldom tried, and have no reafon to fuppofe that they would anfwer the purpofe. In the Me of France in Africa, rice and wheat are thraftied wuth poles, and maize with flicks ; for it has not been poflible to teach the negroes the ufe off the flail. The animals ufed for treading out corn are, oxen, cows, horfes, mules, and even affes when the quantity is not great. The operation is performed in this man¬ ner : The {heaves, after being opened, are fpread in fuch a manner that the ears of the corn are laid as much uppermoft as poflible, and a man, Handing in the centre, holds the halters of the cattle, which are made to trot round as in a manege j whiift other men with 3 F forks THU [41 ,Hiraflung, forks (hake the ftraw up from time to time, and the cat- v tie are trotted ovef it again and again till they have beaten out all the grain. This method is expeditious enough ; but befides bruifing a confiderable quantity of corn, it requires a great many cattle, and injures the legs of the horfes and mules, which are preferred before cows and oxen for this work. The flail is undoubtedly a much better inftrument for thrafliing corn than the feet of animals, for it feparates the grain from the ftraw and hulks both more effectual¬ ly and more expeditioufly j yet it is liable to many ob¬ jections. It is a very laborious employment, too fevere indeed even for a ftrong man ; and as it is ufually the intereft of the thralher rather to thrafti much than to thralh clean, a good deal of corn will generally be left upon the ftrawn It is therefore an objeCt of great im¬ portance in hulhandry to procure a proper machine for feparating the corn from the ftraw. The firft thralhing machine attempted in modern times, of which we have received any account, was in¬ vented in Edinburgh by Mr Michael Menzies about the year 1732. It confifted of a number of inftruments like flails, fixed in a moveable beam, and inclined to it at an angle of ten degrees. On each fide of the beam in which the flails were fixed, floors or benches were pla¬ ced for fpreading the fheaves on. The flails were mo¬ ved backwards and forwards upon the benches by means of a crank fixed on the end of an axle, which made about 30 revolutions in a minute. The fecond thralhing machine was invented by Mr Michael Stirling, a fanner in the parilh of Dunblane, Perthlhire. Of this difeovery we have received a very accurate and authentic account from his fon, the reve¬ rend Mr Robert Stirling minifter of Crieff. It is an old proverb, that neceflity is the mother of in¬ vention. This was verified on the prefent occafion. Be¬ fides his ordinary domeftic fervants, Mr M. Stirling had occafion fometimes to hire an additional number to thralh out his grain, and frequently found it difficult to procure fo many as he needed. This naturally led him to refleft whether the operation of thralhing could not cafily be performed by machinery. Accordingly, fo early as the year 1753, under the pretence of joining in the amufements of his children, he formed in miniature a Water mill, in which two iron fprings, made to rife and fall alternately, reprefented the motion of two flails, by which a few ftalks of corn put under them might be fpeedily thraffied. This plan he executed on a fcale fufficiently large within twro years after, making the fprings about ten feet long, each of which had one end firmly ferew^ed into a folid plank, and the other termi¬ nated in a round batoon of folid iron, two feet long and above an inch in diameter. Under thefe the (heaves were conveyed gradually forward in a narrow channel or trough, by paffing between twx> indented horizontal cylinders, fimilar to thofe now ufed in the moft of the thralhing mills in that part of the country, and called feeders. In this manner the thralhing was executed completely, and with confiderable rapidity 5 but as the operation was performed on a low floor, and no me¬ thod contrived for carrying off the ftraw, the accumu¬ lation of it produced fuch confufion, and the removal of it w^as attended with fuch danger, that this fcheme was very foon entirely abandoned. The mortification arifing from difappointment, and efpecially the feoffs of 0 ] T H R his neighbours, for what was univerfally accounted an Thrafliing. abfurd and ridiculous attempt, ferved only to ftimulate ' v——' the exertions of the inventor to accomplilh his defigns on another plan. Laying afide therefore the iron fprings with the feed¬ ers, and all the apparatus adapted to them, he retained only an outer or water wheel, with an inner or cog wheel moving on the fame axle: to this inner w heel, which had 48 teeth or cogs, he applied a vertical trun¬ dle or pinion, with feven notches, the axle of which paffed through a floor above the wffieel, and having its upper pivot fecured in a beam fix feet above that floor. At the diftance of three feet three inches above the floor two ftraight pieces of fquared wood, each four feet long, paffed through the axle of the trundle at right angles, forming four arms, to be moved round hori¬ zontally. To the extremities of thefe arms w ere fixed four iron plates, each 20 inches long, and eight broad at the end next the arms, but tapering towards a point at the other end. This large horizontal fly, conftitu- ting four thraffiers, was inclofed within a wooden cylin¬ drical box three feet and a half high and eight in dia¬ meter. On the t®p of the box was an opening or port (two or three ports were made at firft, but one was found fufficient) eight inches wdde, and extending from the circumference a foot and a half towards its centre, through which the corn (heaves defeended, being firft opened and laid one by one on a board with two ledges gently declining towards the port j on which board they were moderately preffed down with a boy’s hand, to prevent them from being too haftily drawn in by the repeated ftrokes of the thraffiers. Within the box w^as an inclined plane, along which the draw' and grain fell down into a wide wire riddle two feet fquare, placed immediately under a hole of nearly the fame fize. The riddle received a jerk at every revolution of the fpindle from a knob placed on the fide of it, and w’as inilantly thruft backward by a fmall fpring preffing it in the op- pofite dire&ion. The (liort ftraw, wuth the grain and chaff which paffed through the wide riddle, fell imme¬ diately into an oblong ftrait riddle, which hung with one end raifed and the other depreffed, and was moved by a contrivance equally fimple as the other; and ha¬ ving no ledge at the lower end, the long chaff which could not pafs through the riddle dropped from thence to the ground j while the grain and moft of the chaff falling through the riddle into a pair of common barn- fanners that flood under it on the ground floor, the ftrong grain, the weak, and the chaff, were all fepa- rated with great exaftnefs. The fanners were moved by a rope or band running circuitoufly in a (hallow niche cut on the circumference of the cog-wheel. The ftraw collefted gradually in the bottom of the box over the wide riddle, and through an opening two and a half feet wide, and as much in height, left in that fide of the box neareft the brink of the upper floor, was drawn down to the ground with a rake by the perfon or perfons employed to form it into (heaves or rolls. Such was the thraftiing mill invented by Mr Michael Stirling, which, after various alterations and improve¬ ments he completed in the form now deferibed, A. D. 1758. By experiment it was found that four bolls of oats, Linlithgow meafure, could be thralhed by it in 25 minutes. From that period he never ufed a common flail in thrafhing, except for humbling or bearding bar- THRASHING MACIHINK Tlute PA'XXN - T H R [ 41 Thrafliing. ley. In every other kind of grain he performed the L“—V" whole operation of thrathing with the mill j and con- ' tinned always to ufe it till 1772, when he retired from bufmefs, and his thralhing mill became the property of his fecond fon, who continues to ule it with, equal ad¬ vantage and fatisfa&ion. Several machines were con- ftru&ed on the fame plan, particularly one near Stir¬ ling, under Mr Stirling’s direction, for Mr Moir of Leckie, in 1765, which, we underhand, has been ufed ever fince, and gives complete fatisfa&ion to the pro¬ prietor. There was another erefted in 1778 by Mr Thomas Keir (in the parilh of Muthil and county of Perth), wTho has contrived a method of bearding barley with it: and by the addition of a fmall fpindle with Ihort arms contiguous to the front of the box, and moved by a band common to it and the great fpindle to which it is parallel, the ftraw is fliaken and whirled out of the box to the ground. That this machine did not come immediately into general ufe, was owing partly to the fmallnefs of the farms in that part of the country, whofe crops could eafdy be thrafhed by the few hands necef- farily retained on them for other purpofes; and chiefly to an apprehenfion that the machine could only be moved by water j an apprehenlion which experience proves to be entirely groundlefs. The machine how¬ ever, w’as, ingenious, and did great credit to the worthy inventor, and certainly deferved a better fate than it was deftined to undergo. A third thrafhing mill was invented in 1772, by two perfons nearly about the fame time, and upon the lame principles. The inventors were, Mr Alderton who lived near Alnwick, and Mr Smart at Wark in North¬ umberland. The operation was performed by rubbing. The Iheaves were carried round between an indented drum of about fix feet diameter, and a number of in¬ dented rollers arranged round the circumference of the drum, and attached to it by means of fprings; fo that while the drum revolved, the fluted rollers rubbed the corn off- from the ftraw by rubbing againft the flutings of the drum. But as a confiderable quantity of the grain was bruifed in palling between the rollers, the ma¬ chine was foon laid afide. In 1776 an attempt was made by Mr Andrew Mei- kle, an ingenious millwright in the parilh of Tyning- ham, Eaft Lothian, to conftruft a new machine upon the principles which had been adopted by Mr Menzies already mentioned. This confifted in making joints in the flails, which Mr Menzies had formed without any. But this machine, after much labour and expence, was loon laid afide, on account of the difficulty of keeping it in repair, and the fmall quantity of work performed, which did not exceed one boll or fix Winchefter bulhels of barley per hour. Some time after this, Mr Francis Kinloch, then junior of Gilmerton, having vifited the machine invented in Northumberland, attempted an improvement upon it. He inclofed the drum in a fluted cover •, and inftead of making the drum itfelf fluted, he fixed upon the outfide of it four fluted pieces of wood, which by means of fprings could be raifed a little above the circumference of the drum, fo as to prefs againft the fluted covering, and thus rub off the ears of corn as the Iheaves palled round between the drum and the fluted covering. But not finding this machine to anfwer his expe&ation (for it bruifed the grain in the fame manner as the Northum- 1 j t H R berland machine did), he fent it to Mr Meikle, that he 1 might, if poflible, rectify its errors. ~»' ‘ Mr Meikle, who had long directed his thoughts to this fubjeft, applied himfelf with much ardour and per- feverance to the improvement and correction of this ma¬ chine j and after fpending a good deal of time upon it, found it was conftruCted upon principles fo erroneous, that to improve it was impracticable. At length, however, Mr Meikle’s own genius invent¬ ed a model, different in principle from the machines which had already been conftruCted. This model was made in the year 1785 5 and in the following year the firft thralhing machine on the fame principles was ereCt- ed in the neighbourhood of Alloa, in the county of Stirling, by Mr Gedrge Meikle the fon of the inven¬ tor. This machine anfwered completely the wilhes of Mr Stein, the gentleman for whom it was ereCted, who gave the molt ample teftimony of his fatisfaCtion both to the inventor and to the public. The fame of this difeovery foon fpread over the whole country, and a great many farmers immediately applied to Mr Meikle, defiring to have thralhing mills ereCted on their farms. The difeovery, it appeared, would be profitable, and it was reafonable that the inventor Ihould enjoy the profits of his invention. He accordingly applied for a patent-, which, after confiderable expence, arifing from the op- pofition of fome perfons, who claimed a lhare in the dil- covery, was granted.—Thefe machines are now becom¬ ing very common in many parts of Scotland, and are increafing very confiderably in number every year over all the united kingdom. We will now endeavour to deferibe this machine iu its moft improved ftate j which is fo fimple that with the afliftance of a plate, exhibiting the plan of eleva¬ tion, fig. 1. the ground plan, fig. 2. and the 3d Ihowing its effential parts in a diftinCt manner, we hope it will DXXX' * be eafily underftood by all our readers who have not had an opportunity of feeing it. The power employed for turning that part of the machine which feparates the corn from the ftraw is produced by four wheels (when moved by horfes), the teeth of which move in one ano¬ ther and turn the drum, on which four fcutchers are fixed. The Iheaves are introduced between two fluted rollers, which hold them firm, and draw them in gradual¬ ly, while the fcutchers ftrikeoff the grain from the ftraw as it paffes through. This will fuifice for a general idea of this machine. We will now be more parti¬ cular. The large fpur-wheel A, fig. 1. and 2. which has Fig. 1. an* 276 cogs, is horizontal, and moves the pinion B, which *• has 14 teeth. The pinion B moves the crown-wheel C, which has 84 teeth $ the wheel C moves a fecond pinion D, which has 16 teeth ; and the pinion D moves the drum HIKL. The drum is a hollow cylinder three feet and a half diameter, and placed horizontally ; on the outfide of which the fcutchers are fixed by ftrong ferew bolts. The fcutchers confift of four pieces of wood, faced on one fide with a thin plate of iron, placed at an equal diftance from each other, and at right angles to the axis of the drum. The iheaves are fpread on an inclined board F, fig. 3* from which they are introduced between two fluted rol¬ lers GG made of cart iron, about three inches and a half in diameter, and making about 35 revolutions in a minute. As thefe rollers are only about three quarters 3 F 2 T HR [4 c- of an inch diftant from the fcutchers or leaves of the drum HIKL, they lerve to hold the iheaves faft, while the fcutchers a, b, c, d, moving with prodigious veloci¬ ty, feparate the grain completely from the draw, and at the fame time throw out both grain and draw upon the concave rack M, lying horizontally with Header parallel ribs, fo that the corn paffes through them into a hopper N placed below. From the hopper it paffes through a harp or riddle O into a pair of fanners P, fnm which, in the mod improved machines, it comes out clean and fit for the market. The draw, after be¬ ing thrown by the fcutchers a, b, c, d, into the rack, is removed from it by a rake QRST into a place contigu¬ ous V. The rake confids ot four thin pieces of wood or leaves ; on the end of each ol thele leaves is ranged a row of teeth e,fg,h, five inches long. The rake moves in a circular manner in the concave rack, while the teeth catch hold of the draw, and throw it out of the rack. Thefe are all the effential parts of the ma¬ chine ; the red may be eafily underdocd by the refer¬ ences to the Plate. W is the horfe-courfe, N° I, which is 27 feet diameter. X is the pillar for lupporting the beams on which the axle of the fpur-wheel is fixed. YYY are three fpindles for moving the two fluted rol¬ lers, the rake, and fanners. To the defcription now given we have only to add, that the drum has a cover¬ ing of wood Z at a fmall didance ^bove it, for the pur- pofe of keeping the {heaves clofe to the fcutchers. The advantages of this machine are many. As the drum makes 300 revolutions in a minute, the four fcutchers together make 200 drokes in the fame fpace of time. From fuch power and velocity, it is evident that much work mud be performed. When the horfes go at the rate of two and one-third miles per hour, from three to fix bolls will be thralhed ; but as the quantity thradied will be lefs when the draw' is long than when it is fhort, we lhall take the average at four bolls. One gentleman, whofe veracity and accuracy we can depend on, affures us, that his mill thradied 63 bolls in a day j by which, w'e fuppofe, he meant 10 hours. To prove the fupeiior advantage of this machine to the common method of thrafhing with flails, a gentleman ordered two equal quantities of oats to be thraflied by the mill and by flails. When the corn was cleaned and meafur- ed, he obtained one-fixteenth more from the flieaves thradied by the mill than from thofe thraflied by the flail. We are alfo informed by another gentleman who has dudied this machine with much attention, and cal¬ culated its advantages with care, that, independently of having the corn much cleaner feparated from the draw than is ufually done by dails, there is a faving of 30 or 40 per cent, in the expence of thrafhing. ‘ The number of perfons requifite for attending the mill when working is fix: One perfon drives the horfesj a fecond hands the fheaves to a third, who unties them, while a fourth fpreads them on the inclined boards and preffes them gently between the rollers; a fifth perfon 12 ] T H R is neceffary to riddle the corn as it falls front the fanners, Tlirajliine and a iixlh to remove the draw (a). || ^ This machine can be moved equally well by water , Tbr01ie- wind, or hories. Mr Meikle has made fuch improve- ' ments on the wind-mill as to render it much more ma¬ nageable and convenient than formerly; and wre are in¬ formed many wind-mills are now erecting in different parts ot the country. As to the comparative expence of thefe different machines, the ereftkin of the horfe machine is leaft j but then the expence of employing hories muff be taken into confideration. One of this kind may be erected for 70I. A water mill will cod 10I. more on account of the expence of the water-wheel. A wind-mill will cod from 200I. to 300I. iterling. THRAVE of COHN, an expredion denoting 24 fheaves or four fhocks of fix fheaves to the fhock ; though in fome countries they only reckon 12 dieaves to the. thrave. iHRASYRULUS, a renowned Athenian general and patriot, the deliverer of his country from the yoke of the 30 tyrants, lived about 294 B. C *. * See At~ THRASYMENUS lacus, in Ancient Geography,tica, N° a lake of Etruria, near Perufia, and not far from the^S—174* Jiber, fatal to the Romans in the Punic war. Now // Logo de Perugia in the Ecclefiadical State. iHREAD, a fmall line made up of a number of fine fibres of any vegetable or animal fubdance, fuch as flax, cotton, or filk j from which it takes its name of linen, cotton, or filk thread. THREATENING LETTERS. Knowingly to fend any letter without a name, or with a fidtiiious name, demanding money, or any other valuable thing, or threatening (without any demand) to kill or fire the houfe of any perfon, is made felony without benefit of clergy. And fending letters, threatening to accufe any perfon of a crime punifliable with death, tranfportation, pillory, or other infamous punifhment, with a view to extort from him any money or other valuable chattels, is punifliable by flatute 30 Geo. II. cap. 24. at the dif- cretion of the court, with fine, imprifonment, pillory, whipping, or tranlportation for feven years. rl HRESHING. See Thrashing. THRIFT. See Statice, Botany Index. IHRINAX, Small Jamaica Fan-palm, a genus of plants belonging to the clafs of palmse. See Botany Index. THRIPS, a genus of infe&s belonging to the order of hemiptera. See Botany Index. THROAT, the anterior part of an animal, between the head and the flioulders. '1 HROAT-wort. See Campanula, Botany //*- dex. THRONE, a royal feat or chair of date, enriched with ornaments of architedlure and fculpture, raifed on one or more deps, and covered with a kind of canopy. Such are the thrones in the rooms of audience of kings and other fovereigns. THROSTLE. (a) We add, on the authority of an experienced farmer, that of the fix perfons neceffary to attend the thrafhing machine, only two can in judice be charged to the account of the machine ; namely, the perfon who manages the horfes, and the one who feeds the machine : For in the ufual mode of thradiing by the dail, it requires the fame number of perfons as the thradiing machine does to clear an equal quantity of corn from the chaff in the fame time. THU [ 413 ] THU Throftle !! Thucy¬ dides. Lernpri- ere's Dic¬ tionary. THROSTLE. See Turdus, 1 Ornithology In- THRUSH. SeeTuRDUs, | dex. Thrush, or Aphtha. See Medicine Index, i THRYALLIS, a genus of plants belonging to the clafs decandria, and order of monogynia j and in the natural fyftern ranging under the 38th order, Tricoccce. See Botany Index. THUANUS, Jacobus Augustus, youngeft fon of the prefident de Thou, was tamous for hjis erudition. He was born in 1553 and having finilhed his Itudies and travels, was made prefident a-mortier, and took poffeflion thereof in 1595. He was employed in feveral important offices of Hate, and in reforming the univer- fity of Paris. He wrote the hiflory of his own time in Latin, from the year 1543 to 1608, in 138 books j a wrork, both for fubjefl and ftyle, worthy of the ancients. He alfo left memoirs of his own life, belides poems $ and died at Paris, 1617. TPIUCYDIDES, a celebrated Greek hiftorian, was born at Athens 471 B. C. He was the fon of Olorus, and grandfon of Miltiades, who is thought to have been defcended from Miltiades the famous Athenian general, and to have married the king of Thrace’s daughter. He was educated in a manner fuitable to his quality, that is, in the Itudy of philofophy and eloquence. His mailer in the former was Anaxagoras, in the latter An¬ tiphon 5 one, by his defcription in the eighth book of his Hiltory, for power of fpeech almoft a miracle, and feared by the people on that account. Suidas and Pho- . tius relate, that when Herodotus recited his hiltory in public, a falhion in ufe then and many ages after, Thu¬ cydides felt fo great a Hing of emulation, that it drew tears from him j infomuch that Herodotus himfelf took notice of it, and congratulated his father on having a fon who Ihowed fo wonderful an affeftion to the Mufes. Herodotus was then 29 years of age, Thucydides a- bout 16. When the Peloponnelian war began to break out, Thucydides conje&ured truly, that it would prove a fubjedl worthy of his labour j and it no fooner com¬ menced than he began to keep a journal. This explains the reafon why he has attended more to chronological order than to unity of delign. During the fame war he was commiffioned by his countrymen to relieve Amphi- polis } but the quick march of Bralidas the Lacedaemo¬ nian general defeated his operations j and Thucydides, unfuccefsful in his expedition, was banilhed from A- thens. This happened in the eighth year of this cele¬ brated war 5 and in the place of his banilhment the ge¬ neral began to write an impartial hiftory of the import¬ ant events which had happened during his adminillra- tion, and which Hill continued to agitate the feveral Hates of Greece. This famous hiflory is continued only to the 21H year of the war, and the remaining part of the time till the demolition of the walls of Athens was defcribed by the pen of Theopompus and Xenophon. Thucydides wrote in the Attic dialed!, as being poffef- ied of moH vigour, purity, elegance, and energy. He fpared neither time nor money to procure authentic ma¬ terials •, and the Athenians, as well as their enemies, furniffied him with many valuable communications, which contributed to throw great light on the different tranfadlions of the wTar. His hiflory has been divided into eight books 5 the lafl of which is imperfedt, and fuppofed to have been written by his daughter. The hiflorian of Halicarnaffus has often been com- Ttmcy- pared with the fon of Olorus, but each has his peculiar t of the mountains of Tibet as in Switzerland at the Tickell. ^00t ^Ps> a glandular fwelling in the throat — V ‘ . commonly called goitre. The language fpoken in Tibet is different from that of the Tartars. The aftronomers are acquainted with the motion of the heavenly bodies, and able to cal¬ culate eclipfes; but the lamas are generally ignorant; few of them can read, much lefs underhand Their an¬ cient books. 11BULLUS, Aulus Albius, a Roman knight, and a celebrated Latin poet, was born at Rome 43 B. C. He was the friend of Horace, Ovid, Macer, and other great men in the reign of Auguftus. He accompanied Meffala Corvinus in his expedition againft the ifland of Corcyra : but falling lick, and being unable to fupport the fatigues of war on account of the weaknefs of his conlfitution, he quitted the profeflion of arms, and re¬ turned to Rome, where he died before the year 17 j when Ovid fhowed his grief for his death by writing a fine elegy upon him. Tibullus wrote four books of ele¬ gies, which are hill extant: they are written in a ten¬ der and agreeable ftyle, and in very elegant Latin. Mu- ret and Jofeph Scaliger have written learned and curi¬ ous commentaries on the works of this poet. The belt edition of Tibullus is that of Janus Bronckhufius, pu- bhihed at Amfterdam in 1708, in one volume quarto. We have an Englifh poetical verfion by Mr Grainger. TIBUR, in Ancient Geography, a town of Latium, pleafantly fituated on the Anio. Here Horace had his villa and houie j and here he wifhed to end his days. Here Adrian built an extraordinary villa called Tibur- ttna, inferibed with the names of the provinces and of the moft confiderable places, (Spartian) 5 near which Zenobia had a houfe called Zenobia, (Trebellius, Pollio). Hither Auguftus often retreated on account of its falu- brity, (Suetonius): for which it is greatly recommend- -ed, (Martial). Anciently, when the Romans had far extended their territory, it was the utmoft place of ba- nilhment, (Ovid). It had a temple of Hercules 5 and therefore called Hercu/eum. In the temple was a li- brary, (A. Gellius). Now Tivoli in the Campagna di Roma, on the Teverone. 1ICINUS, in Ancient Geography, a river in Infubria, rifing in Mount Adula, traverfmg the Lacus Verbanus fouthwards, and falling into the Po near Ticinum. Be¬ tween this river and the Po Hannibal gained his firft viaory over the Romans under P. Scipio. The general himfelf efcaped with the utmoft difficulty, and that by the bravery of his fom the firft S. ipio Africanus. Now the lejino, rifing in Mount Godard, running fouth through the Lago Maggiore and Milan, by Pavia, into the Po. TICK. See Acarus, Entomology Index. TICKELL, Ihomas, an excellent Engliffi poet, was the fon of the Reverend Richard Tickelf, and was born in 1686, at Bridekirk in Cumberland. He was educated at Queen’s college, Oxford, of which he was made fellow j and while he continued at that univerfity, he addreffed to Mr Addifon a complimentary copy of verfes on his Opera of Rofamond, which introduced him to an acquaintance with that gentleman, who difeover- ing his merit, became his fincere friend. On Mr Ad¬ difon being made fecretary of ftate, he appointed Mr J ickell his under-fecretary 5 and on his being obliged to refign that office on account of his ill health, he xe- 1 6 ] T I D commended him fo effectually to Mr Craggs his fuccef- Xi. keIi for, that he was continued in his poft till that gentle- |j * mans death. In 1724, Mr Jickell was appointed fe- Tide, cretary to the lords jufticts in Ireland, and enjoyed that place as long as he lived. He wrote feme poems, which, when feparately publiftied, met with a favourable reception, and paffed through feveral editions : they are now printed in the fecond volume of the Minor Poets. After Mr Addifon’s death Mr Tickell had the care of the editioB of his works printed in 4 vols. 410 j to which he prefixed an account of Mr Addifon’s life, and a poem on his death. Mr Tickell died in the’ year 1740. IICKERA, a confiderable article of merchandile in Jezzan in Africa j it is valued by travellers as a porta¬ ble and highly falubrious food. It is a preparation of pounded dates, and the meal of Indian corn, formed into a pafte, and highly dried in an oven. TrCKSEED, Sun-flower. See Coreopsis, Bo¬ tany Index. TICUNAS. See Poison. TIDE, is a word which expreffes that rifing and falling of the waters which are obferved on all maritime coafts. There is a certain depth of the waters of the ocean which wmuld obtain if all were at reft : but obfervation (hows that they are continually varying from this le¬ vel, and that fome of thele variations are regular and periodical. \ft, It is obferved, that on the fhores of the ocean, and in bays, creeks, and harbours, which communicate freely with the ocean, the waters rife up above this mean height twice a-day, and as often fink below it, forming what is called a flood and an ebb, a high and low water. The whole interval between high and low w^ater is call¬ ed a tide ; the water is faid to flow and to ebb j and the rifing is called the flood-tide, and the falling is called the EBB tide. id, It is obferved, that this rife and fall of the wa¬ ters is variable in quantity. At Plymouth, for inftance, it is fometimes 21 feet between the greateft and leaf! depth of the water in one day, and fomelimes only 12 feet. Thefe different heights of tide are obferved to fuc- ceed each other in a regular feries, diminifhing from the greateft to the leaft, and then increafing from the leaft to the greateft. The greateft is called a spring tide and the leaft is called a neap tide. ’, ^d. This feries is completed in about 15 days. More careful obfervation (hows that two feries are completed in the exatt time of a lunation. For the fpring tide in any place js obferved to happen precifely at a certain in¬ terval 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, more accurately fpeaking, it is obferved that the fpring tide always happens when the moon has got a certain number of degrees eaftw’ard of the line of conjundlion and oppofition, and the neap tide happens when ftie is a certain number of degrees from her firft or laft quadrature. Thus the whole feries of tides appears to be regulated by the moon. 4*//, It is oblerved that high water happens at new and full moon, when the moon has a certain deter¬ mined pofition with refpedt to the meridian of the place of obfervation, preceding or following the moon’s fouthing t i d r 41 Tide, fouthing a certain interval of time; which is con- fiant with refpett to that place, but very different in different places. $t/i, The time of high water in any place appears to be regulated by the moon j for the interval between the time of high water and the moon’s foitthing never changes above three quarters of an hour, whereas the in¬ terval between the time of high water and noon changes fix hours in the courfe of a fortnight. 6//q The interval between two fucceeding high wa¬ ters is variable. It is leaft of all about new and full moon, and greatefl when the moon is in her quadra¬ tures. 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 is fhorteft about new and full moon, being then about ,24h 31''■> about the time of the moon’s quadratures it is 25h 27'. Thefe values are taken from a mean of many obi'ervations made at Barbadoes by Dr Mafke- lyne. llh, The tides in fimilar circumdances are greateft when the moon is at her fmallefi diftance from the earth, or in her perigee, and, gradually diminifhing, are fmall¬ efi when (lie is in her apogee. 8^, The fame remark is made with refpeft to the fun’s diftance, and the greateft tides are obferved during the winter months of Europe. 9//;, The tides in any part of the ocean increafe as the moon, by changing her declination, approaches the ze¬ nith of that place. 10th, 'The tides which happen while the moon is above the horizon are greater than the tides of the fame day when the moon is below the horizon. Such are the regular phenomena of the tides. They are important to all commercial nations, and have there¬ fore been much attended to. It is of the tides, in all probability, that the Bible fpeaks, when God is faid to fet bounds to the fea, and to fay, “ thus far fhall it go, and no farther.” Homer is the earlieft profane author who fpeaks of the tides. Indeed it is not very clear that it is of them that he fpeaks (in the 12th book of the Odyffey) when he fpeaks of Charybdis, which rifes and retires thrice in , every day. Herodotus and Diodorus Siculus fpeak more diftinftly of the tides in the Red fea. Pytheas of Mar- feilles is the firft who fays any thing of their caufe. Ac¬ cording to Strabo he had been in Britain, where he muff have obferved the tides of the ocean. Plutarch fays ex- piefsly that Pytheas aferibed them to the moon. It is fomewhat wonderful that Ariftotle fays fo little about the tides. The army of Alexander, his pupil, were ftart- led at their firft appearance to them near the Perfian gulf; and w^e ftiould have thought that Ariftotle would be well informed of all that had been obferved there. But there are only three paffages concerning them in all Arirtotle’s writings, and they are very trivial. In one place he fpeaks of great tides obferved in the north of Europe , in another, he mentions their having been aferi¬ bed by fome to the moon ; and in a third, he fays, that the tide in a great fea exceeds that in a fmall one, I he Greeks had little opportunity of obferving the tides. The conquefts and the commerce of the Romans gave them more acquaintance with them. Csefar fpeaks of them in the 4th book of h!s Gallic War. Strabo, arter Pofidonius, claffes the phenomena into dailv. VOL. XX. Part II. 7 ] T I D ly, and annual. He obferves, that the fea rifes as the Tide, moon gets near the meridian, whether above or below v— the horizon, and falls again as (he rifes or falls; alfo, that the tides increafe at the time of new and full moon, and are greateft at the fummer fclftice. Pliny explains the phenomena at fome length ; and fays, that both the fun and moon are their caufe, dragging the rvaters along with them (B. II. c. 97). Seneca {Nat. ^ucjl. III. 28.) fpeaks of the tide with corredlnefs ; and Macrobius {Sonin. Scip. I. 6.) gives a very accurate defeription of their motions. It is impoftible that fuch phenomena ftiould not exer- cife human curiofity as to their caufe. Plutarch {Plant. P/uV. UL 17.), Galileo {Sy/l. Hand. Dial. 4.), Ric- cioli in his Ahnagejl, ii. p. 374, and Gaffendi, ii. p. 27. have collefled moil of the notions of their predeceffors on the fubje£t; but they are of fo little importance, that they do not deferve our notice. Kepler fpeaks more like a philofopher {De Stella Mortis, and Epit. AJlron. p. 555-)* He fays that all bodies attraft each olher, and that the waters of the ocean would all go to the moon were they not retained by the attra&ion of the earth ; and then goes on to explain their elevation under the moon and on the oppofite fide, becaufe the earth is Ids attracted by the moon than the nearer waters, but more than the waters which are more remote. "The honour of a complete explanation of the tides was referved for Sir Ifaac Newton. He laid hold of this clafs of phenomena as the mod inconteftable proof of univerfal gravitation, and has given a moft beautiful and fynoptical view of the whole fubjedt ; contenting him- felf, however, with merely exhibiting the chief conic- quences of the general principle, and "applying it to the phenomena with lingular addrefs. But the wide (teps taken by this great philofopher in his inveftigation leave ordinary readers frequently at fault : many of his af- fumptions require the greateft mathematic xl knowledge to fatisfy us o( their truth. The academy of Paris there¬ fore propofed to illuftrate this among other parts of the principles of natural philofpphy, and publiftied the the¬ ory of the tides as a prize problem. This produced three excellent diflertations by M‘Laurin, Dan. Bernoulli, and Euler. Aided by thefe, and chiefly by the lecond’ we fhall here give a phyfical theory, and accommodate it to the purpofes of navigation by giving the rules of calculation. We have demonftrated in ©ur diflerta- tions on the phyfical principles of the celeftial mo¬ tions, that it is an unexcepted faft, that every particle of matter in the folar fyftem is actually ckflefted toward e\ery other particle ; and that the defiedlion of a parti¬ cle of matter toward any diftant fphere is proportional to the quantity of matter in that fphere dire&ly, and to the fquare of the diftance of the particle from the centre of that fphere inverfely : and having found that the hea- vmels of a piece of terreflrial matter is nothing but the fuppofed. opponent to the force which we exert in car¬ rying this piece of matter, we conceive it as poffefiing a property, that is, diftinguifhing quality, manifelted by its being gravis or heavy. This is heavinefs, gravitas gravity ; and the manifeftation of this quality, or the event in which it is feen, whether it be diredly falling or defleding m a parabolic curve, or firetching a coiled fpnng, or breaking a rope, or fimply preffing on its fup- P0iT is gravitatio, gravitation ; and the body is faid to gravitate. When all obftacles are removed from the 3 G body, T I D [ 418 ] T I D Tide, body, as when we cut the ftnng by which a (lone is 1 V— ' hung, it moves direftly downwards, tendit ad terrain. Si dijcindatur funis tenderet lapis ad terrain. Dum vero funis integer perfet, lapis terrain verfus niti cenfetur. By fome metaphyiical proceis, wilich it is ncedleis at prei'ent to trace, this ni/iis ad motum has been called a tendency in our language. Indeed the word has now come to fignity the energy of any adlive quality in thole cafes where its limpiel! and molt immediate mani- feilation is prevented by fome obltacle. The ftone is now faid to tend towards the earth, though it does not actually approach it, being withheld by the firing. The ftretchmg the tiring in a diredlion perpendicular to the horizon is conceived as a lull manifeltauon of this ten¬ dency. This tendency, this energy ol its heavinefs, is therefore named by the word which diitinguilhes the qua¬ lity ; and it is called gravitation, and it is faid \.ogravi¬ tate. But Sir Ifaac Newton difeovered that this defledtion of a heavy body differs in no refpedl from that general delleCtidn obfeived in all the bodies of the folar lyllem. For 16 feet, which is the defledlion of a llone in one fccond, has the very fame proportion to -rg-th of an inch, ivhich is the limultaneous deiledtion of the moon, that the fquare of the moon’s dillance from the centre of the earth has to the fquare of the Hone’s diftance from it, namely, that of 3600 to 1. Thus we are enabled to compare all the effedls of the mutual tendencies of the heavenly bodies with the ten¬ dency of gravity, whole effedls and meafures are fami¬ liar to us. If the earth were a fphere covered to a great depth with water, the water would form a concentric fpherical (hell 5 for the gravitation of every particle of its furface would then be diredied to the centre, and would be equal. The curvature of its lurface therefore w’ould be every where the lame, that is, it would be the uniform curvature of a fphere. It has been demonflrated in former articles, after Sir Ifaac Newton, that the gravitation of a particle C Plate (fig- I-) t0 centre O, is to that of a particle E at iDXXXVI. the furface as CO to EO. In like manner the gravita- Fig. 1. tion of 0 is to that of / as 0 to p O. If therefore EO and Op are two communicating canals, of equal lengths, the water in both would be in equilibrio, becaufe each column w-ould exert the fame total pieffure at O. But if the gravitation of each particle in / O be diminilhed by a certain proportion, fuch as -rl^th of its whole weight, it is plain that the total preffure of the column p O will be x^th part lefs than that of the column EO. Therefore .they will no longer be in equilibrio. The weight of the column EO will prevail y and if a hollow- tower be built at the mouth of the pit p ot the w-ater will fink in EO and rife in Op, till both are again in equilibrio, exerting equal total picffures at O. Or we may prevent the finking at E by pouring in more w-ater into the tower Pp. The fame thing mull happen in the canalperpendicular to EO, if the gra¬ vitation of every particle be diminilhed by a force adting in the diredhon CF, and proportional to the dillance of the particle from C, and fuch, that when c C is equal to 0 O, ihe force adling on c is equal to the force adling on 0. In order that he former equilibrium may be re- flored after this diminution of the gravitation of the co¬ lumn yC, it is plain that more water mult be poured in¬ to the oblique tow-er fF. All this is evident when we confider the matter hydroflatically. The gravitation of the particle c may be reprefented by 0 O ; but the dimi¬ nution of the preffure occafioned by this at O is repre- fented by C c. Hence we can colledt this much, that the whole di¬ minution of prelfure at C is to the whole diminution of preffure at O as the fum of all the lines c C to the fum of all the lines 0 O, that is, as fC* to PO2. But the weight of the fmall quantity of w-ater added in each tower is diminilhed in the lame proportion y therefore the quantity added at F/mult be to the quantity added at P/> asyC to p O. Therefore we mult have Fy: Bp=fC : p O, and the points E, F, P, muff be in the circumference of an elliple, of which PO and EO are the tranfverfe and conjugate ftmx-axes. What w-e have here fuppoied concerning the diminu¬ tion of gravity in thefe canals is a thing which really obtains in nature. It w-as demonllrated, when treating of tiie PRECESSION of the Equinoxes, that if the fun or' moon lie in the diredtion OP, at a very great diftance. there refults from the unequal gravitation of the differ¬ ent particles of the earth a diminution of the gravity of each particle ; which diminution is in a diredtion paral¬ lel to OP, and proportional to the diftance of the par¬ ticle from a plane palling through the centre of the earth at right angles to the line OP. Thus it happens that the waters of the ocean have their equilibrium difturbed by the unequal gravitation of their different particles to the fun or to the moon ; and this equilibrium cannot be reftored till the waters come in from all hands, and rife up around the line joining the centres of the earth and of the luminary. The fpherical ocean mull acquire the form of a pro¬ late fpheroid generated by the revolution of an ellipfe round its tranlverfe axis. The waters will be highelt in that place which has the luminary in its zenith, and in the antipodes to that place 5 and they will be moll depreffed in all thofe places which have the luminary in their horizon. P and P' will be the poles, and EO£) will be the equator of this prolate fpheroid. Mr Fergufbn, in his Aftronomy, affigns another caufe of this arrangement, viz. the difference of the centrifu¬ gal 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 miftake. It would be juft if the earth and moon were attached to the ends of a rod, and the earth kept always the fame face toward the moon. it is evident that the accumulation at P and P', and the depreffion at the equator, muft augment and diminiflr in the fame proportion with the difturbing force. It is alfo evident that its abfolute quantity may be difeovered by our knowledge of the proportion of the difturbing force to the force of gravity.—Now this proportion is known 5 for the proportion of the gravitation of the earth’s centre to the fun or moon, to the force of gravi¬ ty at the earth’s furface, 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 furface, is alfo known, being very nearly the propor¬ tion of the diilance of the luminary to twice the radius of the earth. Although this reafonii.*, by which we have afeertain- ed the elliptical form of the watery fpheroid, be fuffi- ciently / T I D [ 41 Title, ciently convincing, it is very imperfeft, being accom- —V modated to one condition only of equilibrium, viz. the equilibiium of the canals/V and c 0. There are feveral other conditions equally neceflary to which this lax rea- foning will not apply, fuch as the dire&ion of the whole remaining gravitation in any point F. This mull be perpendicular to the furface, &c. &c. Nor will this mode of inveftigation afcertain the eccentricity of the fpheroid without a molt intricate procefs. We muft therefore take the fubje£l mare generally, and (how the proportion and dire£tions of gravity in every point of the fpheroid. We need not, however, again demon- ftrate that the gravitation of a particle placed any where without a perfc-ft fpherical fhell, or a fphere confining of concentric fpherical Ihells, either of uniform denlity, or of denfities varying according to fome fun&ion of the radius, is the fame as if the whole matter of the {hell • or fphere were colledled in the centre. This has been demonftrated in the article Astronomy. We need only remind the reader of fome confequences of this the¬ orem which are of continual ufe in the prefent inveftiga¬ tion. 1. The gravitation to a fphere is proportional to its quantity of matter direftly, and to the fquare of the diftance of its centre from the gravitating particle in- verfely. 2. If the fpheres be homogeneous and of the fame den- fity, the gravitations of particles placed on their furfaces, or at diftances which are proportional to their diame¬ ters, are as the radii j for the quantities of matter are as the cubes of the radii, and the attractions are inverfe- ly as the fquares of the radii j and therefore the whole . . rs gravitations are as —, or as r. 3. A particle placed within a fphere has no tendency to the matter of the {hell which lies without it, becaufe its tendency to any part is balanced by an oppolite ten¬ dency to the oppofite part. Therefore, 4. A particle placed any where within a homogene¬ ous fphere gravitates to its centre with a force propor¬ tional to its diftance from it. It is a much more difficult problem to determine the gravitation of particles to a fpheroid. To do this in ge¬ neral terms, and for every fttuation of the particle, would require a train of propofitions which our limits will by no means admits we muft content ourfelves with as much as is neceffary for merely afcertaining the ratio of the axes. This will be obtained by knowing the ra¬ tio of the gravitation at the pole to that at the equator. Therefore. fig. 2. Let N S y N (fig. 2.) be a feaion through the axis of an oblate homogeneous fpheroid, which differs very little from a fphere. NS is the axis, m q is the equato¬ rial diameter, O is the centre, and NMSQ is the fec- tion of the infcribed fphere. Let P be a particle fi- tuated at any diftance without the fphere in its axis produced ; it is required to determine the gravitation of this particle to the whole matter of the fpheroid ? Draw two lines PAC, PBD, very near to each other, cutting off two fmall aiches AB, CD; draw GA a, HB b, IC c, KD d, perpendicular to the axis; alfo draw OE and AL perpendicular to PAC, and OF perpendi¬ cular to PD, cutting PC in f. Join OA. Let OA, the radius of the infcribed fphere be r, and OP the diftance of the gravitating particle be d, and 9 ] TIB M ot, the elevation of the equator of the fpheroid, or the ellipticity, be e. Alfo make AErzAr, and OE~?/, rzjy/V*—a*. Then AE—BF= x and F/izry. Tide. Suppofe the whole figure to turn round the axis OP. The little fpace AB b a will generate a ring of the re¬ dundant matter 5 fo will CD dc. This ring may be confidered as confifting of a number of thin rings gene* rated by the revolution of A a. The ring generated by A a is equal to a parallelogram whofe bafe is the cir¬ cumference defcribed by A and whofe height is A a. Therefore let c be the circumference of a circle whofe radius is 1. The ring will be A oX^X AG. But be¬ caufe a N is an arch of an ellipfe, we have Mm : A« —MO : AGrzrr : AG, and A a=M m X ——, = ~ r r € AG. Therefore the furface of this ring is — c - AG* We have fuppofed the fpheroid to be very nearly fpherical, that is, e exceedingly fmall in comparil’on of r. This being the cafe, all the particles in A a, and confequently all the particles in the ring generated by the revolution of A a, will attra6I the remote particle P with the fame force that A does very nearly. We may fay the fame thing of the whole matter of the ring gene¬ rated by the revolution of AB b a. This attraction is exerted in the direflron PA by each individual particle. But every aftion of a particle A is accompanied by the aClion of a particle A1 in the direflion PA'. Thefe two compofe an attraftion in the diredtion PO. The whole attradtion in the diredlions fimilar to PA is AG* PA* plates e = cX- X GH, for GH meafures the number of parallel of which the folid ring is compofed. This (> being decompofed in the diredtion PG is zz c x ~ X AG* • PG A Cr * XGH. But—- OE* PO*’ and^ = PE PO* PA3 ~ PA*— PO*’ PA Therefore the attradlion of the ring, eftimated in the di- e OE* . PE X GH. redtion PO, is zr r X ~ X r PO3 Further, by the nature of the circle, we have HG : ABzz AG : AO; alfo AB : BLz= AO : OE. But PA: a n v. po AGzzPO : OE, and OErz —Therefore AB : BLssAO: AG . PO PA z=AO. PA : PO AG : PE. PA . PA Alfo BL : LAzzEO : EA, And LA : Fy— PA : Py :z= ultimately PA Therefore, by equality, HG : FfzzAG . AO EO . PA : AO . PO'. AG . EA . PE. Or HG : Fy=EO . PA* : PO . EA . PE. . , TJ„ „ - EO . PA* n H - yx po p£ . EA’ Now fubftitute this value of HG in the formula ex- preffing the attradlion of the ring. This changes it to * OE* . PE OE . PA* ^ e c t'^13 ^ a ^ Fy or e -• X OE3 PO4 . EA PO3 PA* -j-i r X F/ PO.PE.EA In like manner, the altradlion of 3 G 2 the Tide. T I D the ling generated by the revolution cf CD ac is c - x OE3 . PC* EA X OE3 PU4 Therefore the attraction of both is crxF/x */3 EAJ X PA* -f- PC*. x P£*4-.v*. C TT* */ 2C-—-X F/— r A a; Therefore F_/ A, — ^ X FO^EAX 1>A,+PC''= A >< FT But PA* -f PC* = 2 PE* + Therefore the attraction is But 2 PE* 2 ar r/J F/=y, =-P. y y — y x, ~ r h herefore the attraction of the two rings is 2 c - x . r a'4 xl X PE* -f ** X a:. But PE*—PO* — OE*,— (r* — x1).—d3 — r*-j-.v*. Therefore the attrac¬ tion ot the two rings is e 2c v/4 X r1 — x* X d1 —>l + 2x3x, — 2c r1 d3 x — r* x-\-2 r* .vs •d*' ■d3 x3x-\-r%x1 x— 2x* x~7c —--x — ^ * / ' r3 d3 x-\-$ r3 x3x — r*x — d3x3 x—2\*x. I he attraction of tne whole fhell of redundant mat¬ ter will be had by taking the fluent of this formula, which is 2 c —r-X r d* A d3 3 r3 x3 d3 2 and then make x~r. This gives 2c—(d3 r3 -\-r* 420 1 t I D fmali in comparifon of r, a particle on the equator of the oblong fpheroid will be ns much attracted by thefe ' cncles of equal areas, with their correfponding eliiples, as by the ellipfes. Now the attraction at the pole of an oblate fpheroid was \ c r-\- c e. Therefore putting 4 e in p'ace of e, the attraction on the equator of the oblong fpheroid will be equal to *- c r-f yt c e. I bus we have afcertained the gravitations of a parti¬ cle fituated in the pole, and of one fituated in the equa¬ tor, of a homogeneous oblong ipheroid. This will en¬ able us to lolve the following problem ; If the particles of a homogeneous oblong fluid Ipheroid attraCt each other with a force inverfely as the fquares of their diltances, and if they are attracted by a very diltant body by the fame law, and if the ratio of the equatorial gravity to this external force be given •, to find what muit lie the proportion of the femi-axis, fo that all may be in equilibrio, and the fpheroid preferve its form ? Let r be the equatorial radius, an dr-fe be the polar femi-axis. Then the gravitation at the pole m is ^ c r + tV c c, and the gravitation at the equator is ^-cr-p tt c e- Now by the gravitation towards the ditfant body placed in the direCHon of the polar axis, the polar gravitation is diminifhed, and the equatorial gravitation is increafed j and the increafe of the equatorial gravita¬ tion is to the diminution of the polar gravitation as NO to 2 to O. Therefore if the whole attraCHon of the ob- long fpheroid for a particle on its equator be to the force which the diftant body exerts there, as G to P, and if the fpheroid is very nearly fpherical, the abfolute weight P And —d3 r3—J-rs), which is 4 c ^ r* 4 ?-4 d3 5 d* * infcribed fphere, wdiich is traCIion of the whole fpheroid _ c r3 To this add the attradion of the c r3 and w7e have the at- d3 + c e r* d3 _r7 dl b d* Cor. i. If the particle' P is fituated precifely in N, tbe pole of the fpheroid, the attraftion of the Ipheroid Is 4 c ;-q- r8j c c. If the fpheroid is not oblate, but oblong, and if the greater femiaxis he r, and the depreflion at the equator be e, the analyfis is the lame, taking e negatively. I. aeiefoie the attradion for a particle in the pole, or the gravitation of a particle in the pole, is | c r 4rce. But if the polar femiaxis be r-f , when e is very at the equator will be | c ?•-}-TA c e-f the abfolute weight at the pele will be 2 P -c r —. Gr Tcr+-xh P Their difference is ■r\ce+2cr G ^ g Now if we fuppofe this fpheroid to be compofed of fimilar concentric fhells, all the forces will decreafc in the fame ratio. Therefore the weight of a particle in a column reaching from the equator to the centre will be to the weight of a fimilarly fituated particle of a column reaching from the pole to the centre, as the weight of a particle at the equator to the weight of a particle at the pole. But the whole weights of the two columns muft be equal, that they may balance each other at the cen¬ tre. Their lengths mult therefore be reciprocally as the weights of fimilarly fituated particles ; that is, the polar femi-axis mult be to the equatorial radius, as the weight of a particle at the equator to the weight of a particle at the pole. Therefore we muft have t^c c-j-2c r~ ; , , . P c r-y- Hence we derive 2 r — T*x from the longer axis of the furroundir.g fpheroid S N 7. Let TR, TW be perpendicular to the equa¬ torial diameter and to the axis, fo that they are the co¬ fine and the fine of TO(^ to the radius TO or QO. Let S'.7 N7 be a feftion of the circumfcribed fphere. Draw OT cutting the fphtroid in Z and the circum¬ fcribed fphere in t. Alfo let r 0 « be a feclion of a fphere which has the fame capacity with the fpheroid, and let it cut the radius in r. Then, 1. The elevation TZ of the point Z of the fphertid above the inferibed fphere is ~Q q X cof.2 Z, and the deprefiion t Z below the ci cumfcribed fphere is —£) 7 X fine2 Z. Produce R F till it meet the furface of the fpheroid in V. The minute triangle VTZ may be con- fidered as retlilineal, right-angled at Z, and iherefore fimilarto OTR. Therefore OT : TRrrTV : TZ. But in the ellipfe 0<^, or OT : TR—(^7 : TV. There¬ fore OT2 : TR2—(I q : TZ, and TZ- Q <7 X cof.2 Z = 0.7 : > =Q 7X cof.2 Z. And in the very fame manner it may be fhown, that t Z—O 7 x find Z* 2. The elevation of the point T above another point T', whole angular-diftance TOT' from the point T is 90°, is — O 0 X cold Z—fin.2 £. Call the angle QOT' Z'. Then T'Z'—Q 7 X cof.2 Z', and TZ—T', Z', — 0.7 Xcol.2Z—cof.2 Z'. But the arch QT' is the complement of QT, and therefore cof.2 Z'— fin.2 Z. Therefore TZ—T', Z'=r(^7 X coldZ—tin.2 Z. 3. O 0^7. For the inferibed fphere is to ihe fpheroid as 0() to O 7. But the infcrlbed fphere is to the fphere j 0 n as OQ3 to O o3. Therefore becaufe the fphere son is equal to the fphereid S 7 N, we have OQq O 7—OQ3 : O 03, and O 0 is the fir ft of two mean propoilionals between OQ and O 7. But £>7 is very final] in comparifon with OQ^. Therefore Q^o is very nearly y of Q7. Since .r 0 « is the fphere of equal capacity, it is the form of the undifturbed ocean. The belt way therefore of conceiving the changes of form produced by the fun or moon, or by both together, is to confider the eleva¬ tions or depreflions which they produce above or below . this furface. Therefore, . 4. The T I D T 1 D [42 4. The elevation r Z of the point Z above the equi- capacious fphere is evidently =rO ^Xcof.*Z—-fQ.?' Alfo the depreflion r'7J of the point Z'isrr fin.* Z —4 Q q. N. B. Either of thefe formulge will anfwer for either the elevation above, or the depreflion below, the natural ocean : For if cof.* Z is lefs than 4» the elevation given by the formula will be negative 5 that is, the point is below the natural furface. In like manner, when fin.* Z' is lefs than 4* the deprefiion is negative, and the point is above the furface. But if cof.* Z be =4? or fin.* Z' be —4, the point is in the natural iiirface. This marks the place where the fpheroid and the equal fphere interfeft each other, viz. in P', the arch P' 0 being 540 44' very nearly, and PS=35° 16'. Let S reprefent the whole elevation of the pole of the folar tide above its equator, or the difference between high and low water produced by the fun 5 and let M reprelent the whole elevation produced by the moon. Let x and y reprefent the zenith diftances of the fun and moon with refpedl to any point whatever on the ocean. Then x and y will be the arches intercepted between that point and the fummits of the folar and lunar tides. Then the elevation* produced by both lu¬ minaries in that plane is S • cof.* x-—4^ + ^'c0^*y — 4 M $ or, more concifely, S • cof.* ar-f-M • cof.*y — 4 S-f-M, and the depreflion is S • fin.* #-{-M • iuPy—4 S+M. Let the fun and moon be in the fame point of the heavens. The folar and lunar tides will have the fame axis; the cofines of x and y will each be 1, and the elevation at the compound pole will be S-}-M—4 S-|-M=4b-j-M. The depreflion at any point 90° from this pole will be 4 S-f-M, and the whole tide is S + M. Let the moon be in quadrature, as in a (fig. 3.). The appearance at s will be known, by confidering that in this place the cofine of x is 1, and the cofine of y is o. There¬ fore the elevation at r = S — 4 S + M, —4 S—4 M. The depreflion at a ~ S — 4 S+M =4 S—4 M. The difference or whole tide = S— M. In like manner, the whole elevation at a above the in- fcribed fphere is M—S. * Hence we fee that the whole tide, when the moon is in quadrature, is the difference of S and M. We alfo fee, that if M exceeds S, the water will be higher at a than at j. Now it is a matter of obfervation, that in the quadratures it is high water under the moon, and low water under the fun. It is alfo a matter of obfervation, that in the free ocean, the ebb tide, or the water at s, immediately under the fun, is below the natural furface of the ocean. Hence we muft conclude, that 4 S is lefs than 4 M, or that M is more than double of S. This agrees with the phenomena of nutation and precefiion, which feem to make S=4 of M. In all other pofitions of the fun and moon, the place of high water will be different. It is high water where the fum of the elevations produced by both luminaries above the natural ocean is greateft ; and the place of low water is where the depreflion below the natural ocean is greateft. Therefore, in order that it may be high water, we muft have S • cof.* at + M • cof.* y—4 S+M a maximum; or, neglecting the conftant quan- 4 ] tity S+M maximum. we muft have S • cof.* # + M • cof.* y In like manner, to have low water in a place where the zenith diftances of ihe fun and moon are v and w, we muft have S • fin.* zi+M • fin. % w a maximum. Lemma 1. If we confider the fines and cofines of angles as numeral fractions of the radius 1, then we have cof.* Z=z-|+i cof.* Z, and fin.* Z=:^— i cof.* Z. Let a m s (fig. 3.) be a quadrant of a circle of which O is the centre, and O j is the radius. On O r de-F!^3' feribe the femicircle OMS, cutting O m in M. Draw s M, and produce it till it cut the quadrant in n. Al¬ fo draw MC to the centre of the femicircle, and MD and « d perpendicular to O s. It is plain that j- M is perpendicular to OM ; and if O r be radius, j- M is the fine of the angle s OM, which we may call Z; OM is its cofine : and becaufe O r r OM=OM : OD, and O j : OD =:Of* : OM*, and OD may reprefent cof.* Z. Now OD—OC+CD. If O s=z 1, then OC=:+ CD=CM • cof. MCD, — CM • cof. 2 MOD, =4 * c°f 2 Z. Therefore cof.* Z = 4 + | cof. 2 Z. In like manner, becaufe Oj: J-Mrrj-M.-j'D, j-D is =: fin * Z. This is evidently = 4 — 4 cof. 2 Z. Lemma 2. Cof.* Z—fin.*Z=cof. 2 Z. For, becaufe j M is perpendicular to OM, the arch j- « is double of the arch s m, and becaufe MD is parallel to n d, s d i$ = 2s D, and dD— fin.* Z. Therefore Od= cof.*Z —-fin.* Z. But Od'is the confine of ns. —cof. 2Z and cof.* Z—fin.*Z=cof. 2 Z. By the firft Lemma we fee, that in order that there may be high water at any place, when the zenith di¬ ftances of the fun and moon are x and y, we muft have S * cof. 2x +M • cof. 2y a maximum. That this may be the cafe, the fluxion of this for¬ mula muft be = o. Now we know that the fluxions of the cofines of two arches are as the fines of thofe arch.es. Therefore we muft have S • fin. 2 A'+M • fin. 2 y=o, or S • fin. 2x~ — M*fin. 2y, which gives us fin. 2x : fin. 2y M : S. In like manner, the place of low water requires fin. 2 v : fin. 2 = M : S. From this laft circumftance w’e learn, that the place of low water is o, removed 900 from the place of high water ; whereas we might have expe&ed, that the fphe¬ roid would have been moft protuberant on that fide on which the moon is: For the fines of 2^ and of 2 w have the fame proportion with the fines of 2 * and of 2 y. Now we know that the fine of the double of any arch is the fame wdth the fine of the double of its complement. Therefore if low water be really diftant 90° from high wrater, we {hall have fin. 2 x : fin. 2y= fin. 2v : fin. 2 w. But if it is at any other place, the fines cannot have this proportion. Now let s be the point of the earth’s furface which has the fun in the zenith, and m the point which has the moon in the zenith. Let h be any other point. Draw O h cutting the femicircle OM j in H. Make CM to CS as the difturbing force of the moon to that of the fun; and draw Si< parallel, and S/, M r per¬ pendicular to HH\ Join MH and MH'. The angle HC j- is double of the angle FIO s, and MCH is double of MH'H, or of its equal MOH. Becaufe HMH is a femicircle, HM is perpendicular to MO. There¬ fore T I D [ 423 ] T I D Fig. 4. «ld 5- Tice, fore if HH' be confidered as radius, HM is the fine, ""V**' and H'M is the cofine of MH'H. And C r is = MC* cof. 2y, zz M • cof. 2y. And C / is SC • cof. 2x. Therefore tr or is cnS • cof. • cof. 2 y. Therefore / r or Sv will exprefs the whole difference of elevation between h and the points that are 90 degrees from it on either fide (by Lemma 2.) ; and if h be the place of high water, it will exprefs the whole tide, be caufe the high and low waters were fhown to be 90° afunder. But when h is the place of high water, S v is a maximum. Becaufe the place of the moon, and therefore the point M, is given, S v will be a maxi¬ mum when it coincides with SM, and CH is parallel to SM. This fuggeftcd to us the following new, and not in¬ elegant, folution of the problem for determining the place of high water. Let s Qo q s (fig. 4. and 5 ) be a feftion of the ter¬ raqueous globe, by a plane palling through the fun and moon, and let O be its centre. Let J' be the point which is immediately under the fun, and m the place immediately under the moon. Bifeft Or in C, and defcribe round C the circle OM j- LO, cutting O m in M. Take C j to reprefent the dillurbing force of the moon, and make C r to CS as the force of the moon to that of the fun (fuppofing this ratio to be known). Join MS, and draw CH parallel to it. Draw GH^, and / OL /' perpendicular to it. And laftly, draw Cl per¬ pendicular to SM. Then we fay that m and its oppo- fite ni are the places of high water, / and /' are the places of low water, MS is the height of the tide, and MI, SI are the portions of this tide produced by the moon and fun. For it is plain, that in this cafe the line S v of the laft propofition coincides with MS, and is a maximum. We may alfo obferve, that MC : CS=fin. MSC : fin. SMC, =rfin. HCS : fin. MCH, —fin. 2tOs : fin. 2 A O m, = fin. 2 x : fin. 2y, or M : S — fin. 2 x : fin. 2 y, agreeably to what was required few the maxi¬ mum. It is alfo evident, that MI—MC • cof. CMI, = M • cof. 2y, and SI =; SC • cof. ISC, — S • cof. 2x; and therefore MS is the difference of elevation between fi and the points / and which are 90° from it, and is therefore the place of low water j that is, MS is the whole tide. The elevation of every other point may be determin¬ ed in the fame way, and thus may the form of the fphe- roid be completely determined If we fuppofe the figure to reprefent a fe£lion through the earth’s equator (which is the cafe when the fun and moon are in the equator), and farther fuppofe the two luminaries to be in conjunftion, the ocean is an oblong fpheroid, whofe axis is in the line of the fyzigies, and whofe equator coincides with the fix hour circle. But if the moon be in any other point of the equator, the figure of the ocean will be very complicated. It will not be any figure of revolution j becaufe neither its equator (or mod depreffed part) nor its meridians are circles. The moft depreffed part of its equator will be in that feftion through the axis which is perpendicular to the plane in which the luminaries are fituated. And this greatefi: depreffion, and its ihorteff equatorial dia meter, will be conftant, while its other d’menfions vary ¥i’ith the moon’s place. We need not inquire more mi¬ nutely into its form } and it is fufficient to know that all the feftions perpendicular to the plane palling through the fun and moon are ellipfes. This conftruftion will afford us a very fimple, and, we hope, a very perfpicuous explanation of the chief phenomena of the tides. The well informed reader will be pleafed with obferving its coincidence with the alge¬ braic folution of the problem given by Daniel Bernoulli, in his excellent differtation on the Tides, which {hared with M‘Laurin and Euler the prize given by the Aca¬ demy of Sciences at Paris, and with the eafe and per- fpicuity with which the phenomena are deducible from it, being in fome fort exhibited to the eye. In our application, we (hall begin with the fimpleft cafes, and gradually introduce the complicating circum- flances which accommodate the theory to the true ffate of things. We begin, therefore, by fuppofing the earth covered, to a proper depth, with water, forming an ocean concen¬ tric with its folid nucleus. In the next place, we fuppofe that this ocean adopts in an inllant the form which is confillent with the equi¬ librium of gravity and the ditlurbing forces. Thirdly, We fuppofe the fun ftationary,and the moon to move eaftward from him above 1 27° every day. Fourthly, We fuppofe that the folid nucleus turns round its proper axis to the eaftward, making a rotation in 24 folar hours. Thus any place of obfervation will fuccelfively experience all the different depths of water. Thus we lhall obtain a certain Succession of pheno¬ mena, precifely limilar to the fucceflion obferved in na¬ ture, with this foie difference, that they do not cor- refpond to the contemporaneous fituations of the fun and moon. When we ftiall have accounted for this differ¬ ence, we ftiall prefume to think that we have given a-* juft theory of the tides. We begin with the fimpleft cafe, fuppofing the fun and moon to be always in the equator. Let the feries begin with the fun and moon in conjunction in the line O J. In this cafe the points j, m, and h coin¬ cide, and we have high water at 12 o’clock noon and midnight. While the moon moves from s to £), Om cuts the upper femicircle in M 5 and therefore CH, which is al¬ ways parallel to MS, lies between MC and C j. There¬ fore h is between m and s, and wre have high water after 1 2 o’clock, but before the moon’s fouthing. The fame thing happens while the moon moves from 0 to y, during her third quarter. But while the moon moves from her firft quadrature in Q to oppofition in 0 (as in fig. 5.), the line m Q drawn from the moon’s place, cuts the lower femicircle in M and CH, parallel to SM, again lies between M and s, and therefore h lies between m and 0. The jdace of high water is to the eaftward of the moon, and we have high water after the moon’s fouthing. The fame thing happens while the moon is moving from her laft quadrature in q to the next fyzigy. In Ihort, the point H is always between M and s, and the place of high water is always between the moon and the tiearejl fyzigy. The place of high water overtakes the moon in each quadrature, and is overtaken by the moon in each fyzigy. Therefore during the firft and third quar¬ ters, the place of high water gradually falls behind the moon for fome time, and then gains upon her again, fo as Tide. / T I D as to overtake her in the next quadrature. But during the fecond and fourth quarters, the place of high wa¬ ter advances before the moon to a certain diftance, and then the moon gains upon it, and overtakes it in the next fyzigy. If therefore we fuppofe the moon to advance uniform¬ ly along the equator, the place of high wTater moves un¬ equally, floweit in the times of new and full moon, and Twifteft in the time of the quadratures. There muft be fome intermediate fituations where the place of high water neither gains nor lofes upon the moon, but moves with the fame velocity. The rate of motion of the point h may be determined as follows : Draw C z, S «, making very fmall and equal angles with HC and MS. Draw' n C, and about S, with the diftance S zz, deferibe the arch n i/, which may be confidered as a ftraight line perpendicular to n S, or to MS. Then, becaufe SM and S n are parallel to CH and C /, the points n and i are contemporaneous fituations of M and H, and the arches n M, z’H, are in the ratio of the an gular motions of m and h. Alfo, becaufe n v and n M are perpendicular to « S and n C, the angle v « M Is equal to the angle S rz C, or SMC. Alfo, be¬ caufe the angles nv M and MIC are right angles, and the angles v n M, CMI, are alfo equal, the triangles v n M, CMI, are fimilar. Therefore n M : zzu—MC : MI. And n v : z'H— n S : z C, or — MS : MC ; therefore «M : zH= MS : MI. Therefore the angular motion of the moon is to the angular motion of the place of high water as MS to MI. Therefore, when M'S is perpendicular to SC, and the point I coincides with S, the motion of high water is equal to that of the moon. But when M'S is perpen¬ dicular to SC, H'C is alfo perpendicular to C,r, and the angle h'Os is 450, and the high water is in the oftant. While the moon paftes from ,r to m’, or the high water from s to //, the point I falls between M and S, and the motion of high water is flower than that of the moon. The contrary obtains while the moon moves from m' to p, or the high wrater from the odlant to the quadrature. It is evident, that the motion of /i in the third quar¬ ter of the lunation, that is, in pafling from 0 to y, is fimilar to its motion from s to Q. Alio, that its mo¬ tion from Q to 0 mu^ relarc^ by the fame degrees as it accelerated in pafling from s to Q, and that its motion in the laft: quarter from q to s is fimilar to its motion from Q to 0. At new and full moon the point I coincides with C, and the point M coincides with j-. Therefore the mo¬ tion of the high w'ater at full and change is to the mo¬ tion of the moon as j C to j- S. But when the moon is in quadrature, I coincides with C, and M with 0. Therefore the motion of the moon is to that of high water as OS to OC or sC. Therefore the motion of high water at full and change is to its motion in the quadratures as OS to S J-, or as the difference of the difturbing forces to their fum. The motion of the tide is therefore floweft in the fyzigies and fwifteft in the quadratures •, yet even in the fyzigies it paffes the fun along with the moon, but more flowdy. Let the interval between the morning tide of one day and that of the next day be called a tide-day. T I D This is always greater than a folar day, or 24 hours, Tide, becaufe the place of high W'ater is moving iafter to t—-v”- the eaftward than the fun. It is lefs than a lunar day, or 24b, 50', while the high water paffes from the fe¬ cond to the third obfant, or from the fourth to the firft. It is equal to a lunarday when high water is in theoftants, and it exceeds a lunar day while high w'ater paffes from the firft to the fecond oftant, or from the third to the fourth. The difference between a folar 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 de- feribing in its rotation an angle equal to the motion of the high water in a day from the fun. The fmalleft of tbefe retardations is to the greateft as the difference of the difturbing forces to their fum. Of all the pheno¬ mena of the tides, this feems liable to the feweft: and moft inconfiderable derangements from local and acci¬ dental circumftances. It therefore affords the beft means for determining the proportion of the difturbing forces. By a comparifon of a great number of obferva- tions made by Dr Maikelyne at St Helena, and at Bar- badoes (places ficuated in the open fea), it appears that the fhorteft tide day is 24]!. 3'7', and the longeft is 25b. 27'. This gives M—S : M-f-S=37 : 87, and S : M ~2 : 4 96 j which differs only 1 part in 1 24 from the proportion of 2 to 5, which Daniel Bernoulli collebled from a variety of different obfervations. We (hall there¬ fore adopt the proportion of 2 to 5 as abundantly exa£l. It alfo agrees exactly wdth the phenomena of the nuta¬ tion of the earth’s axis and the preceflion of the equi¬ noxes 5 and the altronomers affeft to have deduced this proportion from thefe phenomena. But an intelligent reader of their writings will perceive more finefie than juftice in this affertion. The nutation and ‘precef- fion do not afford phenomena of which we can aflign the ftiare to each luminary with fufficient precilion for de¬ termining the proportion of their difturbing forces 5 and it is by means of many arbitrary combinations, and without neceflity, that D’Alembert has made out this ratio. We cannot help being of opinion, that D'Alem¬ bert has accommodated his diftribution of the pheno¬ mena to this ratio of 2 to 5, which Daniel Bernoulli (the beft philofopher and the moft candid man of that illuftrious family of mathematicians) had, with fo much fagacity and juftnefs of inference, deduced from the phe¬ nomena of the tides. D’Alembert could not but fee the value of this inference ; but he wanted to fhow his own addrefs m deducing it propria marte foriooth from the nutation and preceftion. His procedure in this re- fembles that of his no lefs vain countryman De la Place, W'ho affefts to be highly pleafed with finding that Mr Bode’s difeovery that Meyer had feen the Georgium Sidus in 1756, perfeftly agreed with the theory oi its motions which he (De la Place) had deduced from his own do&rines. Any w'ell informed mathematician will fee, that De la Place’s data afforded no fuch precifion j and the book on the Elliptical Motions of the Planets, to which he alludes, contains no grounds for his infe¬ rence. This obfervation we owe to the author of a pa¬ per on that fubjeft in the Tranfaftions of the Royal So¬ ciety of Edinburgh. We hope that our readers will ex- cufe this occafional obfervation, by which wTe w'ifti to do juftice to the merit of a modeft man, and one of the greateft philofophers of his time. Our only claim in the prefent differtation is the making his excellent per¬ formance [ 424 1 T I D T I D [ 425 ] Tide. - formance on the tides acceflible to an Englifh reader “-v not much verfant in mathematical reiearches j and we are forry that our limits do not admit any thing more than a {ketch of it. But to proceed. Affuming 2 : 5 as the ratio of SC to CM', we have the angle CM'S=:230 34' nearly, and m' oh'=ii° 47'} and this is the greatelf difference between the moon’s place and the place of high water. And when this ob¬ tains, the moon’s elongation m' 0 s is 56° 47' from the neared fyzigy. Hence it follows, that while the moon moves uniformly from 56° 47' weft elongation to 36° 47'eaft, or from 1230 13'eaft to 123* 13'weft, the tide day is fhorter than the lunar day \ and while (lie moves from 56° 47' eaft to 123° 13', or from 123° 13' weft to 56° 47', the tide-day is longer than the lunar- dry. We now fee the reafon why ————The fwelling tides obey the moon. The time of high water, when the fun and moon are in the equator, is never more than 47 minutes different from that of the moon’s fouthing (-f- or — a certain fixed quantity, to be determined once for all by obferva- tion). It is now an eafy matter to determine the hour of high water correfponding to any pofition of the fun and moon in the equator. Suppofe that on the noon of a certain day the moon’s diftance from the fun is m s. The conftrudftion of this problem gives us s h, and the length of the tide-day. Call this T. Then fay 360° : s m~T : t, and t is the hour of high water. Or, if we choofe to refer the time of high water to the moon’s fouthing, v:e muft find the value o{ m h at the time of the moon’s fouthing, and the difference d between the tide-day and a mean lunar day L, and fay 360 : h~d : 3, the time of high water before the moon’s fouthing in the firft and third quarters, but after it in the fecond and fourth. The following table by Daniel Bernoulli exhibits thefe times for every 10th de¬ gree of the moon’s elongation from the fun. The firft or leading column is the moon’s elongation from the fun or from the point of oppofition. The fecond column is the minutes of time between the moon’s fouthing and the place of high water. The marks — and -f- diflin- guifh whether the high water is before or after the moon’s fouthing. The third column is the hour and minute of high water. But we muft remark, that the firft column exhibits the elongation, not on the noon of any day, but at the very time of high water. The two remaining columns exprefs the heights of the tides and their daily variations. Vol, XX. Part II. The height of high water above the low water confti- tutes what is ufually called the tide. This is the inte- refting circumftance in pradlice. Many circumftances render it almoft impoflible to fay what is the elevation of high water above the natural furface of the ocean. In many places the furface at low water is above the na¬ tural furface of the ocean. This is the cafe in rivers at a great diftance from their mouths. This may appear abfurd, and is certainly very paradoxical; but it is a fad eftablilhed on the moft unexceptionable authority. One inftance fell under our own obfervation. The low- water mark at fpring tide in the harbour of Alloa W'as found by accurate levelling to be three feet higher than the top of the ftone pier at Leith, which is feveral feet above the high-water mark of this harbour. A little attention to the motion of running waters will explain this completely. Whatever checks the motion of water in a canal muft raife its furface. Water in a canal runs only in confequence of the declivity of this furface : (See River). 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 cur¬ rent farther up, and therefore the waters accumulate there alfo j and this checking of the ftream, and confe- quent rifing of the waters, is gradually communicated up the river to a great diftance. The water rifes every¬ where, though its furface ftill has a flope. In the mean time, the flood tide at the mouth paffes by, and an ebb fucceeds. This muft accelerate even the ordi¬ nary courfe of the river. It will more remarkably ac¬ celerate the river now raifed above its ordinary level, becaufe the declivity at the mouth will be fo much greater. Therefore the waters near the mouth, by ac¬ celerating, will fink in their channel, and increafe the declivity of the canal beyond them. This will accele¬ rate the waters beyond them *, and thus a ftream more rapid than ordinary will be produced along the whole 3 PI river. Tide. \ T I D T I D [426 Tide. river, and the waters will fink below their ordinary le- 1 vel. Thus there will be an ebb below the ordinary fur- face as well as a flood above it, however floping that furface may be. Hence it follows, that we cannot tell what is the na¬ tural furface of the ocean by any obfervations made in a river, even though near its mouth. Yet even in rivers we have regular tides, fubje&ed to all the varieties de¬ duced from this theory. We have feen that the tide is always proportional to MS. It is greateft therefore when the moon is in con- jun&ion or oppofition, being then S s, the fum of the fe par ate tides produced by the fun and moon. It gra¬ dually decreafes as the moon approaches to quadrature j and when fire is at £) or q, it is SO, or the difference of the feparate tides. Suppofing Sr divided into 1000 equal parts, the length of MS is expreffed in thefe parts in the. fourth column of the foregoing table, and their differences are expreffed in the fifth column. We may here obferve, that the variations of the tides in equal fmall times are proportional to the fine of twice the diftance of the place of high water from the moon. For fince M « is a conftant quantity, on the fuppofi- tion of the moon’s uniform motion, M u is proportion¬ al to the variation of MS. Now M « : M ti—MC : Cirri : fin. 2y, and M n and MC are conftant quan¬ tities. Thus we have feen with what eafe the geometrical conftrudlion of this problem not only explains all the in- terefting circumftances of the tides, but alfo points them out, almoft without employing the judgement, and ex¬ hibits to the eye the gradual progrefs of each phenome¬ non. In thefe refpedls it has great advantages over the very elegant algebraic analyfis of Mr Bernoulli. In that procefs we advance almoft: without ideas, and ob¬ tain our folutions as detached faffs, without perceiving their regular feries. This is the ufual pre-eminence of geometrical analyfis , and we regret that Mr Bernoulli, who was eminent in this branch, did not rather employ it. We doubt not but that he would have fhown ftill more clearly the conneflion and gradual progrefs of every particular. His aim, however, being to inftruft thofe who were to calculate tables of the different affec¬ tions of the tides, he adhered to the algebraic method. Unfortunately it did not prefent him with the eafiefi: formulae for praffice. But the geometrical conftruffion which we have given fuggefts feveral formulae wdiich are exceedingly fimple, and afford a very ready mode of -calculation. The fundamental problems are to determine the angle j O ^ or ot O //, having m O s given j and to determine MS. Let the given angle mOf be called a; and, to avoid the ambiguity of algebraic figns, let it always be reckoned from the neareft fyzigy, lo that wre may al¬ ways have a equal to the fum of a? and y. Alfo make X^‘ °— , which reprefents the Sr M*4-S*-}-2MxSxcof. 2a’ S X fin» 2 a 6M-°ffiS-4-or fin-’ ^ a,,dmake'^=M+s3<73^;’ S r which is the expreflion of of that figure, or of tan, ay. Then we (hall have. 1. Sin. For we {hall have ccf. 2y V x—d*. But fin.*y = ■cof. 2y: V1—d' and fin. y 2. Tan. y =r“ For becaufe /> is = tan. I+\Z1 + />* 1-{-is the lecant of 2y, and —P : tan. y. Theie proceffes for obtaining y direffly are abundantly fimple. But it will be much more expeditious and eafy to content ourfelves wdth obtaining 2y by means of the . f. . S • fin. 2 a value or its tangent, viz. . Ur, we may by means of fig. 4. M -f- S ' col. 2 a of the fimilar value of its tangent find x M d ~S7 There is ftill an eafter method of finding both 2 x and 2 y, as follows. Make M-f-S : M — S = tan. a : tan. b. Then b is the difference of x and y, as a is their fum. For this analogy evidently gives the tangent of half the differ¬ ence of the angles CSM and CMS of fig. 4. or ol 2 x and 2 y. Therefore to a, which is half tlfe fum of 2x a-\-b -f-2y, add b, and we have 2x—a-{-by or x—— A a~~b and y—— . J 2 By either of thefe methods a table may be readily computed of the value of # or y for every value of a. But we mult recollect that the values of S and M are by no means conftant, but vary in the inverfe tripli¬ cate ratio of the earth’s diftance from the fun and moon; and the ratio of 2 to 5 obtains only when thefe lumina¬ ries are at their mean diftances from the earth. The forces correfponding to the perigean, medium, and apo- gean diftances are as follow. Apogean Medium Perigean Sun. 1.901 2. 2.IO5 Moon. 4.2j8 5- 5-925 Tide. Hence we fee that the ratio of S to M may vary from 1.901 : 5*925 to 2.105 : 4.258, that is, nearly from 1 : 3 to x : 2, or from 2 : 6 to 2 : 4. The folar force does not vary much, and may be retained as conftant without any great error. But the change of the moon’s force has great effedts on the tides both as to their time and their quantity. I. In refpedt of their Time. 1. The tide day following a fpring tide is 24 h. 2^ when the moon is in perigee, but 24 h. 33' when flie is in apogee. 2. The tide day following neap tide is 25 h. 15', and 25 h. 40' in thefe two fituations of the moon. 3. The greateft interval of time between high wa¬ ter and the moon’s fouthing is 39' and 6x' $ the angle £ T I D t 427 1 Til) Tide. y being 90 45' in the firfl cafe, and 150 ij' in the fe- cond. II. In refpeft of their Heights. I. If the moon is in perigee when new or full, the fpring tide will be 8 feet inftead of 7, which correfponds to her mean diftance. The very next fpring tide hap¬ pens when flie is near her apogee, and will be 6 feet in¬ ftead of 7. The neap tides happen when fire is at her mean diftance, and will therefore be 3 feet. But if the moon be at her mean diftance when new or full, the two fucceeding fpring tides will be regular or 7 feet, and one of the neap tides will be 4 feet and the other only 2 feet. Mr Bernoulli has given us the following table of the time of high water for thefe three chief fituations of the moon, namely, her perigee, mean diftance, and apo¬ gee. It may be had by interpolation for all interme¬ diate pofilions with as great accuracy as can be hoped for in phenomena which are fubjeft to fuch a complica¬ tion of difturbances. The firft column contains the moon’s elongation from the fun. The columns P, M, A, contain the minutes of time which elapfe between the moon’s fouthing and high water, according as (he is in perigee, at her mean diftance, or in apogee. The fign — indicates the priority, and -p the pofteriority, of high water to the moon’s fouthing. fiderable refemblances ; but he will alfo find fuch great differences as will make him very doubtful of its juftnefs. In very few places does the high water happen within three-fourths of an hour of the moon’s fouthing, as the theory leads him to expeft; and in no place whatever does the fpring tide fall on the day of new and full moon, nor the neap tide on the day of her quadrature. Thefe always happen two or three days later. By com¬ paring the difference of high wrater and the moon’s fouthing in different places, he will hardly find any connedfting principle. This fhows evidently that the caufe of this irregularity is local, and that the juftnefs of the theory is not affedted by it. By confidering the phenomena in a navigable river, he will learn the real caufe of the deviation. A flood tide arrives at the mouth of a river. The true theoretical tide differs in no refped from a rvave. Suppofe a fpring tide actually formed on a fluid fphere, and the fun and moon then annihilated. The elevation muft fink, preffing the un¬ der waters afide, and caufing them to rife where they were depreffed. The motion will not flop when the furface comes to a level j for the waters arrived at that, pofition with a motion continually accelerated. They will therefore pafs this pofition as a pendulum paffes the perpendicular, and will rife as far on the other fide, forming a high water where it wras low rvater, and a low water where it was high water ; and this wmuld go on for ever, ofcillating in a time which mathematicians can determine, if it were not for the vifcidity, or fome- thing like fri£tion, of the waters. If the fphere is not fluid to the centre, the motion of this wave ufill be dif¬ ferent. The elevated waters cannot fink without diffu- fing themfelves fidewife, and occafioning a great hori¬ zontal motion, in order to fill up the hollow at the place of low water. This motion will be greateft about half way between the places of high and low water. The fliallower we fuppofe the ocean, the greater muft; this horizontal motion be. The refiftance of the bot¬ tom (though perfe&ly fmooth and even) will greatly retard it all the way to the furface. Still, however, it will move till all be level, and will even move a little farther, and produce a fmall flood and ebb where the ebb and flood had been. Then a contrary motion will obtain ; and after a few ofcillations, which can be cal¬ culated, it will be infenfible. If the bottom of the ocean (which we ftill fuppofe to cover the whole earth) be uneven, with long extended valleys running in va¬ rious directions, and with elevations reaching near the furface, it is evident that this muft occafion great irre¬ gularities in the motion of the undermoft waters, both in refpect of velocity and direction, and even occafion fmall inequalities on the furface, as we fee in a river with a rugged bottom and rapid current. The devia¬ tions of the under currents will drag with them the con¬ tiguous incumbent waters, and thus occafion greater fu- perficial irregularities. Now a flood arriving at the mouth of a river, muff aft precifely as this great wave does. It muft be pro¬ pagated up the river (or along it, even though perfect¬ ly level) in a certain time, and we thall have high wa¬ ter at all the different places in fuccefilon. This is di- ftinftly feen in all rivers. It is high water at the mouth of the Thames at three o’clock, and later as we go up the river, till at London bridge we have not high water till three o’clock in the morning, at which time it is again high water at the Nore. But, in the mean time, there has been low water at the Nore, and high water about half way to London ; and while the high water is proceeding to London, it is ebbing at this interme¬ diate place, and is low water there when it is high wa¬ ter at London and at the Nore. Did the tide extend as far beyond London as London is from the Nore, we 3^2 ihoultl T I D [ 428 ] T I D Tide. (hould have three high waters with two low waters in- terpofed. The moft remarkable inftance of this kind is the Maragnon or Amazon river in South America. It appears by the obfervations of Condamine and others, that between Para, at the mouth of the river, and the conflux of the Madera and Maragnon, there are feven coexiflent high waters, with fix low waters between them. Nothing can more evidently {how that the tides in thefe places are nothing but the propagation of a wave. The velocity of its fuperficial motion, and the diftance to which it will fenfibly go, muft depend on many circumflances. A deep channel and gentle ac¬ clivity will allow it to proceed much farther up the ri¬ ver, and the dillance between the fucceflive fummits will be greater than when the channel is (hallow and fteep. If we apply the ingenious theory of Chevalier Euat, delivered in the article River, we may tell both the velocity of the motion and the interval of the fuc¬ ceflive high waters. It may be imitated in artificial canals, and experiments of this kind would be very in- ftruftive. We have faid enough at prefent for our pur- pofe of explaining the irregularity of the times of high water in different places, with refpeft to the moon’s fouthing. For wTe now fee clearly, that fomething of the fame kind muft happen in all great arms of the fea which are of an oblong fhape, and communicate by one end with the open ocean. The general tide in this ocean muft proceed along this channel, and the high water will happen on its {bores in fucceftion. This alfo is diftinffly feen. The tide in the Atlantic ocean pro¬ duces high water at new and full moon at a later and later hour along the fouth coaft of Great Brit ain in pro¬ portion as we proceed from Scilly iflands to Dover. In the fame manner it is later and later as we come along the eaft coaft from Orkney to Dover. Yet even in this progrefs there are confideraMe irregularities, owing to the finuofities of the fhores, deep indented bays, promi¬ nent capes, and extenfive ridges and valleys in the chan¬ nel. A fimilar progrefs is obferved along the ccafts of Spain and France, the tide advancing gradually from the fouth, turning round Cape Finifterre, ranging along the north coaft of Spain, and along the weft and north coafts of France. The attentive confideration of thefe faffs will not only fatisfy us with refpefl to this difficulty, but will enable us to trace a principle of connexion amidft all the irregularities that we obferve. We now add, that if we note the difference between the time of high water of (bring tide, as given by the¬ ory, for any place, and the obferved time of high water, we ftiall find this interval to be very nearly conftant through the whole feries of tides during a lunation. Suppofe this interval to be 40 hours. We fha'.l find every other ohenomenon fucceed after the fame inter¬ val. And if we fuppofe the moon to be in the place where (he was 40 hours before, the obfervation will agree pretty -well with the theory, as to the fucceffion of tides, the length of tide day, the retardations of the tides, and their gradual diminution from fpring to neap tide. We fay pretty well 5 for there ftill remain feve- ral (mail irregularities, different in different places, and not following any obfervable law. Thefe are therefore local, and owing to local caufes. Some of thefe we fhall afterwards point out. There is alfo a general de¬ viation of the theory from the real feries of tides. The neap tides, and thofe adjoining, happen a little earlier Tide, than the correfted theory points out. Thus at Breft V” (where more numerous and accurate obfervations have been made than at any other place in Europe), when the moan changes precifely at noon, it is high water at 3 h. 28'. When the moon enters her fecond quarter at noon, it is high water at 8 h. 40', inftead of 9 h. 48', which theory afligns. Something fimilar, and within a very few minutes equal, to this is obferved in every place on the fea-coaft. This is therefore fomething general, and indicates a real defe6t in the theory. But this arifes from the fame caufe with the other ge¬ neral deviation, viz. that the greateft and leaft tides do not happen on the days of full and half moon, but a certain time after. We fhall attempt to explain this. We fet out with the fuppofilion, that the water ac¬ quired in an inftant the elevation competent to its equi¬ librium. But this is not true. No motion is inftanta- neous, however great the force ; and every motion and change of motion produced by a fenfible or finite force increafes from nothing to a fenfible quantity by infinitely fmall degrees. Time elapfes before the body can ac¬ quire any fenfible velocity and in order to acquire the fame fenfible velocity by the action of different forces afting fimilarly, a time muff elapfe inverfely propor¬ tional to the force. An infinitely fmall force requires a finite time for communicating even an infinitely fmall velocity *, and a finite force, in an infinitely fmall time, communicates only an infinitely fmall velocity •, and it there be any kind of motion which changes by in fenfi¬ ble degrees, it requires a finite force to prevent this change. Thus a bucket of water, hanging by a cord lapped round a light and eafily moveable cylinder, will run down with a motion uniformly accelerated 5 but this motion will be prevented by hanging an equal bucket on the other fide, fo as to aft with a finite force. This force prevents only infinitely fmall accele¬ rations. Now let ALKF (fig. 6.) be the folid nucleus of the Fig. e. earth, furrounded by the fpherical ocean bhdg. Let this be raifed to a fpheroid BHDG by the aftion of the moon at M, or in the direction of the axis CM. If all be at reft, this fpheroid may have the form precifely competent to ifs equilibrium. But let the nucleus, with its fpheroidal ocean, have a motion round C in the di- reffion AFKL from weft to eaft. When the line of water BA is carried into the fituation s q infinitely near to BA, it is no longer in equilibrio } for s is too eleva¬ ted, and the part now come to B is too much depreffed. There is a force tending to deprefs the waters at r, and to raife thofe now at B ^ but this force is infinitely fmall. It cannot therefore reftore the fhape competent to equilibrium till a fenfible time has elapfed ; therefore the difturbing force of the moon cannot keep the fum- mit of the ocean in the line MC. The force muft be of a certain determinate magnitude before it can in an inftant undo the inftantaneous effecl of the rotation of the waters and keep the fummit of the ocean in the fame place. But this effeft is poflible j for the depref- fion at s neceffary for this purpofe is nearly as the di¬ ftance from B, being a depreflion, not from a ftraight line, but from a circle deferibed with the radius CB. It is therefore an infinitefimal of the firft order, and may be reftored in an inftant, or the continuation of the de- preflion TIB [ 429 ] T I D Tide. preflion prevented by a certain finite force. Therefore —v there is fome diftance, fuch as B y, where the diiturb- ing force of the moon may have tfie necetTary intenfity. Therefore the fpherical ocean, inftead of being kept continually accumulated at B and D, as the waters turn round, will ne kept accumulated at y and y', but at a height fomewhat fmaller. It is much in this way that we keep melted pitch or other clammy matter Irom run¬ ning off from a brufh, by continually turning it round, and it hangs protuberant, not from the loweft point, but from a point beyond it, in the di reft ion of its mo¬ tion. The fafts are very fimilar. The following expe¬ riment will illullrate this completely, and is quite a pa¬ rallel faft. Conceive GDH, the lower half of the el- lipfe, to be a fupple heavy rope or chain hanging from a roller with a handle. The weight of the rope makes it hang in an oblong curve, juft as the force of the moon raifes the waters of the ocean. Turn the roller very flowly, and the rope, unwinding at one fide and winding up on the other fide of the roller, will continue to form the fame curve : but turn the roller very briikly in the direftion FKL, and the rope will now hang like the curve uy' v, confiderably advanced from the per¬ pendicular, fo far, to wit, that the force of gravity may be able in an inftant to undo the infinitely fmall eleva¬ tion produced by the turning. We are very anxious to have this circumftance clear¬ ly conceived, and its truth firmly eftabliftied ; becaufe We have obferved it to puzzle many perfons not unaccuf- tomed to fuch difcuflions: we therefore hope that our readers, who have got over the difficulty, will indulge us while we give yet another view of this matter, which leads to the fame conclufion. It is certain that the interval between high and low water is not fufficient for producing all the accumulation neceffary for equilibrium in an ocean fo very (hallow. The horizontal motion neceffary for gathering together fo much water along a (hallow fea would be prodigious. Therefore it never attains its full height; and when the waters, already raifed to a certain degree, have palled the fituation immediately under the moon, they are (fill under the aftion of accumulating forces, although thefe forces are now diminifhed. They will continue rifing, till they have fo far paft the moon, that their fituation fubjefts them to depreffing forces. If they have acqui¬ red this fituation with an accelerated motion, they will rife dill farther by their inherent motion, till the depref¬ fing forces have deftroyed all their acceleration, and then they will begin to fink again. It is in this way that the nutation of the earth’s axis produces the greateft incli¬ nation, not when the inclining forces are greateft, but three months after. It is thus that the warmeft time of the day is a confiderable while after noon, and that the warmeft feafon is confiderably after midfummer. The warmth increafes till the momentary wafte of heat ex¬ ceeds the momentary fupply. We conclude by faying, that it may be demonftrated, that, in a fphere fluid to the centre, the time of high water cannot be lefs, and may be more, than three lunar hours after the moon’s fouthing. As the depth of the ocean diminifhes, this interval alfo diminifhes. It is perhaps impoffible to affign the diftance B y at which the fummit of the ocean may be kept while the earth turns round its axis. We can only fee, that it muft be lefs when the accumulating force is greater, and therefore lefs in fpring tides than in neap tides j but the difterence may be infenfibie. Ail this depends on cir- cumftances which we are litile acquainted with : many of thefe circumitances are local ; and the fituation of the fummit of the ocean, with refpeft to the moon, may be dift'erent in different places. Nor h ave we been able to determine theoretically what will be the height of the fummit. It will certainly be lefs than the height neceffary for perfeft equilibrium. Daniel Bernoulli fays, that, after very attentive conli- deration, he is convinced that the height at new or full moon will be to the theoretical height as the cofine of the angle BCy to radius, or that the height at y will be p 1 b * B4*cV The refult of all this reafoning is, that we muft al¬ ways fuppofe the fummit of the tide is at a certain di¬ ftance eaftward from the place afligned by the theory. Mr Bernoulli concludes, from a very copious compari- fon of obfervations at different places, that the place of high water is about 20 degrees to the eaftward of the place aifigned by the theory. Therefore the table for¬ merly given will correfpond with obfervation, if the lead¬ ing column of the moon’s elongation from the fun be al¬ tered accordingly. We have inferted it again in this place, with this alteration, and added three columns for the times ef high water. Thus changed it will be of great ufe. We have now an explanation of the acceleration of the neap tides, which ftiould happen 6 hours later than the fpring tides. They are in faft tides correiponding to pofitions of the moon, which are 20° more, and not the real fpring and neap tides. Thefe do not happen till two days after; and if the really greateft and leaft tides be ob¬ ferved, the leaft will be found 6 hours later than the firft o . . r b£ O O IO 20 30 40 5° 603 70 80 90 too 110 120 I30 I40 150 1603 170 180 High Water before or after Moon’s Southing. Perigee M. Dift. Apogee. 1 8 after qi do. o do. pf bet. 18 do 26 3 37i 384 33t 22 o 22 after 33 4aftei 384 374 3 26 18 22 afte ni o 1 if bef. 22 3j4 40 45 464 4°4 25 o 25 after 404 464 45 40 31* 22 27^ after J4 o 14 bef. 274 394 50 56' 58 5of 31 o 31 after 5°4 58 56 5°' 294 2 74 Time of High Water Perigee. M. Dill; Apogee O.lS 0-494 1.20 I-504 2.22 2.54 3- 27 4- 024 4.414 5.264 6.19 7.20 8.21 9-134 9-584 1 o-3 74 11.13 11.46 0.18 0.22 0.5x1 1.20 1.48 2 18 2.48 3.20 3- 55 4- 33 5I9 6.15 7.20 8.25 9.20 10.06 IO-45 11.20 11.51 0.22 o. o. 1. 1. 2. 2 3 3- 4- 5- 6 ?■ 8. 9- 10. 10 11 11. o. .274 '54 20 46 12 40 10 44 22 °9 09 20 3i 30 18 56 3° 59 27 This table is general, and exhibits the time of high- watery Tide. T I D [ 430 J T I I) 'Tile. water, and their difference from thofe of the moon’s fouthing, in the open fea, from all local obftrudtions. If therefore the time of high water in any place on the earth’s equator (for we have hitherto confidered no other) be different from this table (fuppofed corredt), we muft attribute the difference to the diftinguifhing cir- cumftances of the fituation. Thus every place on the equator fhould have high water on the day that the moon, fituated at her mean diftance, changes precifely at noon, at 22 minutes pafl noon j becaufe the moon pafles the meridian along with the fun by fuppofition. Therefore, to make ufe of this table, we muft take the difference between the firft number of the column, in- titled time of high water, from the time of high water at full and change peculiar to any place, and add this to all the numbers of that column. This adapts the table to the given place. Thus, to know the time of high water at Leith, when the moon is 50° eaft of the fun, at her mean diftance from the earth, take 22' from qh. 30', there remains 4.08. Add this to 2h. 48' and we have 6° 56' for the hour of high water. The hour of high wa¬ ter at new and full moon for Edinburgh is marked qh. 30' in Mafkelyne’s tables, but we do not pretend to give it as the exadf determination. This would require a feries of accurate obfervations. It is by no means an eafy matter to afeertain the time of high water with precifion. It changes fo very flowly, that we may eafily miftake the exadf minute. The belt method is to have a pipe with a fmall hole near its bot¬ tom, and a float with a long graduated rod. The water gets in by the fmall hole, and raifes the float, and the fmallnefs of the hole prevents the hidden asd irregular ftaris which waves would occafion. Inftead of obferving the moment of high water, obferve the height of the rod about half an hour before, and wait after high water till the rod comes again to that height. Take the middle between them. The water rifes fenfibly half an hour before the top of the tide, and quickly changes the height of the rod, fo that we cannot make a great miftake in the time. Mr Bernoulli has made a very careful comparifon of the theory thus corredfed, with the great colledtion of obfervations preferved in the Depot de la Marine at Breft * Se“ Mr an^ Rochefort * j and finds the coincidence very great, Caffini, and far exceeding any rule which he had ever feen. In- Mem. Acad.Attd. we have no rules but what are purely empirical, or Tar. 1734* which fuppofe a uniform progreflion of the tides. The heights of the tides are much more affedted by local circumftances than the regular feries of their times. The regular fpring tide Ihould be to the neap tide in the fame proportion in all places j but nothing is more dif¬ ferent than this proportion. In fome places the fpring tide is not double of the neap tide, and in other places it is more than quadruple. This prevented Bernoulli from attempting to fix the proportion of M to S by means of the heights of the tides. Newton had, however, done it by the tides at Briftol, and made the lunar force almoft five times greater than the folar force. But this was very ill-founded, for the reafon now given. Yet Bernoulli faw, that in all places the tides gra¬ dually decreafed from the fyzigies to the quadratures. He therefore prefumed, that they decreafed by a fimi- lar law with the theoretical tides,'and has given a very ingenious method of accommodating the theory 4o any tides which may be obferved. Let A be the x fpring tide, and B the neap tide in any place. Then Tide. A q_B form an M and an S from thefe, by making M =. f A b and S —-—j fo that M -f- S may be = A, and M — S = B agreeable to the theory. Then with this M and S compofe the general tide T, agreeable to the conftruftion of the problem. We may be perfuaded that the refult cannot be far from the truth. The following table is calculated for the three chief diftances of the moon from the earth. Obferve that this table is corre&ed for the retardation arifing from the inertia of the waters. Thus when the moon is 20 degrees from the fun, the mean diftance tide is i.ooA-j-o.ooB, which is the theoretical tide corre- fponding to conjundfion or oppofition. We have now given in fufficient detail the phenomena of the tides along the equator, when the fun and moon are both in the equator, fhewing both their times and their magnitude. When we recolledl that all the fec- tions of an oblong fpheroid by a plane palling through an equatorial diameter are ellipfes, and that the com¬ pound tide is a combination of two fuch fpheroids, we perceive that every fedlion of it through the centre, and perpendicular to the plane in which the fun and moon are fituated, is alfo an ellipfe, whofe fliorter axis is the equatorial diameter of a fpring tide. This is the great- eft depreflion in all fituations of the luminaries •, and the / points of greateft depreflion are the lower poles of every compound tide. When the luminaries are in the equa¬ tor, thefe lower poles coincide with the poles of the earth. The equator, therefore, of every compound tide is alfo an ellipfe : the whole circumference of which is lower than any other fedlion of this tide, and gives the place of low water in every part of the earth. In like manner, the feftion through the four poles, upper and low'er, gives the place of high water. Thefe two fec- tions are terreftrial meridians or hour circles, when the luminaries are in the equator. Hence T I D [ 43i 3 TIB Hence it follows, that all we have already faid as to ; the times of high and low water may be applied to every place on the furface of the earth, when the fun and moon are in the equator. But the heights of tide will diminilh as we recede from the equator. The heights mull be re¬ duced in the proportion of radius to the cofine of the la¬ titude of the place. But in every other fituation of the fun and moon all the circumfiances vary exceedingly. It is very true, that the determination of the elevation of the waters in any place whatever is equally eafy. The difficulty is, to exhibit for that place a connefted view of the whole tide, with the hours of flood and ebb, and the difference between high and low water. This is not indeed difficult ; but the procefs by the ordinary rules of fpherical trigonometry is tedious. When the fun and moon are not near conjunffion or oppofition, the fhape of the ocean refembles a turnip, which is flat and not round in its broadeft part. Before we can determine with precifion the different phenomena in connedtion, we muff afcertain the pofition or attitude of this turnip ; marking on the furface of the earth both its elliptical equators. One of thefe is the plane paffing through the fun and moon, and the other is perpendicular to it, and marks the place of low water. And vve muff mark in like manner its firft meridian, which paffes through all the four poles, and marks on the furface of the earth the place of high water. The pofition of the greateft fec- tion of this compound fpheroid is frequently much incli¬ ned to the earth’s equator j nay fometimes it is at right angles to it, when the moon has the fame right afcenfion with the fun, but a different declination. In thefe cafes the ebb tide on the equator is the greatefl: pcffible j for the lowTer poles of the compound fpheroid are in the equator. Such fituations occafion a very complicated calculus. We muft therefore content ourfelves with a good approximation. And firft, with refpeft to the times of high wTater. It will be fufficient to conceive the fun and moon as always in one plane, viz. the ecliptic. The orbits of the fun and moon are never more inclined than 54 degrees. This will make very little difference ; for when the lu¬ minaries are fo fituated that the great circle through them is much inclined to the equator, they are then very near to each other, and the form of the fpheroid is little different from what it would be if they were really in conjunftion or oppofition. It will therefore be fuffi¬ cient to confider the moon in three different fituations. 1. In the equator. The point of higheft water is ne¬ ver farther from the moon than 150, when fhe is in apo¬ gee, and the fun in perigee. 'I herefore if a meridian be drawn through the point of higheft water to the equator, the arch mh of fig. 4. will be reprefented on the equator by another arch about of this by reafon of the inclination of the equator and ecliptic. There¬ fore, to have the time of high water, multiply the num¬ bers of the columns which exprefs the difference of high water and the moon’s fouthing by -5%%-, and the products give the real difference. 2. Let the moon be in her greateft declination. The arch of right afcenfion correfponding to mh will be had by multiplying mh, or the time correfponding to it in the table, by 3. When the moon is in a middle fituation between thefe two extremes, the numbers of the table will give the right afcenfion correfponding to m h without any correction, the diflance from the equator compenfating Tide, for the obliquity of the ecliptic arch m h. ——y—« The time of low water is not fo eafily found 5 and we muft either go through the whole trigonometrical procefs, or content ourfelves with a lefs perfeCt appro¬ ximation. The trigonometrical procefs is not indeed dif¬ ficult : we muft find the pofition of the plane through the fun and moon. A great circle through the moon perpendicular to this is the line of high water; and an¬ other perpendicular circle cutting this at right angles is the; circle of low water. But it will be abundantly exaft to confider the tide as accompanying the moon only. Let NQSE (fig. 7.) be a feftion of the terraqueous j-- „ globe, of which N and S are the north and fouth poles and EO(^ the equator. Let the moon be in the direc¬ tion OM, having the declination BQ. Let D be any place on the earth’s furface. Draw the parallel LDC of latitude. Let B'F b'f be the ocean, formed into a fpheroid, of which B^ is the axis and f¥ the equator. As the place D is carried along the parallel CDL by the rotation of the earth, if will pais in fucceflion through different depths of the watery fpheroid. It will have high water when at C and L, and low water when it croffes the circleyOF. Draw the meridian N G, and the great circle ¥>db. The arch G(^, when converted into lunar hours (each about 62 minutes), gives the du¬ ration of the flood dc and of the fubfequent ebb cd, which happen while the moon is above the horizon : and the arch EG will give the durations of the flood and of the ebb which happen when the moon is below the hori¬ zon. It is evident, that thefe two floods and two ebbs have unequal durations. When D is at C it has high water, and the height of the tide is CC'. For, the fphe¬ roid is fuppofed to touch the fphere on the equator /OF, fo that of CC' is the difference between high and low water. At L the the height of the tide is LL' j and if we defcribe the circle LNy, Cy is the difference of thefe high waters, or of thefe tides. Hence it appears, that the two tides of one lunar day may be confiderably different, and it is proper to diftin- guifh them by different names. We fhall call that a/?/- perior tide which happens when the moon is above the horizon during high water. The other may be called the mfenor tide. The duration of the fuperior tide is meafured by 2G£), and that of the inferior tide by 2EG ; and 4GO meafures the difference between the whole duration of a fuperior and of an inferior tide. From this conftruftion we may learn in general, I. When the moon has no declination, the durations and alfo the heights of the fuperior and inferior tides are equal in all parts of the world. For in this cafe the tide equator f¥ coincides with the meridian NOS, and the poles ¥>’b' of the watery fpheroid are on the earth’s equa¬ tor. 2. When the moon has declination, the duration and alfo the height of a fuperior tide at any place is greater than that of the inferior ; or is lefs than it, according as the moon’s declination and the latitude of the place are. of the fame or oppofite names.. This is an important circumftance. It frequently happens that the inferior tide is found the greateft when it ffiould be the leaft 5 which is particularly the cafe at the Nore. I his {hows, without further reafoning, that the tide at the Nore is only a branch of the regular tide,. T I D [ 432 ] T I The regular tide comes in between Scotland and fupplements of the angle ICB. 'Tide. tide. ' the continent j and after travelling along the coaft reaches the Thames, while the regular tide is juft coming in again between Scotland and the continent. 3. If the moon’s declination is equal to the colati¬ tude of the place, or exceeds it, there will be only one tide in a lunar day. It will be a fuperior or an inferior tide, according as the declination of the moon and the latitude of the place are of the fame or oppofite kinds. For the equator of the tide cuts the meridian in f and I. Therefore a place which moves in the parallel c f has high water when at c, and 12 lunar hours after¬ wards has low water when at f. And any place k which is ftill nearer to the pole N has high water when at £, and 12 lunar hours afterwards has low water at tn. Therefore, as the moon’s declination extends to 300, all places farther north or fouth than the lati¬ tude 6o° will fometimes have only one tide in a lunar day. 4. The fine of the arch GO, which meafures -Jth of the difference between the duration of a fuperior and in¬ ferior tide, is = tan. lat. X tan. deck For in the ipherical triangle d OG Rad. : cotan. rf,'2l A y^-/- \ 1 / ^ ^ "l \ Wat \ T~y^ <7 -£^— Ar f II o \\ r c ° ]Q w cv- I V. T/yn/i xXcu tn ? ' T 1 D [ 433 ] T I D Tide. i. The greateft tides happen when the moon is in the ■~V ' zenith or nadir of the place of obfervation : for then the point B coincides with A, and DF becomes DB j that is, — M, indicating the fall tide BB'. 2. When the moon is in the equator, the fuperior and inferior tides have equal heights, in ?»! • coi.1 lat. For then A and I coincide with C, and the points F and K coincide in z, and D z is ~ DB • col.* BL)C, —hi • col.1 lat. If the place of obfervation is in the equator, the inferior and fuperior tides are again equal, whatever is the moon’s declination : For then B coincides with C, and the points F, K, and H, coincide with G j and PG X PC • cof.* APG, = M • cof.* decl. moon. 4. The fuperior tides are greater or lefs than the in¬ ferior tides according as the latitude and declination are of the fame or of oppofite names. For by making ~QZ, and drawing £ C n, cutting the fmall circle in /3, we tee that the figure is reverfed. The difference be¬ tween the fuperior and inferior tides is KF, or IA X cofin. of the angle formed by IA and DB ; that is, of the angle BD^, which is the complement of twice ZQ4 becaufe BOC = 2ZCQ. Now IA is 2 GA, — 2OA • fin. 2 MO = PC 'fin. 2 M£) , — M ' fin. 2 deck Therefore the difference of the fuperior and in¬ ferior tides is M* fin. 2 declin. fin. 2 lat. 5. If the colatitude be equal to the declination, or lefs than it, there will be no inferior tide, or no fupeiior tide, according as the latitude of the place and declination of the moon are of the fame or oppofite names. For when PZ Mf), D coincides with I, and IK vaniffies. When PZ is lefs than MO, the point D is between C and I, and the point Z never paffes through the equator of the wTatery fpheroid ; and the low water of its only tide is really the fummit of the inferior tide. 6. At the pole there is no daily tide : but there are two monthly tides “ M * fin.* declin. and it is loiv wTa- ter when the moon is in the equator. 7. The medium tide, reprefented by DH, is ~M X I’+cof. 2to. xrof. sdccii^ For DH=DO+OH. 2 Now OH is equal toOGxcof. GOHmrOG'cof. 2Z£F And OGzrOA'Cof. GOA, rzOA-cof. 2MO. There¬ fore OHmrOA • cof. 2ZO • cof. 2MQ. Therefore DH rrOA + OA-cof. 2ZQ^cof. 2M<£ = - I 4-Cof. 2Z0 " cof. 2 MO 1 • r if M x — ^ li. Let this for the fu- 2 ture be called m. N. B. The moon’s declination never exceeds 30°. Therefore cof. 2MC) is always a pofitive quantity, and never lefs than which is the cofine of 60®. While the latitude is lefs than 450, cof. 2 lat. is alfo a pofi¬ tive quantity. When it is precifely 450 the cofine of its double is 0 ; and when it is greater than 45, the co¬ fine of its double is negative. Hence we fee, 1. That the medium tides are equally affefted by the northern and fouthern declinations of the moon. 2. If the latitude of the place is 450, the medium tide is always § M. This is the reafon why the tides along the coafts of France and Spain are fo little affefted by the declination of the moon. 3. If the latitude is lefs than 450, the mean tides in- creafe as the moon’s declination diminifties. The con¬ trary happens if ZO is greater than a;0. For DH in- VOL. XX. Part II. creafes or diminifties wdiile the point G feparates from C Tide, according as the angle COD is greater or lefs than [ v COB $ that is, according as PCZ is greater or lefs than zc£- 4. When Z is in the equator, H coincides with G, and the effeft of the moon’s declination on the height of the tides is the moil fenfible. The mean tide is then — M 1 -j- cof. 2 MQ 2 All that we have now faid may be faid of the folar tide, putting S in place of M. Alfo the fame things hold true of fpring tides putting M-fS in place of M. But in order to afcertain the effeffs of declination and latitude on other tides, we mult make a much more complicated conftrudfion, even though we fuppofe both luminaries in the ecliptic. For in this cafe the two de- preffed poles of the watery fpheroid are not in the poles of the earth ; and therefore the leffions of the ocean, made by meridians, are by no means eilipfes. In a neap tide, the moon is vertical at B (fig. 7. or 8.), Fig. 7. orS. and the fun at fome point off¥, 90° from B. If O lie 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 1V1 -f- 0 — D'F or DK Xfin.* z/O, sue M + S — tide X —r;—4re, as is evi¬ cof.* MQ/ dent. But if the fun be vertical at s very irregularly •, and the perceptible high water on the Spanilh coad differs four hours from that of the fouthern coad. Thus it happens, that one tide ranges round Europa point, and another along the (Lore near Ceuta, and there is a third current in the middle different from both. Its general direftion is from the 3 I 2 Atlantic T -I D [ 43^ 1 T I D Atlantic ocean into the Mediterranean fea, but it fome- times comes out when the ebb tide in the Atlantic is conliderable. Suppofe the moon over the middle of the Mediter¬ ranean. The furface of the lea 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 with¬ in half an hour of high water. Therefore there will be a current fetting in from the Atlantic. About three and an half hours after, it is high water within and half ebb without. The current now fets out from the Me¬ diterranean. Three hours later, it is low wrater wdth- out the Straits and half ebb within \ therefore the cur¬ rent has been fetting out all this while. Three hours later, it is half flood without the Straits and low' water within, and the current is again fetting in, &c. Were the earth fluid to the centre, the only fenfible motion of the waters would be up and down, like the waves on the open ocean, which are not brufhed along by ftrong gales. But the fhallownefs of the channel makes a horizontal motion neceflary, that water may be fupplied to form the accumulation of the tide. When this is formed on a flat fhelving coaft, the water mull: flow in and out, on the flats and fands, while it rifes and falls. Thefe horizontal motions mult be greatly modified by the channel or bed along which they move. When the channel contradls along the line of flowing water, the wave, as it moves up the channel, and is checked by the narrowing fhores, muft be reflefted back, and keep a-top of the w'aters flill flowing in un¬ derneath. Thus it may rife higher in thefe 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 fre¬ quently rifes 50 feet. But we cannot give any thing like a full or fatisfaflory account of thefe Angularities. In the bay of Fundy, and particularly at Annapolis Royal, the wTater fometimes rifes above ico feet. This feems 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 ar'e unqueftion- ably 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 wrater are frequently feen on a fmall fcale in the motions of brooks and rivers ; but we are too little acquainted with hy¬ draulics to explain them with any precifion. We have feen that there is an ofcillation of waters formed under the fun and moon ; and that in confe- quence of the rotation of the earth, the inertia and the wrant of perfeft fluidity of the waters, and obftruftions in the channel, this accumulation never reaches the place where it would finally fettle if the earth did not turn round its axis. The confequence of this muff be a general current of the w'aters from eaft to weft. This may be feen in another wray. The moon in her orbit round the earth has her gravity to the earth diminifhed by tbe fun’s difturbing force, and therefore moves in an orbit lefs incurvated than flie wTould defcribe independent of the fun’s aflion. 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 fup- pofe the moon turning round the earth, almoft in con- tad with the equator, with her natural undifturbed pe¬ riodic time, and that the earth is revolving round its axis in the fame time, the moon would remain continu¬ ally above the fame fpot of the earth’s furface (fuppofe the city of Quito), and a fpedator in another planet would fee the moon always covering the fame fpot. Now let the fun ad. This will not affed the rotation of the earth, becaufe the adion on one part is exadly balanced by the adion on another. But it will affed the moon. It will move more (lowly round the earth’s centre, and at a greater diftance. It will be left behind by the city of Quito, which it formerly covered. And as the earth moves round from weft to eaft, the moon, moving more (lowly, will have a motion to the weft with refped to Quito. In like manner, every particle of water has its gravity diminifhed, and its diurnal motion retarded ; and hence arifes a general motion or current from eaft to weft. This is very diftindly perceived in the At¬ lantic and Pacific oceans. It comes round the Cape of Good Hope, ranges along the coaft of Africa, and then fets diredly over to America, where it meets a fimilar ftream which comes in by the north of Europe. Meet¬ ing the (bores of America, it is defteded both to the fouth along the coaft of Brazil, and to the north along the North American fhores, where it forms what is call¬ ed the Gulf Stream, becaufe it comes from the gulf of Mexico. This motion is indeed very (low, this being fufticient for the accumulation of feven or eight feet on the deep ocean •, but it is not altogether infenfible. We may exped differences in the appearances on the weftern (bores of Europe and Africa, and on the weftern (bore of America, from the appearances on the eaftern coafts of America and of Afia, for the general current obftruds the waters from the weftern (bores, and (ends them to the eaftern (bores. 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 exped differences between the appearances on the weft ccafls of Europe and of Ame¬ rica. 'The obfervations made during the circumnaviga¬ tions of Captain Cook and others (how 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 fur- rounds this globe, confiding of an elevation and de- preffion, which move gradually from eaft to weft. Nei¬ ther does this tide ever attain that pofition with refped 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 eaft to weft ; and this is the principal caufe of the trade-winds. They are a little accelerated by being heated, and therefore expanding. They ex¬ pand more to the weftward than in the oppofite direc¬ tion, becaufe the air expands on that fide into air which is norv cooling and contrading. Thefe rvinds very evi¬ dently follow the fun’s motion, tending more to the fouth or north as he goes fouth or north. Were this motion corfiderably affeded by the expanfion of heated air, we (hould find the air rather coming northward and fouthward from the torrid 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 verv formation of this tide. We cannot perceive the accumulation. It cannot affed the barometer, as many T I D [ 437 ] TIL many think, becaufe, though the air becomes deeper, it becomes deeper only becaufe it is made lighter by the gravitation to the fun. Inttead of prefling more on the ciltern of the barometer, vve imagine that it prefles lefs; becaufe, like the ocean, it never attains the height to which it tends. It remains always too low for equili¬ brium, and therefore it fhould prefs with lefs force on the ciftern of a barometer. There is an appearance precifely flmilar to this in the planet Jupiter. He is furrounded by an atmofphere which is arranged in zones or belts, probably owing to climate differences of the different latitudes, by which each feems to have a different kind of Iky. Something like this will appear to a fpe&ator in the moon looking at this earth. The general weather and appearance of the Iky is confiderably different in the torrid and tem¬ perate zones. Jupiter’s belts are not of a conftant lhape and colour ; but there often appear large fpots or trafts of cloud, which retain their fhape during feveral revo¬ lutions of Jupiter round his axis. To judge of his rota¬ tion by one of thefe, w’e fhould fay that he turns round ’n 9-55* There is alfo a brighter fpot which is frequent¬ ly 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 traft of clouds hovering over fome volcano. This fpot turns round in 9-5 ^ And thus there is a general current in Jffs atmofphere from eaft to w’eft. _ Both the motion of the air and of the water tend to diminiih the rotation of the earth round its axis 5 for they move flower than the earth, becaufe they are re¬ tarded by the luminaries. They muft communicate this retardation to the earth, and muff take from it a quan¬ tity of motion precifely equal to what they w^ant, in or¬ der to make up the equilibrated tide. In all probability this retardation is compenfated. by other caufes j for no retardation can be obferved. This would have altered the length of tne year flnce the time of Hipparchus, giving it a fmaller number of days. We fee caufes of compenfation. The continual waffling down of foil from the elevated parts of the earth muft produce this effeft, by communicating to the valley on which it is brought to reft the excefs 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 IVIr Saint Pierre. This author fcouts the Newtonian theory of the tides, as erroneous in principle, and as quite in- fufflcient for explaining the phenomena ; and he afcribes all phenomena of the tides to the liquefadion 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 w^e wifli to fpeak with re- fpedt, for his conftant attention to final caufes, and the proof thence refulting of the wifdom and goodnefs of God. For this he is entitled to the greater praife, that it required no fmall degree of fortitude to reftft; the in¬ fluence of national example, and to retain his piety in the midft of a people who have drunk the very dregs of t ie atheifm 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 colledled manv important faffs. J he argument which he em¬ ploys to prove that the earth is a prolate fpheroid, is a direfl demonftration 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 ten times more ice and fnow floating on the northern fea than there is, and wrere it all to melt in one minute, there would be no flux from it } for it would only fill up the fpace which it formerly occupied in the water. Of this any perfon will be convinced, who (hall put a handiui of fnowT fqueezed hard into a jar of water, and note the exaff height of the water. Let the fnow melt, and he will find the water of the fame height as before. 7 IDE-lVaiters, or Tide/men, are inferior officers be- longing to the cuftomhoufe, whofe employment is to watch or attend upon ftiips until the cuftoms be paid : they get. this name from their going on board fliips on their arrival in the mouth of the Thames or other ports, and fo come up with the tide. TIEND, in Scots Lazo. See Teind. . TIERCE, or Ieirce, a mealure of liquid things, as wine, oil, &c. containing the third part of a pipe, or 42 gallons. TIERCED, in Heraldry, denotes the Afield to be divided by any part of the partition-lines, as party, coupy, tranchy, or tailly, into three equal parts of dif¬ ferent colours or metals. TIGER. See Felis, Mammalia Index. TlGER-Wolf, the name of the hyaena at the Cape of Good Hope. See Canis, Mammalia Index. 1IGRIS, a river of Afia, which has its fouvee near that of the Euphrates in the mountain Tchildir in Tur¬ komans : afterwards it feparates Diarbeck from Erze- rum, and Khufiftan from Irac-Arabia 5 and uniting with the Euphrates at Gorno, it falls into the gulf of Baf- forab, under the name of Schat el-Arab. This river paffes by Diaroekir, Gezira, Mouful, Bagdad, Gorno and Bafforah. - & ’ 1 ILI A, Lime or Linden-tree, a genus of plants belonging to the clafs of polyandria } and in the natu¬ ral fyftem ranging under the Columnferce. See Bota¬ ny Index. 1ILLEMONT, Sebastian le Nain de. See Nain. FILLER o/*SHIR, a ffrong piece of wood faftened in the head of the rudder, and in fmall flrips and boats called the helm. TILLOEA, a genus of plants belonging to the clafs of letrandria } and in the natural fyftem ranging under the 13th order, Succulents. See Botany index. IILLOI SON, John, a celebrated archbilhop of Canterbury, was the fon of Robert Tillotfon of Sower- by, in the parilh of Halifax in Yorkftfire, clothier } and was born there in the year 1630. He ftudied in Clare-hall, Cambridge} and in 1636 left this college, in order to become tutor to the fon of Edmund Pri- deaux, Efq. of Ford abbey in Devonlhire. Fie was afterwards curate to Dr Hacket vicar of Chelhunt, in Hertfordfliire. In 1663, he was prefented by Sir Tho¬ mas Barnardifton to the reftory of Ketton or Kedding- ton in the county of Suffolk ; but was the next year . chofen preacher to Lincoln’s Inn, when he procured Ketton to be beftowed on his curate. He was greatly admired in London for his fermons } and in the fame year was chofen Tuefday-lefturer at St Lawrence’s church, London, where his leftures were frequented by sll J TIM [ 438 ] TIM Til lot fon all the divines of the city, and by m&ny perfons of qua- Jl lity and diftinftion. In 1666, he took the degree of Time . ©oftor 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 Shrewlbury, whom he converted from Popery 5 and the next year refufed to fign the clergy of London’s addrefs of thanks to King Charles II. for not agreeing to the bill of ex- elulion of the duke of York. In 1683, he vilited the unfortunate Lord Ruffel when under condemnation 5 and attended him in his lalt moments on the fcafFold. In J689, he was inftalled dean of St Paul’s ; made clerk of the clofet to King William and Queen Mary 5 and ap¬ pointed one of the commiffioners to prepare matters to be laid before the convocation, in order to a compre- henfion of all Proteftants, as well diflenters as church¬ men ; but this attempt was fruftrated by the zeal of thofe members of that body, w’ho refufed to admit of any alteration in things confeffedly indifferent. In 1691, Dr Tillotfon was, notwithftanding the warmeft remon- ftrances and intreaties on his part, confecrated archbi- fhop of Canterbury, and four days after was fvvorn one of the privy council; their majelties always repofing an entire confidence in his prudence, moderation, and integrity. In 1694, ^ie was ^ei'zecf with a palfy, of which he died in the 65th year of his age. He was in¬ terred in the church of St Lawrence Jewry, London, w'here a handfome monument is erected to his memory. This learned and pious divine, while living, wTas greatly inveighed againft by the enemies of the revolution. Af¬ ter his death there was found a bundle of bitter libels which had been publifhed againft him, on which he had written with his own hand, “ I forgive the authors of thefe books, and pray God that he may alfo forgive them.” It is remarkable, that while this truly great man was in a private ftation, he always laid afide two- tenths of his income for charitable ufes. One volume in folio of Dr Tillotfon’s fermons w7as publilhed in his life-time, and correfted by his own hand ; they were tranflat?d into French by Baibeyrac. Thofe which came abroad after his death, from his chaplain Dr Barker, made tw’O volumes in folio, the copy of which was fold for 2500k 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. King William, however, gave two grants to his widow •, the Hrft of which was an annuity of 400!. during the term of her natural life, and the fecond of 200I. as an addi¬ tion to the former annuity. Dr Tillotfon wrote fome other works befides his Sermons ; and alfo publiftied Dr Barrow’s works, and Dr Wilkins’s Treatife of the Prin¬ ciples 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 (hip, or the incurvated pieces of wood, branching outward from the keel in a vertical direiflion, fo as to give ftrength, figure, and fo- lidity, to the whole fabric. See SHIP-BUILDING, book i. chap. ii. TIME, a fucceflion of phenomena in the univerfe, or a mode of duration marked by certain periods or 4 meafures, chiefly by the motion and revolution of the Time fun. 1) The general idea which time gives in every thing to, limon which it is applied, is that of limited duration. Thus ^ we cannot fay of the Deity, that he exifts in time ; be- caufe eternity, which he inhabits, is abfolutely uniform, neither admitting limitation nor fucceflion. See Meta¬ physics, N° 209. Time, in Mufc, is an affeftion of found, by which it is faid to be long or ftvort, with regard to its continu¬ ance in the fame tone or degree of tune. Mufical time is diftinguiihed 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 minims, a minim to two crotchets, a crotch¬ et to two quavers, &c. Common or double time is of two kinds. The firft when every bar or meafure 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 meafure are various, but there are three common di- ftimftions; the firftyftno, denoted at the beginning of the line by the mark ^ ; the fecond brifk, marked thus and the third very brifk, thus marked ffi- 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. TlME.-Kecpers, or Inftruments for meafuring Time. See Clock, Dial, Watch, &c. Harrifoti's TlME-Keeper. See Harrison and Lon¬ gitude. TIMOLEON, a celebrated Corinthian general, who reftored the Syracufans to their liberty, and drove the Carthaginians out of Sicily. See Syracuse, N° 5c — 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 Philadel- phus. He took fo little pains to invite difcipleS to his fchool, that it has been faid of him, that as the Scy¬ thians {hot flying, Timon gained pupils by running from them. He was fond of rural retirement •, and was fo much addidled to wine, that he held a fuccefsful conteft with feveral celebrated champions in drinking. Like Lucian, he wrote with farcaftic humour againft the wdiole body of philofophers. The fragments of his fati- rical poem Silli, often quoted by the ancients, have been carefully colledled by Henry Stephens in his Poefs Pltilofophica. 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 detefted all the reft of the human race ? on which he replied, “ It is becaufe I forefee that he will be the ruin of the Athenians.” He carefully avoided all forts of company ; yet went one day to an affembly of the people, and cried with a loud voice, “ That he had a fig-tree cn which feveral perfons had hanged themfelves; TIM [ 439 ] TIP Timon, themfelves but as he intended to cut it down, in order 1 imotheus. tQ a houfe on place where it flood, he gave v them notice of it, that if any of them had a mind to hang themfelves, they muft make hafte and do it fpee- dily.” He had an epitaph engraved on his tomb, filled with imprecations againft thofe who read it. Shake- fpcare has formed a tragedy on his ftory. TIMOR, an ifland of Afia, in the Eaft Indian fea, to the fouth of the Moluccas, and to the eaft of the ifland of Java, being 150 miles in length, and 37 in breadth. It abounds in fandal-wood, wax and honey j and the Dutch have a fort here. The inhabitants are Pagans, and are little better than favagesj and fome pretend they had not the ufe of fire many years ago. TIMOTHEUS, one of themoft celebrated poet-mu- ficians of antiquity, was born at Miletus, an Ionian city of Caria, 446 years B. C. He was contemporary with Philip of Macedon and Euripides 5 and not only ex¬ celled in lyric and dithyrambic poetry, but in his per¬ formance upon the cithara. According to Paufanias, he perfected that inftrument by the addition of four new ftrings to the feven which it had before; though Suidas fays it had nine before, and that Timotheus only added two, the 10th and nth, to that number. See Lyre. With refpefl to the number of ftrings upon the lyre of Timotheus : The account of Paufanias and S«idas is confirmed in the famous fenatus-confultum againft him, ftill extant, preferved at full length In Boethius. Mr Stillingflcet has given an extra£l from it, in proof of the fimplicity of the ancient Spartan mufic. The fa£t is mentioned in Athenaeus; and Cafaubon,. in his notes upon that author, has inferted the whole original text from Boethius, with corre&ions. The following is a faithful tranflation of this extraordinary Spartan a£t of parliament. “ Whereas Timotheus the Milefian, com¬ ing to our city, has dilhonoured our ancient mufic, and, defpifing the lyre of feven ftrings, has, by the introduc¬ tion of a greater variety of notes, corrupted the ears of our youth ; and by the number of his ftrings, and the novelty of his melody, has given to our mufic an effe¬ minate and artificial drefs, inftead of the plain and orderly one in which it has hitherto appeared •, rendering me¬ lody infamous, by compofing in the chromatic inftead of the enharmonic : The kings and the ephori have therefore refolved to pafs cenfure upon Timotheus for thefe things : and, farther, to oblige him to cut all the fuperfluous ftrings of his eleven, leaving only the feven tones ; and to baniftr him from our city ; that men may be warned for the future not to introduce into Sparta any unbecoming cuftbm.^ The fame ftory, as related in Athenaeus, has this ad¬ ditional circumftance, That when the public executioner was on the point of fulfilling the fentence, by cutting off the new ftrings, Timotheus, perceiving a little ftatue in the fame place, with a lyre in his hand of as many ftrings as that which had given the offence, and fliowing it to the judges, was acquitted. It appears from Suidas, that the poetical and mufical compofitions of Timotheus were very numerous, and of various kinds. He attributes to him 19 nomes, or can¬ ticles, in hexameters •, 36 proems, or preludes; 18 dithy- rambics ; 21 hymns j the poem in praife of Diana j one panegyric j three tragedies, the Perfians, Phinidas, and Laertes; to which muft be added a fourth, mentioned Timotheus by feveral ancient authors, called Niobe, without forget- H ' ting the poem on the birth of Bacchus. Stephen of SY’f Byzantium makes him author of 18 books of nomes, or airs, for the cithara, to 8000 verfes j and of 1000 or preludes, for the nomes of the flutes. Timotheus died in Macedonia, according to Suidas, at the age of 97 ; though the Marbles, much better au¬ thority, fay at 90 ; and Stephen of Byzantium fixes his death in the fourth year of the 105th Olympiad, two years before the birth of Alexander the Great j whence it appears, that this Timotheus was not the famous player on the flute fo much efteemed by that prince, who was animated to fuch a degree by his performance as to feize his arms; and w ho employed him, as Athe¬ naeus informs us, together with the other great mufi- cians of his time, at his nuptials. However, by an inattention to dates, and by forgetting that of thefe two muficians of the fame name the one was a Milefian and the other a Theban, they have been hitherto often- confounded. TIMUR-beck. See Tamerlane. TIN, a metallic fubftance. See CHEMISTRY and Mineralogy Index for an account of its qualities and ores; and for the method of reducing its ores, fee Ores, ReduBion of. TINCAL, the name by which crude or impure bo¬ rax is fometimes known. See Borax, Chemistry Index. TINCTURE, in Pharmacy. See Materia Me¬ dic a Index. TINDAL, Dr Matthew, a famous Englifti writer, was the fon of the reverend Mr John Tindal of Beer- Ferres in Devonfliire, and wtis born about the year 1657. He ftudied at Lincoln college in Oxford, whence he removed to Exeter, and was afterwards ele&ed felldw of All-Souls. In 1685 he took the degree of debtor of law, and in the reign of James II. declared himfelf a Roman Catholic ; but foon renounced that religion. After the revolution he publiftied feveral pamphlets in favour of government, the liberty of the prefs, &.c. His “ Rights of the Chriftian Church afferted,” occa- fioned his having a violent conteft with the high- church clergy \ and his treatife “ Chriftianity as old as the Creation,” publiihed in 1730, made much noife, and was anfwered by feveral writers, particularly by Dr Conybeare, Mr Forfler, and, Dr Leland. Dr Tin¬ dal died at London in Auguft 1733. kft *n manufeript a fecond volume of his “ Chriftianity as old as the Creation the preface to which has been pu'- blifhed. Mr Pope has fatirized Dr Tindal in his Dunciad. TINDALE, William. See Tyndale. TINNING, the covering or lining any thing with melted tin, or tin reduced to a very fine leaf. Looking- glaffes are foliated or tinned with plates of beaten tin, the whole bignefs of the glafs, applied or faftened thereto by means of quickfilver. See FOLIATING of Looking Glaffes. TINNITUS aurium, a noife in the ears like the con¬ tinued found of bells, very common in many diforders, particularly in nervous fevers. TIPPERARY, a county of the province of Munfter in Ireland, bounded on the weft by thofe of Limerick and Clare, on the eaft by the county of Kilkenny and Queen’s county, on the fouth by the county of Water¬ ford, T I R Tipperary ford, and on the north and north-ead by Iving’s-county .!i and the territory of the ancient O’Carols. It extends , Tiro1- , about 42 miles in length, 27 in breadth, containing Goal's 599,5°o acres, divided into 12 baronies, in which are edn\of feveral market towns and boroughs. It fends eight Camden's members to parliment, viz. two for the county, two for Britannia- jjie c;ty 0f Cathel, and two for each of the boroughs of Clonmell, Fetherd, and Thurles. The north part of it is mountainous and cold } but in the fouth the air is milder, and the foil much more fertile, producing plenty of corn, and good padure for the numerous herds of cat¬ tle and flocks of flreep with which it abounds. The north part is called Ormond, and for a long time gave the title of earl, and afterwards of marquis and duke, to the no¬ ble family of Butler, defcended from a After of Thomas a Becket archbilhop of Canterbury, till, at the acceffion of George I. the laft duke vras attainted of high-treafon, and died abroad. In that part of the county, the family had great prerogatives and privileges granted them by Edward III. Another diftrift in this county was an¬ ciently called the County of the Holy Crofs of Tippera¬ ry, from a famous abbey in it ftyled Holy Crofs, on account of a piece of Chrift’s crofs that tvas hud to be preferved there. This abbey and diftrift enjoyed alfo fpecial privileges in former times. The remains of the abbey, or rather the fpot where it flood, are ftill held in great veneration, and much refortcd toby the Roman Catholics. TIPSTAFF, an officer who attends the judges with a kind of flaff tipped with filver, and takes into his charge all prifoners who are committed or turned over at a judge’s chambers. TIPULA, the Crane-fly-, a genus of infedls be¬ longing to the order of diptera. bee Entomology Index. / _ ^ TIRE, in the fea language, is a i-ow of cannon placed along a (hip’s fide, either above upon deck, or below, diftinguifned by the epithets of upper and lower tires. TIROL, or Tyrol, a county of Germany in the circle of Auftria, under which may be included the territories belonging to the bifhops of Brixen, I rent, and Chur, the Teutonic Order, and the prince of Dei- trichftein, the Auftrian feigniories before the Arlberg, and the Auftrian diftridls in Swabia. It is 150 miles in length, and 120 in breadth, and contains 28 large towns. The face of the country is very mountainous. Of thefe mountains^ fome have their tops always buried in fnow ; others are covered with woods, abounding with v a variety of game; and others are rich in metals, and marble of all colours. Of the lower, fome yield plenty of corn, others wine, and woods of chefnut trees. The valleys are exceeding fertile alio, and pleafant. In fome places confiderable quantities of flax are railed, in others there is a good breed of horfes and horned cattle j and, among the mountains, abundance of chamois and wild goats. In this country are alfo found precious ftones of feveral forts ; as garnets, rubies, amethyfts, emeralds, and a fpecies of diamonds, agates, carnelians, calcedo- nies, malachites, &tc. \ nor is it without hot baths, acid waters, fait pits, mines of filver, copper, and lead, mi¬ neral colours, alum, and vitriol. The principal river of Tirol is the Inn, which, after traverfing the country, and receiving a number of leffer dreams into it, enters 4 T I T Bavaria, in which, at Paffau, it falls into the Danube. Tirol, The men here are very tall, robuft, and vigorous j the Tltan’ women alfo are flout, and generally fair -, and both fexes ”'v have a mixture of the Italian and German in their tem¬ pers and cbarafters. As there is little trade or manu¬ facture in the country, except what is occafioned by the mines and fait works, many of the common people are obliged to feek a fubfiftence elfewhere. A particular kind of falutation is ufed all over Tirol. When a per- fon comes into a houfe, he fays, “ Hail ! Jefus Chriit the anfwer is, “ May Chrift be raifed, and the Holy- Virgin his mother.” Then the mafter of the houfe takes the vifitor by the hand. This falutation is fixed up in print at all the doors, wdtlr an advertifement tacked to it, importing, that Pope Clement XI. granted 100 days indulgence, and a plenary abfolution, to thofe who (hould pronounce the falutation and anfwer, as often as thev did it. The emperor has forts and citadels fo ad- vantageoufly fituated on rocks and mountains all over the country, that they command all the valleys, avenues, and pafles that lead unto it. The inhabitants, however, to keep them in good humour, are more gently treated, and not fo highly taxed as thofe of the other hereditary countries. As to the dates, they are much the fame in this country as in the other Auftrian territories, except that the peafants here fend deputies to the diets. Tirol came to the houfe of Auftria in the year 1363, when Margaret, countefs thereof, bequeathed it to her un¬ cles the dukes of Auftria. The arms of Tirol are an eagle gules, in a field argent. The counts of Trap are hereditary ftewards 5 the lords of Glolz, chamberlains j the princes of Trautfon, marfhals , the counts of Wol- kenftein, mafters of the horfe and caivers; the houfe of Spaur, cup-bearers ; the counts of Kungl, fewers and rangers ; the counts of Brandis, keepers of the jewels j the houfe of Welfperg, purveyors and ftaff-bearers; and the counts of Coalto, falconers. Befides the governor^ here are three fovereign colleges, fubordinate to the court at Vienna, which fit at Infpruck, and have their different departments. Towards the expences of the military eftablifhment of this country, the proportion is 100,000 florins yearly ; but no more than one regiment of foot is generally quartered in it. Tirol is divided into fix quarters, as they are called 5 namely, thofe of the Lower and Upper Innthal, Vintf- gow, Etch, Eifack, and Pufterthal. TITAN, in fabulous hiflory, the fon of Coelus and Terra, and the elder brother of Saturn, fuffered the latter to enjoy the crown, on condition that he fliould bring up none of his male iffue, by which ineans th» crown fhould at length revert to him ; but Jupiter being fpared by the addrefs of Rhea, Saturn’s wife, Titan and his children were fo enraged at feeing their hopes fruf- trated, that they took up arms to revenge the injury; and not only defeated Saturn, but kept him and his wife prifoners till he was delivered by Jupiter, who defeated the Titans; when from the blood of thefe Titans flain in the battle, proceeded ferpents, fcorpions, and all ve¬ nomous reptiles. See Saturn. Such is the account given by the poets of this family of Grecian and Roman gods. From the fragments of Sanchoniatho, however, and other ancient writers, many learned men have inferred that the Titans were an early race oY ambitious heroes, who laid the foundation of that idolatry which quickly overfpread the world, and that r 44° ] TIT - [ 44i ] TIT Titan, that by aflumlng the names of the luminaries of heaven v— “'l they contrived to get themfelves every where adored as the Dii tnajorum gentium. That the word Titan figni- bes the lun, there can indeed be very little doubt. Kvery one knows that fuch was its lignification in the yfiohc dialeft ; and as it is evidently compounded of 2V, which, in fome oriental tongues, fignifies bright or cieary and Tan, which figntfies a country or the earth, it may be lately concluded that Titan was the name of the lun before the word was imported into Greece. But the great queltion among antiquarians is, of what coun¬ try was that race wdrich, affuming to themfelves the names of the heavenly bodies, introduced into the world that fpecies of idolatry which is known by the appella¬ tion of Hero-worjhif) ? M. Pezron, in a work publilhed many years ago, and entitled The Antiquities of Nations, maintains that the Titans were a lamiiy ot bacae or Scythians, who made their firft appearance beyond Media and Mount Imaus, in the upper regions of Alia ; that they w7ere the de . fcendants of Gomer the fon of Japheth and grandfon of Noah j and that alter conquering a great part of the world, upon entering Upper Phrygia, they quitted their ancient name of Gomerians or Cimmerians, and aflumed that of Titans. All this, he fays, happened before the birth of Abraham and the foundation of the Affyrian monarchy j and he makes Uranus, their fecond prince in the order of fucceflion, to have conquered Thrace, Greece, the illand of Crete, and a great part of Europe. Uranus was fucceeded by Saturn, and Saturn by Jupiter,wTho flourilhed, he lays, 300 years before Mo¬ les, and divided his valt empire between himfelf, his bro¬ ther Piuto, and his coulin-german Atlas, who was called Telamon. For the truth ol this genealogy of the Ti¬ tans M. Pezron appeals to the molt approved Greek hi- ftorians j but unluckily for his hypothecs, thefe writers have not a Angle fentence by which it can be fairlv fup- ported. It fuppofes not only the great antiquity of the Scythians, but Ukewife their early progrefs in arts and fciences, contrary to what we have proved in other ar¬ ticles of this work. See Sculpture, n° 4 and 5. and Scythia. Others, taking the fragment of Sanchoniatho’s Phe- nician hiftory for their guide, have fuppofed the Titans to have been the defcendants of Ham. Of this opinion was Bilhop Cumberland ; and our learned friend Dr Doig, to whom we have been indebted for greater fa¬ vours, indulged us with the perufal of a manufcript, in which, with erudition and ingenuhy ftruggling for the pre-eminence, he traces that impious family from the profane fon of Noah, and (how's by what means they fpread the idolatrous worfhip of themfelves over the greater part ©f the ancient wwld. Cronus, of whofe exploits fome account has been given elfev here (fee Sanchoniatho), he holds to be Ham ; and tra¬ cing the progrefs of the family from Phoenicia to Cy¬ prus, from Cyprus to Rhodes, thence to Crete, and from Crete to Samothrace, he finds reafon to conclude that the branch called Titans or Titanides flourilhed about the era of Abraham, with whom, or with his fon Ifaac, he thinks the Cretan Jupiter muft have been contem¬ porary. As they proceeded from countries wrhich were the original feat of civilization to others in which man¬ kind had funk into the groflelt barbarifm, it w^as eafy for them to perfuade the ignorant inhabitants that they Vol. XX. Part II. derived the arts of civil life from their parent the fun, Titaor and in confequence of their relation to him to alfume to [nhes. themfelves divine honours. To alk how they came to " ^ think of fuch grofs impiety, is a queltion as foolilh as it would be to alk how Ham their ancellor became lb wicked as to entail the curfe of God upon himlelf and his pofterity. The origin of evil is involved in dif¬ ficulties ; but leaving all inquiries into it to be profe- cuted by the metaphyfician and moralift, it is furely more probable that the worlhip of dead men originated among the defcendants of Ham than among thofe of Shem and Japheth ; and that the fragment of Sancho- niatho, when giving an account of the origi.* of the Titans, the undoubted authors of that wrorlhip, is more deferving of credit than the fabulous and comparatively late writers of Greece and Rome. TITHES, in ecclefiaftical law, are defined to be the tenth part ot the increale, yearly arifing and renewing from the profits of lands, the Hock upon landsj and the perlbnalindultry of the inhabitants: the firft fpecies be¬ ing ufually called predial, as of corn, grafs, hops, and wood ; the fecond mixed, as of wool, milk, pigs, &.c, confifting of natural products, but nur'ured and pre- ferved in part by the care of man ; and of thefe the tenth muft be paid in grofs; the third pcrfonal, as of manual occupations, trades, filheries, and the like ; and of thefe only the tenth-part of the clear gains and pro¬ fits is due. We fhall, in this article, confider, 1. The original of the right of tithes. 2. In w’hom that right at prefent fubfifts. 3. Who may be difcharged, either totally or in part, from paying them. 1. As to their original, we will not put the title of the clergy to tithes upon any divine right; though fuch a right certainly commenced, and wre believe as certain¬ ly ceafed, with the Jewifh theocracy. Yet an honour¬ able and competent maintenance for the minifters of the gofpel is undoubtedly jure divino, whatever the particu- Blnck/ld lar mode of that maintenance may be. For, befides the pofitive precepts of the New Teftam nt, natural reafon wall tell us, that an order of men who are fepa- rated from the world, and excluded from other lucra¬ tive profeflions for the fake of the reft of mankind, have a right to be furnilhed with the neceffaries, conve¬ niences, and moderate enjoyments of life, at their ex¬ pence ; for whofe benefit they forego the ufual means of providing them. Accordingly all municipal laws have provided a liberal and decent maintenance for their national priefts or clergy j ours, in particular, have e- ftablilhed this of tithes, probably in imitation of the Jewilh law : and perhaps, confidering the degenerate ftate of the wrorld in general, it may be more beneficial to the Englifti clergy to found their title on the law> ot the land, than upon any divine right whatfoever, unac¬ knowledged and unfupported by temporal fanftions. We cannot precifely afcertain the time when tithes were firft introduced into this country. Poflibly they were contemporary with the planting of Chriftianity among the Saxons by Auguftin the monk, about the end of the fixth century. But the firft mention of them which w^e have met with in any written Englifh law, is a conftitutional decree, made in a fynod held A. D. 786, wherein the payment of tithes in general is ftrong- ly enjoined. This canon or decree, which at firft bound not the laity, was effe&ually confirmed by two g K kingdoms TIT [ 442 ] TIT kingdom*, of the heptarchy, in their parliamentary con¬ ventions of eftates, refpedlively confifting of the kings of Mercia and Northumberland, the bifhops, dukes, lena- tors, and people. Which was a few years later than the time that Charlemagne ellablilhed the payment of them in France, and made that famous divifion of them into four parts 5 one to maintain the edifice of the church, the fecond to fupport the poor, the third the bifhop, and the fourth the parochial clergy. The next authentic mention of them is in the fadus Edwardi et Guthruni; or the laws agreed upon between King Guthrun the Dane, and Alfred and his fon Ed¬ ward the Elder, fuccefiive kings of England, about the year 900. This was a kind of treaty between thofe monarchs, which may be found at large in the Anglo- Saxon laws: wherein it wTas neceffary, as Guthrun was a Pagan, to provide for the fubfiftence of the Chrillian clergy under his dominion ; and accordingly, we find ihe payment of tithes not only enjoined, but a penalty added upon non-oblervance : which law is feconded by the laws of Athelftan, about the year 930. And this is as much as can certainly be traced out with regard to their legal original. 2. We are next to confider the perfons to whom tithes are due. Upon their firft introduftion, though every man was obliged to pay tithes in general, yet he might give them to what priefts he pleafed 5 which were called arbitrary confecratwns of tithes; or he might pay them into the hands of the bithop, who diftributed among his diocefan clergy the revenues of the church, which were then in common. But when diocefes were divided into parilhes, the tithes of each parilh were al¬ lotted to its own particular minilter j firft by common confent or the appointments of lords of manors, and afterwards by the wuitten law of the land. Arbitrary confecrations of tithes took place again afterwards, and were in general ufe till the time of King John. This was probably owing to the intrigues of the regular clergy, or monks of the Benediffine and other orders, under Archbilhop Dunftan and his fvcef- fors •, who endeavoured to wean the people from pay¬ ing their dues to the fecular or parochial clergy (a much more valuable fet of men than themfelves), and were then in hopes to have drawn, by fandlimonious pretences to extraordinary purity of life, all ecclefiafii- cal profits to the coffers of their own focieties. And this will naturally enough account for the number and riches of the monafteries and religious houfes w'hich were founded in thofe days, and which were frequently endowed with tithes. For a layman, who was obliged to pay his tithes fomewhere, might think it good policy to ereft an abbey, and there pay them to his own monks, or grant them to fome abbey already ere&ed : fince for this donation, which really coft the patron lit¬ tle or nothing, he might, according to the fuperftition of the times, have maffes for ever fung for his foul. But in procefs of years, the income of the poor laborious parifh-priefts being fcandalcafly reduced by thefe ar¬ bitrary confecrations of tithes, it wras remedied by Pope Innocent III. about the year 1200, in a decretal epiftle fent to the archbilhop of Canterbury, and dated from the palace of Lateran : which has occafioned Sir Henry Hobart and others to miftakeit for a decree of the coun¬ cil of Lateran, held A. D. 1179, which only prohibit¬ ed what was called the infeodation of tithes, or their be¬ ing granted to mere laymen ; whereas this letter of Tithes. Pope Innocent to the archbilhop enjoined the payment y— of tithes to the parfons of the refpeftive parilhes where every man inhabited, agreeable to what was afterwards direcled by the fame pope in other countries. This epiftle, fays Sir Edward Coke, bound not the lay fub- jthts of this realm ; but being reaionable and juft, it was allowed of, and fo became /ex terrce. This put an effedtual Hop to all the arbitrary conlecrations of tithes $ except fome footfteps which ftiil coniinue in thofe por¬ tions of tithes which the parfon of one parilh hath, though rarely, a right to claim in another: for it is nowT univer- fally held, that tithes are due, of common right, to the par¬ fon of the parilh, unlefs there be a fpecial exemption. This parfon of the parilh may be either the ahtual incumbent, or elle the appropriator of the benefice j appropriations being a method of endowing monafteries, which feems to have been deviled by the regular clergy, by way of fubftitution to arbitrary confecrations of tithes. 3. We obferved that tithes are due of common right to the parfon, unlefs by fpecial exemption ; let us there¬ fore lee, thirdly, wrho may be exempted from the pay¬ ment of tithes, and how lands and their occupiers may be exempted or difcharged from the payment of tithes, either in part or totally ; firft, by a real compofition \ or, fecondly, by cuftom or prefcription. Firf, A real compofition is when an agreement is made between the owner of the lands and the parfon or vicar, with the confent of the ordinary and the patron, that fuch lands lhall for the futuie be dilcharged fiom payment of tithes, by realon of fome land or other real recompenfe given to the parfon in lieu and fatisfaftion thereofi This was permitted by law, becaufe it wras fuppofed that the clergy would be no lofers by fuch compofition 5 fince the confent of the ordinary, whofe duty it is to take care of the church in general, and of the patron, whofe intereft it is to protedf that particular church, were both made neceffary to render the com- polition effedlual: and hence have arifen all fuch cora- pofitions as exift at this day by force of the common law*. But experience Ihowing that even this caution was ineffedtual, and the pcffelfions of the church being by this and other means every day diminilhed, the dif- abling ftatute 13 Eliz. c. 10. was made; which pre¬ vents, among other fpiritual perfons, all parfons and vi¬ cars from making any conveyances of the ertates of their churches, other than for three lives of 21 years. So that now, by virtue of this ftatute, no real compofition made fince the 13 Eliz. is good for any longer term than three lives or 21 years, though made by confent of the patron and ordinary : w hich has indeed effedtu- ally demolilhed this kind of traffic ; fuch compofitions being now' rarely heard of, unlefs by authority of par¬ liament. Secondly, a difeharge by cuftom or prefcription, is wdiere time out of mind fuch perfons or fuch lands have been either partially or totally difcharged from the pay¬ ment of tithes. And this immemorial ufage is binding upon all parties; as it is in its nature an evidence of uni- verfal confent and acquiefcence, and with reaibn fup- pofes a real compofition to have been formerly made. This cuftom or prefeription is either de modo decimandi, or de non decimando, A modus decimandi, commonly called by the fimple name of a modus only, is where there is by cuftom a • particular TIT [' 443 ] T I T particular manner of tithing allowed, different from the general law of taking tithes in kind, which are the a&ual tenth-part of the annual increafe. This is fome- times a pecuniary compenfation, as twopence an acre for the tithe of land : fornetimes it is a compenfation in work and labour, as that the parfon (hall have only the twelfth cock of hay, and not the tenth, in confideration of the owner’s making it for him : fometimes, in lieu of a large quantity of crude or imperfeft tithe, the parfon lhall have a lefs quantity when arrived at greater ma¬ turity, as a couple of fowls in lieu of tithe-eggs, and the like. Any means, in fliort, whereby the general law of tithing is altered, and a new method of taking them is introduced, is called a modus decimandiy or fpe- cial manner of tithing. A prefeription de non decimando is a claim to be en¬ tirely difeharged of tithes, and to pay no compenfation in lieu of them. Thus the king by his prerogative is difeharged from all tithes. So a vicar fhall pay no tithes to the reftor, nor the redlor to the vicar, for ecclcjla de- cimas non folvit ccclcjicr. But thefe perfonal privileges (not arifing from or being annexed to the land) are per- fonally confined to both the king and the clergy ; for their tenant or leffee {hall pay tithes, though in their awn occupation their lands are not generally tithable. And, generally fpeaking, it is an eftablKhed rule, that in lay hands, modus de non decimando non valet. But fpiritual perfons or corporations, as monafteries, abbots, bilhops, and the like, were always capable of having their lands totally difeharged of tithes by various ways: as, i. By real compofition. 2. By the pope’s bull of exemption. 3. By unity of poffeffion $ as ■when the redtory of a parifh, and lands in the fame parifti, both belonged to a religious houfe, thofe lands were difehar¬ ged of tithes by this unity of poffeffion. 4. By pre¬ feription ; having never been liable to tithes, by being always in fpiritual hands. 5. By virtue of their order ; as the Knights Templars, Ciftercians, and others, whofe lands were privileged by the pope with a difeharge of tithes. Though, upon the diffolution of abbeys by Henry VIII. moft of thefe exemptions from tithes would have fallen with them, and the lands become tithable again, had they not been fupported and upheld by the ftatute 31 Henry VIII. c. 13. which enadls, that all perfons who ffiould come to the pofieffion of the lands of any abbey then diffolved, (hould hold them free and difeharged of tithes, in as large and ample a man¬ ner as the abbeys themfelves formerly held them. And from this original have fprung all the lands which be¬ ing in lay hands, do at prefent claim to be tithe-free : for if a man can (how his lands to have been fuch ab¬ bey-lands, and alfo immemorially difeharged of tithes by any of the means before mentioned, this is now a good prefeription de non decimando. But he muft ffiow both thefe requifites : for abbey-lands, without a fpecial ground of difeharge, are not difeharged of courfe ; neither will any prefeription de non decimando avail in total difeharge of tithes, unlefs it relates to fuch ab¬ bey-lands. It is univerfally acknowledged that the payment of tithes in kind is a great difeouragement to agriculture. They are inconvenient and vexatious to the hufband- man, and operate as an impolitic tax upon induftry. The clergyman, too, frequently finds them troublefome aqd precarious j his expences in colledling are a confi- derable drawback from their value, and his juft rights Tithes are with difficulty fecured : he is too often obliged to fubmit to impofition, or is embroiled with his pariffiion-, V " ^ ers in difputes and litigations, no lefs irkfome to his feel¬ ings than prejudicial to his intereft, and tending to pre¬ vent thofe good effedts which his precepts {hould pro¬ duce. It is therefore of the utmoft: importance to pa¬ rochial tranquillity, and even to religion, that fome juft and reafonable ftandard of compofition could be fixed. Land has been propofed, but in the prefent ftate of the divifion of property this is impoffible : and as money i*. continually changing in its value, it would alfo be a very improper ftandard, unlefs fome plan could be form ¬ ed by which the compofition could be increafed as the value of money diminiffies. A plan of this kind has been publifhed in the Tranfadlions of the Society infti- tuted at Bath, vol. iv. which thofe who are interefted in this fubjedt may confult for farther information. TITHING, (Tit king a, from the Sax. T/teothungc, i. e. Decuriam), a number or company of ten men, with their families, knit together in a kind of fociety, and all bound to the king, for the peaceable behaviour of each other. Anciently no man was fuffered to abide in Eng¬ land above forty days, unlefs he were enrolled in fome tithing.—One of the principal inhabitants of the tithing was annually appointed to prefide over the reft, being called the tit/iing-man, the head-borough, and in fome countries the borfeholder, or borough’s ealder, being luppofed the difereeteft man in the borough, town, or tithing. The diftribution of England into tithings and hundreds is owing to King Alfred. See BoRSE- HOLDER. TITIANO Vecellt, or Titian, the moft univer- fal genius for painting of all the Lombard-fchool, the beft colourift of all the moderns, and the mod. eminent Pilkingtori’r for hiftories, portraits, and landfcapes, was born at C?i- dore, in the province of Friuli, in the ftate of Venice, °f ^aintet r» in 1477, or in 1480 according to Vafari and Sandrart. His parents fent him at ten years of age to one of his uncles at Venice, who finding that he had an inclina¬ tion to painting, put him to the fchool of Giovanni Bel- lino. But as foon as Titian had feen the works of Giorgi¬ one, whofe manner appeared to him abundantly more elegant, and lefs conftrained than that of Bellino, he determined to quite the ftyle to which he had fo long been accuftomed, and to purfue the other that recom¬ mended itfelf to him, by having more force, more re¬ lief, more nature, and more truth. Some authors affirm, that he placed himfelf as a difciple with Giorgione 3 yet others only fay, that he cultivated an intimacy with him 3 but it is undoubtedly certain that he ftudied with that great matter 3 that he learned his method of blend¬ ing and uniting the colours ; and praflifed his manner fo effectually, that feveral of the paintings of Titian were taken for the performances of Giorgione 5 and then his fuccefs infpired that artift with an invincible- jealoufy of Titian, which broke off their connexion for ever after. The reputation of Titian rofe continually 3 every new work contributed to extend his fame through all Eu¬ rope 3 and he was confidered as the principal ornament of the age in which he flouriftied. And yet, Sandrart ob- feryes that amidft all his applaufe, and conftant employment at Venice, his income and fortune were inconfiderable ; 3 K ^ and TIT [ 444 ] TIT Titiano. and be was more remarkable for the extenfivenefs of his "“—v" talents, than for the affluence of his circumltances. But when his merit was made known to the emperor Charles V. that monarch knew how to fet a juft value on his fuperior abilities *, he enriched him by repeated bounties, allowed him a confiderable penfion, conferred on him the honour of knighthood, and what was ftill more, honoured him wuth his friendfhip. He painted the por¬ trait of that benefaftor feveral times } and it is record¬ ed by Sandrart, tnat one day, wfflile the emperor was iuling for his pi£lure, a pencil happening to drop from the painter, he ftooped, took it up, and returned it j obligingly anfwering to the modeft apology of the artift (who blulhed at the > ondelcenfion ot lo great a mo¬ narch), that the merit ot a Titian was worthy of the at¬ tendance of an emperor. The excellence of Titian was not fo remarkably ap¬ parent in the hiftorical compofitions which he painted as in his portraits and landfcapes, which feem to be lupe- rior to all competition ; and even to this day, many of them preferve their original beauty, being as much the admiration of the prefent age as they have defervedly been of the ages paft.—It is obferved of Titian by moft writers, that in the different periods of his life he had four different manners; one refembling his firft inftruftor Beliino, which was fomew'hat iiiff; another, in imita¬ tion of Giorgio .e, more bold, and full of force j his third manner was the refult of experience, knowledge, and judgement, beautifully natural, and finifhed with exquifite care, which manner w'as peculiarly his own j and in thofe piffures which he painted between the years of approaching old age and his death may be noticed his fourth manner. His portraits were very differently finifhed in his early, and in his latter time, according to the teftimony of Sandrart. At firft he laboured his pi&ures highly, and gave them a polifhed beauty and luftre, fo as produce their effedft full as well when they were examined clofely as when vieived at a diftance ; but afterwards, he fo managed his penciling, that their greateft force and beauty appeared at a more remote view, and they pleafed lefs when they were beheld more nearly. So that many of thofe artifts who ftudied to imitate him, being mifled by appearances which they did not fufficiently confider, have imagined that Titian executed his work with readinefs and a mafterly rapidi¬ ty and concluded that they fhould imitate his manner moft tffeflually by a freedom of hand and a bold pen¬ cil : Whereas in reality, Titian took abundance of pains to work up his pi&ures to fo high a degree of perfec¬ tion ; and the freedom that appears in the handling w as entirely efft&ed by a fk’dful combination of labour and judgement. It cannot be truly affirmed, that Titian equalled the great mafters of the Roman fchool in defign ; but he al¬ ways took care to difpofe his figuies in fuch attitudes as fhowed the moft beautiful parts of the body. His tafte in defigning men w^as not generally fo correft or elegant as it appeared in bis boys and female figures 5 but his colouring had all the look of real flefh, his figures breathe. He was not fo bold as Giorgione, but in tendernefs and' delicacy he proved himfelf much fuperior to him and all other artifts. The expreffion of the paf- fions was not his excellence, though even in that refpedt many of his figures merited the jufteft commendation ; but he always gave his figures an air of eafe and digni¬ ty. His landfcapes are univerfally allowed to be un- Titiano equalled, whether we confider the forms ot his trees, the II, grand ideas of nature wduch appear in his feenery, or 1 e' his diftances which agreeably delude and delight the eye of every oblerver j and they are executed with a light, tender, and mellow pencil. He learned from nature the harmony of colours, and his tints feem afton- ilhing, not only for their force, but their fwreetnefs j and in that relpedf his colouring is accounted the ftandard of excellence to all proieffors of the art. It would prove almoft an endlefs talk to enumerate the variety of works executed by this illuftrious artift, at Rome, Venice, Bologna, and Florence, as w7ell as thofe which are to be feen in other cities of Italy, in England, Spain, Germany, and France; but there are twm, which are mentioned as being truly admirable. One is, a Laft Supper, prelerved in the refe&oiy at the Efcurial in Spam, which is inimitably fine j the other is at Milan, reprelenting Chrift crowned with thorns. The principal figure in the latter has an attitude lull of grace and digni y more than mortal, and the counte¬ nance (hows a benevolence and humility, combined with dignity and pain, which no pencil but that of Ti¬ tian could lo feelingly have delcribed. It is admirably coloured, and tenderly and delicately penciled ; tl>e heads are wonderfully beautiful, the compofition excel¬ lent, and the whole has a charming effedt by the chiaro- feuro. He was of fo happy a conftitution, that he was never ill till the year 1576, when he died of the plague, at 99 years of age. His difciples were Paulo Veronefe, Giacomo Tintoret, Giacomo de Porte Baffa- no, and his Tons. TITLARK. See Alauda, Ornithology Index. TITLE, an appellation of dignity or rank given to princes and perfons of ditiinftion. Titles were not fo common among the ancient Greeks or Romans as they are in modern times. Till the reign of Conftantine the title of Ilhtftrious wras never given except to thofe w7ho were diltinguifhed in arms or let¬ ters : But at length it became hereditary in the families of princes, and every fon of a prince was illuftrious. The title of Highnefs w-as formerly given only to kings. The kings of England before the reign of Henry VIII. were addreffed by the title of your Grace. That mo¬ narch firft affumed the title of Highnefs, and afterwards that of Majejly. The title of majefty was firft given him by Francis I. in their interview in 1520. Charles V. was the firft king of Spain who aflumed the fame title. Princes, nobles, and clergy, generally have one title derived from their territories and eflates, and another derived from their rank or from fome other remarkable circumftance. The pope is called the Bijhop of Rome, and has the title of Holinefs. A cardinal has his name generally from fome church, and is faluted by the name ot Eminent, or mof Eminent. An archbilhop, befides being named from his diocefe, is called his Grace and mof Reverend: a bilhop is alfo diftinguifhed by the name of his diocefe, and has the title of his Lordfhip and right Reverend. Inferior clergymen are denominated Reverend. The titles of crowmed heads derived from their domi¬ nions it is unneceffary to mention. It will be fufficient to mention thofe by which they are addreffed. To an emperOJE T O B [ 445 ] T O B 'Title emperor is given the title of Imperial Majefty; to kings, It that of Majefty ; to the princes of Great Britain, Royal Tolr.cio. ipighnefs; to thofc of Spain, Infant; to electors, Eleiilo- ral H’gknefs ; to the grand duke of Tufcany, Mojl Se¬ rene Highnefs ; to the other princes of Italy and Ger¬ many, Highnefii to the doge of Venice, Mojl Serene Prince ; to the grand-malfer of Malta, Eminence ; to nuncios and ambaffadors of crowned heads, Excellency; to dukes, Grace; to marquiffes, cans, and barons, Lord- (hip. The emperor of China, among his titles, takes that of Tien Su, “ Son of Heaven.” The Orientals, it is obferved, are exceedingly fond of titles: the fimple go¬ vernor of Schiras, for inllance, after a pompous enume¬ ration of qualities, lordfhips, &c. adds the titles of Flower of Courtefy, Nutmeg oj Conflation, and Rofe of Delight. Title, in Law, denotes any right which a perfon has to the pofl'eflion of a thing, or an authentic inifru- ment whereby he can prove his right. See the articles Right, Property, &c. Title to the Crown in the Britijh Conjlitution. See Succession. TITMOUSE. See Parus, Ornithology Index. TI TULAR, denotes a perfon invetfed with a title, in virtue of which he holds an office or benefice, whether he perform 'he funffions thereof or not. TITUS Vespasianus, the Roman emporer, the fon of Vefpafian ; of whom it is related, that not being able to recolleil any remarkable good aftion he had done on a certain day, he exclaimed, “ I have loll a day !” He might truly be called the father of his people; and though Rome laboured under various public calamities during his reign, fuch was his equitable and mild admi- niftration, that he conffantly preferved his popularity. He was a great lover of learning, and compofed feveral poems. He reigned but two years ; and it is thought Domitian his brother poifoned him, A. D. 81. aged 41. See ( Hiftory of) ROME. TIVIOT hills. See Cheviot. TIVOLI, the modern name of Tibur. R OAD. See Rana, Erpetology Index. TOAD-Fifh. See LoPHIUS, ICHTHYOLOGY Index. ToAD-Flax. See Antirrhinum, Botany Index. TOAD Stone, an argillaceous ftone. See Geology. TOBACCO. See Nicotiana, Botany Index, and Snuff. ToeAcco-Pipe-Fifh. See Fistularia, Ichthyolo¬ gy Index. TOBACCO Pipes, Manufacture of. The art of making tobacco-pipes, or, as it is commonly called, pipe-making, though one of the fimpleft fpecies of pottery, isfufheient- ly curious to merit defeription in a didfionary of arts and feiences. The procefs of pipe-making may be divided in¬ to fix ftages ; viz. 1.. Beating or preparing the clay ; 2. Rolling ; 3. Moulding} 4. Trimming*, 5. Drying} and 6. Burning. Preparation of the Clay.—The fine white clay em¬ ployed by the pipe-makers, is dug from the quarries in maffes of about a cubic foot each. Before it can be ufed in the manufadture of tobacco-pipes, it muff be re¬ duced to the confiftence of a tough pafte. To effedl this, after its outer furface has been cleared from dirt pr duft, it is broken into fmall pieces about as large as a goofe’s egg, and thrown into a tub with fuch a quan- Tobacce.^ tity of loft water as experience has fhewn to be fuffi- v cent to bring it to the proper confidence. After lying till it has foaked up all the water, which ufually re¬ quires from 1 2 to 24 hours, it is taken from the tub and laid on a thick ilrong wooden bench. Here it is beat¬ en by a heavy four-fquare iron initrument, in lucn a manner as to cut it from one end to the other into very thin llices. It requires confiderable adtiiefs to perform this operation and it is furprifing how aha die work¬ men will fometimes cut the flices, and how equally they Vill thus divide the clay. This beating is con¬ tinued, alternately folding up the clay and flicing it, till the whole is perfedtly fmootk. It is then ready tor rolling. Rolling.—The operation of rolling reduces the clay into pieces of a proper fize and length for making pipes* and almoft to the proper form. The roller fits at a bench with a fmooth board before him, and holds in his hand another fmooth board about 18 inches long, four broad, and about half an inch thick, having one end rounded off on one fide, fo as to produce a corre- fponding hollow in the clay. He now takes a piece of the beaten clay, and rolls it out, firll with his hands, and then with the board, till it acquire the form of a- long (lender cylinder, with one end confiderably larger than the reft. This large end is to form the bole, and the cylinder the (hank of the future pipe. The pieces of clay thus formed are laid befide each other on a tlat board, and are nowT ready lor moulding. Moulding.—This is the molt complex operation, and requires the greateft number of inftruments. The prin¬ cipal of thefe is the mould, which is compofed of two long pieces of iron, formed fo as to join together, and having their correfponding fides cut into the lhape of half a tobacco pipe, each piece being hollowed fo as to form half a (lender cylinder, with a larger cavity at the upper end, and at fuch an angle as it is intended the bole of the pipe fhall make with the fhank. Juft above that part of each fide of the mould which Hands be¬ yond what is intended to form the bole, there is a notch for admitting a knife to cut off the fuperfluous clay. To receive the united mould there is a vice, having at one end two upright polls, between which moves a long lever, and to this lever, near the polls, there is loofely attached a piece of iron ending below in a fmoothr conical head, capable of entering the large opening of the mould, but rather fmaller than that opening, fo as that when forced down into it, a fufficient thicknefs of clay may be left between the cone and the fides of the mould, to form the bole of the pipe. One fide of this vice is fixed, and the other moveable, towards the form¬ er. The moveable fide has attached to it an iron ferew with a very long lever as its handle, fo that by turning the ferew one way or the other, the moveable fide of the vice may be forced nearer the fixed tide, or fuffered to return to its original pofition.. Befides thefe principal inftruments, the moulder re¬ quires a {lender fteel wire, fixed in a handle at one end,, and having its other extremity formed into a very ('mail head} a faucer containing wool well impregnated with oil, and a fmall woollen or cotton bruftn When about to mould his pipes, he lays hold of the fhank of one of the rolled pieces, and with great dexte- rity^ which pra&ice alone can teach, he paifes up the oiled 1 T O B [ 44-6 J T O B Tobacco, oiled wire through its whole length, till he finds it ar- y rived at the commencement of the larger extremity of the clay. This extremity he then bends to the proper angle, and having oiled the infide of each part of his mould, he lays the piece of clay with the wire in it, in¬ to one part of the mould, and covers it with the other. He now puts the mould containing the clay into the vice, and with the left hand turning round the handle of the fcrew, fo as to fix the mould firmly within the vice, he, with the right hand, preffes down the lever with its conical head, and thus forms the cavity of the bole. He now withdraws the mould, cuts off with his’knife the fuperfluous clay from the bole, opens the mould, takes out the pipe, and now only withdraws the wire. He then lays the moulded pipe on a fiat board, in the fame manner as the rolled pieces before defcribed. The pipes thus moulded require to be trimmed, that is, to have the prominences arifing from the joining of the mould, and other fuperfiuous pieces of clay taken off, fo as to render the furface fmooth and round. Trimming.—The operation of trimming is generally performed by boys and girls, as it requires very little ikill. The trimmer has before him a fmooth block of wood, about the length of the pipe, and of confiderable thicknefs, elevated a little at the remote end. He has alfo a thick piece of fmooth iron, one edge of which has acrofs it two or more femicylindrical grooves, capa¬ ble of receiving half the (hank of a pipe. Taking one of the rough moulded pipes, the trimmer carefully paffes up the hollow of the thank, a wire fimilar to that em¬ ployed in moulding, and holding the pipe by the bole, while the thank lies before hhn on the wooden block, he pares off with a blunt knife all the excrefcences of clay, both from the thank and bole, and rubs the for¬ mer, while lying on the block, with the grooved part of his iron, fo as to render it as fmooth as pofifible. He now cuts off the ragged piece at the extremity of the ftiank, withdraws the wire, and lays the pipe on the drying frame. One great objeft of the trimmer is, to fee that the pipe is completely perforated, vvhich he dif- covers by blowing through it; and if he finds the hole choked up, he muff open it by pulhing the wire as far as pofiible. If this does not faceted, he breaks the pipe as ufelefs. Drying.—The pipe has now received all the work that can be beftowed on it by the maker, previous to its being burned •, but as the expofing of it to heat, while foft and pliable, would make it crack, it is neceffary that it be properly dried. For this purpofe, a frame is prepared, compofed of three or four long pieces of wood, faftened to two end pieces in fuch a manner, as that the middle of the frame (hall be the loweft, to give the fhanks of the pipes that curve which they generally poffefs. After being trimmed, the pipes are laid befide each other in this concave frame, with their boles hang¬ ing down over the edges of the frame, and their thanks bending within its hollow. In this petition they are ex- pofed to the air till they are dry and firm. They are then ready for burning or baking. Burning.—For burning or baking the pipes, there is to be prepared a kiln of a fimple but peculiar conftruc- tion. It is built in the form of a cylinder, clofe at the bottom and on the tides, and open at the top. Below the bottom is a grate for receiving the fuel, and round the fides are conilrufted vertical or fpiral Hues, opening 1 at the top, and communicating below with the grate. Tobacco* The fides of the furnace on its interior are pretty thin, 1 obagQ' and are formed of a cement compofed of clay mixed ^ with frefh cow dung. In the middle of the cavity is placed a pedeffal compofed of the fame materials, for the pipes to lean againft. When the pipes are fuffi- ciently dried, they are arranged round this pedeftal, reiling againft it, and againft each other, with their boles next the bottom of the furnace. They are thus placed in fuccefiive layers, till the furnace be fufficiently full, when the open ipace at top is filled up with bricks placed over each other, fo as to leave interftices for the free circulation of the air, and of the fmoke and flame which iffue through the flues. In thefe interftices are laid feveral pieces of broken dried pipes, to ferve as py¬ rometers for afeertaining the ftate of the included pipes during the burning. The fire is now lighted, and kept up, till, on examining the pieces of clay laid in the in¬ terftices of the bricks, it is concluded that the pipes within the furnace are fufficiently baked. The fire is then fuffered to go out, and the whole to cool till the next day, when the bricks are taken down, the pipes removed, and packed in barrels for fale. After being burnt, the pipes are fometimes glazed, which is done by rubbing them, while warm, with flan¬ nel and a little white wax. In fome places the extre¬ mities of the (hanks are rendered fmooth by dipping them before burning in the ordinary potters glazing, which prevents that adhefion to the lips fo unpleafant in new unglazed pipes. TOBAGO, one of the Caribbee iflands, ceded to Great Britain by the treaty of Paris in 1763, taken by the French in 1781, and retaken by the Britifli in 1793. It lies in the latitude of 11 degrees 10 minutes north, and 59 degrees 40 minutes longitude weft from London, about 40 leagues fouth-by-weft from Barba- does, 35 fouth-eaft from St Vincents, 20 fouth-eaft from Grenada, 12 north-eaft from the Spanifli ifland of Trinidada, and between 30 and 40 north-eaft from the Spanifti main. According to the lateft accounts, it is fomewhat more than 30 miles in length from north-eaft to fouth-weft, between 8 and 9 in breadth, and from 23 to 25 leagues in circumference. The Englifh vifited this ifland very early, Sir Robert Dudley being there in the reign of Queen Elizabeth. In that of Charles I. William earl of Pembroke procured a grant of this, with two other fmall iflands ; but died before he was able to cany into execution his defign of fettling them. In A. D. 1632 fome merchants of Zealand fent over a fmall colony thither, and gave it the name of New Wal- cheren ; but before they were able thoroughly to efta- blifh themfelves, they were deftroyed by the Indians af- fifted by the Spaniards. Ten years after, James duke of Courland fent a colony thither, who fettled them- felves upon Great Courland bay, and made a confider¬ able progrefs in planting. A. D. 1654, Meffieurs A- drian and Cornelius Lampfius, two opulent merchants of Flufhing, fent a confiderable number of people thi¬ ther, who fettled on the other fide of the ifland, and lived in amity with the Courlanders, until they learned that the king of Sweden had feized the perfon of their duke and difpofleffed him of his dominions, when they attacked and forced his fubje&s to fubmit. The duke being afterwards reftored, he obtained from Charles II. a grant of this ifland, dated the 17th of November 1664. T O B r 447 ] T O K Tobago, j 664. In the fecond Dutch war the count d’Eftrees, Iobohki. order of his mafter, totally ruined it at the clofe of ■—~v“~ the year 1677 j and from that time it continued wafte till Britain took pofleffion of it after the treaty of Paris. The climate, notwithflanding its vicinity to the line, is fo tempered by the breezes from the fea, as to be very fupportable even to Europeans ; and hath the fame ad* vantages with that of Grenada, in having regular fea- lons, and alfo in being exempt from the hurricanes. There are throughout the iiland many rifing grounds, though, except at the north-eaft extremity, there is no part of it that can be ftyled mountainous; and even there the country is far from being rugged or impalfable. The foil, if we may credit either Dutch or French wri¬ ters, is as fertile and luxuriant as any of the iflands, and very finely diverfified. Ground provifions of all forts have been raifed in great plenty, a vatf variety of vegetables, excellent in their kind, fome for food, fome for phyfic. Almoft every Ipecies of ufeful timber is to be found here, and fome of an enormous fize 5 amongft others, the true cinnamon and nutmeg tree, as the Dutch confefs, and of which none could be better judges j whole groves of faffafras, and of trees that bear the true gum copal, with other odoriferous plants that render the air wholefome and pleafant. It is as well watered as can be wifiied, by rivers that fall into the fea on both fides, many fmaller ftreams, and fine frdh fprings in almoft every part of the ifland. The fea- coaft is indented by 10 or 12 fair and fpacious bays, and there are amongft thefe one or two ports capable of receiving as large fliips as ever vifited thofe feas. There are wild hogs in great plenty, abundance of fowls of different kinds, and a vaft variety of fea and river fifh. At the north-eaft extremity lies Little Tobago, which is two miles long, and about half a mile broad, very capable of improvement. TOBOLSKI, the capital of Siberia, is fituated at the confluence of the rivers Tobol and Irtifti, in N. Lat. 58° 12', E. Long. 68° 18'. The city ftands upon the afcent of a high hill, the lower part of which is inha¬ bited by Mahometan Tartars, who carry on a confider- able traffic upon the river Irtifh, and convey their mer- chandife quite acrofs Great Tartary, as far as China. The river Irtifti is reckoned as rapid as the Danube j runs from the fouth, and empties itfelf into the Oby : the Tobol wafties the other fide of the town, and a lit¬ tle below it falls into the Irtifh. By means of thefe two rivers, there is a conftant flow of merchandife into the city during the fummer feafon. Tobolfki is there¬ fore a great mart for the commodities of Mufcovy, Tar¬ tary, and other countries : and here is a great concourfe of merchants. All forts of provifions are plentiful and cheap. An hundred weight of rice is fold for 16 co- pecs, equal to about eightpence fterling j a fturgeon weighing 40 pounds, for half that money ; an ox for tivo rix-dollars, and every other article in proportion : the adjacent country abounds with game in great va¬ riety. rJ'he fupreme court of judicature for all Siberia is held in this city, which is alfo the feat of a metropo¬ litan, fent hither from Mofcow to exercife fpiritual ju- rifdiftion over the whole kingdom. ToboHki is well fortified, and defended by a ftrong garrifon, under the command of the waiwode, who refides in the place, and takes charge of the fur tribute, which is here depofited in proper magazines.. This governor enjoys a very ex- tenfive command, and can occafionally bring into the Toboliki, field 9000 men, befides a ftrong body of Tartars on -^°kriy horfeback, to make head againft the Kalmucks and , ‘j1 ’ j Coflacks, in their repeated incurfions. A iufficient num¬ ber of Ruffians, called Jemjkoiks, are kept in continual pay by the government, on the banks of the Irtifh, to fupply travellers on the czar’s account with men, boats, or carriages, to convey them as far as Surgut on the Oby, a voyage of 200 leagues by water. This is the common method of travelling in the fummer 5 but in winter the journey by land is not half fo long, being performed in fleds over the ice and fnow, with which the country is covered. Thefe fleds are moved by a pair of dogs, which will draw a load of 300 pounds with furprifing expedition. They are hired at eaiy rates, and during one half of the year may be feen fly¬ ing over the fnow in great numbers. The city is fup- pofed to contain 15,000 inhabitants. It is 800 miles eaft from Molcow, and 1000 from Peteifburgh. TODDA Panna. See Cycas, Botany Index. TODDY, a name given to the juice of the cocoa- nut tree. See Arack.—Toddy is alio a name given to a mixture of fpirits, wrater, and fugar. TODDT-Bird. See Loxia, Ornithology Index. TODUS, the Tody j a genus of birds belonging to the order of picae. See Ornithology Index. TOGA, in Roman antiquity, a wide woollen gown or mantle, which feems to have been of a femicircular form, without fleeves j differing both in richnefs and largenefs, according to the circumifances of the wearer, and ufed only upon occafion of appearing in public. Every body knows that the toga was the diiiinguifli- ed mark of a Roman : hence, the jus togee, or privilege of a Roman citizen ; i. e. the right of wearing a Roman habit, and of taking, as they explain it, fire and water through the Roman empire. TOKAY wine, derives its name from a town of Hungary, where it is produced. There are four forts of wine made from the fame grapes, diftinguifhed at Tokay by the names of ejfence, oufpruch, majslack, and the common wine. The effence is made by picking out the half-dried and fhrivelled grapes, and putting them into a perforated veffel, where they remain as long as any juice runs off by the mere preffure of their own weight. This is put into fmall calks. The aufprucb is made by pouring the expreffed juice of the grapes from which the former had been picked on thofe that yielded the effence, and treading them with the feet. The liquor thus obtained ftands for a day or two to ferment, and then is poured into fmall calks, which are kept in the air for about a month, and afterwards put into calks. The fame procefs is again repeated by the addition of more juice to the grapes which have already undergone the two former preffures, and they are now wrung with the hands ; and thus is had the mafslach. The fourth kind is made by taking all the grapes together at firft, and fubmitting them to the greateft preffure : this is chiefly prepared by the peafants. The effence is thick, and very fweet and lufeious : it is chiefly ufed to mix with the other kinds. The aufpruch is the wine com¬ monly exported, and which is known in foreign coun¬ tries by the name of Tohay. The goodnefs of it is determined by the following rules. The colour fliould neither be reddifh nor very pale, but a light filver ; in trying it, the palate and tip of T O L [ 448 ] T O L Tokay cf the tongue (hould be wetted without fwallowing it, 1'V‘ne and if it manifeft any acrimony to the tongue it is not Toledo. g0°d > but the tafte ought to be foft afid mild : when y—poured out, it (hould form globules in the glafs, and have an oily appearance : when genuine, the (trongeft is always of the bed quality : when (wallowed, it ihould have an earthy aftringent tafte in the mouth, which is called the tafte of the root. All tokay wine has an aro¬ matic tafte, which diftinguifhes it from every other fpe- cies of wine. It keeps to any age, and improves by time : but is never good till about three years old. It is the beft way to tranfport it in calks •, for when it is on the feas, it ferments three times every feafon, and thus refines itfelf. When in bottles, there muft be an empty fpace left between the wine and the cork, other- wife it would burft the bottle. A little oil is put upon the (urface, and a piece of bladder tied over the cork. The bottles are always laid on their fides in fand. Phil. Tranf. vol. Ixiii. part ii. p. 292, &c. TOKENS. See ABES MENS Tokens. TOISE, a French meafure containing fix of their feet, or a fathom. TOLAND, John, a famous writer, was born near Londonderry in Ireland in 1670, and educated in the Popiftr religion 5 but at 16 years of age embraced the principles of the Proteftants. He ftudied three years at the univerfity of Glafgow $ wras created mafler of arts in the univerfity of Edinburgh j and afterwards completed his ftudies at Leyden, wEere he refided two years. He then went to Oxford, where, having the advantage of the public library, he colledfed materials upon various fubjefts, and compofed home pieces j among which was, A Difiertation to prove the received hiftory of the tra¬ gical death of Atilius Regulus, the Roman conful, to be a fable. He began likewife a work of greater con- (equence, in which he undertook to (howr that there are no myfteries in the Chriftian religion. He publiftied it in 1696 at London, under the title of Chriftianity not mysterious. This book gave great offence, and was at¬ tacked by feveral writers. He afterward wrote in fa¬ vour of the Hanoverian fucceftion, and many other pieces. In 1707 he went into Germany, where he vi- fited feveral courts 5 and in 1710 he was introduced to Prince Eugene, who gave him feveral marks of his ge- nerofity. Upon his return to England he wras for fome time fupported by the liberality of the earl of Oxford 1 rd-treafurer, and kept a country boufe at Epfom •, but focn lofing his lordftiip’s favour, he publifhed feveral pamphlets againft that minifter’s meafures. In the laft four years of his life he lived at Putney, but ufed to fpend moft part of the winter in London. Mr 'Poland died at London in 1722. He wras a man of uncommon abilities, publilhed a number of curious trafts, and was pe'haps the moft learned cf all the infidel waiters •, but hu private charafler was far from being an amiable one 5 for he was extremely vain, and w’anted thofe focial vir¬ tues which are the chief ornaments as well as duties of life. H's pofthumous works, twm volumes oflavo, were publiftied in 1726, with an account of his life and wait¬ ings, by Mr Des Maizeaux. TOLEDO, an ancient and trading city of Spain in Bonrgoan- New7 Caftile, of which it was formerly the capital. ne'i Tru itt About two centuries ago it is faid to have contained than 200 oco inhabitants; but they are now di- minifticd io 20,000, or at moft to 30,000. It is ad- 2 vantageofly feated on the river Tajo, wdiich furrounds it Toledo, on tw'O fides; and on the land fide, it has an ancient roleratiun. w7all built by a Gothic king, and fianked with ico towers. It is feated on a mountain, which renders the ftreets uneven, and which are narrow7; but the houfes are fine, and there are a great number of fuperb ftruc- tures, befides 17 public fquares, where the markets are kept. The finelt buildings are the royal caftle and the cathedral church •, which laft is the richeft and mod confiderable in Spain. It is feated in the middle of the city, joining to a handfome ftreet, with a fine fquare before it. Several of the gates are very large, and of bronze. There is alfo a fuperb fteeple, extremely high, from whence there is a very diftant profpedf. The ba- grariro, or piincipal chapel, is a real treafury, in which are 15 large cabinets let into the wall, full of prodigious quantities of gold and (iiver veffels, and other works. There are tw-o mitres of filver gilt, fet all over with pearls and precious (tones, with three collars of maffy gold, enriched in like manner. There are two brace¬ lets and an imperial crown of ihe Virgin Mary, confid¬ ing of large diamonds and other jewels. The weight oi the gold in the crown is 15 pounds. The vtffel W'hich contains the confecrated wafer is of fiiver gilt, as high as a man, and fo heavy, that it requires 30 men to cany it \ within it is another of pure gold enriched with jewels. Here are 38 religious houfes, moft of which are worthy a traveller’s notice, with many other facred buildings, a great number of churches belonging to 27 parifties, and lome hofpitals. Without the town are the remains of an amphitheatre, and other antiqui¬ ties. Toledo is an archbifliop’s fee, and the feat of the pri¬ mate of Spain. His revenue is faid to be wmrth 400,000 ducats, but there are large deduftions to be made from it. It pays 15,000 ducats to the monks oi,ymin, the Efcuml, befides feveral other penfions. Toledo has alfo a univerfity. It was formerly celebrated for the exquifite temper of the fword blades made there. It is fituated in E. Long. 3. 15. N. Lat. 39. 50. and is 37 miles fouth from Madrid. TOLERATION, in matters of religion, is either civil or ecclefiaftical. Civil toleration is an impunity and fafety granted by the (late to every fed! that does not maintain dotffrines inconfiftent with the public peace : and ecclefiaftical toleration is the allowance which the church grants to its members to differ rti cer¬ tain opinions, not reputed fundamental. As the gods of Paganifm were almoft all local and tutelary, and as it was a maxim univerfally received that it was the duty of every man to worftup, together with his owrn deities, the tutelary gods of the country in udiich he might chance to refide, there was no room for perfecution in the Heathen world, on account of dif¬ ferent fentiments in religion, or of the different rites with which the various deities were woi(hipped. Had the primitive Chriftians joined their fellow-citizens in the worffiip of Jupiter, Juno, and the reft of the rabble of Roman divinities, they wmuld have been fuffered to worftiip, without moleftation, the Creator of the world and the Redeemer of mankind ; for in that cafe the God of the Chriftians w7ould have been looked upon as a Being of the fame kind with the gods of the empire j and the great principle of intercommunity would have remained unviolated. But the true God had exprefsly prohibited T O L [ 449 1 T O L T6lcnaior. prohibited both Jews and Chrifiians from worfhipping ' ^ •r—~J any other god befides Himftlf j and it was their refufal to break that precept of their religion which made their Heathen mafters look upon them as Atheifts, and per- fecute them as a people inimical to the Hate. Utility, and not truth, was the objeft for which the Heathen Jegiflatures fupported the national religion. They well knew' that the dories told by their poets of their differ¬ ent,divinities,, of the rewards of Elyftum, and of the puni/lnnents of Tartarus, were a colle&ion of fenfelefs fables; but they had nothing better to piopofe to the vulgar, and they were not fuch Ihrangers to the human heart, as to fuppofe that mankind could live together in . fociety without being influenced in their conduct by fome religion* Widely different from the genius of Paganifm was the fpirit of the Jewifh difpenfation. Truth, which is in fabf always coincident wdth general utility, was the great objedl of the Mofaic law. The children of Ifrael were feparated from the reft of the world, to preferve the knowledge and worftiip of the true God, at a time when all the other nations on earth, forgetting the Lord that made them, were falling proftrate to llocks and fton'es, and wTorftiipping devils and impure fpirits. Such was the contagion of idolatry, and fo ftrong the propen- fity of the Ifraelites to the cuftoms and manners of the Egyptians, and other polytheiftic nations around them, that the purpofe of their feparation could not have been ferved, had not Jehovah condelcended to become not only their tutelary God, but even their fupreme civil Magiftrate (fee Theology, N° 151.) ; fo that under .the Mofaic economy, idolatry was the crime of high treafon, and as fuch juftly punithed by the laws of the ftate. Among the .Tews, the church and ftate were not indeed different focieties. They were fo thoroughly in¬ corporated, that what wras a fin in the one was a crime in the other; and the forfeiture of ecclefiaftical privile¬ ges w'as the forfeiture of *he rights of citizens. In many refpefls the Chriftian religion is direffly op- pofite to the riiual law of Moles. It is calculated for all nations, and intended to be propagated among all. Inftead of feoarating one people from another, one of its principal objects is to dilfeminate univerfal benevo¬ lence, and to inculcate upon the whole human race, that mutual love wLich naturally fprings from the knowledge that all men are brethren. Its ultimate end being to train its votaries for heaven, it concerns itfelf no farther with the affairs of earth than to enforce by eternal fanftions the laws of morality ; and the king¬ dom of its Founder not being of this world, it leaves every nation at liberty to fabricate its own municipal laws, fo as beft to ferve its own intereft in the various circumftances in which it may be placed ; and denounces a curfe upon all who pay not to thofe laws the fulleft obedience, •when they are not obvioufly inconfiftent with the laws of piety and virtue, which are of prior .obligation. The Chriftian church therefore muft always remain a d'ftinft fociety from the ftate ; and though, ti1l the prefent age of hazardous innovations, it has been deemed expedient in everv country, where the truth of the gofpel is admitted, to give to the religion of Chrift: a legal eftahl’lhment, and to confer immunities on its Tninifters, this meafure has been adopted, not to fecure tl’e nuritv of the faith, which appeals to the private judgement of each individual, but merely to preferve ^ Vol. XX. Part II. the peace of iociety, and to put a reftraint upen thofe Toleration, ablions of which human lawrs cannot take cogmz.i ,ce. ^ With religion, Chriftian governments have no farther concern than as it tends to promote the prablice of vir¬ tue. The early Clniftians, however, not underftanding the principle upon which penal laws were employed to preferve the purity of the Jewilh religion ; and, as our bleffed Lord obierved to two of his apoftles, not know¬ ing what fpirit they were of—baftily concluded that they had a right to enforce the dodtrines and w'orlhip of the New leftament, by the fame means which had been uled to preferve the Ifraelites fteady to the doc¬ trines and worihip of the Old. Hence, though they had fuffered the cruelleft -perfecutions themfelves (fee Persecution), they no fooner got the power of the ftate in their hands, than they perfecuted the Pagans for their idolatry ; and afterwards, when herefies arofe in the church, perfecuted one another for exprefling in difterent phrafes metaphylical propofitions, of fuch a na¬ ture as no human mind can fully comprehend. The apoftle had forewarned them that there muft be herefies in the church, that they who are approved may be made manifeft ; but it did not occur to them that perfecution for opinion is the worft of all herefies, as it violates at once truth and charity. Hitherto thefe unhallowed means of bringing Chri- ftians to uniformity of faith and pra&ice, had been only occafionally employed, from their not accurately diftin- guifhing between the fpirit of the gofpel and that of the law ; but as foon as the bifhops of Rome had brought the inhabitants of Europe to recognize their infallibility in explaining articles of faith and deciding points of controverfy, perfecution became a regular and perma¬ nent inilrument of ecclefiaftical difeipline. To doubt or to deny any do&rine to which thefe unerring inftruc- tors had given the fanftion of their approbation, was held to be not only a refitting of the truth, but an aft of rebellion againft their facred authority ; and the fecular power, of which, by various arts, they had acquired the abfolute direftion, was inftantly employed to avenge both. “ T. bus Europe had been accuftomed, during many Robertforft centuries, to fee fpeculative opinions propagated or de- ^j^0,y °f fended by force; the charity and mutual forbearance which Charles V- Chriftianity recommends with fo much warmth, were forgotten, the facred rights of confcience and of private judgement were unheard of, and not only the idea of toleration, but even the word ilfelf, in the fenfe now af¬ fixed to it, was unknown. A right to extirpate error by- force, was univerfally alkwved to be the prerogative of thofe who poffeffed the knowledge of truth ; and though the firft reformers did not arrogate to themfelves in di- reft terms that infallibility which they had refufed to the church of Rome, they were not lefs confident of the truth of their own doftrines, and required with equal ardour the princes of their party to check fuch as prefu¬ med to impugn or to oppofe them. To this requeft too many of thefe princes lent a willing ear. I fl ittered at once their pietv and their pride to be confidered as pof- fefting all the rights of Jewifh princes ; and Henry the VIII. of England, after labouring to make his divines declare that all authority ecclefiaftical fvs well as civil flows from the crown, perfecuted alternately the Papifts and Proteftants. Many of his fucceffors, whofe charac¬ ters were much better than his, thought thenifdves duly 3 ^ authorized T O L r 450 ] TOM Toleration, authorized, in virtue of their acknowledged fupremacy over all Hates and conditions of men, to enforce by- means of penal laws a uniformity of faith and worlhip gmong their fubjefls : and it was not till the revolution that any fe6t in England feems to have fully under- Hood, that all men have an unalienable right to worlhip God in the manner which to them may leem mofl fuit- able to his nature, and the relation in which they Hand to him ; or that it is impoflible to produce uniformity of opinion by any other means than candid difquifition and found reafoning. That the civil magiflrate has a right to check the propagation of opinions which tend only to fap the foundations of virtue, and to diiturb the peace of fociety, cannot, we think, be queHioned ; but that he has no right to reHrain mankind from publicly profefling any fyftem of faith, which comprehends the being and providence of God, thl great laws of mora¬ lity, and a future Hate of rewards and punifhments, is as evident as that it is the objeft of religion to fit man¬ kind for heaven, and the whole duty of the magiHrates to maintain peace, liberty, and property, upon earth. We have elfewhere obferved (fee Test), that among a number of different fefts of Chriflians, it is not the fuperior purity of the fyfiem of faith profeffed by one of them, that gives it a right to the immunities of an efia- blifhment in preference to all its rivals $ but though the legiflature is authorized, in certain circumHances, to make a lefs pure fyfiem the religion of the Hate, it would be the height of abfurdity to fuppofe that any man, or body of men, can have authority to prevent a purer fyfiem from being acknowledged as the religion of indi¬ viduals. For propagating opinions and purfuing pra£fi- ces which neceffarily create civil difiurbance, every man is anfwerable to the laws of his country; but for the foundnefs of his faith, and the purity of his worfhip, he is anfwerable to no tribunal but that which can fearch the heart. When churches are eflablilhed, and creeds drawn up as guides to the preaching of the national clergy, it is obvious that every clergyman who teaches any thing direflly contrary to the doflrine of fuch creeds, violates the condition on which he holds his living, and may be juflly deprived of that living, whether his obnoxious opi¬ nion be in itfelf true or falfe, important or unimportant ; but his punifhment fhould be extended no farther. To expel a Chriflian from private communion for teaching any do&rine which is neither injurious to the Hate nor contrary to the few fimple articles which comprife the fum of the Chrifiian faith, is the grofiefi tyranny; and the governors of that church which is guilty of it, ufurp the prerogative of the bleffed Lord, w'ho commanded the apofiles themfelves not to be called mafiers in this fenfe ; for one (fays he) is your mafler * x»6riyrlns'), even Chrifi. It is indeed a hardfliip to deprive a man of his living for confcientioufiy illuftrating what he believes to be a truth of the gofpel, only becaufe his illufiration may be different from that which had formerly been gi¬ ven by men fallible like himfelf; but if the eflablifti- ment of human compilations of faith be neceffary, this hardlhip cannot be removed, but by making fuch com¬ pilations as fimple as poffible, and drawing them up in fcripture language. Such a reformation, could it be ef- fe£!ed peaceably, would ferve other good purpofes ; for while it would fufficiently guard the purity of the faith, it would withdraw that temptation which too many efia- blifhments throw in the way of men, to fubfcribe to the Toleration truth of what they do not really believe ; and it would >1 effectually banifli from the Chnfiian church every thing , r°mb- which can be called by the name of perfecution. See J Nonconformists. TOLL, a tax or cufiom paid for liberty to vend goods in a market or fair, or for keeping roads in pro¬ per repair. I he firfi appointment of a toll on highways of which wfe read, took place in 1346. See Road. TOLOUSE. See Toulouse. TOLU, a town of South America in Terra Firma, and in the government of Carthagena; famous for the fine balfam of Tolu, brought into Europe from thence, and produced from a tree like a pine. It is feated on a bay of the North fea, 60 miles fouth of Carthagena. W. Long. 72. 55. N. Lat. 9. 40. TOLU1FERA, the Balsam-oLTolu tree ; a ge¬ nus of plants belonging to the clafs of decandria. See Botany, p. 182. and Chemistry, N° 2483. TOMATOES. See Solanum, Botany Index. TOMB, includes both the grave or fepulchre wherein a defunft is interred, and the monument erefted to pre- ferve his memory. The word is formed from the Greek rvftQos, tumulus^ “ fepulchre or, according to Me¬ nage, from the Latin tumba, which fignifies the fame. In many nations it has been cuflomary to burn the bodies of the dead, and to colled the allies with pious care into an urn, which was depofited in a tomb or fe¬ pulchre. See Burning. Among many nations it has alfo been the pradice to lay the dead body in a tomb, without confuming it, after having wrapped it up de¬ cently, and fometimes placing it in a coffin. See Cof¬ fin. The tombs of the Jew's w'ere generally hollow places hewn out of a rock. Abraham buried Sarah in a cave. Such was the place too in which the kings of Judah and Ifrael were interred : and fiich wras the place in which the body of our Saviour was depofited by Jofeph of Ari- mathea. But it is probable that the common people bu¬ ried their dead in graves ; for our Saviour compares the Pharifees to “ graves which appear not, and the men that walk over them are not aware of them.” Over the tombs, perhaps only of people of difiindion, a Hone or monument was ereded, to intimate to paffengers that they were burying places, that they might not pollute themfelves by touching them. With the fame intention, as Lightfoot informs us, they whitened them every year on the 15th of February. The Egyptians alfo buried their dead in caves, called catacombs. See Catacomb. The pyramids, as fome think, were alfo employed for the fame purpofe. Some¬ times alfo, after embalming their dead, they placed them m niches in fome magnificent apartment in their hou- fes. The Greeks and Romans burned their dead, and depo¬ fited their affies in a tomb. The Greeks interred the affies without the cities, by the fides of their highways. Sometimes indeed, by way of particular honour, they were buried in an elevated part of the town; and the Lacedemonians were allowed by Lycurgus to bury in the city and round their temples : But this was forbid¬ den among the Romans by the law of the twelve tables,. In urbe ne fepelito, neve urito ; yet Valerius Publicola, Poffhuttius Tubertius, and the family of the Claudii, were buried iu the Capitol. To bury by the fides of public TOM [ 45* 1 TON Tomb, public roads was common among the Romans alfo j v ' ' hence their epitaphs frequently began with JiJle viator. Highways were made choice of probably for two rea- fons: i. That the dead might not be offenfive or injure the health of the living, which they certainly would if buried in towns or populous places ; and, 2dly, That they might hold out to travellers a ieffon of mortality, and teach the ruftic moralift to die. As it would fwell this article to too great a fize to de- fcribe all the difterent kinds of tombs which have been ufed by different nations and ages, we muft consent our- felves with Ihortly defcribing the tombs of a few nations, and adding a few concomitant circumifances. The tombs of the Parfees are Angular. The deceafed, after lying a proper time in his own houfe, for the pur- pofes of mourning, is carried, followed by his relations and friends, the females chanting a requiem, and depo- fited in a tomb of the following conftruftion. It is a circular building, open at top, about 55 feet diameter, and 25 feet in height, filled to within 5 feet of the top, excepting a well of 15 feet diameter in the centre. The part fo filled is terraced, with a flight declivity toward the well. Two circular grooves three inches deep are railed round the well j the firft at the diftance of four, the fecond at ten, feet from the well. Grooves of the like depth or height, and four feet diftant from each other at the outer part of the outer circle, are carried ftraight from the wall to the well, communicating with the circular ones, for the purpofe of carrying off the water, &c. The tomb, by this means, is divided into three circles of partitions : the outer, about feven feet by four : the middle fix by three : the inner, four by two : the outer for the men, the middle for the women, the inner for the children j in which the bodies are re- fpedtively placed, wrapped loofely in a piece of cloth, and left to be devoured by the vultures 5 which is very foon done, as numbers of thofe animals are always feen hovering and watching about thefe charnel houfes, in expe&ation of their prey. The friends of the deceafed, or the perfons who have charge of the tomb, come at the proper time, and throw the bones into their recep¬ tacle, the well in the centre ; for which purpofe, iron rakes and tongs are depofited in the tomb. The en¬ trance is clofed by an iron door, four feet fquare, on the eaftern fide, as high up as the terrace, to which a road is raifed. Upon the wall, above the door, an additional wall is raifed, to prevent people from looking into the tomb, which the Parfees are particularly careful to pre¬ vent. A Perfian infcription is on a ftone inferted over the door, which we once copied, but have forgotten its tenor. From the bottom of the wall fubterraneous paf- fages lead to receive the bones, &c. and prevent the well from filling. Of the ancient fepulchres found in Ruflia and Siberia, fome are perfedt tumuli, raifed to an enormous height, Archteolo. while others are almoft level with the ground. Some of g.a, vol. vii. them are encompaffed with a fquare wall of large quarry Rones placed in an eredt pofition; others are covered only with a fmall heap of ftones, or they are tumuli adorned with ftones at top. Some are walled with brick within, and vaulted over j others are no more than pits or common graves. In fome the earth is excavated feve- ral fathoms deep j others, and efpecially thofe which are topped by a lofty tumulus, are only dug of a fufticient depth for covering the carcafe. In many of thefe fe- Tomb pulchres the bones of men, and frequently of horfes, are II found, and in a condition that renders it probable the , ^ or'e‘ bodies were not burnt before they were inhumed. Other ' bones fhow clearly that they have been previoufly burnt 5 becaufe a part of them is unconfumed, and becaufe they lie in a difordered manner, and fome of them are w anting. Urns, in which other nations of antiquity have depofited the afties of their dead, are never met with here. But fometimes what remained of their bodies after the combuf- tion, and even whole carcafes, are found wrapped up in thin plates of gold. Many dead bodies are frequently feen depofited together in one tomb ; a certain indication that either a battle had been fought in the neighbour¬ hood of the place, or that fome families buried their rela¬ tions in an hereditary tomb. The Moors, like all other Mahometans, hold it a thing irreverent, and contrary to the fpirit of religion, to bury their dead in mofques, and to profane the temple of the Moft High by the putrefa&ion of dead bodies. In the infancy of the church the Chriftians had the like Chenier’’t piety, and gave example of the refpedl in which they M°r?cc*> held temples dedicated to religious worfliip j but ill-vol,1‘ guided devotion, mingled with fuperftitious vanities, and that contagious fpirit of felf-intereft which pervades all human affairs, without refpe&ing the altar of God, have> together, infenfibly perverted men’s ideas. The burial grounds of the Mahometans are moft of them without the city ; the emperors have their fepulchres diftinft and diftant from the mofque, in fandluaries, built by them- felves, or in places udiich they have indicated : their tombs are exceedingly fimple * the Moors do not imitate the oftentation of Europeans, where fuperb monuments are raifed rather to gratify the pride of the living than the merit of the dead. All Mahometans inter the dead at the hour fet apart for prayer. The defunft is not kept in the houfe, ex¬ cept he expires after f'unfet j but the body is tranfported to the mofque, whither it is carried by thofe who are going to prayer. Each, from a fpirit of devotion, is de- firous to carry in his turn. The Moors fing at their bu¬ rial fervice; which ufage perhaps they have imitated af¬ ter the Chriftians of Spain, for the oriental Mahome¬ tans do not fing. They have no particular colour ap¬ propriated to mourning; their grief for the lofs of rela¬ tions is a fenfation of the heart they do not attempt to exprefs by outward fymbols. Women regularly go on the Friday to weep over and pray at the fepulchres of the dead, whofe memory they hold dear. Among the northern nations it was cuftomary to bury their dead under heaps of ftones called cairns, or under barrows: (See the articles Cairns and Barrow). The inhabitants of Tibet, it is faid, neither bury nor bum their dead, but expofe them on the tops of mountains. See Tibet. TOMPION; a fort of bung or cork ufed to ftop the mouth of a cannon. At fea this is carefully encircledi with tallow or putty, to prevent the penetration of the water into the bore, wdiereby the powder contained in the chamber might be damaged or rendered incapable of lervice. TON, a meafure or weight. See Tun. TONE, or Iune, in Mujic, a property of found, thereby it comes under the relation of grave and acute $ 3 L 2 or TON r 45 Tone or the degree of elevation any found has, from the de- rr, II gree . f fwiftnefs of the vibrations of the parts of the fo- ronnaee. 0 , ^ ^ norous body. The variety of tones in human voices arifes partly frotn the dimenfions of the windpipe, which, like a flute, the longer and narrower it is, the (harper the tone it gives ; but principally from the head of the larynx or knot of the throat: the tone of the voice being more or lefs grave as the rima or cleft thereof is more or lefs open. The wmrd tone is taken in four different fenfes among the ancients : i. For any found ; 2. For a certain in¬ terval, as when it is faid the difference between the dia- pente and diatelfaron is a tone ; 3. Fora certain locus or compafs of the voice, in which lenfe they ufed the " Dorian, Phrygian, Lydian tones 5 4. For tenfion, as when they fpeak of an acute, grave, or a middle tone. Tone is more particularly ufed, in muflc, for a cer¬ tain degree or interval of tune, wflrereby a found may be either raifed or lowered from one extreme of a concord to the other, fo as ftill to produce true melody. TONGUE. See Anatomy, N° 102. TONIC, in Mujic, lignifies a certain degree of ten¬ fion, or the found produced by a vocal firing in a given degree of tenflon, or by any fonorous body when put in vibration. Tonic, fays Rouffeau, is like wife the name given by Anffoxenus to one of the three kinds of chromatic mu- fic, whofe divifions he explains, and which was the or¬ dinary chromatic of the Greeks, proceeding by -two femitones in fucceflion, and afterwards a third minor. TONIC Dominant. See DOMINANT. TONNAGE and Poundage, an ancient duty on wine and other goods, the origin of which feems to have been this: About the 2ift of Edward III. complaint was made that merchants were robbed and murdered on the feas. The king thereupon, with the confent of the peers, levied a duty of 2s. on every ton of wine, and 12d. in the pound on all goods imported ; which was treated as illegal by the commons. About 25 years after, the king, wdien the knights of (hires were re¬ turned home, obtained a like grant from the citizens and burgeffes, and the year after it was regularly grant¬ ed in parliament. Thefe duties were diminifhed fome- times, and fometimes increafed j at length they feem to Blaekft. have been fixed at 3s. tonnage and is. poundage. They Comment. wrere at firft ufually granted only for a (fated term of vo1, u years, as, for two years in 5 Ric. II. ; but in Henry VI.’s time they were granted him for life by a ftatute in the 31(1 year of his reign ; and again to Edward IV. for the term of his life alfo : fince which time they were regularly granted to all his fucceffors for life, fometimes at the firft, fometimes at other fubfequent parliaments, till the reign of Charles 1.5 when, as the noble hiftorian expreffes it, his minifters wTere not fuf- ficiently folicitous for a renewal of his legal grant. And yet thefe impofts were imprudently and unconftitution- ally levied and taken, without confent of parliament, for 1 5 years together; which was one of the caufes of thofe unhappy difcontents, juftifiable at firft in too many in (lances, hut wfljich degenerated at laft into caufe- lefs rebellion and murder. For, as in everya^ther, fo in this particular cafe, the king (previous to the com¬ mencement of hoftilities) gave the nation ample fatisfac- tion for the errors of his former conduct, by palling an 2 i TON a£l, whereby he renounced all power in the crown of Tonnage, levying the duty of tonnage and poundage, -without the Tonqum; exprels confent of parliament; and alio all power of im- ~ - v • pofition upon any merchandiies whatever. Upon the. reftoration this duty was granted to King Charles II. for life, and fo it was to his two immediate fuccellbis j but now, by three feveral (latutes, 9 Ann. c. 6. I Geo. I. c. 12. and 3 Geo. I. c. 7. it is made perpetual, and mortgaged for the debt of the public. TONQUIN, a kingdom of Afia, in the Eaft Indies, beyond the Ganges ; bounded on the north by the pro¬ vince of Yunnan in China, on the eaft by the province of Canton and the bay ofTonquin, on the fouth by Cochin China, and on the weft by the kingdom of Laos. It is about 1200 miles in length and 5'co in breadth ; and is one of the fined and moil coi.fideiable kingdoms of the Eaft, as. well on account of the num¬ ber of inhabitants as the riches it contains and the trade it carries on. The country is thick fet with villages j and the natives in general are of a middle (iature and clean limbed, with a tawny complexion. Their faces are oval and flattiih, and their nofes and lips ivell pro¬ portioned. Their hair is black, long, lank, and coarfe ; and they let it hang down their (houlders. They are generally dexterous, nimble, adlive, and ingenious iu mechanic arts. They weave a multitude of fine filks, and make curious lacker-works, which are tranfported to other countries. There is fuch a number of people, that many want employment ; for they feldom go to work but when foreign (hips arrive. The money and goods brought hither by the Engliih and Dutch put them in aftion ; for they have not money of their own fufficient to employ themfelves } and therefore one-third at lead muft be advanced beforehand by the merchants: and the (hips muft (lay here till the goods are finiftred, which is generaliy-five or fix months. I hey are fo ad- didled to gaming, that when every thing elfe is loft, they will (lake their wives and children. The garments of the Tonquinefe are made either of filk or cotton ; but the poor people and foldiers wear only cotton of a dark tawny colour. Their houfes are fmall and low $ and the walls either of mud, or hurdles daubed ovef with clay. They have only a ground floor, with two or three partitions ; and each room has a fquare hole to let in the light. The villages confift of 30 or 40 houfes, furrounded with trees ; and in fome places there are banks to keep the water from overflowing their gar¬ dens, where they have oranges, betels, melons, and la- lad-herbs. In the rainy feafon they cannot pafs from one houfe to another without wading through the wa¬ ter *, they fometimes have boats. In the capital city called Cacho there are about 20,000 houfes with mud- walls, and covered with thatch j a few are built with brick, and roofed with pan-tiles. In each yard is a fmall arched building like an oven, about fix feet high, made of brick, which ferves to fecure their goods in cafe of fire. The principal ftreets are very wide, and paved with fmall (tones. The king of Tonquin has three pa¬ laces in it, fuch as they are j and near them are (fables for his horfes and elephants. The houfe of the Engiiih factory is feated at the north end of the city, fronting the river, and is the bed in the city. The people in general are courteous, and civil to ftrangers ; but the great men are proud, haughty, and ambitious ; the fol- dieis infolent, and the poor thievifti. They buy all TON r 453 I TOP ■fonquin their wives, of which the great men have feveral ; but II. the poor are {tinted for want of money. In hard times Tontine- , the men will fell both their wives and children to buy rice to maintain themlelves. The women offer them- felves to flrangers as wives wdiile they flay, and agree with them for a certain price. Even the great men will offer their daughters to the merchants and officers who are likely to day fix months in the country. They are not afraid of being with child ; for if they are girls they can fell them w'ell when they are young, becaufe they are fairer than the other inhabitants. Thefe wo¬ men are faid to be very faithful j and are trulied w’ith money and goods by the Europeans during their ab- fence, and will make great advantage with them. The firft new moon in the year that happens after the mid¬ dle of January, is a great feftival -7 when they rejoice for'io or 12 days together, and fpend their time in all manner of fports. Their common drink is tea, but they make themfelves merry with arrack. The language is fpoken very much in the throat j and fome of the wyords are pronounced through the teeth, and has a great re- femblance to the Chinefe. They have feveral mechanic arts or trades ; fuch as fmiths, carpenters, joiners, tur¬ ners, weavers, taylors, potters, painters, money-changers, paper-makers, workers in lacker, and bell-founders.— Their corhmodities are gold, mufk, filks, calicoes, drugs of many forts, woods for dyeing, lacquered wares, earthen wares, fait, anifeeds, and worm-feeds. The lac¬ quered xvare is not inferior to that of Japan, which is accounted the beft in the world. With all thefe mer- chandifes, one would expert the people to be very rich, but they are in general very poor ; the chief trade be¬ ing carried on by the Chinefe, Engliffi, and Dutch. The goods imported, befides filver, are faltpetre, ful- phur, Engliffi broad-cloth, pepper, fpices, and great guns. TONSILS. See Anatomy, N° 102. TONSURE, in Ecclefiaflical Hi/lory, a particular manner of (having or clipping the hair of ecclefialtics or monks. The ancient tonfure of the clergy was nothing more than polling the head, and cutting the hair to a moderate degree, for the fake of decency and gravity : and the fame obfervation is true with refpedt to the tonfure of the ancient monks. But the Romans have carried the affair of tonfure much farther 5 the candidate for it kneeling before the bi- ftiop, who cuts the hajr in five different parts of the head, viz. before, behind, on each fide, and on the crown. TONTINE, a loan given for life annuities with be¬ nefit of furvivorlhip ; fo called from the inventor Lau¬ rence Tonti, a Neapolitan. He propofed his fcheme in 1653 to reconcile the ueople to Cardinal Maza¬ rine’s government, by amufing them with the hope of becoming fuddenly rich. He obtained the confent of the court, but the parliament would not regifier the edif natural hiftory at large, ancient and modern geography, *""" religion, manners, and commerce. He fpent three years in this learned voyage 5 and then refuming his profeflion, was made profeffor of phyfic in the college- royal. He died in conlequence of an accidental crufti of his breaft by a cart-wheel, which brought on a Ipit- ting ol blood and hydrothorax, that carried him off in 1708. He wrote Elements of Botany, both in French and Latin 5 A Relation cf his Voyage into the Levant j with other pieces of lefs conffderation. TOURNIQUET, in Surgery, an inftrument form¬ ed with ferews, for compitfling any part with rollers, &c. for the flopping of hsemorrhagies. See Surgery Index. '1 OWER, a tall building confifting of feveral {lo¬ ries, ulually of a round form, though feme are fquare or polygonal. Towers are built for fortrefles, &c. as the Tower of London. See London, N° 46. TOWN, a place inhabited by a confiderable num¬ ber of people, being of a middle fize between a city and a village. TOXICODENDRON. See Rhus, Botany In¬ dex. TRAAS. See Terras. TRACHEA. See Anatomy, N° 119. TRACH1NUS, the Weever, a genus of fifties be¬ longing to the order of jugulares. See Ichthyology Index. TRACT, in Geography, an extent of ground, or a portion of the earth’s furtace. Tract, in matters of literature, denotes a fmall trea- tife or written difeourfe upon any fubjeft. TRADE, in general, denotes the lamp with com¬ merce, confifting in buying, felling, and exchanging of commodities, bills, money, &c. See Commerce, Coin, Money, Company, &c. TRADE-Wmds, denote certain regular winds at fea, blowing either coniianlly the lame way, or alternately this way and that 5 thus called from their ufe in naviga¬ tion, and the Indian commerce. See Meteorology. TRADESMEN’S tokens, a term lynonymous a- mong medalifts with provincial coins. - This is a fubjeft curious enough to deferve attention, though we will not go fo far as Mr Pinkerton does, who fays that it is a fubjeft in which the perpetual glory of the nation is interefted. Since the year 1789 provin¬ cial halfpence have been made and circulated in confi¬ derable quantity. As ancient medals and coins have been frequently of ule to hiftorians, it is to be regretted that many of thefe provincial halfpence are rendered ufe- lefs in this refpeft by unmeaning figures and puerile de¬ vices. Utility and elegance ought to be ftuditd : for this view it has been propofed by a gentleman of tafte on this fubjt £1, that all coins Ihould be diftinguilhed by one of the following five charafteriftics. 1. Fac fimiles of magnificent beautiful buildings. 2. Reprefentations of great and ufeful undertakings. 3. Emblems of the induftry and commerce of the age 4. The illuftrious men, &.c. to whom the nation has given birth. 5. Im¬ portant hiftoriral events. TRADITION, fomething handed down from one generation to another without being written. Thus the Jews T H A [ 459 T T R A Tradition Jetvs pretended, that befides their written law contained ii in the Old Teftament, Mofes had delivered an oral Tra-los- jaw ^ich had been conveyed down from father to fonj muiae^^ ^ thus the Roman Catholics are faid to value particu¬ lar doctrines fuppofed to have defcended from the apo- ftolic times by tradition. TRAGACANTH. See Astragalus, Materia Medica Index. TRAGEDY, a dramatic poem, reprefenting fome fignal a£Hon performed by illuftrious perfons, and which has frequently a fatal iffue or end. See Poetry, Part II. left. i. TR AGI-COMEDY, a dramatic piece, partaking both of the nature of tragedy and comedy •, in which a mix¬ ture of merry and ferious events is admitted. TRAGOPOGON, Goat’s-beard •, a genus of plants belonging to the clafs of lyngenefia ; and in the natural fyftem ranging under the 49th order, Compojitce. See Botany Index. TRAJAN, Marcus Ulpius, a celebrated Roman emperor, urho gained many victories over the Parthians and Germans, pufhing the empire to its utmoft extent on the call and north fides. He died at Silinunte, a city of Cilicia, which from him was called Trajanopolis, in the year 117. TRAJAN'S Column, a famous hiflorical column erect¬ ed in Rome, in honour of the emperor Trajan. It is of the Tufcan order, though fomewhat irregular : its height is eight diameters, and its pedeftal Corinthian : it w'as built in a large fquare called Forum Romanum. Its bafe confifls of 12 Hones of an enormous fize, and is railed on a focle, or foot, of eight Heps : withinfide is a ftaircafe illuminated with 44 windows. It is 140 feet high, which is 35 feet (hoit of the Antonine column, but the workmanlhip of the former is much more va¬ lued. It is adorned from top to bottom with baffo re¬ lievos, reprefenting the great actions of the emperor againft the Dacians. TRAIN, a line of gunpowder laid to give fire to a quantity thereof, in order to do execution by blowing up earth, works, buildings, &c. TRAIN of Artillery, includes the great guns and other pieces of ordnance belonging to an army in the field. TRAIN-Oil, the oil procured from the blubber of a wdiale by boiling. TRALLIAN, Alexander, a Greek writer on phyfic, a native of Tralles in Lydia, wTho lived about the middle of the fixth century. His works are divided into 12 books ; in which he treats of diftempers as they occur, from head to foot. He was the firft who opened the jugular vein, and that ufed cantharides as a blifter for the gout. Dr Freind, in his Hiflory of Phyfic, flyles him one of the moft valuable authors fince the time of Hionocrates. Though he appears on the whole to have been a rational phyfician, yet there are things in his writings that favour of enthufiafm and fu- perftition. TR A-LOS-MONTES, a province of Portugal,-cal¬ led in Latin Tranfmontana, becaufe fituated on the call: fide of a chain of hills that feparate it from Entre Du- ero-e-Minho. It is bounded on the north by Galicia ; on the fouth by the provinces of Beira and Leon ; by the laft of which it is bounded alfo to the eaft. Its length from north to fouth is upwards of 120 miles, and its breadth about 80. It is full of mountains, and pro- Tranfac- • duces little corn, but plenty of wine, fruits of feveral tl is about 162 miles in length, and 150 in breadth. The adminiftration of affairs is conducted by 12 perfons j namely, three Roman Catholics, three Lutherans, three’ Calvinifts, and three Socinians. The militia is com¬ manded by the governor, whofe commiflion is the more important, as Tranfylvania is the bulwark of Chxiften- dom. It is divided into feveral fmall diftriCts, called palatinates and counties; and is inhabited by three dif¬ ferent nations, Saxons, Silefians, and Hungarians. Her- manftadt is the capital town. TRAPEZIUM, in Geometry, a plane figure con¬ tained under four unequal right lines. TRAPEZIUS, a mufcle. See Anatomy, Part II. TRAPP, a compound rock. See Geology. TRAVELLERS joy. See Clematis, Botany Index. 'TRAVERSE, or Transverse, in general, denotes fomething that goes athwart another ; that is, croffes and cuts it obliquely. Traverse, in Navigation, implies a compound courfe, or an affemblage of vaiious courfes, lying at different angles with the meridian. See Navigation. 1R A VERSE Board, a thin circular piece of board, marked with all the points-of the compafs, and having eight holes bored in each, and eight fmall pegs hang¬ ing from the centre of the board. It is ufed to de¬ termine the different courfes run by a {hip during the period of (he watch, and to afeertain the diftance of each eeurfe. TRAVESTY, a name given to an humorous tranf- lation of any author. The word is derived from the French travejier “ to difguife.” TREACLE, or Melasses. See Sugar. Treacle Beer. See Spruce. Treacle Mufard. See Clypeola, Botany Index. TREASON, a general appellation, made ufe of by the law, to denote not only offences againft the king and government, but alfo that accumulation of guilt which arifes whenever a fuperior repofes a confidence in a fubjedt or inferior, between whom and himfelf there fubfifts a natural, a civil, or even a fpiritual relation ; and the inferior fo abufes that confidence, fo forgets the obligations of duty, fubjedlion, and allegiance, as to de- ftroy the life of any fuch fuperior or lord. Hence trea- fon is of two kinds, high and petty. High Treafon, or Treafon Paramount (which is equi¬ valent to the crimen Icefce majefatis of the Romans, as Glanvil denominates it alfo in our Englifh law'), is an offence committed againft the fecurity of the king or kingdom, whether by imagination, word, or deed. In order to prevent the inconveniences which arofe in Eng¬ land from a multitude of conftrudfive treafons, the fta- tute 25 Edw. III. c. 2. was made ; which defines what offences only for the future fliould be held to be treafon • and this ftatute comprehends all kinds of high-treafon under feven diftindf branches. “ 1. When a man doth compafs or imagine the death of our lord the king, of our lady his queen, or of their eldeft fon and heir.” Under this defeription it is held that a queen-regnant (fuch as Queen Elizabeth and Queen Tranfyl¬ vania II Treaibn. ——V——J Treafon. T R E [ 462 ] T R E Oueen Anne) is within the words of the act, being in¬ verted with royal power, and intitled to the allegiance of her fubjedts : but the huihand of fuch a queen is not comprifed within thefe words ; and therefore no treafon can be committed againft him. Let us next fee what is a compajjing or imagining the death of the king, &c. Thefe are fynonymous terms : the word compafs fignifying the purpofe or defign of the mind or will ; and not, as in common fpeech, the car¬ rying fuch defign to effcd. And therefore an acciden¬ tal ftroke, which may mortally wound the fovereign, per infortuniam, without any traitorous intent, is no trea¬ fon : as was the cafe of Sir Walter Tyrrel, who, by the command of King William Rufus, (hooting at a hart, the arrow glanced againft a tree, and killed the king upon the fpot. But as this compafling or imagination is an aft of the mind, it cannot poffibly fall under any ju¬ dicial cognizance, unlefs it be demonftrated by fome open or overt aft. The ftatute exprefsly requires, that the accufed “ be thereof upon fufticient proof attainted of fome open aft by men of his own condition.” Thus, to provide weapons or ammunition for the purpofe of killing the king, is held to be a palpable overt aft of treafon in imagining his death. To confpire to imprifon the king by force, and move towards it by affembling company, is an overt aft of comparting the king’s death ; for all force ufed to the perfon of the king, in its confe- quence may tend to his death, and is a ftrong prefump- tion of fomething worfe intended than the prefent force, by fuch as have fo far thrown off their bounden duty to . their fovereign : it being an old obfervation, that there is generally but a Ihort interval between the prifons and the graves of princes. It feems clearly to be agreed, that by the common law and the ftatute of Edw. III. ■words fpoken amount only to a high mifdemeanor, and no treafon. For-they may be fpoken in heat, without any intention ; or be miftaken, perverted, or mifremem- bered by the hearers ; their meaning depends always on their conneflion with other words and things j they may fignify differently even according to the tone of voice with which they are delivered and fometimes filence itfelf is more expreflive than any difcourfe. As there¬ fore there can be nothing more equivocal and ambiguous than words, it would indeed be unreafonable to make them amount to high treafon. And accordingly, in 4 Car. I. on a reference to all the judges, concerning fome very atrocious words fpoken by one Pyne, they certified to the king, “ that though the words wrere as wicked as might be, yet they w7ere no treafon ; for un¬ lefs it be by fome particular ftatute, no words will be treafon.” If the words be fet down in writing, it argues more deliberate intention ; and it has been held, that •writing is an overt afl of treafon •, for fcribere eji agere. But even in this cafe the bare words are not the treafon, but the deliberate aft of writing them. 2. The fecond fpecies of treafon is, “ if a man do vio¬ late the king’s companion, or the king’s eldeft daughter unmarried, or the wife of the king’s eldeft fon and heir.” By the king’s companion is meant his wife 5 and by vio¬ lation is underftood carnal knowledge, as well without force as with it : and this is high treafon in both parlies if both be confer,ting ; as fome of the wives of Hen¬ ry VIII. by fatal experience evinced. 3. The third fpecies of treafon is, “ if a man do levy war againft our lord the king in his realm.” And this may be done by taking arms, net only to dethrone the king, but under pretence to reform religion, or the lawTs, or to remove evil counfellors, or other grievances whe¬ ther real or pretended. For the law does not, neither can it, permit any private man, or fet of men, to inter¬ fere forcibly in matters of fuch high importance j efpe- cially as it has eftabiilhed a fufficient power for thefe purpofes in the high court of parliament : neither does the conftitution juftify any private or particular refin¬ ance for private or particular grievances j though, in cafes of national oppreffion, the nation has very juftifi- ably rilen as one man, to vindicate the original -contraft (ubfifting between the king and his people. 4. “ If a man be adherent to the king’s enemies in his realm, giving to them aid and comfort in the realm or elfewhere,” he is alfo declared guilty of high-treafon. This muft likewife be proved by fome overt aft $ as by giving them intelligence, by fending them provifions, by felling them arms, by trcacheroufiy furrendering a fortrefs, or the like. 5. “ If a man counterfeit the king’s great or privy feal,” this is alfo high-treafon. But if a man takes wax bearing the impreflion of the great feal off from one pa¬ tent, and fixes it to another, this is held to be only an abufe of the feal, and not a counterfeiting of it: as was the cafe of a certain chaplain, who in fuch a manner framed a difpenfation for non-refidence. But the knav- iffi artifice of a lawyer much exceeded this of the divine. One of the clerks in chancery glued together two pieces of parchment •, on the uppermoft of which he wrote a patent, to which he regularly obtained the great feal, the label going through both the (kins. He then dif- folved the cement, and taking off the written patent, on the blank (kin, wrote a frefh patent of a different import from the former, and publifired it as true. This was held no counterfeiting of the great feal, but only a great mifprifion ; and Sir Edward Coke mentions it with fome indignation that the party was living at that day. 6. The fixth fpecies of treafon under this ftatute is, “ if a man counterfeit the king’s money ; and if a man bring falfe money into the realm counterfeit to the mo¬ ney of England, knowing the money to be falfe, to mer- chandife and make payment withal.” As to the firft branch, counterfeiting the king’s money \ this is trea¬ fon, whether the falfe money be uttered in payment or not. Alfo if the king’s own minters alter the ftandard or alloy eftabliftied by law, it is treafon. But gold and filver money only are held to be within this ftatute. With regard likewife to the fecond branch, importing foreign counterfeit money in order to utter it here ; it is held that uttering it, without imparting it, is not within the ftatute. 7. The lad: fpecies of treafon afcertained by this fta¬ tute is, “ if a man flay the chancellor, treafurer, or the king’s juftices of the one bench or the other, jnftices in eyre, or juftices of aflize, and all other juftices affigned to hear and determine, being in their places doing their offices.” Thefe high magiftrates, as they reprefent the king’s majefty during the execution of their offices, are therefore for the time equally regarded by the law. But this ftatute extends only to the aftual killing of them j and not to wounding, or a bare attempt to kill them. It extends alfo only to the officers therein fpecified ; and therefore the barons of the exchequer, as fuch, are not Treafori. with^ 4 \ T R E [ 4S3 ] T R E Trcafon. within the protection of this aft j but the lord keeper or commiffioners of the great feal now feem to be within it, by virtue of the ftalutes c Eliz. c. 18. and 1 W. and M. c. 21. The new treafons, created fince the ftatute I M. c. 1. and not comprehended under the defcription of ftatute 25 Edw. Hi. may be comprifed under three heads. The firlt ipecies relates to Papifts j the fecond to falfifying the coin or other royal lignatures, as falfely forging the fign manual, privy fignet, or privy feal, which fhall be deemed high treaion (1 M. flat. ii. c. 6.). The third new fpecies of high treai'on is fuch as was created for the fecuniy of the Proteftant fucceflion in the houfe of Hanover. For this purpofe, after the aft of fettlement was made, it was enafted by ftatute 13 and 14 W. III. c. 3. that the pretended prince of Wales, affuming the title of .King James III. ftiould be attainted of high trea- fon ; and it was made high-treafon for any of the king’s fubjcfts to hold correfpondence with him or any perfon employed by him, or to remit money for his ufe. And by 17 Geo. II. c. 39. it is enafted, that if any of the fons of the pretender flrall land or attempt to land in this kingdom, or be found in the kingdom or any of its dominions, he fliall be adjudged attainted of high-trea¬ fon j and correfponding with them or remitting money to their ufe is made high-treafon. By 1 Ann. flat. 2. c. 17. the offence of hindering the next in fucceflion from fucceedxng to the crown is high-treafon : and by 6 Ann. c. 7. if any perfon fhall malicioufly, advifedly, and direftly, by writing or printing, maintain, that any other perfon hath any right to the crown of this realm, otherwife than according to the aft of fettlement, or that the kings of this realm with the authority of par¬ liament are not able to make laws to bind the crown and its defcent; fuch perfon flrall be guilty of high- treafon. The punifhment of high treafon in general is very fo- lemn and terrible. 1. That the offender be drawn to the gallows, and not be carried or walk ; though ufual- ly (by connivance, at length ripened by humanity into law) a fledge or hurdle is allowed, to preferve the of¬ fender from the extreme torment of being dragged on the ground or pavement. 2. That he be hanged by the neck, and then cut down alive. 3. That his entrails be taken out, and burned while he is yet alive. 4. That his head be cut off. 5. That his body be divided into four parts. 6. That his head and quarters be at the king’s difpofal. , bhe king may, and often doth, difcharge all the pu¬ nifhment except beheading, efpecially where any of noble blood are attainted. For beheading being part of the judgement, that may be executed, though all the reft be omitted by the king’s command. But where be¬ heading is no part of the judgement, as in murder or other felonies, it hath been faid that the king cannot change the judgement, although at the requeft of the party, from one fpecies of death to another. In the cafe of coining, which is a treafon of a diffe¬ rent complexion from the reft, the punifhment is milder for male offenders; being only to be drawn and hanged by the neck till dead. But in treafons of every kind the punifhment of women is the fame, and different from that of men. For as the natural modefty of the fex for¬ bids the expofing and publicly mangling their bodies, their fentence (which is to the full, as terrible to fenfe as. the other) is to be drawn to the gallows, and there to be Treafon ' burned alive. II For the confequences of this judgement, fee Attain- , rrca,lirer‘i der, Forfeiture, and Corruption of Blood. Betty or Petit Treafon, according to the ftatute 25 Edward III. c. 2. may happen three ways : by a fer- vant killing his mafter, a wife her hufband, or ajj eccle- fiaftical perlbn (either lecular or regular) his fuperior, to whom he owes faith and obedience. A fervar.t who kills his mafter whom he has left, upon a grudge con¬ ceived againft him during his fervice, is guilty of petty treafon : for the traitorous intention was hatched while the relation fubliiled between them, and this is only an. execution of that intention. So if a wife be divorced a metfe et thoro, ftill the vinculum matrimonii fubfifts ;. and if fhe kills fuch divorced hufband, fhe is a traitrefs. And a clergyman is underftood to owe canonical obedi¬ ence to the bifhop who ordained him, to him in whofe diocefe he is beneficed, and alfo to the metropolitan of fuch fuffragan or diocefan bilhop ; and therefore to kill any of thefe is petit treafon. As to the reft, whatever ' has been faid with refpeft to wilful Murder, is alfo applicable to the crime of petit treafon, which is no other than murder in its moft odious degree ; except that the trial fhall be as in cafes of high treafon, before the improvements therein made by the ftatutes of Wil¬ liam III. But a perfon indrfted of petit treafon may be acquitted thereof, and found guilty of manflaughter or murder : and in fuch cafe it thould feem that two witnefles are not neceffary, as in cafes of petit treafon they are. Which crime is alfo diftinguifhed from mur¬ der in its punifhment. The punifhment of petit treafon in a man, is to be drawn and hanged, and in a woman to be drawn and burned : the idea of which latter punifhment feems to have been handed down to us from the laws of the an¬ cient Druids, which condemned a woman to be burned for murdering her hufband ; and it is now the ufual punifhment for all forts of treafons committed by thofe of the female fex. Perfons guilty of petit treafon were firft debarred the benefit of clergy by ftatute 12 Henry VII. c. 7. which has fince been extended to their aiders, abettors, and counfellors, by ftatutes 23 Henry VIII. c, I, 4, and 5 P. and M. c. 4. TREASURE, in general, denotes a ftore or flock of money in referve. TkEASURE-Trove, in derived from the French word trover, “ to find,” called in Latin thefaurus inven-* ■ tus, is where any money or coin, gold, filver, plate, or bullion, is found hidden in the earth or other private place, the owner thereof being unknown ; in which cafe the treafure belongs to the king : but if he that had hid it be known, or afterwards found out, the owner and not the king is infilled to it. TREASURER, an officer to whom the treafure of a prince or corporation is committed to be kept and duly difpofed of, in payment of officers and other expences. See Treasury. Of thefe there is great variety. His majefty of Great Britain, in quality of eleftor of Hanover, is arch-trea- furer of the Roman empire. In England, the principal officers under this denomination are, the lord high-trea- furer, the treafurer of the houffehold, treafurer of the navy, of the king’s chamber, &c. The lord high-treafurer of Great Britain, or firft com- miffionsr THE [ 464 ] T R E Treafurer miflioner of the treafury, when in commiflion, has under Trebuchet c^arSe an(^ government all the king’s revenue ■ - which is kept in the exchequer. He holds his place during the king’s pleafure j being inftituted by the de¬ livery of a white Half to him. He has the check of all the officers employed in collefling the cuftoms and royal revenues: and in his gift and difpofition are all the offices of the cuftoms in the feveral ports of the king¬ dom ; efcheators in every county are nominated by him j he alfo makes leafes of the lands belonging to the crown. The office of lord-treafurer is now in comm'flion. The number of lords commiffioners is five j one of whom is the firft lord, whole annual falary was formerly 3,83!. but is now 4000I.; and who, unlefs he be a peer, is alfo chancellor of the exchequer, and prime minifter in the government of this country; the other lords commiflioners have an annual falary of 1600I. * ■ each. TREASURER of the Houfehold, is an officer who, in the abfence of the lord-fteward, has power, with the comptroller and other officers of the green-cloth and the fteward of the Marftialfea, to hear and determine treafons, felonies, and other crimes committed within the king’s palace. See Household. There is alfo a treafurer belonging to the eftabliffiment of her majefty’s houfehold, &c. TREASURER of the Navy, is an officer who receives money out of the exchequer, by warrant from the lord high-treafurer, or the lords commiffioners executing that place ; and pays all charges of the navy, by warrant from the principal officers of the navy. TREASURER of the County, he that keeps the county flock. There are two of them in each county, chofen by the major part of the juftices of the peace, &c. at their general quarter feffion 5 under previous fecurity given for the money entrufted with them, and the faith¬ ful execution of the trulls repofed in them. TREASURY, the place wherein the revenues of a prince are received, preferved and dilburfed. In Eng¬ land the treafury is a part of the exchequer j by fome called the lower exchequer. The officers of his ma¬ jefty’s treafury, or the lower exchequer, are the lords commiffioners, one of wffiom is chancellor, two joint fe~ cretaries, private fecretary to the firft lord, two cham¬ berlains, an auditor, four tellers, a clerk of the pells, ulhers of the receipt, a tally-cutter, &c. See each officer under his proper article, Chancellor, Teller, Tal¬ ly, &c. Lords of the TREASURE. In lieu of one fingle di- reftor and adminiftrator of his majefty’s revenues under the title of lord high treafurer, it is at prefent thought proper to put that office in commiffion, i. e. to ap¬ point feveral perfons to difcharge it with equal au¬ thority, under the title of lords commifjioners of the treafury. TREATISE, a fet difcourfe in writing on any fub- jeft. TREATY, a covenant between two or more na¬ tions ; or the feveral articles or conditions ftipulated and agreed upon by trvo fovereign powers. TREBLE, in Mufc, the higheft or moft acute of the four parts in fvmphony, or that which is heard the cleareft and (hrilleft in a concert. TREBUCHET, Trebucket, Tribuch (Terbicke- tum), a tumbrel or cucking ftool. Alfo a great engine to call ftones to batter walls. TREE, a large vegetable rifmg with one woody ftem to a confiderable height. Trees may be divided into two claffes, timber and fruit-trees; the firft including all thole trees which are ufed in machinery, ffiip-building, &c. or, in general, for purpofes of utility j and the fecond comprehending thofe trees valued only, or chiefiy, for their fruit. It is not neceffary to form a third clafs to include trees ufed for fuel, as timber is ufed for this purpofe where it is abundant; and where it is not abundant the branches of the timber trees, or fuch of them as are dwarfilh, un¬ healthy, or too fmall for mechanical purpofes, are ufed as fuel. Tim anatomy and phyfiolo^y of trees have already been given under the generic name Plant and Sap. Certain trees, it is well known, are natives of parti¬ cular diftrifts ; but many of them have been tranfplant- ed from their native foil, and now flouriffi luxuriantly in diftant countries, fo that it becomes a matter of very confiderable difficulty to afcertain their original foil. The following rules are given for this purpole by the Honourable Daines Barrington. 1. They mull grow in large mafies, and cover confi¬ derable trails of ground, the woods not ending abrupt¬ ly, by a change to other trees, except the fituation and ftmta become totally different. 2. They mult grow kindly in copfes, and ftioot from the ftool, fo as to con¬ tinue for ever, if not very carefully grubbed up. 3. The feed muft ripen kindly 5 nature never plants but where a fucceffion in the greateft profufion wall continue Laft- ly, _ trees that give names to many places are probably indigenous. T he growth of trees is a curious and interefting fub- jeft ; yet few experiments have been m&de to deter¬ mine what the additions are which a tree receives an¬ nually in different periods of its age. The only obfer- vations which we have feen on this fubjedl worth re¬ peating were made by the ingenious Mr Barker, to whom the Philofophical Tranfadlions are much indebt¬ ed for papers containing an accurate regifler of the weather, which he has kept for many years. He has drawn up a table to point out the growth of three kinds of trees, oaks, affies, and elms j which may be feen in the Philofophical Tranfa6lions for 1788. We ftiall give his conclufions. “ I find (fays he) the growth of oak and affi to be nearly the fame. I have fome of both forts planted at the fame time, and in the fame hedges, of which the oaks are the largeft ; but there is no certain rule as to that. The common growth of an oak or an afh is about an inch in girth in a year; fome thriving ones w’ill grow an inch and a half; the unthriving ones not fo much. Great trees grow more timber in a year than fmall ones; for if the annual growth be an inch, a coat of one-fixth of an inch is laid on all round, and the timber added to the body every year is its length mul¬ tiplied into the thicknefs of the coat and into the girth, and therefore the thicker the tree is, the more timber is added.” We will prefent our readers with a table, fhownng the growth of 17 kinds of trees for two years. The trees grew at Cavenham in Suffolk. Tree. 4 j Oak THE [ 46 1 Oak 2 Larch 3 Scotch fir 4 Spruce fir 5 Spanifh chefnut 6 Elm 7 Pin after 8 Larch 9 Weymouth pine 10 Acacia 11 Beech 12 Plane, occidental 13 Lombardy poplar 14 Black poplar 15 Willow 16 Silver fir 17 Lime July 1785. F. In. O ICf 1 of 1 3i o n 2 7i 2 3i 1 Si o 5 I 2l o 6j o 6i 1 8 1 2i 2 9f o 7i 1 8i July 1786 F In. O Ilf 1 3 1 if o 6f o 7i 2 9 2 4f 1 6 o 6 1 if o 6f o 7f July 1787. F In. I Of 1 4 1 7f o 7f o 8 2 11 2 7f 1 7 o 7t 1 6f o 7f o 8f 2 3f 1 if 3 3 o 94- See Husbandry, N° 165, where the growth of 11 kinds of trees in 21 years is given. Trees fometimes attain a very great fize : this muft depend in a great meafure on the richnefs of foil, but no lefs on the degree of heat. Indeed heat is fo effen- tial to the growth of trees, that as we go from the place within the polar circles where vegetation begins, and advance to the equator, we find the trees increafe in fize. Greenland, Iceland, and other places in the fame latitude, yield no trees at all 5 and the fhrubs which they produce are dwarfifh; whereas, in warm climates, they often grow to an immenfe fize. Mr Marfham faw fpruce and filver firs in the dock-yard in Venice above 40 yards long, and one of 39 yards was 18 inches dia¬ meter at the fmall end. He was informed that they came from Switzerland. The largeft tree in Europe, mentioned by travellers, Is the chefnut tree on Mount Etna, already defcribed under the article Etna, N° 18. It is a certain fa& that trees acquire a very great fize in volcanic coun¬ tries. Befide the multitude of fine groves in the neigh¬ bourhood of Albano in Italy, there are many detached oaks 20 feet in circumference, and many elms of the fame fize, efpecially in the romantic way to Eaftello, called the Galleria. In travelling by the fide of the lake of Bolfena, the road leads through an immenfe number of oaks, fpread upon beautiful hills. Where the lava has been fufficiently foftened, they are clean and ftraight, and of a confiderable fize ; but where the lava has not been converted Into a foil proper for ftrong vegetation, they are round-headed, and of lefs fize j however, taken all together, they make a magnificent appearance ; and the fpot itfelf ought to be ranked among the fine parts of Italy. The fame may be obferved of the fmall lake of Vico, encompaffed with gentle rifings, that are all clothed with foreft-trees. Some yews have been found in Britain 60 feet round. P ilms in Jamaica attain the height of 200 feet j and fome of the pines in Norfolk illand are 280 feet high. Of all the different kinds known in Europe, oak is beft for building j and even when it lies expofed to air and water, there is none equal to it. Fir-timber is the Vol. XX. Part II. 5 ] T R E next in degree of goodnefs for building, efpecxally in England, where they build upon leales. It differs from oak in this, that it requires not much feafonmg, and therefore no great ftock is required before-hand. Fir is ufed for flooring, wainfcoting, and the ornamental parts of building within doors. Elm is the next in ufe, efpe¬ cially in England and France : it is very tough and pliable, and therefore eafiiy worked : it does not readily fplit 5 and it bears driving of bolts and nails better than any other wood j for which reafon it is chiefly ufed by wheel-wrights and coach-makers, for (hafts, naves, See. Beech is alfo ufed for many purpofes : it(is very tough and white when young, and of great ftrength 5 but liable to warp very much when expoled to the weather, and to be worm eaten when ufed within doors $ its greateft ufe is for planks, bedfteads, chairs, and other houfehold goods. Afti is like wife a very ufeful wood, but very fcarce in moft parts of Europe 5 it ferves in buildings, or for any other ufe, when fereened from the weather j handfpikes and oars are chiefly made of it. Wild .chefnut timber is by many efteemed to be as good as oak, and feems to have been much ufed in old build¬ ings ; but whether thefe trees are more fcarce at prefent than formerly, or have been found not to anfwer fo well as was imagined, it is certain that this timber is now but little ufed. Walnut-tree is excellent for the joiner’s ufe, it being of a more curious brown colour than beech, and not fo fubjeft to the worms. The poplar, abele, and afpen trees, which are very little different from each other, are much ufed inftead of fir $ they look well, and are tougher and harder. The goodnefs of timber not only depends on the foil and fituation in which it Hands, but likewife on the fea- fon wherein it is felled. In this people difagree very much ; fome are for having it felled as foon as its fruit is ripe, others in the fpring, and many in the autumn. But as the fap and moifture of timber is certainly the caufe that it perifties much fboner than it otherwife would do, it feems evident, that timber ftrould be felled where there is the leaft fap in it, viz. from the time that the leaves begin to fall till the trees begin to bud. This work ufually commences about the end of April in England, becaufe the bark then rifes moft; freely j for where a quantity of timber is to be felled, the ftatute requires it to be done then, for the advantage of tan¬ ning. The ancients chiefly regarded the age of the moon in felling their timber $ their rule was to fell it in the wane, or four days after the new moon, or fometimes in the laft quarter. Pliny advifes it to be in the very in- ftant of the change •, which happening to be in the laft day of the winter folftice, the timber, fays he, will be incorruptible. Timber fttould likewife be cut when of a proper age; for when it is either too young or too old, it will not be fo durable as w'hen cut at a proper age. It is faid that oak fliould not be cut under 6o years old, nor above 200. Timber, however, Ihould be cut in its prime, when almoft fully grown, and before it begins to decay ; and this will be fooner or later according to the drynefs and moiftnefs of the foil where the timber grows, as alfo according to the bignefs of the trees $ for there are no fixed rules in felling of timber, ex¬ perience and judgment muft dire& here as in moft other cafes. Great attention is neceffary in the feafoning of tim- 3 N ber. THE [ 466 ] T R E tier. Some advife the planks of timber to be laid for a few days in fome pool or running ftream, in order to extract the fap, and afterwards to dry them in the fun or air. By this means, it is faid, they will be prevented from either chopping, carting, or cleaving ; but againft fhrinking there is no remedy. Some again are for bury¬ ing them in the earth, others in a heat; and fome for fcorching and feafoning them in fire, efpecially piles, ports, &c. which are to ftand in water or earth. The Venetians firft found out the method of feafoning by fire ; which is done after this manner: They put the piece to be feafoned into a ftrong and violent flame j in this they continually turn it round by means of an en¬ gine, and take it out when it is everywhere covered with a black coaly cruft j the internal part of the wood is thereby fo hardened, that neither earth nor water can damage it for a long time afterwards. Dr Plott fays, it is found by long experience, that the trunk or body of the trees, when barked in the fpring, and left Handing naked all the fummer expofed to the fun and wind, are fo dried and hardened, that the fappy part in a manner becomes as firm and durable as the heart itfelf. This is confirmed by M. Buffon, who, in 1738, prefented to the royal academy of fciences at Paris a memoir entitled, “ An eafy method of increaf- ing the folidity, ftrength, and duration of timber j” for which purpofe he obferves, “ nothing more is neceflary than to ft rip the tree entirely of its bark during the fea- fon of the rifing of the fap, and to leave it to dry com¬ pletely before it be cut down.” By many experiments, particularly defcribed in that eflay, it appears, that the tree rtiould not be felled till the third year after it has been ftripped of the bark j that it is then perfectly dry, and the fap become almoft as ftrong as the reft of the timber, and ftronger than the heart of any other oak tree which has not been fo ftripped ; and the whole of the timber ftronger, heavier, and harder •, from which he thinks it fair to conclude, that it is alfo more durable. “ It would no longer (he adds) be neceffary, if this method were pra&ifed, to cut off the fap •, the whole of the tree might be ufed as tim¬ ber j one of 40 years growth would ferve all the pur- pofes for which one of 60 years is now required 5 and this praftice would have the double advantage of in- creafing the quantity, as well as the ftrength and folidi¬ ty, of the timber.” The navy board, in anfwer to the inquiries of the eommiffioners of the land revenue, in May 1789, in¬ formed them, that they had then Handing fome trees ftripped of their bark two years before, in order to try the experiment of building one half of a Hoop of war with that timber, and the other half with timber felled and ftripped in the common w’ay. This very judicious mode of making the experiment, if it be properly exe¬ cuted, will undoubtedly go far to afcertain the effetts of this pra&ice. We are forry that we are not able to inform our readers w7hat was the refult of the experi¬ ment. After the planks of timber have been w7ell feafoned and fixed in their places, care is to be taken to defend ©r preferve them •, to which the fmearing them writh linfeed oil, tar, or 'the like oleaginous matter, contri¬ butes much. The ancients, particularly Hefiod and Virgil, advife the fmoke-drying of all inftruments made of wood, by hanging them up in the chimneys where w7ood fires are ufed. The Dutch preferve their gates, Tree, portcullices, drawbridges, fluices, &c. by coating them 'r~mJ over with a mixture of pitch and tar, whereon they ftrew fmall pieces of cockle and other {hells, beaten al¬ moft to powder, and mixed with fea-fand, which in¬ crufts and arms them wonderfully againft all affaults of Wind and weather. When timber is felled before the fap is perfeftly at reft, it is very fubjeft to worms ; but to prevent and cure this, Mr Evelyn recommends the foi- kwing remedy as the moft approved : Put common ful- phur into a cucurbit, with as much aquafortis as will cover it three fingers deep j diftil it to drynefs, which is performed by two or three reftifications. Lay the ful- phur that remains at bottom, being of a blackifh or fand-red colour, on a marble, or put it in a glafs, and it will diffolve into an oil ; with this oil anoint the timber which is infe&ed with worms. This, he fays, will not only prevent worms, but preferve all kinds of woods, and many other things, as ropes, nets, and mafts, from putrefaction, either in water, air, or fnow. An experiment to determine the comparative durabi¬ lity of different kinds of timber, when expofed to the weather, was made by a nobleman in Norfolk 5 of which jn„a!s ef an account is given by Sir TL homas Beevor. 1 his no- Agricul- bleman, in the year 1774, ordered three polls, forming ture, vol. two fides of a quadrangle, to be fixed in the earth on a v1, P1 ^ rifing ground in his park. Into thefe ports were mor- tifed planks, an inch and a half thick, cut out of trees from 30 to 45 years growth. Thefe, after {landing 10 years, w^ere examined, and found in the following ftate and condition : The cedar w7as perfeClly found; larch, the heart found, but the fap quite decayed ; fpruce fir, found j filver fir, in decay j Scotch fir, much decayed j pin- after, quite rotten $ chefnut, perfeflly found; abele, found ; beech, found ; w7alnut, in decay ; fycamore, much decayed ; birch, quite rotten. Sir Thomas Bee¬ vor juftly remarks, that the trees ought to have been of the fame age ; and Mr Arthur Young adds, they ought to have been cut out of the fame plantation. The immenfe quantity of timber confirmed of late years in {hip-building and other purpofes has diminifh- ed in a very great degree the quantity produced in this country. On this account, many gentlemen who wilh w7ell to their country, alarmed with the fear of a fcarci- ty, have ftrongly recommended it to government to pay fome attention to the cultivation and prefervation of tim- her. We find, on the beft authority, that of Mr Irving in- fpeftor general of imports and exports, that the {hip¬ ping of England in 1760 amounted to 6107 in num¬ ber, the tonnage being 433,922; and the {hipping in Scotland amounted to 976 in number, the tonnage be¬ ing 52,818. In 1788 the whole {hipping of Britain and Ireland and their colonies amounted to 13,800, be- ing 1,359,752 tons burden, and employing 107,925 men. The tonnage of the royal navy in the fame y^ar w7as 413,667. We are informed alfo, on what we con- Elwenfh fider as the beft authority (the report of the commiflion-i?^0,f‘ ers of the land revenue), that the quantity of oak timber, of Englifh growth, delivered into the dockyards from 1760 to i 788 was no lefs than 768,676 loads, and that the quantity ufed in the merchants yards in the fame time w7as 1516,630 loads 5 in all 1,285,306 loads. The foreign oak ufed in the fame period was only 137,766 loads. THE [ 467 ] T R E Tree, loads. So that, after deducing the quantity remaining -V-—' in the dock-yards in 1760 and 1788, and the foreign oak, there will remain about 1,054,284 loads of Englilh oak, confumed in 28 years, which is at an average 37,653 loads per annum, befides from 8300 to 10,000 loads expended annually by the Eaft India company within the fame period (a). The price of wood has rifen in proportion to the de¬ mand and to its diminution. At the conqueft, woods were valued, not by the quantity of timber which they contained, but the number of fwine which the acorns could fupport. In 1608, oak in the forefts was fold at 1 os. per load, and fire-wood for 2s. per load. In 1663 or 1665, in navy contracts from 2l. to 2l. 15s. 6d. per load was given. In 17 :6 it rofe to 4I. 5s. per load, and 3s. in addition, becaufe no tops are received. Plank four inch fold in 1769 for 7I. a load, three inch 61.; which prices were the fame in 1792. So great an expenditure of valuable timber within fo (hort a period, gives reafon to fear that the forefts of this country will foon be entirely difmantled, unlefs fomething is done to raife frelh fupplies. The building of a 70 gun ftiip, it is faid, would take 40 acres of timber. This calculation is indeed fo exceflive, that it is fcarcely credible. This, however, is no exaggeration. According to the prevailing opinion of experienced fur- veyors, it will require a good foil and good manage¬ ment to produce 40 trees on an acre, which, in a hun¬ dred years, may, at an average, be computed at two loads each. Reckoning, therefore, two loads at 81. 16s. one acre will be worth 350I. and confequently 40 acres will only be worth 14,200!. Now a 70 gun (hip is ge¬ nerally fuppofed to coil 70,000!.; and as {hips do not laft a great many years, the navy continually requires new fhips, fo that the forelts muft be {tripped in a cen¬ tury or two, unlefs young trees are planted to fupply their place. Many plans have been propofed for recruiting the forefts. Premiums have been held forth to individuals; and it has been propofed that the crown-lands Ihould be fet apart for the fpecial purpofe of railing timber. With refpeft to individuals, as they muft generally be difpofed to fow or plant their lands with thofe vege¬ tables which will beft reward their labours, it is not to be expefted that they will fet apart their fields for planting trees unlefs they have a greater return from them than other crops. But bad muft that land be which will not yield much more than 350I. produce in loo years. But though it be evident that good land will produce crops much more lucrative to the proprietor than timber, yet ftill there are lands or pieces of land which might be applied with very great advantage to the produdlion of wood. Uneven ground, or the fides of fields where corn cannot be cultivated, might very properly be fet apart for this purpofe j barren lands, or fuch as cannot be cultivated without great labour and *xpence, might alfo be planted. Hedge-rows and clumps of trees, and little woods fcattered up and down. Tree, would Ihelter and defend the fields from deftrudtive ' winds, would beautify the face of the country, render the climate warmer, improve barren lands, and furnilh wood for the arts and manufa&ures. But to cultivate foreft timber has alfo been thought of fuch national importance, that it has been deemed wor¬ thy of the attention of government. It has been pro¬ pofed to appropriate fuch part of the crown-lands as are fit for the purpofe folely of producing timber for the na¬ vy. This appears a very proper fcheme in fpeculation $ but it has been objedled, that for government to attempt the farming of forefts would be really to eftablifti groups of officers to pocket falaries for doing what, it is well known, will never be done at all. But to this objeftion we reply, that fuch an agreement might be made with the infpeftors of forefts, as to make it their own intereft to cultivate trees with as much care as poflible. Their falary might be fixed very low, and raifed in proportion to the number of trees which they could furnilh of fuch a fize in a certain number of years. After all, we muft: acknowledge that we muft depend greatly on Ruftia, Sweden, Norway, and America, for fupplying us with . timber j and while thefe countries take our maaufadtures in exchange, we have no reafon to complain. Still, how¬ ever, we ought furely not to negledl the cultivation of w-hat is of fo much importance to our exiftence as a na¬ tion, for it may often be impoffible in time of war to ob¬ tain timber from foreign countries. In the beginning of this article we mentioned the ge¬ neral divifion of trees into timber or foreft-trees and fruit trees. We have already faid all that our limits will permit refpe&ing the former : we will now, there¬ fore, fay fomething of the latter. Our obfervations {ball be confined to the methods of preferving fruit trees in bloffom from the eftedls of froft, and from other difeafes to which they are liable. The Chevalier de Dienenberg of Prague, we are told, has difcovered a method of effeftually preferving trees in bloffom from the fatal effe&s of thofe frofts which fome-1^1, times in the fpring deftroy the moft promifing hopes of a plentiful crop of fruit. His method is extremely fimple. He furrounds the trunk of the tree in bloffom with a wifp of ftraw or hemp. The end of this he finks, by- means of a ftone tied to it, in a veffel of fpring water, at a little diftance from the tree. One veffel will conve¬ niently ferve two trees : or the cord may be lengthened fo as to furround feveral, before its end is plunged into the water. It is neceffary that the veffel be placed in an open fituation, and by no means {haded by the branches of the neighbouring trees, that the froft may produce all its effeft on the water, by means of the cord communi¬ cating with it.—This precaution is particularly neceffary for thofe trees the^ flowers of which appear nearly at the fame time as the leaves 5 which trees are peculiarly ex- poled to the ravages of the froft. The proofs of its effi¬ cacy, which he had an opportunity of obferving in the 3 2 ^Pnng (a) A writer in the Bath Tranfaftions fays, that the aggregate of oaks felled in England and Wales for 30 years paft has amounted to 320,000 loads a-year ; and affirms that he has documents in his poffeflion founded on indifputable fafts.. The difference between this account, and that which we have given in the text from the re¬ port of the commiftioners, we leave to be reconciled by thofe who have proper opportunities. We give the fads merely on the authority of others. & THE [ fpring of 1787, were remarkably fhiking. Seven apri¬ cot efpaliers in bis garden began to bloffom in the month of March. Fearing that they would fuffer from the late frolts, he furrounded them with cords as above direfted. In effeft, pretty ftiarp frofts took place fix or eight nights: the apricot-trees in the neighbouring gardens were all frozen, and none of them produced any fruit, whilll each of the chevalier’s produced fruit in abun¬ dance, which came to the greateft perfeftion. The following is the method propofed by Mr Wil¬ liam Forfyth for curing injuries and defefts in trees ; for which a reward was given to him by his Majefty, on condition that he (hould make it public. It is equally applicable to foreft as to fruit trees (b). Take one bufhel offrefh cow-dung, half a bufhel of lime rubbifh of old buildings (that from the ceilings of rooms is preferable) j half a bufhel of wood allies j and a fixteenth part of a bufhel of pit or river fand. The three laft ar¬ ticles are to be fifted fine before they are mixed $ then work them well together with a fpade, and afterwards with a wooden beater, until the fluff is very fmooth,like fine plafler ufed for the ceilings of rooms. The compo- fition being thus made, care muff be taken to prepare the tree properly for its application by cutting away all the dead, decayed, and injured parts, till you come to the frefh found wood, leaving the furface of the wood very fmooth, and rounding off the edges of the bark with a draw-knife, or other inftrument, perfe&ly fmooth, which muft be particularly attended to. Then lay on the plaf- ter about one-eighth of an inch thick all over the part where the wood or bark has been fo cut away, finifhing off the edges as thin as poffible. Then take a quantity of dry powder of wood afhes, mixed with a fixth part of the fame quantity of the afhes of burnt bones ; put it into a tin box, with holes in the top, and fhake the pow¬ der on the furface of the plafler, till the whole is covered over with it, letting it remain for half an hour to abforb the moiflure ; then apply more powder, rubbing it on gently with the hand, and repeating the application of the powder, till the whole plafter becomes a dry fmooth fuiface. All trees cut down near the ground fhould have the farface made quite fmooth, rounding it off in a fmall de¬ gree, as before mentioned j and the dry powder direfted to be ufed afterwards fhould have an equal quantity of powder of alabafter mixed with it, in order the better to refift the dripping of trees and heavy rains. If any of the compofiiion be left for a future occafion, it fhould be kept in a tub or other veffel, and urine of any kind poured on it, fo as to cover the furface *, otherwife the atmofphere will greatly hurt the efficacy of the applica¬ tion. Where lime rubbifh of old buildings cannot be eafily got, take pow’dered chalk, or common lime, after having been flaked a month at leaft. As the growth of the tree will gradually affect the plafler, by raifing up its edges next the bark, care fhould be taken, where that 468 ] the happens, to rub it over with the finger when occafion Tree- may require (which is bell done when moiltened by Trj|it rain), that the plafler may be kept whole, to prevent. - > the air and wet from penetrating into the wound. By this procefs, fome old worn-out pear trees, th&t Forfyth’*' bore only a few fmall, hard fruit, of a kcrnelly texture, were made to produce pears of the beft quality and finefi^0/" th* flavour the fecond fummer after the operation j and in ^ four or five years they bore fuch plenteous crops, as a young healthy tree would not have produced in four times that period. By this procefs, too, fome large ancient elms, in a moft decayed flate, having all their upper parts broken, and a fmall portion only of the bark remaining, fhot out flems from their tops, abave thirty feet in height, in fix or feven years from the firfl application of the compofi- tion. Thus may valuable trees be renovated j and forefl trees, which are ufeful or ornamental from their particu¬ lar fituation, be preferved in a flourifliing flate. But what is far more interefling, a perfedl cure has been made, and found timber produced, in oak trees, which had received very confiderable damage from blows, brui- fes, cutting of deep letters, the rubbing off the bark by the ends of rollers, or wheels of carts, or from the breaking of'branches by {forms. TREFOIL. See'J RiFOLiuM, Botany/wr/c.v. TREMELLA, a genus of plants belonging to the clafs of cryptogamia. See Botany Index. TREMOR, an involuntary fhaking, chiefly of the hands and head, fometimes of the feet, and lometimes of the tongue and heart.—Tremors arifing from a too free ufe of fpirituous liquors require the fame treatment as palfies. TRENCHES, in fortification, are ditches cut by the befiegers, that they may approach the more fecurely to the place attacked, whence they are alfo called lines of approach. TRENT, Bishopric of, a province of Germany, in the circle of Auftria, near the frontiers of Italy 5 is bounded on the north by Tirol j on the eaft by the Fel- trino and Bellunefe j on the fouth, by Vincentino, the Veronefe, Brefciano, and the lake de Garda ; and on the weft, by the Brefciano and the lake de Garda. The foil is faid to be very fruitful, and to abound in wine and oil. Trent, a city of Germany, and capital of the bi- (hopric of that name, is a very ancient place, and Hands in a fertile and pleafant plain, in the midft of the high mountains of the Alps. The river Adige wafties its walls, and creeping for fome time among the hills, runs fwiftly into Italy. Trent has three confiderable church¬ es, the principal of which is the cat hedral: this is a very regular piece of architefture. The church of St Maria Major is all of red and white marble *, and is remark¬ able for being the place where the famous council of Trent (b) A pafte for covering the wounds of trees, and the place w-here grafts are inferted, w-as difcoyered long ago. It is recommended in a Treatife on Fruit Trees, publilhed by Thomas Hitt in 1755 i a third edition of which, with additions, was pubhfhed in 1768. It confifts of a mixture of clay and cow'’s dung diluted with water. This pafte he ditefts to be laid on the wound with a brulh j it adheres firmly, he fays, without cracking till the wound heals. We are informed by a gentleman, to whofe opinion and experience we pay great refpe£t, that this pafte anfwers every purpofe which Mr Forfyth’s can ferve. T R E r 469 j T R I Treves. Trent Trent was heid, w'hofe decifions are now the (landing rule of the Romilh church. E. Long. 11. 5. N. Lat. - 46. 10. Trent, one of the larged rivers in England, which rifes in the moorland of Staffordlhire, and runs fouth- weft by Newcadle-under-Line 5 and afterwards dividing the county in two parts, runs to Burton, then to Not¬ tingham and Newark : and fo continuing its courfe due north to Gainfborough on the confines of Lmcolnthire, it joins feveral rivers, and falls into the Humber. Trent, Council ofy in Ecclejiajlical HJlory, denotes the council affembled by Paul III. in 1545, and conti¬ nued by 35 fedions till the year 1563, under Julius III. and Pius IV. in order to correft, illullrate, and fix with perfpicuity, the doftrine of the church, to redore the vigour of its difeipline, and to reform the lives of its mi- niders. The decrees of this council, together with the creed of Pope Pius IV. contain a fummary of the doc¬ trines of the Roman Catholics. Thefe decrees were fubferibed by 255 clergy, confiding of four legates, 2 other cardinals, 3 patriarchs, 25 archbidiops, 168 bi- (hops, befides inferior clergy. Of thefe 150 came from Italy, of courfe the council was entirely under the influ¬ ence of the pope. For a more particular account of the council of Trent, fee Molheim’s Church Hidory, the Modern Univerfal Hiflory, vol. xxiit. and Father Paul’s Hidory of the Council of Trent. TRENTON. See New Jekset. TREPANNING. See Surgery Index. TRES TABERNiE, in Ancient Geography, a place in Latium, Iving on the Via Appia, on the left or fouth fide of the river Adura, to the north of the Paludes Pomptinae. Its ruins are now feen near Ciderna, a vil¬ lage in the Campagna di Roma, 21 miles from Rome, whence the Chridians went out to meet St Paul. TRESPASS, in Law, fignifies any tranfgreflion of the law, under treafon, felony, or mifprifion of either : but it is commonly ufed for any wrong or damage that is done by one private perfon to another, or to the king in his fored. TRESSLE TREES, in Ship-Building, two drong bars of timber fixed horizontally on the oppofite fides of the lo wer mad-head, to fupport the frame of the top and the weight of the top-mad. TRESSURE, in Heraldry, a diminutive of an orle, ufually held to be half the breadth thereof. TRET, in Commerce, an allowance made for the wade or the dirt that may be mixed with any commodi¬ ty ; which is commonly four pounds in every 104 pounds weight. TREVERI, or TrEviri, in Ancient Geography, an ancient and a poweiful people, both in horfe and foot, according to Caefar j extending far and wide between the Meufe and the Rhine. Their chief town was called Tre- ’Deris. Now Triers or T re-ves. TREVES, or Triers (in Latin Trevere, Trevers, Treviris, or Augufia Trevirorum), the capital of the German archbithopric of the fame name, dands 60 miles wed of Mentz, 52 fouth of Cologne, and 82 north of Strafburg. This city vies with mod in Europe for anti¬ quity, having been a large and noted town before Au- gudus fetlled a colony in it. It was free and imperial till the year 1560, when it was furprifed and fubje&ed by its archbilhop James III. It dands on the Mofelle, over which it has a fair done bridge. The cathedral is a large building ; and near it dands the ele£lor’s palace, Treves-, which not long ago was rebuilt. Here are three colie- giate and five paridr churches, three colleges of Jefuits, ^ thirteen monaderies and nunneries, an univerfity founded in 1472, a houfe of the Teutonic order, and another of that of Malta, with fome remains of the ancient Roman theatre. Roman coins and medals are often found in the ruins of the old city. In the cathedral they pretend to have oui Saviour’s coat and St Peter’s daff, to which they aferibe miracles. The private houfes here are mean ; and the city is neither well fortified nor inhabi¬ ted. E. Long. 6. 41. N. Lat. 49. 45. TRIAL, in Law, the examination of a caufe accor¬ ding to the laws ol the land before a proper judge j or it is the manner and order obferved in the hearing and determining of caufes. Trials are either civil or criminal. I. Civil TRIALS. The fpecies of trials in civil cafes are feven : By record; by infpeEtion or examination j by certificate; by wunejjes ; by wager of battel; by wager of law ; and by^W' y. The fird fix are only had in cer¬ tain fpecial or eccentrical cafes, where the trial by jury would not be fo proper or effe6lual : (See them explain¬ ed under their refpe£tive titles). The nature of the lad, that principal criterion of truth in the law of England, fhall be explained in this article. As trial by jury is edeemed one of the mod impor¬ tant privileges which members of fociety can enjoy, and the bulwark of the Britidi conditution, every man of reflexion mud be dimulated by the defire of inquiring^ into its origin and hiflory, as well as to be acquainted with the forms and advantages by which it is accompa¬ nied. We will therefore begin with tracing it to its ori¬ gin. Its inllitution has been aferibed to our Saxon an- cedors by Sir William Blackdone. “ Some authors (fays that illudrious lawyer) have en- Blarkjl. deavoured to trace the original of juries up as high as the Britons themfelves, the firll inhabitants of our iflandj^ ^j. but certain it is that they were in ufe among the earlied Saxon colonies, their inditution being aferibed by Bidrop Nicholfon to Woden himfelf, rheir great legidator and captain. Hence it is, that we may find traces of juries in the laws of all thofe nations which adopted the feodal fydem, as in Germany, Fiance, and Italy j who had all of them a tribunal compofed of twelve good men and true, boni homines, ufually the vaffals or tenants of the lord, being the equals or peers of the parties litigant j and, as the lord’s vaflais judged each other in the lord’s courts, fo the king’s vafials, or the lords themfelves, judged each other in the king’s court. In E: gland we find aftual mention of them fo early as the laws of King Ethelred, and that not as a new invention. Stiernhock aferibes the invention of the jury, which in the Teuto¬ nic language is denominated nembda, to Regner king of Sweden and Denmark, who wTas contemporary with our King Egbert. Juft as we are apt to impute the inven¬ tion of this, and fome other pieces of juridical polity, to the fuperior genius of Alfred the Great j to whom, on account of his having done much, it is ufual to attri¬ bute every thing : and as the tradition of ancient Greece placed to the account of their ow-n Hercules whatever atchievement wTas performed fuperior to the ordinary prowefs of mankind. Whereas the truth feems to be, that this tribunal was univerfally eftablilhed among all the northern nations, and fo interwoven in their very conftitution. T R I t 4: Trial, conftitution, that the earlieft accounts of the one give us alio fome traces of the other.” This opinion has been controverted with much learn¬ ing and ingenuity by Dr Pettingal in his Inquiry into the Ufe and Practice of Juries among the Greeks and Romans, who deduces the origin of juries from thefe an¬ cient nations. He begins with determining the meaning of the word itxxrxt in the Greek, and judices in the Roman, writers. “ The common acceptation of thefe words (fays he), and the idea generally annexed to them, is that of pre- Jidents of courts, or, as we call them, judges; as fuch they are underllood by commentators, and rendered by critics. Dr Middleton, in his life of Cicero, exprefsly calls the judices, of the bench : and Archbilhop Potter, and in Ihort all modern writers upon the Greek or Roman orators, or authors in general, exprefs Zixxrctt and judices by fuch terms as convey the idea of pref dents in courts of jufice. The propriety of this is doubted of, and hath given occafion for this inquiry j in which is Ihown, from the bell Greek and Roman authorities, that neither the Sixxrxi of the Greeks, or the judices of the Romans, ever fignified pref dents in courts of judicature, or judges of the bench; but, on the contrary, they were diitin- guilhed from each other, and the difference of their duty and fun&ion was carefully and clearly pointed out by the orators in their pleadings, who were the befl author¬ ities in thofe cafes, where the queftion related to forms of law, and methods of proceeding in judicial affairs and criminal procefs. The prefidents of the courts in criminal trials at A- thens were the nine archons, or chief magiftrates, of which whoever prefided was called tyipm ^tKxc^u, or prefident of the court. Thefe nine prefided in different caufes peculiar to each jurifdidlion. The archon, pro¬ perly fo called, had belonging to his department all pu¬ pillary and heritable cafes j the l&xnMvf or rex facro- rum, the chief prieft, all cafes where religion was con¬ cerned } the polemarchus, or general, the affairs of the army and all military matters •, and the fix thefmothetae, the other ordinary fuits. Wherever then the av^e? iixxcxi, or judicial men, are addreffed by the Greek orators in their fpeeches, they are not to be underftood to be the prefiding magiftrates, but another clafs of men, wh« were to inquire into the ftate of the caufe before them, by witneffes and other methods of coming at truth $ and after inquiry made and witneffes heard, to report their opinion and verdift to the prefident, who was to declare it. The feveral fteps and circumftances attending this ju¬ dicial proceeding are fo fimilar to the forms obferved by our jury, that the learned reader, for fuch I muft fup- pofe him, cannot doubt but that the nature, intent, and proceedings of the among the Greeks were the fame with the Englifh jury} namely, for the pro¬ tection of the lower people from the power and oppref- fion of the great, by adminiftering equal law and juftice to all ranks ; and therefore when the Greek orators di¬ rected their fpeeches to the itxxrxi, as we fee in Demofthenes, Alfchines, and Lyfias, we are to under- ftand it in the fame fenfe as when our lawyers at the bar fay, Gentlemen of the jury. So likewife among the Romans, the judices, in their pleadings at the bar, never fignified judges of the bench, or prefidents of the court, but a body or order of men, whole office in the courts of judicature was diftinCt from o ] T R . 1 that of the praetor or judex quefionis, which anfwered | TnA to our judge of the bench, and was the fame with the 'r~' archon, or vyipai Gli of Tri¬ arch or angle are commonly written thus, 23° 29' 32"Sonometr'1" 20"', which expreffion means 23 degrees 29 minutescal iUbles‘. 32 feconds and 20 thirds. v III. Two angles which make together two right angles, alfo two arches which make together a femi- circle, are called the Supp/ements of one another. IV. A tlraight line BG drawn through B, one of the extremities of the arch AB, perpendicular to the di¬ ameter palling through the other extremity A, is called the Sine of the arch AC, or of the angle ACB, having arch AB for its meafure. Cor. 1. '1 he fine of a quadrant or of a right angle is- equal to the radius. Cor. 2. The fine of an arch is half the chord of twice the arch. V. The fegment AG of the diameter intercepted between its extremity and the fine BG is called the; Ferfed Sine of the arch AB, or of the angle ACB. VI. A Itraight line AH touching the circle at A one extremity of the arch AB, and meeting the diame¬ ter CB which paffes through B the other extremity, is called the Tangent of the arch AB, or of the angle ACB. s Cor. The tangent of half a right angle is equal to the radius. VII. The ftraight line CH between the centre and the extremity of the tangent AH is called the Secant of the arch AB or of the angle ACB. Cor. to Def. 4, 6, 7. The fine, tangent, and fe- cant of any angle ACB, are alfo the fine, tangent, and fecant of its fupplement BCE. For by the de¬ finition, BG is the fine of the angle BCE ; and if BC be produced to meet the circle in I, then AH is the tangent and CH the fecant of the angle ACI or BCE. 6 Cor. to Def. 4, 5, 6, 7. The fine, verfed fine, tan¬ gent, and fecant of an arch which is the meafure of the ingle ACB is to the fine, verfed fine, and fecant of any other arch which is the meafure of the fame angle as the radius of the firft arch is to the radius of the le- cond. Let BG, fig. 2. be the fine, AG the verfed fine, Fig. a, AH the tangent, and CH the fecant of the arch AB to the radius CA ; and bg, ag, a h, ch the fame things to the radius C a. From fimilar triangles BG : bg :: E’C : bC; and becaufe CG : Cg (::CB : C &) :: CA : Co ; therefore, by divifion AG : ag :: CA : Ca. Alfo AH : a h :: CH : Ch :: CA : Ca. _ Hence it appears that if tables be conftrutted exhi¬ biting in numbers the fines, tangents, and verfed fines of certain angles to a given radius, they will exhibit the ratios of the fines,- tangents, and verfed fines of the fame angles to any radius whatever. In fuch tables, which are called trigonometrical tables, the radius is either fuppofed 1, or feme number in the feries 10, 100, icoo, &c, - 4/8 Nature and Conftruc- tion of Tri¬ gonometri¬ cal Tables. Fie. i. TRIGONOMETRY. £kc. The cemftru&Ion and ufe of thefe tables we fliall prefently explain. VIII. The difference between any angle and a right angle, or between any arch and a quadrant, is called the Complement of that angle, or of that arch. Thus, if the angle ACD, fig. i. be aright angle, and confe- quently the arch AD, which is its meal'ure, a quadrant, the angle BCD is the complement of the angle BCA, and the arch BD is the complement of the arch AB. Alfo the complement of the obtufe angle BCE is BCD, its excefs above a right angle j and the complement of the arch BDE is the arch BD. IX. The fine, tangent, or fecant of the complement of any angle is called the cofine, cotangent, or cofecant of that angle. Thus, fuppofing the angle ACD to be a right angle, then BF=CG, the fine of the angle BCD, is the cofine of the angle BCA 5 DK, the tan¬ gent of the angle BCD, is the cotangent of the angle BCA, and CK, the fecant of the angle BCD, is the co¬ fecant of the angle BCA. The following properties of the lines which have been defined flow immediately from their pofition. 1. The fum of the fquares of the fine and cofine of any angle is equal to the fquare of the radius. For, in the right-angled triangle BGC, BC* — BG1 -}- GC*, (Geometry, Seft. IV. theor. 13.') Now BG is the fine, and CGrrrBF is the cofine of the angle BCA. 2. The radius is a mean proportional between the tangent of any angle and its cotangent, or tan. ACB X cot. ACBrrrad.a. For fince DK, CA are parallel, the angles DKC, HCA are equal; now CDK, CAH are right angles, therefore the triangles CDK, HCA are fimilar, and therefore AH : AC :: CD or AC : DK, and AC*zrAHxDK. 3. The radius is a mean proportional between the co¬ fine and fecant of any angle. Or cof. ACB'X fee. ACB rrrrad*. For the triangles CGB, CAH are fimilar $ therefore CG : CB or CA :: CA : CH. 4. The tangent of an arch is a fourth proportional to its cofine, its fine and the radius, or tan. ACB = fin. ACB ^ £rom fimiiar triangles CG : GB cof. ACBA ’ 6 :: CA : AH. Trigonometrical tables ufually exhibit the fines, tan¬ gents, and fecants of all angles which can be expreffed by an exa& number of degrees and minutes from I mi¬ nute to 90 degrees, or a right angle. Thefe may be computed in various w’ays, the moft elementary is to calculate them by the help of principles deducible im¬ mediately from the elements of geometry. It has been demonftrated in Geometry, (Se6I. V. prob. 22.) that the chord of one-fixth of the circumfer¬ ence, or an arch of 6o°, is equal to the radius; therefore, if BD be an arch of 30°, its fine BF will be half the radius (cor. 2. def. 4.). Xet us fuppofe the radius to be expreffed by unity, or I, then fin. 3o°=:4-*, nowr fince a being put for any arch, cof. * tf-j-fin.* tfrzrad.* (w'here by cof.1 a is meant the fquare of the number ex- prefiing the cofine of the arch <7, &c.) and as fin.* 30° rr-J, therefore cof.1 30°= 1—^=3:, Cof. 30*= !V'3=:-866o254038. It has been demonftrated in the arithmetic of fines (Algebra, § 356.) that 2cof.177m -j-cof. la; hencewe have the following formula for finding the cofine of an arch, having given the cofine of its double) cof a = By this formula from the cofine of 30oJConftruc- 2 ' r r fi°n Tri- we may find that of 150, and again from cof. 150 we gonometri- may find cof. 70 30', and proceeding in this wray we cal Tables, may find the cofines of 30 45', l° 52' 30", and fo on,'"■"’’v till after 11 bife£Hons the coline of 5 2" 44"' 3lT 4jT is found j we may then find the fine of this arch by the formula fin. a-=z^{\—cof.*fl). Nowq as from the na¬ ture of a circle the ratio of an arch to its fine appi caches continually to that of equality, when the arch is conti¬ nually diminilhed, it follows that the fines of very ifnall arches will be very nearly to one another as the arches themfelves : Therefore, as 52" 44"/ 35t 45t to 1' fo is the fine of the former arch to the fine of the latter. By performing all the calculations which we have here indicated, it will be found that the fine of i' is .0002908882. It has been fhewm in the arithmetic of fines (Alge¬ bra, § 35J-) that a and b being put for any twx> arches, fin. (d-J-£)— 2 cof. b fin. a — fin (a—Z>), hence putting 1' for b, and i', 2', 3', &c. fucceffively for <7, we have, fin. 2'= 2 cof. i'xfin* 1', fin. 3'= 2 cof. I'xfin* 2'—fin. i', fin. 4,= 2 cof. x'xfin* 3'—fin- 2.', &c. In this way the fines for every minute of the quadrant may be computed, and as the multiplier cof. i' remains always the fame, the calculation is eafy. If inftead of l', the common difference of the feries of arches were any other angle, the very fame formula would apply. The fines, and confequently the cofines of any num¬ ber of arches being fuppofed found, their tangents may be found by confidering that tan. 77=—j:— j and their fecants from the formula fee. flrr:-—?.—. col. a We have here very briefly indicated the manner of conftra&ing the trigonometrical canon, as it is fometimes called. There are, however, various properties of fines, tangents, &c. which greatly facilitate the actual cal¬ culation of the numbers, thefe the reader will find de¬ tailed in Algebra, Seft. XXV. which treats exprefsly of the Arithmetic of Sines. The moft expeditious mode of computing the fine or cofine of a fingle angle is by means of infinite feries : The inveftigation of thefe is given in Fluxions, § 70. j and it is there fhewn that if a denote any arch, then, the radius being expreffed by 1, fin. a—a- 2*3 1 ’2 * 3 * 4‘5 &c. cof. 77 = 1- i-2 1*2-3-4 &c. To apply thefe we muft have the arch expreffed m parts of the radius, which requires that we know the pro¬ portion of the diameter of the circle to its circumference. We have inveftigated this proportion in Geometry, Prop. 6. Sett. vi.; alfo in Fluxions, § 137.; and fub- fequently in the article entitled Squaring the Circle. From thefe feries others may be found which (hall exprefs the tangent and fecant. Thus becaufe tan. a= TRICON ^Conftruc^ a=:S7r~ ’ we gct> after dividing the feries for the fine tion of Tri- gonometri- b7 tbat for the cofine, cal Tables. ^3 » tan. a— 3 2 s 17 rt7 + &c. And in like manner, dividing unity by the ferics for cof. a, becaufe fee. a= —we get col.o fee. a~l c a* , 61a5 24 720 + &c. We (hall conclude what we propofed to fay on the conftru&ion of the tables, by referring fuch of our readers as wifh for more extenfive information on this fubjedt to Dr Hutton’s Introduftion to his excellent Mathematical tables j alfo to the treatifes which treat exprefsly of trigonometry, among which are thofe of Emerfon, Simpfon, Bonmjca/Ile, Cagnoli, Mauduit, La¬ croix, Legendre. In particular, we refer to an excel¬ lent treatife on the fubjeft by Mr R. Woodhoufe of Caius college, Cambridge. Defcription of the Table of Logarithmic Sines, isfe. That trigonometrical tables may be extenfively ufe- ful, they ought to contain not only the fine, tangent, and fecant to every minute of the quadrant, but alfo the logarithms of thefe numbers •, and thefe are given in Dr Hutton’s Mathematical Tables, a work which we have already mentioned ; as, however, the fines, &c. or the natural fines, &c. as they are called, are much lefs frequently wanted than their logarithms, we have only given a table of the latter. See Logarithms. This table contains the logarithms of the fines and tangents, or the logarithmicfnes and tangents, to every minute of the quadrant, the degrees at top and minutes defeending down the left-hand fide, as far as 450, and from thence returning with the degrees at the bottom and the minutes afeending by the right hand fide to 90°, in fuch a manner that any arch on the one fide is in the fame line with its complement on the other, the refpe&ive fines, cofines, tangents, and cotangents, being in the fame line with the minutes, and on the columns figured with their refpeftive names at top when the de¬ grees are at top, but at the bottom when the degrees are at the bottom. The differences of the fines and cofines are placed in columns to the right-hand, marked D ; and the differences of the tangents and cotangents are placed in a column between them, each difference belonging equally to the columns on both fides of it. Alfo each differential number is fet oppofite the fpace between the numbers ■whofe difference it is. All this will be evident by infpefting the table itfelf. There are no logarithmic fecants in the table, but thefe are eafily had from the cofines ; for fince fee. a~ rsd ^ —therefore, log. fee. a—l log. rad.—log. cof. a $ now log. rad. mo, therefore the log. fecant of any arch is had by fubtra&ing its log. cofine from 20. The log. fine, log. tangent, or log. fecant of any angle is expreffed by the fame numbers as the log. fine, log. tangent, or log. fecant of its fupplement •, there¬ fore, when an angle exceeds oo°, fubtraft it from 1800 O M E T R Y. 479 and take the log. fine, &c. of the remainder for that of Nature and the angle. Conftruc- To find the log. fine of any angle expreffed by de-^ grees and minutes. If the angle be lefs than 450, look cal Table*, for the number of degrees at the top, and oppofite to —v——* the minutes on the left hand will be found the fine re¬ quired ; thus the log. fine of 8° 10' is 9.15245. But if the angle be 450 or more than 450, look for the degrees at the bottom and the minutes on the right hand, and op- pofitc will be found the log. fine required. Thus the log. fine of 58° 12' is 9.92936. The very fame direc¬ tions apply for the cofine, tangent, and cotangent; and from what has been faid, the manner of finding the angle to degrees and minutes, having given its fine, &c. muft be obvious. If the angle confifts of degrees, minutes, and feconds, find the fine or tangent to the degrees and minutes, and add to this a proportional part of the difference given in the column of differences for the feconds, obferving that the whole difference correfponds to i' or 60". Thus to find the log. fine 30° 23' is 9.70396. 28" - 28x21 of 30° 23' 28"; firft the fine of The dift'erence is 21. As 60" : 21 60 10 nearly, the part of the differ¬ ence to be added, therefore the fine of 20° 22' 28" is 9.70406. On the contrary, let it be required to find the angle correfponding to the tangent IO.14152. The next lefs tangent in the table is 10.14140, which correfponds to 540 10'; the difference between the pro¬ pofed tangent and next lefs is 12 ; and the difference between the next lefs and next greater, as given in the table, is 26 j therefore, 26 : 12 :: 60" 12x60 26 28" nearly, hence the angle correfponding to the propofed log. tangent is 540 10' 28//. SECTION II. PLANE TRIGONOMETRY. The following propofitions exprefs as many of the properties of plane triangles as are effentially neceffary in plane trigonometry. Theor. I. In a right-angled plane triangle, as the hypothe- nufe is to either of the Tides, fo is the radius to the fine of the angle oppofite to that fide ; and as either of the fides to the other fide, fo is the radius to the tangent of the angle oppofite to that fide. Let. ABC be a right-angled plane triangle (fig. 3.), . of which AC is the hypothenufe. On A as a centre ^ ‘5’ with any radius, deferibe the arch DE ; draw1 EG at right angles to AB, and draw DF touching the circle at D, and meeting AC in F. Then EG is the fine of the angle A to the radius AD or AE, and DF is its tangent. The triangles AGE, ADF are manifeftly fimilar to the triangle ABC. Therefore AC : CB :: AE : EG v that is, AC ; CB :: rad ; fin, A. Again, 480 TRIGONOMETRY. Plane Tri¬ gonometry. Again, AB : BC : : AD : ,DF j that Is AB : BC : : rad. : tan. A. Cor. In a right-angled triangle, as the hypothenufe to either of the fides, fo is the fecant of the acute angle adjacent to that fide t® the radius. For AF is the fecant of the angle A to the radius AD j and AC : AB :: AF : AD, that is, AC : AB :: fee. A : rad. Note. This propofition is moft eafily remembered when ftated thus. If in a right-angled triangle the hypo¬ thenufe be made the radius, the fdes become the fnes of the oppofte angles ; and if one of the fides be made the radius, the other fde becomes the tangent of the oppofte angle, and the hypothenufe its fecant. Theor. II. The Tides of a plane triangle are to one another as the Tines of the oppofite angles. Fig. 4. From B any angle of the triangle ABC (fig. 4.), draw BD perpendicular to AC. Then, by lad theorem, AB : BD :: rad. : fin. A, alfo BD : BC :: fin. C : rad. therefore ex equo inverfely (Geometry, Se£t. III. Theor. 7.), AB : BC :: fin. C : fin. A. If Theor. IV. Plane Tri* gonometry. a perpendicular be drawn from any angle of a triangle to the oppofite Tide or bafe j the Turn of the fegments of the bafe is to the fum of the other two Tides as the difference of thefe Tides fo the difference of the fegments of the bafe. Let ABC be a triangle (fig. 6.), and BD a perpen- Fig. 5. dicular drawn to the bafe from the oppofite angle : AD+DC : AB+BC :: AB—BC : AD—DC. On, B as a centre with the radius BC, deferibe a circle meeting AC in E, and AB in G, and the fame line produced in F. Then AC : AF :: AG : AE ; now AF ~ AB-j-BC, and AG~AB—BC, and bc- caufe ED = DC, AE (or AD — DE) — AD —DC, therefore AC : AB-f-BC :: AB—BC : AD—DC. Problem. Having given the fum of any two quantities and alfo their difference, to find each of the quantities. Solution. To half the fum add half the difference of the quantities, and it will give the greater ; and from half the fum fubtracl half the difference, and it will give the lefs. Theor. III. A E D B C. The fum of any two Tides of a triangle is to their difference as the tangent of half the fum of the angles oppofite to thefe Tides to the tangent of half their difference. Fig-5- Let ABC, fig. 5. be a triangle; AB-f-BC : AB —BC :: tan.4-(^BCA-f^BAC) :tan.i(^BCA —^BAC). In AB produced take BE—BC, and on B as a cen¬ tre with BC or BE as a radius, deferibe the femicircle ECF meeting AC in D ; join BD, CF, and CE, and from F draw FG parallel to AC, meeting CE in G. Becaufe the angles CFE, CBE, hand on the fame arch CE, and the former is at the circumference of the circle, and the latter at the centre; therefore, the angle CFE is half the angle CBE (Geometry, Se A .. AB . Bc> Example. In the triangle ABC are given AB 208, and the angle A 350 16', to find AC and BC. To find BC. 10.00000 To find AC. c<>f-A 350 16' 9.91194 Rad. - AB 208 10.00000 2.31806 12.31806 Rad. Tan. A 350 16' 9.84952 AB 208 - 2.31806 BC=i47.i 2.16758 AC=254.7 2.40612 Case 3. The hypothenufe AC and a fide AB being given, to find the angle A (and confequently C) and the fide BC. Solution. CAC \ Rad. AB fin. A rad.-: cof. A, AC : BC. Example. Let the hypothenufe AC be 272, and the fide AB 232. Required the angle A and the fide BC. To find A AC 272 - 2.43457 To find BC. Rad. - - 10.00000 AB 232 - 2.36549 Rad. - - 10.00000 12.36549 Cof. A=3i° 28' 9.93092 Sin. A31° 28' 9-71767 AC 272 - 2.43457 BC 142 - 2.15224 Sin. C : Sin. B :: AB : AC, Sin. C : Sin. A :: AB : BC. The truth of this folution is obvious from Theor. II. Example. In the triangle ABC are given the fide AB=r266, the angle A 38° 40', the angle B 7 2° 16'j to find the fides AC and BC. Firft, A-j-B=r 1 io° 56', and 180°—1 io° 56'=o690 4'=C. Sin. C 69° 4' 9-97°35 Sin. B 720 16' 9.97886 AB 266 - 2.42488 Sin. C 69° 4' 9-97°35 Sin. A 38° 40' 9.79573 AB 266 - 2.42488 12.40374 12.22061 AC—271.3 2-43339 BC=ri77.9 2.25026 Case 2. Two fides AC, CB (fig. 9.), and the angle Fig. 9* A oppofite to one of them, being given 5 to find the other angles B, C, and alfo the other fide AB. Solution. The angle B is found by this propor¬ tion. CB : AC :: fin. A : fin. B. When CB is lefs than CA, the angle B admits of two values, one of which is the fupplement of the other; becaufe, correfponding to the fame value of the fide AC, and the angle A, the fide BC may evidently have two diftinft pofitions, viz. CB, C b. The angle CBA and its fupplement C b A. being found, the angle ACB, alfo the angle AC b may be found, by fub- tra&ing the fum of the two known angles from 180°, and then AB and A b may be found by thefe propor¬ tions. Fig. *. Case 4* The fides AB and BC about the right angle being given, to find the angle A (and thence C) and the hypothenufe AC. Solution ■{ AB : BC : rad. : tan. A, Cof. A : rad.: AB : AC. Example. Let the fide AB be 186, the fide BC 152. Required the angle A, and the hypothenufe AC. To find A. AB 186 - 2.26951 BC 152 Rad. ■ 2.18184 10.00000 12.18184 Tan.A=39°i5' 9.91233 To find AC. Cof. A. 39* 15' 9.88896 Rad. - AB 186 10.00000 2.26951 12.26951 AC—240.2 2.38055 Solution of the Cafes of Oblique-angled Triangles. ^ In oblique-angled triangles there are alfo four cafes, which, with their folutions, are as follows. Case i. Two angles A and B, and a fide AB be¬ ing given,-to find the other fides AC, BC. Vol. XX. Part II. ' Sin. A : Sin. ACB :: CB : AB, Sin. A : Sin. AC b :: CB or C £ : A This is called the ambiguous cafe, on account of the angle B and the fide AB having fometimes two va¬ lues. This folution, like the laft, is deduced from Theo¬ rem II. Example. Suppofe AC 225, BC 180, and the angle A 420 20' \ to find the remaining parts. CB 180 - - 2.25527 AC 225 - - 2.35218 Sin. A 42° 20' - 9.82830 12.18048 Sin. ABC—57® 20 Or fin. A C=i22 40 9-92521 In the triangle ACB we have now the fide AC and the angles CAB, CBA, therefore the remaining angle ACB and fide AB may be found by Cafe 1.} and the fame is true of the triangle AC b. 3 P * Case TRIGONOMETRY. To find A. AC 105 - 2.02119 AD 70.5 - 1.84819 Rad. - io.ocooo 482 Plane Tri- Case 3. Two fides CA, CB and the included angle gonometry q being given, to find the remaining angles B, A, and ^ ' fide AB. Solution. Find AC -4- CB, the fum of the fides, and AC—CB their difference j alfo find the fum of the angles A and B (that fum is the fupplement of C), and half that fum then half the difference of the angles will be got from this proportion. (See Theor. III.). AC-f-CB : AC—CB :: tan. -*- (B-f-A) : tan. -* (B—A). 'Having now the fum and difference of the angles B and A, the angles will be found by the rule given in the problem following Theor. IV. The remaining fide may be found by either of thefe proportions. Sin. B : fin. C :: AC : AB; or fin. A : fin. C :: BC : AB. Example. Let AC be 128, CB 90, and the angle C 48° 12'. Required the remaining parts of the tri¬ angle. AC CB 218 - 2.33846 AC — CB 38 - 1.57978 tan. * (B-j-A) 6j° 54' 10.34938 11.92916 tan. -f (B—A) 210 17' 9.59070 Hence by the given rule in the above-mentioned pro¬ blem, B=87° ii', A —430 37'. As we now know all the angles and two fides, the remaining fide may be found by Cafe 1. Fig. 10. Case 4. The three fides AB, BC and AC (fig. 10.) being given, to find the three angles A, B, C. Solution. Let fall a perpendicular CD upon the greateft of the three fides from the oppofite angle. Then find the difference between AD and DB by this proportion. AB : AC-f-CB :: AC —CB : AD —DB. The fegments AD, DB may now be found feverally by the rule given for finding each of the quantities whofe fum and difference is given, and then the angles A and B may be found by the following propor¬ tions. CA : AD :: rad. : cof. A, CB : BD :: rad. : cof. B. The angles A, B being found, C of courfe is known. The firft part of this folution follows from Theor. IV. The latter part from Theor. I. Example. Let AB be 125, AC 105, and BC 95. Required the angles. In this cafe AC-j-BCrr200, AC — BC=rio, there¬ fore we have * 125 : 200 :: 10 : AD—DB—-00 X T0 —16. Now AD-J-DB=:i25, therefore AD=r70.5 DBzz M-5- 11.84819 Cof. A 470 49' 9.82700 For the application of plane trigonometry, fee Men¬ suration, Se£t. I. SECTION III. SPHERICAL TRIGONOMETRY. Theor. I. If a fphere be cut by a plane through the centre, the fe£lion is a circle. The truth of this propofition is evident from the de¬ finition of a fphere. See Geometry, Seft. IX. Def. 3- Definitions. I. Any circle which is a fe£Hon of a fphere by a plane palling through its centre, is called a great circle of the fphere. Cor. All great circles of a fphere are equal, and the centre of the fphere is their common centre, and any two of them biledt one another. II. The pole of a great circle of the fphere is a point in the fuperficies of the fphere from which all ftraight lines drawn to the circumference of the circle are e- qual. III. A fpherical angle is that which on the fuperficies of a fphere is contained by two arches of great circles, and is the fame with the inclination of the planes of thefe great circles. IV. A fpherical triangle is a figure upon the fuperfi¬ cies of a fphere comprehended by three arches of three great circles, each of which is lefs than a femicixcle. Theor. II. The arch of a great circle between the pole and and the circumference of another circle is a quadrant. Let ABC be a great circle, (fig. ir.) and D ilSpj pole ; let the great circle ADC pafs through D, and let A EC be the common fedtion of the planes of the two circles, which will pafs through E the centre of the circle ; join DA, DC. Becaufe the chord DA is equal to the chord DC, (Def. 2.) the arch DA is equal to the arch DC ; now ADC is a femicircle, therefore the arches AD and DC are quadrants. Cor. i. If DE be drawn, the angle AED is a right angle, and DE being therefore at right angles to every line it meets wuth in the plane of the circle ABC, is at right angles to that plane. Therefore the ftraight line drawn from the pole of any great circle to the centre of the fphere is at right angles to the plane of that circle. Cor. 2. The circle has two poles D, D', one on each Spherical Trigonomfe- BC 95 - I.97772 try. To find B. BD 54-5 Rad. Cof. B 55' i-73640 io.ocooo 11.73640 9.75868 TRIGONOMETRY.. 483 Spherical each fide of its plane, which are the extremities of 1 rigonotne- a diarneter of the fphere perpendicular to the plane ■ ^y-^ABC. Theor. III. A fpherical angle ie meafured by the arch of a great circle intercepted between the great circles containing the angle, and having Jie angular point for its pole. Let AB, AC be two arches of great circles con- Fig. i2. taining the fpherical angle BAG } let EC be an arch of a great circle intercepted between them, and having A for its pole, and let BD, CD, AD be drawn to D the centre of the fphere. The arches AB, AC are qua¬ drants, (Theor. II.), and therefore the angles ADB, ADC right angles; therefore (Geometry, Sedt. VII. Def. 4.), the angle BDC (which is meafured by the arch BC) is the inclination of the planes of the circles EDA, CD A, and is equal to the fpherical angle BAG (Def. 3.). Cor. If AB, AC two arches of great circles meet in A, then A lhall be the pole of a great circle palling through B and C. Theor. IV. Two great circles whofe planes are perpendicular pafs through each others poles. I3* Let ACBD, AEBF be two great circles, the planes of which are at right angles to one another; from G the centre of the fphere, draw GC in the plane ABCD perpendicular to AB, then GC is alfo perpen¬ dicular to the plane AEBF, (Geometry, Sedt. VII. Theor. 12.); therefore C is the pole of the circle AEBF, and if CG be produced to D, D is the other pole of the circle AEBF. In the fame manner, by drawing GE in the plane AEBF perpendicular to AB, and producing it to F, it is fhewn that E and F are the poles of the circle ABCD. Cor. 1. If two great circles pafs through each other! poles, their planes are perpendicular to one another. Cor. 2. If of two great circles the firft paffes through the poles of the fecond, the fecond alfo paifes through the poles of the firft. Theor. V. If the angular points of any fpherical triangle be made the poles of three great circles, another triangle will be formed by their interfedftions, fuch, that the fides of the one triangle will be refpe&ively the fupplements of the meafures of the angles oppofite to them in the other. FI2- r4- Let the angular points of the triangle ABC be the poles of three great circles; which by their interfec- tions form the three lunary furfaces D£), FR, and EO ; A belnp the pole of EF, B the pole of DF, and C the pole of ED. Then the triangle DEF which is com¬ mon to three lunary furfaces will be in every refpedt fupplemental to the triangle ABC, For let each fide of ABC be produced to meet the Spherical fides that contain the angle oppofite to it, in the tri- trigoaome- angle DEF; then, becaufe BC pailes through the poles ' of ED, DF, ED, DF muft alio pafs through the poles of BC. (Thtor. II. Cor. 2.). Therefore the points D, £) are the poles of BC. In like mannner R, F are the poles of AB, and E, O the poles of AC. Hence EL, FK are quadrants, (Theor. II.); and therefore EF is the fupplement of IvL, but fince A is the pole of EF, KL is the meafure of the angle at A ; thus EF is the fupplement of the meafure of the angle at A. In like manner FD is the fupplement of the meafure of the an¬ gle at B, and DE the iupplement of the meafure of the angle at C. Further, it will appear in the fame manner that BC is the fupplement of HM, the meafure of the angle at D ; that AB is the fupplement of NK the meafure of the angle at F ; and that AC is the fupplement of GL, the meafure of the angle at E. Theor. VI. If from any point E, which is not the pole of the ^ great circle ABC, there be drawn arches of great circles EA, EK, EB, Sec. the greateft of thefe is EGA, which pafles through G the pole of ABC, and EC the remainder of the femicircle is the leaft, and of the other, EK, EB, &c. EK which is nearer to EA is greater than EB, which is more remote. Let AC be the common fe&ion of the planes of the great circles AEC, ABC ; draw EH perpendicular to AC, which will be perpendicular to the plane of the circle ABC (Geometry, Sedl. VII. Theor. XII.) and join AE, KE, BE, KH, BH. Then of all the ftraight lines drawn from H to the circumference, HA is the greateft, HC the leaft, and HK greater than HB : Therefore in the right-angled triangles EHA, EHK, EHB, EHC, which have the fide EH common, EA is the greateft hypothenufe, EC the leaft, and EK greater than EB, confequently the arch EGA is the greateft, EC the leaft and EK greater than EB. Theor. VII. Any two fides of a fpherical triangle are together greater than the third, and all the three fides arc together lefs than a circle. Let ABC be a fpherical triangle, let D be the cen'Fig. i-? tre of the fphere, join DA, DB, DC. The folid angle at D is contained by three plane angles ADB, BDC, ADC, any two of which are greater than the third, (Geometry, Sedl. VII. Theor. XV.) ; and therefore any two of the arches AB, BC, AC which meafure thefe angles muft be greater than the third arch. To prove the fecond part of the propofition, pro¬ duce the fides AB, AC until they meet again in E ; then ECA and EB A are femicircles ; now CB is lefs thanCE + EB, therefore CB+CA-f-BA is lefs than CE-j-EB-f-CA-f-BA, but thefe four arches makeup twro femicircles j therefore CB-{-CA-|-BA is lefs than a circle. 3 P 2 Theor. 484- TRIGONOMETRY. Spherical Trigonome¬ try. Fig. 17. Fig. iS. Theor. VIII. If two fides of a fpherical triangle be equal, the angles oppofite to them are equal, and con- verfely. In the triangle ABC, if the lides AB, AC be equal, the angles ABC, ACB are alfo equal. If AB, AC be quadrants, ABC, ACB are right angles. If not, let the tangent to the fide AB at B meet EA the line of common feftion of the planes AB, AC in F, and let the tangents to the bafe BC at its extremities meet each other in G ; alfo, let FC, FG, EC, and EB be joined. I'hen the triangles FEB, FEC have FE common, EB —EC, and the angle AEB—AEC, therefore FB —FC, and the angle FCErrFBE a right angle : hence FC is a tangent, and the triangles FGB, GCF are mutu¬ ally equilateral, therefore the angle FBG=:FCG and confequently the fpherical angle ABC=r ACB. Again, if the angles ABC, ACB be equal, the fide ABrrAC. For if in fig. 14. the angle ABC be equal to ACB, the fide DF of the fupplemental triangle DEF will be equal to the fide DE (Theor. V.)*, there¬ fore the angle DEFcnDFE, and confequently in the triangle ABC, the fide ACrrAB by Theorem V. Cor. In any triangle the greater angle is fubtended by the greater fide •, and converfely. For if the angle ACB be greater than ABC (fig. 18.) let BCDzrABC, then BDzrDC, and AB—AD-f-DC, which is greater than AC (Theor. VII.). The converfe is demonftra- ted in the fame manner as the like property of plane triangles, (Geometry, Seft. I. Theor. XIII.). Theor. IX. All the angles of a fpherical triangle are to¬ gether greater than two, and lefs than fix right ^angles. In the triangle ABC (fig. 14.) the three angles are together lefs than fix right angles, becaufe when add¬ ed to the three exterior angles they only make fix ^ and they are greater than two right angles, becaufe their meafures GH, KL, MNT, added to DE, EF, FD, are equal to three femicircles and DE, EF, FD being lefs than two femicircles (Theor. VII.) GH, KL, MN mull; be greater than one. a fpherical triangle is greater, equal, or lefs than a qua- Spherical drant, half the fum of the oppofite angles will be great- rri80U°nie- er, equal, or lefs than a right angle. , t’'y’ . Theor. XI. In a right-angled triangle, according as either of the fides about the right angle is greater, equal, or lefs than a quadrant, its oppofite angle is greater, equal, or lefs than a right angle ; and converfely. Let ABC (fig. 20.) be a triangle right-angled at B,Fig. 20. and let the fides AB, BC be produced to meet in D j then, becaufe they pafs through each others poles, E the middle point of BAD will be the pole of BCD j let a great circle pafs through the points CE. The arch EC is a quadrant, and the angle ECB a right angle. Now it is plain, that according as AB is greater, equal, or lefs than the quadrant EB, the oppofite angle ACB will be greater, equal, or lefs than the right angle ECB, and converlely. Cor. 1. If the two fides be both greater, or both lefs than quadrants, the hypothenufe will be lefs than a quadrant j but if the one be greater and the other lefs, the hypothenufe wiU be greater than a quadrant, and converfely. For in the triangles ABC, ADC, right-angled at B, in which the fides AB, BC are lefs, and confequent¬ ly AD, DC greater than quadrants, the hypothenufe AC is lefs than a quadrant, becaufe it is nearer to CB than the quadrant CE. But in the triangle «BC, of which the fide # B is greater, and BC lefs than a qua¬ drant, the hypothenufe o C is greater than a quadrant, becaufe it is further from CB than CE is. Cor, 2. Tn every fpherical triangle, of which the two fides are not both quadrants, if the perpendicular from the vertex fall within, the angles at the bafe will be both acute or both obtufe } but if it fall without, the one will be obtufe, and the other acute $ and con¬ verfely. Theor. XII. In any right-angled fpherical triangle, as radius is to the fine of the hypothenufe, fo is the fine of one of the oblique angles to the fine of its oppofite fide. Theor. X. Any two angles of a fpherical triangle are to¬ gether greater, equal, or lefs than two right angles, according as the fum of the oppofite fides is greater, equal, or lefs than a femicircle •, and converfely. Fig- ip* Let the fides AB, AC (fig. 19.) of the fpherical triangle ABC be produced to meet in D; then it is evident that according as the fum of AB, BC is greater, equal, or lefs than the femicircle ABD, the fide BC will be greater, equal, or lefs than BD 5 the angle D or A will be greater, equal, or lefs than BCD, and the fum of the angles BAG, BCA greater, equal, or lefs than the fum of BCA, BCD, which is two right angles. Cor. According as half the fum of any two fides of Let ABC (fig. 21.) be a fpherical triangle, having fig. 31: a right angle at B ; and let AD, BD, CD be drawn to the centre of the fphere. From C, in the plane DCA, let CE be drawn perpendicular to DA, and from E, in the plane DBA, draw EF perpendicular to the fame line, and let CF be joined. Then becaufe DA is perpendicular to the two lines CE, EF, it is perpendicular to the plane CEF, and confequently the plane CEF is perpendicular to the plane DBA j but the plane DCB is alfo perpendicular to DBA j there¬ fore their line of common feriion CF is perpendicular to the fame: Hence CFD, CFE are right angles. Now in the right-angled triangle CFE, rad. : CE :: fin. E : CF j but the angle CEF, being the inclination of the planes DCA, DBA, is the fame with the fphe¬ rical angle CAB, CE is the fine of AC, and CF the fine of BC j therefore rad. ; fin. AC ;; fin. A : fin. BC. Cor* TRIGONOMETRY. Spherical Cor. I. As radius to the cofine of either of the fides, Trigonome- fQ js cofine 0f the other to the ccfine of the hypo- . t^v' thenufe. Fig. 23. For let the great circle of which A is the pole, meet the three lides in D, E, F; then F is the pole of AD ; and applying this propofition to the complemental triangle FCE, rad. : fin. FC :: fin. F : fin. CE ; that is, rad. : cof. EC :: cof. AB : cof. AC. Cor. 2. As radius to the cofine of one of the fides, fo is the fine of its adjacent angle to the cofine of the other angle. 485 Then (Theor. 13. Cor. 2.) rad. : cof. A :: tan. AC : Spherical tan. AB. Trigonome- Therefore, (rad. : tan. AC ::) cot. AC : rad. :: cof. try‘ A : tan. AB, And (Theor. 12. Cor. 2.) rad. : cof. BC :: fin. C : cof. A. Case 3. Let the complement of the fide AB be the middle part. Then (Theor. 13.) rad. : fin. AB :: tan. A : tan. BC. Therefore (rad. : tan. A ::) cot. A : rad. :: fin. AB : tan. BC. Theor. XIII. In any right-angled triangle, as radius to the fine of one of the fides, fo is the tangent of the adjacent angle to the tangent of the other fide. Fig- 23* From B let BE be drawn perpendicular to DA, and from E, EF alfo perpendicular to DA, in the plane DCA, to meet DC in F, and let BF be joined. It may be fhown as in the preceding propofition, that FB is perpendicular to the plane DBA ; hence FB is the tan¬ gent of BC, and FBE is a right-angled triangle ; there¬ fore rad. : EB :: tan. E : FB j that is rad. : fin. AB :: tan A : tan. BC. Cor. I. As radius to the cofine of the hypothenufe, fo is the tangent of one of the angles to the cotangent of the other. For, in the complemental triangle FCE, (fig. 22.) rad. : fin. CE :: tan. C : tan. FE, that is, rad. : cof. AC :: tan. C : cot. A, or, rad. : cof. AC :: tan. A : cot. C. Cor. 2. As radius is to the cofine of one of the angles, fo is the tangent of the hypothenufe to the tan¬ gent of the fide adjacent to that angle. For rad. : fin. FE :: tan F : tan. CE ; that is, rad. : cof. A :: cot. AB : cot. AC, or rad. : cof. A :: tan. AC ; tan. AB. Napier's Rule for Circular Parts. f Let the hypothenufe, the two angles, and the comple¬ ments of the two fides of any right-angled fpherical tri¬ angle be called the five circular parts of the triangle. Any one of thefe being confidered as the middle part, let the two which are next to it be called the adjacent parts, and the remaining two the oppojite parts. Then the two pre¬ ceding theorems, with their corollaries, may be all ex- preffed in one propofition adapted to pra&ice, as follows. In any right-angled fpherical triangle, the reBangle under radius, and the cojine of the middle part, is equal to the reSlangle under the cotangents of the adjacent parts, or to the re Bangle under the fines of the oppofite parts. Fig. 24. Case i. Let the hypothenufe AC be the middle part. Then, rad. : cof. AC :: tan. C : cot.. A (Theor. 13, Cor. 1.). Therefore (rad. : tan. C ;:) cot. C : rad. :: cof. AC : cot. A. And rad. : cof. AB :: cof. BC : cof. AC (Theor. 12. Cor. 1.). Case 2. Let the angle A be the middle part. And (Theor. 12.) rad. : fin. AC :: fin. C : fin. AB. We are indebted for the foregoing rule to Napier, the celebrated inventor of logarithms. It comprehends all the propofitions which are neceffary for the refolution of right-angled triangles, and being eafily remembered, is perhaps one of the happieft inftances of artificial me¬ mory that is known. Theor. XIV. In any fpherical triangle, the fines of the fides are proportional to the fines of the oppofite angle. This propofition has been demonftrated in the cafe of right-angled triangles. Let ABC beany oblique-Fig. 3* angled triangle, divided into two right-angled triangles, ABD, CBD, by the perpendicular BD, falling from the vertex upon the bafe AC. In the former, the complement of BD being the middle part, rad. X fin. BD — fin. AB X fin. A, (Napier’s Rule). In the latter, the complement of BD being the middle part rad. x fm. BD = fin. BC x fin. C. Hence fin. AB X fin. A = fin. BC x fin. C, and fin. AB : fin. BC fin. C : fin. A. Cor. i. The cofines of the two fides are to one another dire&ly as the cofines of the fegments of the bafe. This is proved by making AB, BC the middle part. Cor. 2. The tangents of the two fides are to one another inverfely as the cofines of the vertical angles. This will follow from making the angles ABD, CBD the middle parts. Lemma i. The fium of the tangents of two arches N to their difference, as the reBangle under the fine and cofine of half their fium to the reBangle under the fine and cofine of half their difference. For, putting a and b for any two arches, by the arithmetic of fines (Algebra, § 353.), Sin. a cof. b -f cof. a fin. b ~ fin. (tf-f-£). Let each fide of this equation be divided by cof. <7 cof.£ and we get fin, a t fin. 6_fin. (a + b) cof. « coi. b fin. o cof. 6 that is, tan. a 4- tan. b— ^n;,. T fin. a cof. b In like manner, from the formula fin, (a £) =r fin. a cof. b — cof. a hn. b, we get . fin. (a — b') tan. a — tan. b — —— —L. fin. a cof. b therefore tan. a -f tan. b : tan. <7 — tan. b : fin. fi+b') fin., {a — £), and remarking that fin. (a+b) = 2 fin, i{a+by TRIGONOMETRY. .Spherical \ [a-^-b) Cof. 4- (<7-f-i), and fin. [a — b') — 2 fi i. Tngonome- ^ c0{-> ^ (Algebra, § 358) it follows . t‘y' . that tan. a + tan. b : tan. a — tan. b :: fin. 4 (« + £) cof. £ (a-{-b) : fin. -§-(<* — c°r- \ (a — b). Lemma 2. The fum of the fines of two arches is to their difference, as the rebiangle under the fine of half the fum and cofine of half the difference of thefe arches is to the re&angle under the fine of half the difference and co- fine of half the fum. For it has been Ihown in the arithmetic of fines (Al¬ gebra, § 355), that Sin. fin. (/>—q) = 2 fin. /> cof. q, Sin. (y^-j-y) — fin. (/>—q) ~ 2 cof. p fin. q. 'Let pzz ^ a-\-? b, and y = 4 ^—ib, fo that/>-{-^, zz a and p — q — b, then thefe formulas become Sin. b — 2 fin. 4 c°f- t {a-~d>) Sin. a—fin. bz=. 2 cof. 4 hn* 4 (rt—b). Therefore, fin. a -f- fin. b : fin. a — fin. b :: fin. 4 (tf-j-Z*) cof. ^ (a — b') : cof. 4 4 (fi — b). Lemma 3. The fum of the fines of two arches is to their difference, as the tangent of half the fum of thefe ■arches is to the tangent of half their difference. For, dividing the latter antecedent and confequent of the proportion in the foregoing lemma by cof. 4 (c+^) X cof. 4 — b), we have fin. a + fin. b : fin. a — „ . fin. 4 (<7+^) fin- 4 (tf—b') . . r fin. fin.Z>:: ■■ . ^ ^ tt, that is, becaufe —= coi.4(^ + c’) col.4(«—b) coi. tan. fin. a -j- fin. b : fin. a — fin. b :: tan. 4 : tan. 4 (<*—b'). Lemma 4. The fum of the cofines of two arches is to their difference, as the cotangent of half the fum of ■thefe arches is to the tangent of half their difference. Ly Arithmetic of fines (Algebra, § 355-)> cof. (/>—^)-}-cof. (/)-J-9)=2 cof.p cof. q, cof. (/>—y)—cof. {p-\-q')—2 fin./> fin. q. Let p—\{b-\-a) and q—\(b—a), then p—q~a and p-\-q—b, and the two formulas become cof. a -{-cof. b~2 cof. 4 (bJrns) cof. 4 {b—a), cof. a—cof. b~2 fin. 4 ifif-n) fin. 4 (fi—a) ; Hence, cof. a -{-cof. b : cof. a — cof. b :: cof. 4 {fi-\-a) eof. 4 {fi—a) : fin. 4 (bf-a') fin. 4 {b—o') j and dividing the latter antecedent and confequent by fin. 4 (bffa) cof. 4 {b—«), cof. 4 (Z>-f~'7) cof. tf-j-cof. b : cof. a fin. 4 (Z>—a) -cof. b and * coi. fin. cof. that is, becaufe fin. 4 ifi^-a') cof. 7 ~cot. fin. 4 (*—-o)’ — tan. we have cof. a cof. b : cof. a — cof. b :: cot. 4 (b-\-ai) : tan. 4 [b—a). lhall alfo put j for 4 {a-{-b)-, d for 4 fi—-4), / for Spherics! 4 (/>+?), —?), S for 4(A-{-B), D forTr*gonomc" 4 (A—B), S' for 4 (P + Q), and U for 4 (F—(,)). Theor. XV. In any fpherical triangle, the tangent of half the fum of the fegments of the bafe is to the tan¬ gent of half the fum of the two fides, as the tangent of half their difference to the tangent of half the difference of the fegments of the bafe. For by Theor. XIV. Cor. 1. cof. a : cof. b :: cof. p : cof. q ; therefore, cof. a -{- cof. b : cof. a — cof. b :: cof. p^-cof. q : cof. p — cof. q, hence (Lemma 4.) cot. s : tan. d :: cot. s' : tan. d', or cot. r : cot. s' :: tan. d : tan. d! $ but cot. s '. cot. d :: tan. s' : tan. j, therefore, tan. d : tan. s tan. d : tan. d’. This propofition ex- preffed in words at length is the theorem to be demon- llrated. Theor. XVI. The cotangent of half the fum of the vertical angles and the tangent of half their difference, or the cotangent of half their difference and the tangent of half their fum, according as the per¬ pendiculars fall within or without, are recipro¬ cally proportional to the tangents of half the fum and half the difference of the angles at the bafe. For, taking the cafe in which the perpendicular CD Fig. *7* (fig. 27.) falls within, let EFG be the fupplemental triangle, let the arches GE, GF meet again in L, and produce CA, CB to meet EF in H and K. Becaufe G and L are the poles of AB, the nerpendicular CD, if produced, wall pafs through G and L •, let it meet EF in I 5 then, becaufe C is the pole of EF, the aich GCI is perpendicular to EF, and fince E is the pole of BG, KErra quadrant—FH, and EHrrKF, and IF—IE=r IK—IH. In the triangle LEF, by the preceding pro¬ pofition, tan. 4 (FI-f-IE) : tan. 4 (FL-f-LE) :: tan. 4 (FL—LE) : tan. 4 (FI—IE) or tan. 4 (KI—IH). Now FI-f-IE, or FE, being the fupplement of C, (Theor. 5.), tan. 4 FE—cot. 4 C j and FL, LE being the fupplements of EG and GE, FL and LE are the meafures of the angles A, B *, moreover, IK, IH are the meafures of the angles BCD, ACD, therefore, cet. 4 or cot* 1 (P+QJ : tan- i (A-f-B) : tan; 4 (A—B) : tan. 4 (P—QJ* In {he very fame way it ipay be proved, when the perpendicular falls without the triangle, that cot. 4 (P—QJ : tan. 4 (A-f-B) :: tan. 4 (A—B) : tan f (P+Q.)* Theor. XVII. &g. 26. t^ie demonftration of the remaining theorems, wre fhall put A, B for the angles A and B at the bafe of the fpherical triangle ACB (fig. 26), a and Z> for the fides oppofite to thefe angles, p and q for the fegments of the bafe BD, AD made by the perpendicular arch CD, P and Q_for the vertical angles BCD, ACD;. we 2 In any fpherical triangle, the fine of half the fum of the fides is to the fine of half their difference, as the cotangent of half the vertical angle to the tangent of half the difference of the angles at the bafe. For fince tan. a : tan, b cof. £) : cof, P, therefore, tarn TRIGONOMETRY. Spherical tan. <7-{-tan. b : tan. a — tan b :: cof. Q^+cof. P : cof. trigonome- q—co£ p . by Lemma 2 and 4 fin. f cof. s : fin. d cof. d:: cot. S' : tan. D' . . . {1). i(A+B) : fin. f (A —AC). 487 B) :: tan. AB : tan. spherical Trigonome¬ try. Theor. XX. t——y— Again, becavife (by Theor. XIV.) fin. a : fin. b :: fin. A : fin. B, therefore, fin. tf-ffin. b : fin. a—fin. b :: fin. A + fin. B : fin. A—fin. B 5 hence, (by Lemma 2. and 3.). fin. s cof. d: fin. d cof. s :: tan. S : tan, D . . . (2). In any fpherical triangle, the cofine of half the fum of the angles at the bafe is to the cofine of half their clifierence, as the tangent of half the bafe to the tangent of half the fum of the two fides. Taking now the produ^l of the correfponding terms of the proportions (1) and (2), and rejefHng the faflor cof. r cof. d, which is common to the firft antecedent and confequent of the refulting proportion, we have, fin* s : fin.* d :: cot. S' tan. S : tan D' tan. D. But fince by Theor. XVI. tan. S : tan. D' :: cot. S' : tan. D, therefore cot. S' tan. S : tan. D' tan. D cot.* S' : tan,* D ; therefore, fin.* s : fin.* d :: cot.* S' : tan.* D, and fin. s : fin. d :: cot. S': tan. D,this proportion when exprefled in words is the proportion to be demonilrated. Theor. XVIII. In any fpherical triangle, the cofine of half the fum of the two fides is to the cofine of half their difference, as the cotangent of half the vertical angle to the tangent of half the fum of the angles at the bafe. For in the triangle ELF, cof. f (LF-f-I.E) : cof.Fig. 27. i(LF—LE) :: cot. } L : tan. f (E-f-F) (Th. XVIII.) that is, becaufe of the relation of the triangle FLE to ABC, as expreffed in laft theorem, cof. f (A-}-B) : cof. i(A—B) :: tan. fAB : tan. f (BC +AC). Scholium. Let one of the fix parts of any fpherical triangle be neglefted ; let the one oppofite to it, or its fupplement', if an angle, be called the middle party the two next to it the adjacent parts, and the remaining two the oppojite parts. Then the four preceding propofitions, which are called Napier's Analogies, becaufe firft invented by him, may be included in one, as follows. In any fpherical triangle, the fine or cojine of half the fum of the adjacent parts, is to the fne or cofne of half their difference, as the tangent of half the middle part to the tangent of half the difference or half the fum of the oppofte parts, that is, For it has been proved in laft theorem that fin. s cof. s : fin. d cof. d :: cot. S' : tan. D' fin. j- cof. d: fin. d cof. s :: tan. S : tan. D ; therefore, dividing the terms of the firft of thefe two proportions by the correfponding terms of the fecond, we get, cof. s cof. d cot. S' tan. D' coi. d col. s tan. S ’ tan. 13 Hence, multiplying the firft and fecond terms by cof. s X cof. d, and the third and fourth by tan. S tan. D,wre have, cof.* j- : cof.* d:: cot. S' tan. D : tan. S tan. D'. But fince by Theor. XVI. tan. D : tan. D' :: cot. S' : tan. S, therefore, cot. S'tan. D ; tan. S tan. D':: col.* S' : tan.* S j therefore, cof.* s : cof.* d:: cot.* S' : tan.* S, and coll s : cof. d:: cot. S' : tan. S. Theor. XIX. In any fpherical triangle, the fine of half the fum of the angles at the bafe is to the fine of half their difference, as the tangent of half the bafe to the tangent of half the difference of the two fides. Pig. 27. For the fame conftrufbon being made as in Theor. XVI. in the triangle ELF (fig. 27.) fin. ■§■ (FL-fLE) : fin. 4 (FL—LE) :: cot. 4 L : tan. 4- (E—F) (Tbeor. XVII. ) ; but EfG being the fupplemental triangle of ABC, LF and LE are the meafures of A and B, L is the fuppkment of AB, a; d LEE, LEE are the mea- fures of the fides AC, BC (Theor. V.) > therefore fin. Sin.-f- (A-f-0) : fin. f(A — d) :: tan. f M : tan. i(0—&). Cof. ^ (A -f- «) : cof. f (A — a) :: tan. M : tan. f (O+a). When A, a and M are given, by the firft proportion, f (O—0) is found, and by the fecond 4 (O-f , q denote the fegments into which a fide is di¬ vided by a perpendicular from the oppofite angle, and P, £) the parts into which it divides the angle. Com¬ bining the fix quantities a, b, c, A, B, C, three by three, there are found fix diftind combinations or cafes. Find 4 (a—b) by Theor. XIX. and \ (a+ b) by Theor. XX. and thence a, b. All the Tides and two angles being now known, C is found by Theor. XIV. Case 5. Given a, b, c, the three fides. Sought A, B, C. Draw a perpendicular from any one of the angles, dividing the oppofite fide into the fegments />, q. Find 4 (/>—y) by Theor. XV. and then, from and j (fi—?)> find/*, q. The triangle being now refolved into two right-angled triangles, the angles may be found by Cafe 4. of right-angled triangles. Case 6. Given A, B, C, the three angles. Sought a, b, c. Draw a perpendicular, dividing any one of the angles into the parts P, £. Find 4 (P—QJ by Theor. XVI. and then P, Q. The triangle being now refolved into two right-angled triangles, the Tides may be found by Cafe 6. of right-angled triangles. Case i. Given a, A, b, two fides and an angle op¬ pofite to one of them. Sought c, B, C. B is found by Theor. XIV. •, c by either Theor. XIX.: or Theor. XX. j C by Theor. XVII. or Theor. XVIII. Case 2. Given A, a, B, two angles and a fide op¬ pofite to one of them. Sought b, c, C. b is found by Theor. XIV. j c and C as in Cafe 1. Case 3. Given a, C,b, two fides and the included angle. Sought A, B, c. By Theor. X. XI. and Cor. each of the unknown parts is limited to one value in all the cafes, except in fome of the fubcafes of the firft and fecond. As every oblique-angled triangle may be refolved in¬ to two right-angles, all thefe cafes may be refolved by means of Napier's Rule, and the 15th propofition only. And the cafes may be reduced to three, by ufing the fupplemental triangle. T R I TRIHILATiE, from ires, “ three,” and hilum, “ an external mark on the feed j” the name of the 23d clafs in Linnaeus’s Fragments of a Natural Method $” confifting of plants with three feeds, which are marked with an external cicatrix or fear, where they are faften- ed within the fruit. See Botany. TRIM, implies in general the ftate or difpofition by which a {hip is belt calculated for the feveral purpofes of navigation. Thus the trim of the hold denotes the mod conveni¬ ent and proper arrangement of the various materials con¬ tained therein relatively to the {hip’s motion or {lability at fea. The trim of the mafts and fails is alfo their mod appofite fituation with regard to the condruftion of the fhip and the effort of the wind upon her fails. See Sea¬ manship. TRINGA, Sandpiper j a genus of birds belong- 1 T R I ing to the order of grallae. See Ornithology Index. TRINIDAD, an ifland in the gulf of Mexico, fe- parated from New Andalufia, in Terra Firma, by a drait about three miles over. The foil is fruitful, pro¬ ducing fugar, cotton, Indian corn, fine tobacco, and fruits. It was taken by Sir Walter Raleigh in 1595, and by the French in 1676, who plundered the ifland and then left it. It is about 62 miles in length, and 45 in breadth > and was difeovered by Chridopher Co¬ lumbus in 1498. It is now in the poffeflion of Britain. What was called a bituminous lake in this ifland, appears, from the experiments of Mr Hatchet, to be a porous done from which the mineral pitch exudes. TRINITARIANS, thofe who believe in the Trini¬ ty ; thofe who do not believe therein being called Anti- trinitarians. TRINITY, TH K'.O XOM V, TRY. Plato nxxxv?:. ffZ 7'r'srfr* . I ~ Til 1 G O NOM E T H Y I’jate nxxxvm. //{ Viytrtt iTrttlpf I / i ':'-n T R I [ 4S9 ] T R I TRINITY, in Theology, the ineffable myftery of three perfons in one God ; Father, Son, and Holy Spi¬ rit. See Theology. Trinitr-Houfe. See London, N° 49. TRINITY-Sunday, a festival obferved on the Sunday next after Whitfunday, in honour of the holy Trinity. The obfervation of this feftival was firft enjoined in the council of Arles, anno 1260. TRINOBANTES, in Ancient Geography, a people ©f Britain, fuppofed to have occupied Middlefex and Effex. TRIO, in Mujic, a part of a concert wherein three perfons ling ; or, more properly, a mufical compofition confiding of three parts. TRIPHTHONG, in Grammar, an affemblage or Concourfe of three vowels in one fyllable 5 as quee. TRIPLE, in Mujic, is one of the fpecies of meafure or time. See Music. TRIPOD, in antiquity, a famed facred feat or ftool, fupported by three feet, whereon the priefts and fibyls were placed to render oracles. It was on the tripod that the gods were laid to infpire the Pythias with that divine fury and enthufiafm wherewith they were feized at the delivery of their predictions. 1RIPOLI, a country of Africa, in Barbary 5 bound¬ ed on the north by the Mediterranean fea ; on the fouth, by the country of the Beriberies ; on the weft, by the kingdom of I unis, Biledulgerid, and territory of the Gadamis; and on the eaft, by Egypt. It is about 925 miles along the fea coaft; 5 but the breadth is various. Some parts of it are pretty fruitful j but that towards Egypt is a fandy defert. It had the title of a kingdom; but is now a republic, governed by a dey. He is not abfolute ; for a Turkifh baftraw refides here, who receives his authority from the grand feignior, and has a power of controuling th* dey, and levying taxes on the people. The dey is elefted by the foldiers, who make no fcruple of depofing him when they pleafe. Tripoli, a confiderable town of Africa, and capital of a republic of the fame name in Barbary, and under protection of the grand feignior, with a caftle and a fort. It is pretty large, and the inhabitants are noted pirates. It was taken by Charles V. who fettled the knights oi Pvlalta there j but they were driven away by tne lurks in 1551. It was formerly very llourifhing j and has now fome trade in fluffs, faffron, corn, oil, wool, dates, oftrich feathers, and Ikins : but they make more of the Chnftian Haves which they take at fea ; for they either fet. high ranfoms upon them, or make them perform all forts of work. It is feated on the coaft: of the Mediterranean, in a fandy foil, and furrounded by a wall, {Lengthened by other fortifications. E. Long. 13. 12. N. Lat. 32. 34. Tripoli, called Tripolis of Syria, to diftinguhh it from 1 ripoli in Barb ary, received its name from its bein j- anciently formed of three cities at a fmall diftance from each other, one of which belonged to the Aradians, or ancient kingdom of Arad, the fecond to the Sidonians, and the third to the Tyrians, perhaps as a common mart to. thofe maritime powers. The prefent town of Tripoli is built at the diftance of a mile and a half from tne other, upon the declivity of a hill facing the fea, in 340 20' north latitude, and in 350 50' eaft longitude from Greenwich. It is furrounded with walls, fortified with feven high (Long towers, and a caftle, all of Go- Vol. XX. Part II. thic archite&ure; but the ftreets are narrow, and the Tripoli houfes low. The city contains about 8000 houfes, and II near 60,000 inhabitants, confiding ot Turks, Chrif-,1 rlumPh- tians, and Jews. The balha, or pacha, who refides in the caftle, where there is a garrifon of 200 janizaries, governs the adjacent territory, in which there is plenty of fruit, and a great number of mulberry trees, which enable the inhabitants to carry on a Irik manufacture, from which they draw confiderable profit. All the environs of I ripoli are laid out in orchards, where the nopal grows ipontaneouily, and the white mulberry is cultivated for the filk-worm ; the pomegra¬ nate, orange, and lemon trees for their fruit, which is here very fine. The country, though delightful to the eye, is unhealthy 5 from July to September, epidemic fevers, like thofe of Scanderoon and Cyprus, prevail, and are principally caufed by the artificial inundations made for the purpofe of watering the mulberry trees, to enable them to throw out their iecond leaves, and from a want of free circulation of air, the city being open only to the weftward. Tripoli, a fpecies of argillaceous earth, much ufed in the poliihing of metals. See Mineralogy Index. TRIP! OLEMUS, Laws of. See Mysteries, N° ?4. I RIQUELROUS, among botanifts, denotes a fruit or leaf that has three flat fides or faces. TRIREMIS, in antiquity, a galley with three ranks of oars on a fide. TRISMEGISTUS, an epithet or furname given to one of the two Hermefes. See Thoth. TRISMUS, the Locked Jaw'. See Medicine, N9 280. 1RISSYLLABLE, in Grammar, a word confiding of three fyllables. TRITICUM, Wheat ; a genus of plants belong¬ ing to the clals of triandria ; and in the natural lyftem ranging under the 4th order, Gramina. See Botany and Agriculture Index. TRITON, a fea demigod, held by the ancients to be an officer or trumpeter of Neptune, attending on him, and carrying his orders from lea to fea. TRITURATION, the aft of reducing a folid body into a fubtile powder; called aiib pulverijation and levi- gation. TRIUMPH, in Roman antiquity, a public and fo- lemn honour conferred by the Romans on a victorious general by allowing him a magnificent entry into the city. The greater triumph, called alfo curulis, or Amply the triumph, was decreed by the lenale to a general, upon the conquering of a province or gaining a fignal viftory. The day appointed for the ceremony being arrived, fcaffolds were erefted in the forum and circus and all the other parts of the city where they could beft behold the pomp : the fenate went to meet the con¬ queror without the gate called Capena or Triumphalis and marched back in order to the Capitol ; the ways being cleared and cleanfed by a number of officers and tipilaffs, who drove away fuch as thronged the paffage or ftraggled up and down. The general was clad in a rich purple robe, interwoven with figures of gold, fet- ting forlh his great exploits j his bulkins were befet with pearl ; and he wore a crown, which at firft was only laurel, but afterwards gold ; in one hand he bore 3 Q. a T R O [ 490 ] T R O Triumph a branch of laurel, and in the other a truncheon. He was carried in a magnificent chariot, adorned with ivory 1 Tu)-)a‘ - and plates of gold, drawn ufually by two white horfes j though fometimes by other animals, as that of Pompey, when he triumphed over Africa, by elephants; that of Mark Antony by lions; that of Heliogabalus by ty- gers} that of Aurelian by deer, &c. His children were at his feet, and fometimes on the chariot-horfes. The proceflion was led by the muficians, who played triumphal pieces in praife of the general: thefe were followed by young men, who led the viflims to the fa- crifice, with their horns gilded, and their heads adorn¬ ed with ribbands and garlands j next came the carts and waggons, loaded with all the fpoils taken from the enemy, with their horfes, chariots, &c. j thefe were followed by the kings, princes, and generals, who had been taken captives, loaded with chains: after thefe ap¬ peared the triumphal chariot, before which, as it palfed, they all along ttrewed flowers, and the people with loud acclamations called out, lo triumpheThe chariot was followed by the fenate, clad in white robes j and the fenate by fuch citizens as had been fet at liberty or ran- fbmed ; and the proceffion was clofed by the priells and their officers and utenfils, with a white ox led along for the chief victim. In this order they proceeded through the triumphal gate, along the Via Sacra, to the Capitol, where the vibtims were flain. In the mean time all the temples were open, and all the altars loaded with offerings and incenfe •, games and combats were cele¬ brated in the public places, and rejoicings appeared everywhere. TRIUMVIR, one of three perfons who govern ab- folutely, and with equal authority, in a Hate. It is chiefly applied to the Roman government: Csefar, Pom¬ pey, and Craffus, were the firft triumvirs who divided the government among them. There were alfo other officers fo called 5 as the triumviri or trefviri capitales, who were the keepers of the public gaol : they had the office of punilhing malefablors •, for which purpofe they kept eight liblors under them. TROAS, a country of Phrygia in Alia Minor, of which Troy was the capital. When Troas is taken for the whole kingdom of Priam, it may be faid to contain Myfia and Phrygia Minor ; but if only applied to that part of the country where Troy was fituated, its extent is confined within very narrow limits. Troas was an¬ ciently called Dardania. See Troja. TROCH/EUS, in profody, a foot confiding of a long and ffiort fy 11 able. TROCHANTER, in Anatomy. See there, N° 58. TROCHE, in Pharmacy, a fort of medicine made of .glutinous fubftances into little cakes, and afterw-ards ex- ficcated. See Materia Medica Index. TROCHILUS, Humming Bird, a genus of birds belonging to the order of picse. See Ornithology Index. TROGLODYTES, in the Ancient Geography, a people of Ethiopia, faid to have lived in caves under ground. Pomponius Mela gives a ftrange account of the. Troglodytes : he fays, they did not lo properly fpeak as fhriek ; and that they lived on ferpents. TROGUS Pompeius, a Latin univerfal hiilorian to ?oe time of Auguflus Crefar, of whom we have only an abridgement by Jullin, flouriffied about 41 B. C. TROJA, the capital city of Troas, or, according to others, a country of which Ilium wras the capital. It Troja was built on a fmall eminence near Mount Ida, and the U promontory of Sigaeum, at the diflance of about four, 1°mp't miles from the fea-ffiore. Dardanus the firft king of the country built it, and called it Dardania, and from Tros one of his fucceffors it was called Troja, and from Hus Ition. This city has been celebrated by the poems of Homer and Virgil j and of all the wars which have been carried on among the ancients, that of Troy is the moft famous. A defcription of the plain of Troy has been pub- lilhed in French in the 3d volume of the Philofophi- cal Tranfaftions of the Royal Society of Edinburgh, written by M. Chevalier. The city of Troy, accord¬ ing to him, flood on the prefent file of the modern vil¬ lage of Bounarbachi, diftant four leagues from the fea, and which is the refidence of an aga, ruling with abfo- lute fway the inhabitants of the Trojan plain and the in¬ ferior agas, to whom they are immediately fubje£L Bounarbachi is fituated on the fide of an eminence, ex- pofed to every wind, at the termination of a fpacious plain, the foil of which is rich and of a blackilh colour. Clofe to the village is to be feen a marffi covered with tall reeds j and the fituation is impregnable on all fides except at Erin (Homer’s looses), the hill of wild fg trees, which extended between the Scsean gate and the fources of the Scamander. Thefe circumftances, agree¬ ing with Homer’s defcriptions, ftrongly fupport M. Che¬ valier’s opinion concerning the fituation of Troy. A, very interefting part of this work is the account of co¬ nical mounds or barrows, feveral of them 100 feet in diameter at the bafe and which the author maintains to be the identical tombs raifed over the affies of the heroes of the Trojan war j fome of them he deems more ancient. He defcribes particularly the tombs of Efy- etes, Ilus, Ajax, Heft or, Achilles, Patroclus, and An- tilochus. This differtation, which runs to the length of 9^ quarto pages, is replete with erudition and ingenious reafoning, and is illuftrated and embellifhed by maps of the plain of Troy and feveral tables of infcriptions. It has been tranllated with much accuracy and care by Mr Dalzel profeffor of Greek in the Univerfity of Edinburgh, and accompanied with large notes and iL lutlrations. TROLLIUS, Globe-flower, or Lucken Gowan, a genus of plants belonging to the clafs ot polyandria 5 and in the natural fyftem ranging under the 26th order, Multifiliquce. See Botany Index. TROMP, Martin Happertz Van, a celebrated Dutch admiral, was born at the Bailie, in Holland. He raifed himfelf by his merit, after having diftinguifh- ed himfelf on many occafions, efpecially at the famous engagement near Gibraltar in i6o7- He paffed for one of the greateft feamen that had till that time appeared in the world 5 and was declared admiral ot Holland, even by the advice of the prince of Orange. He in that charafter defeated a large Spanilh fleet in 1630, and gained 32 other viftories at fea-, but was killed when under deck, in an engagement with the Englifh in 1653. The ftates-general caufed medals to be ftruck to his honour, and lamented him as one of the greateft heroes of their republic. Van Tromp, in the mid ft of the greatell glory, conftantly difcovered a re¬ markable modefty ; ior he never afiimud a higher cha¬ rafter T R 0 r 491 1 T R U Tronage rafter than that of a burgher, and that of being the fa¬ ll ther of the failors. _ roug" ■ TRONAGE, an ancient cuftomary duty or toll, for weighing of wool. According to Fleta, trona is a beam to weigh with, mentioned in the flat. Weftm* 2. cap. 25. And tronage was ufed for the weighing wool in a ftaple or public mart, by a common trona or beam j which, for the tronage of wool in London, was fixed at Leaden-Hall. The mayor and commonalty of London are ordained keepers of the beams and weights for weighing merchants commodities, with power to aflign clerks and porters, &c. of the great beam and balance j xvhich weighing of goods and wares is called tronage ; and no ftranger (hall buy any goods in London be¬ fore they are weighed at the king’s beam, on pain of forfeiture. TRONE-WEIGHT, the moft ancient of the different weights ufed in Scotland 5 and, though now forbidden by feveral ftatutes, is ftill ufed by many for home com¬ modities, and that in a very irregular manner j for the pound varies in different places, and for different pur- pofes, from 20 to 24 Dutch ounces. The common al¬ lowance is 214 ounces for wool, for butter and cheefe, 20 for tallow, lint, hemp, and hay. It is di¬ vided into 16 of its own ounces, and 16 pounds make a {tone. TROOP, a fmallbody of horfe or dragoons, about 50 or 60, fometimes more, fometimes lefs, commanded by a captain, lieutenant, comet, quarter-mafter, and three corporals, who are the lowefl officers of a troop. TROPE. See Oratory, N° 52—66. TROPHONlUS’s cave, or Oracle, in Ancient Geo- graphy, a cave near Lebadia in Boeotia, between Heli¬ con and Chseronea (Strabo): fo called from Trophonius, an enthufiaffic diviner •, who, defcending into this cave, pretended to give anfwers and pronounce oracles ; and was hence called Jupiter Trophonius. Such as went down to this cave never after fmiled \ hence the prover¬ bial faying of a man who has loft his mirth, That he is come out of Trophonius’s cave. Though Paufanias, who writes from experience, contradifts this 5 affirming that perfons came out of the cave affefted indeed with a ftupor, but that they foon after recovered themfelves. See Oracle. TROPHY {Tropceum), among the ancients, a mo¬ nument of viftory. TROPIC-Bird. See Phaeton, Ornithology Index. TROPICS. See Geography. TROUBADOURS, poets that fiourifhed in Pro¬ vence during the 12th century. They wrote poems on love and gallantry •, on the il- luftrious charafters and remarkable events of the times 5 fatires which Were chiefly direfted againft the clergy and monks; and a few didaftic pieces. The trouba- tlours were great favourites in different courts, diffufed a tafte for their language and for poetry over Europe, which was about that time funk in ignorance and rude- nefs ; they difappeared in the 14th century. A hiftory of the troubadours in 3 vols 12mo, was begun by M. de Sainte Palaie, and finifhed by the abbe Millot. See Music. TROUGH, Galvanic. See Galvanism. For later difcoveries in galvanic eleftricity, fee Zinc. TROVER, in Law, an aftion that a man hath againtt one that, having found any of his goods, refu- Trout feth to deliver them upon demand. 11 TROUT. See Salmo, Ichthyology Index. Trumpet. TROY. See Troja. v'~j~ TROY-Weight, one of the moft ancient of the differ¬ ent kinds ufed in Britain. The ounce of this weight was brought from Grand Cairo in Egypt, about the time of the cruiades, into Europe, and firft adopted in Troyes, a city of Champagne ; whence the name. The pound Eng/ijh Troy contains 12 ounces, or 5760 grains. It was formerly ufed for every purpoie ; and is ftill retained for weighing gold, filver, and jewels; for compounding medicines ; for experiments in natural phi- lofophy j and for comparing different weights with each other. Scots TROY-Weight was eftablifhed by James VI. in the year 1618, who enafted, that only one weight fhould be ufed in Scotland, viz. the French Troy ftone of 16 pounds, and 16 ounces in the pound. The pound contains 7600 grains, and is equal to 17 oz. 6 dr. avoir¬ dupois. The cwt. or 112 lb. avoirdupois, contains only 103 lb. 24-oz. of this weight, though generally reckon¬ ed equal to 104 lb. This weight is nearly, if not ex- aftly, the fame as that of Paris and Amfterdam 5 and is generally known by the name of Dutch weight. Though prohibited by the articles of union, it is ftill ufed in weighing iron, hemp, flax, moft Dutch and Baltic goods, meal, butcher-meat, unwrought pewter and lead, and fome other articles. TRUE-love. See Paris, Botany Index. TRUFFLES. See Lycoperdon, Botany Index. TRUMPET, a mufical inftrument, the moft noble of all portable ones of the wind kind ; ufed chiefly in war, among the cavalry to direft them in the fervice. Each troop of cavalry has one. The cords of the trum¬ pets are of crimfon, mixed with the colours of the fa¬ cings of the regiments. As to the invention of the trumpet, fome Greek hif- torians afcribe it to the Tyrrhenians •, but others, with greater probability, to the Egyptians 5 from whom it might have been tranfmitted to the Ifraelites. The trumpet was not in ufe among the Greeks at the time of the Trojan war ; though it was in common ufe in the time of Homer, According to Potter {Arch. Grcec. vol. ii. cap. 9.^, before the invention of trumpets, the firft fignals of battle in primitive wars were lighted torches ; to thefe fucceeded fhells of fifties, which were founded like trumpets. And when the trumpet became common in military ufe, it may well be imagined to have ferved at firft only as a rough and noify fignal of battle, like that at prefent in Abyffinia and New Zea¬ land, and perhaps with only one found. But, even when more notes w’ere produced from it, fo noify an in¬ ftrument muft have been an unfit accompaniment for the voice and poetry ; fo that it is probable the trum¬ pet w>as the firft folo inftrument in ufe among the an¬ cients. TRUMPET, Articulate, comprehends both the fpeak- itig and the hearing trumpet, is by much the moft valu¬ able inftrument, and has, in one of its forms, been ufed by people among whom we fhould hardly have expett- ed to find fuch improvements. That the /peaking trumpet, of which the objeft is to increafe the force of articulate founds, ftiould have been known to the ancient Greeks, can excite no wonder j 3 Q. 2 and T R tf [ 402 ] T R U Trumpet, and therefore we eafily admit the accounts which we read of the horn or trumpet, with which Alexander addreffed his army, as well as of the whifpering ca¬ verns of the Syracufan tyrant. But that the natives of Peru were acquainted with this inttrument, will proba¬ bly furprife many of our readers. The fa—2a’ Therefore if we fuppofe X to be the length which will give us n refleaions, we lhall have X=CDx fin. b Hence we fee that the length increafes as fin. b—/ the angle b — n a diminilhes j but is not infinite, unlefs a is equal to b. In this cafe, the immediately pre¬ ceding angle of refleaion muft be a, becaufe thefe angles have the common difference a. Therefore the laft refleaed found was moving parallel to the oppofite fide of the cone, and cannot again meet it. But though WTe cannot affign the length which will give the »th refleaion, we can give the length which will give the one immediately preceding, whofe angle with the fide of the cone is a. Let Y be this length. We have Y = CD X This length will allow every line of found to be refleaed as often, faving once, as if the tube were infinitely long. For fuppofe a fonorous line to be traced backwards, as if a found entered the tube in the direaion ih, and w^ere refleaed in the points hif, d, D, the angles will be continually augmented by the conftant angle a. But this augmentation can never go farther than 900-f-£ a. For if it reaches that value at D, for inftance, the refleaed line DK wflll be perpendicular to the axis CN; and the angle ADK will be equal to the angle DKB, and the found will come out again. This remark is of importance on ano¬ ther account. Now fuppofe the cone to be cut off at D by a plane perpendicular to the axis, KD will be the diameter of its mouth-piece; and if we fuppofe a mouth completely occupying this circle, and every point of the circle to be fonorous, the refleaed founds will proceed from it in the fame manner as light would from a flame which completely T R U [ 495 ] T R U Trumpet, completely occupies its area, and is refle&ed by the in- '“‘'•"V""""’ fide of the cane. The angle FDA will have the greateft poflible line when it is a right angle, and it never can be greater than ADK, which is —90-}-^ a. And lince between and 90-—there mull fall fome multiple of a ; call this multiple b. Then, in order that every found may be retle&ed as often as pof- lible, faving once, we muft make the length of it X~ cd*!4 o, a Now lince the angle of the cone is never made very great, never exceeding to or 12 degrees, £ can never differ from 90 above a degree or two, and its line can¬ not differ much from unity. Therefore X will be very CD nearly equal to ^—- which is alfo very nearly equal to o, a CD —-—— : becaufe a is fmall, and the lines of fmall 2S,4.«’ ’ arches are nearly equal and proportional to the arches themfelves. There is even a fmall compenfation of errors in this formula. For as the line of 90° is fome- what too large, which would give X too great, 2 S, $ is alfo larger than the line of a. Thus let be 12° : then the neareft multiple of a is 84 or 96°, both of which are as far removed as poffible from 90°, and the error is as great as poflible, and is nearly T^th of the whole. This approximation gives us a very limple conftruc- tion. Let CM be the required length of the trumpet, and draw ML perpendicular to the axis in O. It is evident that S, MCO : rad. zrMO : CM, and CM j or ,r MO LM , v CD , r X= —f—= ——f-, but X= —tv T , and therefore S, t a 2 S, ta 2, o, ia LM is equal to CD. If therefore the cone be of fuch a length, that its diameter at the mouth is equal to the length of the part cut off, every line of found will have at leaft as many refleftions, fave one, as if the cone were infinitely long •, and the lafl: reflected line will either be parallel to the oppolite fide of the cone, or lie nearer the axis than this parallel •, confequently fuch a cone will con¬ fine all the reflefted founds within a cone whofe angle is 2 a, and will augment the found in the proportion of the fpherical bafe of this cone to a complete hemifpheri- cal furface. Defcribe the circle DKT round C, and making DT an arch of 90,. draw the chord DT. Then fince the circles deferibed with the radii DK, DT, are equal to the fpherical furfaces generated by the revolu¬ tion of the arches DK and DKT round the axis CD, the found will be condenfed in the proportion of DK* to DT*. This appears to be the beft general rule for con- ftru&ing the inffrument; for, to procure another reflec¬ tion, the tube muft be prodigioufly lengthened, and we cannot fuppofe that one refleftion more will add greatly to its power. It appears, too, that the length depends chiefly on the angle of the cone ; for the mouth piece may be confidered as nearly a fixed quantity. It muft be of a fize to admit the mouth when fpeaking with force and without conftraint. About an inch and a half may be fixed on for its diameter. When therefore we propofe to confine the found to a cone of twice the angle of the trumpet,, the whole is determined by that angle. For fince in this cafe LM is equal to CD, we have DK CD* CD=LM (or CD) : CM and CM= Trumpet. But and therefore And 2 2 8,-3-# 4 S,* ^ i=DK i=CD i=DK CD, CM 5 CM, CM DK 4S,*i-tf’ s,: DK , A , = very nearly. And fince DK is an inch and a half, we get the length in inches, counted from the apex of the cone = , or 2 S,*« DK, S,* a’ From this we muft cut off the part CD, which DK is or very nearly -—, or —^—, b, S, a 2b,a meafured in inches, and we muft make the mouth of the fame width 3 2 S,a' On the other hand, if the length of the trumpet is fix¬ ed on, we can determine the angle of the cone. For let the length (reckoned from C) be L j we have 2 or S *, Br-R, r«Q, Sa; A, Ryx, 6. All the lines between a P and % P have fuffered three refleftions. Draw the tangents T A t, VB v, crofling the axis in w. 7. The whole founds will be propagated within the cone v W t. For to every fonorous point in the line KD there correfponds a point fimilar to £), regulating the firft refleffion from KB ; and a point iimilar to R, regulating the fecond refleflion from DA $ and a point S regulating the third reflection from KB, Sec. And fimilar points will be found regulating the firft reflec¬ tion from DA, the fecond from KB, and the third from DA, &c. \ and lines drawn from all thefe through A and B muft lie within the tangents TA and VB. 8. Thus the centres of reflection of all the fonorous lines which lie in planes pafling through the axis, will be found in the furface of this fphere} and it may be confidered as a fonorous fphere, whofe founds firft con¬ centrate in W, and are then diffufed in the cone aW/. It may be demonftrated nearly in the fame manner, that the fonorous lines which proceed from P, but not jn the plane pafling through the axis, alfo proceed, after various reflections, as if they had come from points in the furface of the fame fphere. The only difference in the demonftration is, that the centres Q, R, S of the fucceflive reflections are not in one plane, but in a fpiral lipe winding round the furface of the fphere according to fixed laws. The foregoing conclufions are therefore general for all the founds which come in all directions from every point in the area of the mouth-piece. Thus it appears, that a-conical trumpet is well fitted for increafing the force of founds by diminiffiing their final divergence. For had the fpeaker’s mouth been in the open air, the founds which are now confined with¬ in the cone w W t would have been diffufed over a he- mifphere : and we fee that prolonging the trumpet muff confine the founds ftill more, becaufe this will make the angde BWA flill (mailer •, a longer tube muft alfo oc- cafion more reflections, and confequently fend more fo¬ norous undulations to the ear at a diftance placed with¬ in the cone ed imperfeft fight. The fubje& is greatly fimplified by the circumftances Trumpet, of the cafe ; for the founds to which we liften generally ' come in nearly one direftion, and all that we have to do is to produce a conftipation of them. And we may conclude, that the audibility will be proportional to this conftipation. Therefore let ACB, fig. 6. be the cone, and CD itspig. axis. The found may be conceived as coming in the direction RA, parallel to the axis, and to be refle&ed in the points A, b, c, d, e, till the angle of incidence in- creafes to 90° j after which the fubfequent refledlions fend the found out again. We muft therefore cut off a part of the cone j and, becaufe the lines increafe their angle of incidence at each refleftion, it wdll be proper to make the angle of the cone an aliquot part of 90°, that the leaft incidence may amount precifely to that quantity. What part of the cone ftiould be cut off may be determined by the former principles. Call the angle ACD, a. We have C — when the lin. a found gets the laft ufeful refle£iion. Then we have the diameter of the mouth AB—2 CA • fin. and that of the other end ef=zC e • 2 fin. a. Therefore the founds will be conftipated in the ratio of CA* to C e1, and the trumpet will bring the fpeaker nearer in the ratio of C A to C e. When the lines of refle61ed found are thus brought together, they may be received into a fmall pipe per- feftly cylindrical, which may be inferted into the exter¬ nal ear. This wfill not change their angles of inclina¬ tion to the axis nor their denfity. It may be conveni¬ ent to make the internal diameter of this pipe y of an inch. Therefore C f • fin. a is — ^ of an inch.. This circumftance, in conjunftion with the magnifying power propofed, determines the other dimenfions of the hearing _ _ I CA * fin. a , ^ . trumpet. lor C c=z — = -— —, and CA oim.a lin. (2 __ fin. (2 ff-f 1 a) 6 fin. * a Thus the relation of the angle of the cone and the length of the inftrument is afcertained,. and the found is brought nearer in the ratio of CA to C e, or of fin. (2«-j-i)o to fin. a. And feeing that we found it pro¬ per to make (2 n-f-1) «=90°, we obtain this very Am¬ ple analogy, 1 : fin. ti=CA : C e. And the line of 4- the angle of the cone is to radius as 1 to the approxima¬ ting power of the inftrument. Thus let it be required that the found may be as au¬ dible as if the voice were 12 times nearer. This gives C A 1 ———— 12. This gives fin. a — —, andand the angle of the cone —9.34. Then CA= 6 fin.: ~=24. Therefore the length of the cone TT*. CA is 24 inches. From this take C e=z——=: I, and the length of the trumpet is 22 inches. The diameter at the mouth is 2 C e, =4 inches. With this inftrument one voice fhould be as loud as 144. If it were required to appreximate the found only four times, making it 16 times ftronger than the natural voice T R U [ SOI ] T R U Trumpet, voice at the fame diftance, the angle ACB muft be 29° j Ae muft be 2 inches, AB muft be iyd inches, and ef muft be -j-d of an inch. It is eafy to fee, that when the fize of the ear-end is the fame in all, the diameters at the outer end are proportional to the approximating powers, and the lengths of the cones are proportional to the magnifying powers. We (hall find the parabolic conoid the preferable ftiape for an acouftic trumpet} becaufe the founds come into the inftrument in a dire&ion parallel to the axis, they are reflefted fo as to pafs through the focus. The parabolic conoid muft therefore be cut off through the focus, that the founds may not go out again by the fubfequent reflexions; and they muft be received into a cylindrical pipe of one-third of an inch in diameter. Therefore the parameter of this parabola is one-fixth of an inch, and the focus is one-twelfth of an inch from the vertex. This determines the whole inftrument 5 for they are all portions of one parabolic conoid. Suppofe that the inftrument is required to approximate the found 1 2 times, as in the example of the conical inftrument. The ordinate at the mouth muft be 1 2 times the 6th of an inch, or 2 inches; and the mouth diameter is four inches, as in the conical inftrument. Then, for the Fig. 7. length, obferve, that DC in fig. 7. is ^th of an inch, and MP is 2 inches, and AC is ^th of an inch, and DC* : MP* = AC : AP. This will give AP ~ 12 inches, and CP — 1 i-J-5-ths 5 whereas in the conical tube it was 22. In like manner an inftrument which approximates the founds four times, is only i-|d inches long, and i-fd inches diameter at the big end. Such fmall inftruments may be very exaXly made in the pa¬ rabolic form, and are certainly preferable to the conical. But fince even thefe are of a very moderate fize when intended to approximate the found only a few times, and as they can be accurately made by any tinman, they may be of more general ufe. One of 12 inches long, and 3 inches wide at the big end, (hould approxi¬ mate the found at leaft 9 times. general rule for making them.— Let m exprefs the approximating power intended for the inftrument. The length of the inftrument in inches is m X w—1 , and the diameter at the mouth is —. The diameter at the fmall 3 end is always one-third of an inch. In trumpets for affifting the hearing, all reverberation of the trumpet muft be avoided. It muft be made thick, of the leaft elaftic materials, and covered with cloth externally. For all reverberation lafts for a fhort time, and produces new founds which mix with thofe that are coming in. We muft alfo obferve, that no acouftic trumpet can Separate thofe founds to which we liften from others that are made in the fame direXion. All are received by it, and magnified in the fame proportion. This is fre¬ quently a very gx-eat inconvenience. There is alfo another imperfection, which we imagine cannot be removed, namely, an odd confufion, which cannot be called indiftinXnefs, but a feeling as if we Vi ere in the mid ft of an echoing room. The caufe feems to be this : Hearing gives us Tome perception of the di- ,reXion cf the founding objeX, not indeed very precife, but fufficiently fo for mod purpofes. In all inftruments Trumpet, which we have deferibed for conftipating founds, the laft refleXions are made in direXions very much inclined to the axis, and inclined in many different degrees. T herelore they have the appearance of coming from dif¬ ferent quarters ; and infteadof the perception of a fingle fpeaker, wre have that of a founding furface of great ex¬ tent. We do not know any method of preventing this, and at the fame time increafing the found. There is an obfervation which it is of importance to make on this theory of acouftic inftruments. Their performance does not feem to correfpond to the compu¬ tations founded on the theory. When they are tried, we cannot think that they magnify fo much : Indeed it is not eafy to find a meafure by which we can eftimate the degrees of audibility. When a man fpeaks to us at the diltance of a yard, and then at the diftance of two yards, we can hardly think that there is any difference in the loudnefs ; though theory fays, that it is four time; lefs in the laft of the two experiments \ and we cannot> but adhere to the theory in this very fimple cafe, and muft attribute the difference to the impoflibility of mea-. Turing the loudnefs of founds with precifion. And be¬ caufe we are familiarly acquainted with the found, we can no more think it four times lefs at twice the di¬ ftance, than we can think the vifible appearance of a man four times lefs when he is at quadruple diftance. Yet we can completely convince ourfelves of this, by obferving that he covers the appearance of four men at that diftance. W^e cannot eafily make the fame experi¬ ment with voices. But, befides this, we have compared two hearing trumpets, one of which (hould have made a found as au¬ dible at the diftance of 40 feet as the other did at 10 feet diftance j but we thought them equal at the di¬ ftance of 40 and 18. The refult was the fame in many trials made by different perfons, and in different circum- ftances. This leads us to fufpeX fome miftake in Mr. Lambert’s principle of calculation •, and we think him miftaken in the manner of eftimadng the intenfity of the- refleXcd founds. He conceives the proportion of inten- fity of the fimple voice and of the trumpet to be the fame with that of the furface of the mouth-piece to the furface of the fonorous hemifphere, which he has fo in- genioufly fubftituted for the trumpet. But this feems to fuppofe, that the whole furface, generated by the revo¬ lution of the quadrantal arch TEG round the axis CG (fig. 4.), is equally fonorous. We are affured that it is not : For even if we (hould fuppofe that each of the points O, R, and S (fig. 3.), are equally fonorous rvith the point P, thefe points of refleXion do not (land fo denfe on the furface of the fphere as on the furface of the mouth-piece. Suppofe them arranged at equal di- ftances all over the mouth-piece, they will be at equal diftances alfo on the fphere, only in the direXion of the arches of great circles which pafs through the centre of the mouth-piece. But in the direXion perpendicular to this, in the circumference of fmall circles, having the centre of the mouth-piece for their pole, they muft be rarer in the proportion of the fine of their diftance from this pole. This is certainly the cafe with refpeX to all fuch founds as have been refleXed in the planes which pafs-through the axis of the trumpet; and we do not fee (for we have not examined this point) that any com- p.enfation is made- by the refleXion which is not in planes - T R Y [ 50 Trumpet planes palling through the axis. We therefore imagine, II that the trumpet does not increafe the found in the pro- Tryphiodo- _ £1 , r^s- portion of g E* to ^ T* (fig. 5.), but in that to CT Mr Lambert feems aware of fome error in his calcu¬ lation, and propofes another, which leads nearly to this ronclufion, but founded on a principle which we do not think in the leaft applicable to the cafe of founds. TbumPET, Marine, is a mufical inftrument confift- ing of three tables, which form its triangular body. It has a very long neck with one Angle firing, very thick, mounted on a bridge, which is firm on one fide, but tremulous on the other. It is firuck by a bow with one hand, and with the other the firing is prefled or flopped on the neck by the thumb. It is the trembling of the bridge, when ftruck, that makes it imitate the found of a trumpet, which it does to that perfection, that it is fcarcely poflible to difiin- guifir the one from the other. And this is what has gi¬ ven it the denomination of trumpet-marine, though, in propriety, it be a kind of monochord. Of the fix divi- fions marked on the neck of the inftrument, the firft makes a fifth with the open chord, the fecond an oc¬ tave, and fo on for the reft, correfponding with the in¬ tervals of the military trumpet. TRUMPET-Flower. See Bignonia, Botany Index. TRUMPETER. See Psophia, Ornithology Index. TRUNCATED, in general, is an appellation gi¬ ven to fuch things as have, or feem to have, their points cut off: thus, we fay, a truncated cone, pyramid, leaf TRUNCHEON, a fhort ftaff or baton ufed by kings, generals, and great officers, as a mark of their command. TRUNDLE, a fort of carriage with low wheels, whereon heavy and cumberfome burdens are drawn. TRUNK, among botanifts, that part of the herb which arifes immediately from the root, and is termina¬ ted by fruftification 5 the leaves, buds, and auxiliary parts of the herb not entering in its defeription. TRUNNIONS, or Trunions, of a piece of ord¬ nance, are thofe knobs or bunches of metal which bear her up on the cheeks of the carriage. TRUSS, a bundle, or certain quantity of hay, flraw, &c. A trufs of hay contains 56 pounds, or half an hundred weight : 36 truffes make a load. Truss is alfo ufed for a fort of bandage or ligature made of fteel, or the like matter, wherewith to keep up the parts in thofe who have hernias or ruptures. Truss, in a fhip, a machine employed to pull a yard home to its refpeftive maft, and retain it firmly in that pofilion. TRUSTEE, one who has an eftate, or money, put or trufted in his hands for the ufe of another. TRUTH, a term ufed in oppofition to falfehood, and applied to propofitions which anfwer or accord to the na¬ ture and reality of the thing whereof fomething is af¬ firmed or denied. TRYPHIODORUS, an ancient Greek poet, who lived fome time between the reigns of Severus and Ana- ilafius. His writings were very numerous j yet none of I 2 ] T U M them have come down to us, except an epic poem, on Tryplfiodo- which Mr Addifon has made fome entertaining remarks in the Spectator, N° 63. The firft edition of this extraordinary work was pub- lifhed by Aldus at Venice, with Quintus Calaber’s Pa- ralipomena, and Coluthus’s poem on the rape of Helen, It has been fince reprinted at feveral places, particularly at Francfort in 1580 by Frifchlinus ; who not only cor¬ rected many corrupt paffages, but added two Latin ver fions, one in verfe and the other in profe. That in verfe W’as reprinted in 1742, with the Greek, at Oxford, in 8vo, with an Englifh tianflation in verfe, and Notes, by Mr Merrick. TUAM, a town of Ireland, in the province of Con¬ naught, and county of Galwray, with an archbifhop’s fee. It wTas once a famous city, though now it is redu¬ ced to a village ; but it ftill retains the title of a city, as being an archiepifcopal fee. W. Long. 8. 46. N» Lat. 53- 33- TUB, in commerce, denotes an indetermined quan¬ tity or meafure : thus, a tub of tea contains about 6» pounds and a tub of camphor from 56 to 86 pounds. TUBE, in general, a pipe, conduit, or canal; a cy¬ linder, hollow within-fide, either of lead, iron, glafs, wood, or other matter, for the air or fotne other matter to have a free conveyance through it. Auricular TUBE, or inftrument to facilitate hearing. See Articulate TRUMPET. TUBERCLES, among phyficians, denote little tu¬ mors wThich fuppurate and difeharge pus ; and are often found in the lungs, efpecially of confumptive per- fons. TUCUMAN, a province of Paraguay, in South A- merica, bounded on the north by the provinces of Los- Chicas and Choco ; on the eaft by Choco and Rio-de- la-Plata, on the fouth by the country of Chicuitos and Pampes, and on the weft by the bithopric of St Jago. The air is hot, and the foil fandy : how-ever, fome pla¬ ces are fruitful enough. The Spaniards poffefs a great part of this country. TUFA, a ftone confifting of volcanic afhes concreted together with various other fpecies of ftone. It is of various colours, blackifti gray, bluifti gray, and yel¬ low ; every colour having a different mixture and foli- dity : but all of them have the bad quality of moulder¬ ing down on long expofure to the wreather ; notwith- ftanding which, they have been ufed in buildings both ancient and modern. The yellow kind refifts the air lefs than any other. TULIP A, Tulip ; a genus of plants belonging to the clafs of hexandria; and in the natural fyftem ranging under the 10th order, Coronarice. See Botany Index ? and for the culture of the tulip, fee Gardening. Tulip-Tree. See Liriodendron, Botany Index. TULL, Jethro, an Oxfordfhire gentleman who farmed his own land, and introduced a new method of culture, to raife repeated crops of wheat from the fame land without the neceffity of manure : the principles of W'hich he pubiilhed about 30 years fince, in a Treatife on Horfe-hoeing Hufbandry. TUMBRELL, Tumbrellum, or Turbichetum, is an engine of punifhment, formerly employed for the cor* reftion of fcolds and unquiet wromen. TUMEFACTION, the act of fwelling or rifing hk to a tumor. TUMOR, Tumor I!. 'i unis. See Obfern). on the City of Tunis by M.r Stan¬ ley, in the F.din. Mag. vol. iv. p. zS. TUN [503 TUMOR, in Medicine and Surgery, a preternatural for riling or eminence in any part of the body. Tumors, in Farriery. See Farriery Index. TUN, a large veffel or calk, of an oblong form, big- geft in the middle, and diminifhing towaids its two ends, girt about with hoops, and ufed for flowing le\e- ral kinds of merchandife for convenience or carriage } as brandy, oil, fugar, fkins, hats, &c. Tun is alfo the name of a meafure. A tun of wine is four hogfheads ; of timber, a fquare of 40 folid feet j and of coals, 20 cwt. Tun is alfo a certain weight whereby the burden of fliips, &c. is effimated. TUNBRIDGE, a town of Kent in England, fitu- ated on a branch of the river Medway, over which there is a bridge. It is a large well built place, noted for the mineral waters four or five miles fouth of the town. E. Long. o. 20. N. Lat. 51. 14. TUNE. See Music and Tone. TUNGSTEN, one of the metals. See Chemistry and Mineralogy Index. TUNICA, a kind of waiftcoat or under garment, in ufe among the Romans. They w'ore it within doors by itfelf, and abroad under the gown. The common peo¬ ple could not afford the toga, and fo went in their tunics j whence Horace calls them populus tunicatus. Tunica, in Anatomy, is applied to the membranes wdiich inveft the veffels, and divers others of the lefs fo¬ lid parts of the body ; thus the inteftines are formed of five tunics or coats. TUNIS, a large and celebrated town of Barbary, in Africa, and capital of a kingdom of the fame name. It is feated on the point of the gulf of Goletta, about eight miles from the place where the city of Carthage flood. It is in the form of a long fquare, and is about four miles in circumference, with ten large ftreets, five gates, and 35 mofques. The houfes are all built with ftone, though but one ftory high; but the nails are very lofty, and flanked with feveral ftrong towers. It has neither ditches nor baftions, but a good citadel, built on an eminence on the weft fide of the city. It is faid to contain 300,000 inhabitants, of whom 30,000 are Jews. The divan, or council of ftate, affembles in an old palace; and the dey is the chief of the republic, who refides there. The harbour of Tunis has a very narrow entrance, through a fmall canal. In the city they have no water but what is kept in cifterns, except one well kept for the bafhaw’s ufe. It is a place of great trade, and is 10 miles from the fea. E. Long. 10. 16. N. Lat. 36. 42. Tunis, a country of Africa, bounded on the north and call by the Mediterranean fea and the kingdom of Tripoli, on the fouth by feveral tribes of the Arabs, and on the weft by the kingdom of Algiers and the country of Efab ; being 300 miles in length from eaft to weft, and 250 in breadth from north to fouth. This country rvas formerly a monarchy ; but a difference arifing be¬ tween a king and his fon, one of whom was for the protection of the Chriftians, and the other for that of the Turks, in 1574 the inhabitants (hook off the yoke of both. From this time it became a republic under the protection of the Turks, and pays a certain tribute to the balhaw who refides at Tunis. The air in general is healthy; but the foil in the eaftern parts is indifferent ] T u R want of water. Towards the middle the moun¬ tains and valleys abound in fruits; but the w'cftern part is the moft fertile, becaufe it is watered with rivers. ^ The environs of Tunis are very dry, upon which ac¬ count corn is generally dear. The inroads of the A- rabs oblige the inhabitants to fow their barley and rye in the fuburbs, and to inclofe their gardens with walls. However, there are plenty of citrons, lemons, oranges, dates, grapes, and other fruits. There are alfo olive trees, roles, and odoriferous plants. In the woods and mountains there are lions, wild beeves, oftriches, mon¬ keys, cameleons, roebucks, hares, pheafants, partridges, and other forts of birds and beafts. The moft remark¬ able rivers are the Guadilcarbar, Magrida, Magerada, and Caps. The form of government is ariftocratic ; that is, by a council, whofe prefident is the dey, not unlike the doge of Venice. The members of the divan or council are chofen by the dey, and he in his turn is elefted by the divan ; which is compofed of foldiers, who have more than once taken oft the dey’s head. The bafhaw is a Turk, redding at Tunis ; whole bufi- nefs is to receive the tribute, and proteCl the republic : the common revenues are only 400,000 crowns a-year, becaufe the people are very poor ; nor can they fend above 40,000 men into the field ; nor more than 12 men of war of the line to fea, even upon the moft extraordinary occafions. There are generally about 12,000 Chriftian flaves in this country; and the inhabitants carry on a great trade in linen and woollen cloth. In the city of Tunis alone there are above 3000 clothiers and weavers. They alfo have a trade in horfes, olives, oil, foap, oftriches eggs and feathers. The Mahometans of this city have nine colleges for ftudents,and 86 petty fchools. The principal religion is Mahometanifm ; but the inha¬ bitants confift of Moors, Turks, Arabs, Jews, and Chrif- tian Haves. However the Turks, though feweft, in num¬ ber, domineer over the Moors, and treat them little bet¬ ter than flaves. TUNKERS, a religious fe£l of Baptifts in Pennfyl- vania, fo called from the word tanker, to put a morfel in fauce. They are alfo called tumblers, becaufe in per¬ forming baptifm they plunge the perfon into the water with the head firft. As the Germans found the letters t and b like d and p, the wmids tankers and tumblers, have been fometimes written dunkers and dumpiers. Their church government and difeipline are the fame with thofe of the Englifh Baptifts, except that every bro¬ ther is allowed to fpeak in the congregation, and the belt fpeaker is ufually ordained to be their mimfter. They are a harmlefs, well-meaning people. TUNNAGE. See Tonnage. TUNNY. See Scomber, Ichthyology Index. TUNNY-Fishing. See Fishery. TURBAN, the head-drefs of moft of the eaftern na¬ tions. It confifts of two parts, a cap and fafti ot fine linen or taffety, artfully wound in divers plates about the cap. The cap has no brim, is pretty flat, though round- ifh at top, and quilted with cotton ; but does not cover the ears. There is a good deal of art in giving the tur¬ ban a fine air; and tbe making of them is a particular trade. The fafli of the Turk’s turban is white linen; that of the Perfians red woollen. Thefe arethediftinguifli- ing marks of their different religions. Sophi king of Perfia, being of the feft of Ali, was the firft who affumed the Tunis Turban. T U R C 504 ] iNjAinate^ the red colour, to diftinguifh himfelf from the Turks, N who are of the fed of Omar, and whom the Perfians ui^L-edeem heretics. TURBINATED, is a term applied by naturalifts to {hells which are fpiral, or wreathed conically from a larger bafis to a kind of apex. TURBITH or Turpeth mineral. See Mercury, N° 1720 and 1728 Chemistry. TURBO, the Wreath, a genus of Ihell-fifti. Se* Conchology Index. TURBOT. See Pleuronectes, Ichthyology Index. TURCAB or Turci, (Mela) j fuppofed to be the Tufci of Ptolemy ; whom he places between Caucafus and the Montes Ceraunii. The name is faid to denote, “ to defolate, or lay wafte.” Herodotus places them among the wild or barbarous nations of the north. There is a very rapid river called Turk^ running into the Cafpian fea, from which fome fuppofe the Turks to take their name. They made no figure in the world till to¬ wards the 7th century; about the beginning of which they fallied forth from the Portae Cafpiae, laid wafte Perfia, and joined the Romans againft Chofroes king of Perfia. In 1042 they fubdued the Perfians, in whofe pay they ferved, and from whom they derived the Mahometan religion ; and afterwards pouring forth, overran Syria, Cappadocia, and the other countries of the Hither Afia, under diftintt heads or princes, whom Ottoman fubduing, united the whole power in him¬ felf, which to this day continues in his family, and who fixed his feat of empire at Prufa in Bithynia. His fuc- ceffors fubdued all Greece, and at length took Conftan- tinople in 1453 j which put a period to the Roman em¬ pire in the Eatt, under Conftantine the laft emperor. It is a {landing tradition or prophecy among the Turks, that their empire will at length be overturned by the Franks or Chriftians ; which feems now to be drawing on apace towards accompliihment. TURCOISE. See Turquoise. TURCOMANIA, a province of Afiatic Turkey, an- „ fwering to the ancient kingdom of Armenia. TURDUS, the Thrush ; a genus of birds belong¬ ing to the order of Pajferes. See Ornithology Index. TURENNE, Viscount. See Tour. TURF,/> This monfter of cruelty had, however, a fuc- ccfsful reign of nine years duration, Du ling the govern- ment of his fon, Achmet I. the affairs of Turkey under- went a material change for the worfe *. On his death, the janizaries and the divan elefted his brother Mufta- pha, whom in two months they declared incapable of reigning, and threw him into prifon } after this they proclaimed his young nephew, Ofman, the Ion of Ach¬ met, emperor. This prince formed a defign of curbing the power of the janizaries, for which he was depofed and murdered ; and Muftapha was again called from his prifon to the imperial throne, but was foon after ftrangled. . Under Amurath, or Morad IV. furnamed Gafi, the Intrepid, every thing again affumed a new appearance. He was fuccefsful in his wars, and took Bagdat from the Perfians. A debauch of wine put an end to his life, and dilhonoured his memory. His fon Ibrahim, wno fucceeded him, had every vice 5 he was a weak prince, and wholly deftitute of courage. He was ftrangled by four mutes. After a long interval of ina&ivity, the Turks again Turkey. in. Amurath IV. An. 1622. Mohammed IV became formidable to Europe, under Mohammed IV. An. 1649. who iucceeded him. His grand vifter Kupuli, M10 at once diretted the councils and conduced the armies of the Porte, took Candia from the Venetians. After car¬ rying on many wars againft the Germans, the Poles, the Ruffians, and other European powers, he was com¬ pelled to refign the turban to Solyman II. in 1687, a An. 16S7. prince happy in his domeftic government, but unfuccefs- f See Ach- ful in his wars. His brother, Achmet II. was hkewife met II. 24 Muftapha II. An. 1695. Achmet III. 26 Muftapha TIL An. 1754. unfortunate in his wars. In his reign the Turks were driven out of Hungary and Tranfylvania f. I he accef- fion of his nephew, Muftapha II. to the Ottoman throne, gave a new turn to the affairs of the Poite. Pofleffed of more vigour than his predcceffor, he refolv- ed to command his troops in perfon. He accordingly took the field, paffed the Danube, ftormed Lippa; feiz- ed Itul, and falling fuddenly on a body of Impelialifts, under Veterani, he killed that officer, difperfed his forces, and clofed with fuccefs the campaign. He was after- wTards defeated bv Prince Eugene in an uncommonly bloody battle at Zenta, a fmall village on the weftern bank of the Thuyfe, in the kingdom of Hungary. A- bout 20,000 Turks were left dead on the field, and 10,000 were drowned in the river, endeavouring to a- void the fury of the fvvord. The magnificent pavilion of the fultan, and all the ftores, fell into the hands of Prince Eugene, and foon after this misfortune the haughty Muftapha was dethroned. His ’brother and fucceffor, Achmet III. gave an a- fylum to Charles XII. king of Sweden, at Bender, a Turkifh town in Moldavia, after his defeat at the battle of Pultava. (See Russia, N° 118. and Sweden, N° 140.). Being unfuccefsful in his war againft Kouli Khan and the Perfians (fee Persia), he was depofed, and fucceeded by Mohammed V. From the depofition of Achmet III. till the acceflion of Muftapha III. in 1754’ no^ng importance oc¬ curs in the hiftory of the Turkifh empire. During the reign of this latter fultan was begun and terminated that deftruaive war with Ruffia, of which the principal events [ 5°7 1 T U R He began his reign have been enumerated in the article Russia, N 143 and 144. . ... 27 In this reign an extraordinary alarm was excuea in _\ppearance Turkey by the fudden appearance of a new prophet m of a new Upper Afia. This man, whole name was Sfaet Marifour, prophet m pretended that he was predoomed by the eternal irn- mutable decrees of heaven to fill up the measure of di¬ vine revelation to mankind j and that, as he was to be the laft, lb he was the greateft of the prophets. 1 he feene of his miniftry was in the wide and defolate re¬ gions on the borders of the Cafpian fea j and though the firft rumour of his proceedings reprefented him as at the head of a multitude of armed enthufiafts, ready to overturn the eftablifhed government, and the religion of Mohammed, it was foon difeovered that all the military fury of his zeal was direfted againft the Chiiftians. 2S About the fame time a formidable rebellion broke A rebellion out in E^ypt, which, though it has never properly form- ^ m • ed a part of the Turkith empire, may be confidered as tributary to the Turks, and as conftituting the granary of that empire. This rebellion, which has been lufh- ciently noticed under the article Egypt, N 125, was fuppreffed chiefly by the wife conduft and intrepid bra¬ very of Hoffan Bey, the captain pacha, who at the age of 70, fought with all the ardour of youth,^ and ah the Ikill of the moft confummate general, lhat veteran, however, was recalled before he was able to carry all his patriotic defigns into execution, that he might aid the divan with his council, in the critical iituation into which the empire was brought by the arrogant claims of the court of Ruffia. The refult of the deliberations was a precipitate declaration of war agaiuft that court, contrary to the better judgement of the old pacha. 1’he war commenced in autumn 1787, and the hordes of Tartars which were firft brought into the field, head¬ ed by the new prophet, were everywhere deleated by the fuperior difeipline of the Ruffian troops commanded by Prince Potemkin. Some enterprifes which were un- dertaken by the Turks againft the ifland of Taman and the Krimea were attended with as little fuccefs as the attempts of the Tartars-, while the emperor Jofeph de¬ clared to the Porte, that he -would affift bis ally the em- prefs of Ruffia with an army of 80,000 pen. four Auftrian armies were accordingly affembled ; one at Carlftadt in Croatia, under the command of General de Vins; another at Peterwaradin in Hungary, command¬ ed by General Langlois ; a third on the borders of Li¬ thuania, under General Febris } and the fourth in t ic Buccowine, under the orders of the prince ot Saxe-Co- boura. Two other generals, 10 lieutenant-generals, and 30 major-generals, were all. ordered to prepare for aftive fervice in the frontier armies. The w-ar betw-een the 1 urks and Auftnans was car¬ ried on w’ith various fuccefs. At firft tne auvantage was evidently on the fide of the Ottomans, and the im¬ perial Jofeph acquired no warlike renown. His declar¬ ed purpofe was to get poffcffion of Belgraoe} , which, however, he w-as repulfed with diigrace. I ne prince of Saxe-Cobourg in his department.of the war difplayed indeed prodigies of valour but being oppofed to a fuperior force, he was long obliged to a- , mee afpers. Fhe principal weight employed is t e kintal, equal to about one cwt. Englilh, divided into 44 oke, and each oke into 400 drahen. 2 10 1 Tun From their jealuufy with refpefl to Grangers, it is ex- Turkey, tremery difficult to form a true eftimate of the national—v—-~ character of the Lurks. An intelligent writer, who,-,, 41 leems well qualified to dire# our judgement in this re- Cfha"aaer Ipecf, has thus delineated the Turkifh charader. “ The lurks Lurks are in general a fugacious, thinking people; in the puiliut of their own intereft, or fortune, their atten¬ tion is fixed on one object, and they perfevere with great ifeadineis until they attain their purpole. They am m common life feemmgly obliging and humane, not without appearances of gratitude : perhaps all or either of theie, when extended towards Chriftians, are practif- ed with a view of lome advantage. Intereft is their fu- preme good ; where that becomes an objedt of competi¬ tion, ail attachment of friendlhip, all ties of confangui- n,ty, diflolved ; they become deiperate, no barrier can. ftop their purfuit, or abate their rancour towards their competitors. In their demeanour they aie rather hypochondriac, grave, fedate, and paffive ; but when agitated by pafljon, furious, raging, ungovernable ; big with diimnulation ; jealous, lufpicious, and vindidlive beyond conception ; perpetuating revenge from genera¬ tion to. generation. In matters of religion, tenacious, lupercihous, and morofe”. * * Pcttet't .1 he manneis and cultoms of the Turks are diftin- Ohfer civil contradt, which either party may break, and is1'13'4’ managed by female mediation, the youth feldom feeing 42 h,s bride till after the ceremony. The dead are perfum. ”r“f ed with mcenfe, and buried in a cloth, open at top and toms. bottom, that the deceafed may be able to lit up and an- Iwer the queftions of the angels of death. The burial- grounds are near the highways, and Hones are often piaced at the heads of the graves, with carved turbans denoting the fex. As they never intrench upon a for¬ mer grave, the cemeteries are very extenfive. In diet the 'I urks are extremely moderate, and their meals are dif- patched with great hafte. Rice is the favourite food, and is drefled in three ways. In boiling, the meat is cut into fmall pieces, and in roafting ftill fmafter, a bit of meat, and an onion being placed alternately on’a very long fpit. The filh of the Archipelago are excellent, and the beef tolerable, except that of the buffalo, which is very hard. The hares, partridges, and other game, are of fupenor flavour. The meal is ufually fpread on a low wooden table, and the mailer of the houfe pro¬ nounces a Ihort prayer. The frugal repaft is followed nuits and coid water, which are fucceeded by hot coffee and pipes with tobacco. The houfes of the Turks are feldom expenfive ; the chief furniture is the car¬ pet which covers the floor, with a low fofa on one fide of the room. In regard to drefs, Tournefort obferves that the ufe of the turban is unhealthy. The fliirt is 0^aLi_co, and the loofe robe is faftened by a girdle, in which is ftuck a dagger, while the tobacco box, pocket- book, &c. are worn in the bofom. The robe is gene¬ rally of European broad cloth, trimmed with various tirs. F Itr»r* Hi **c nil! L 1 1 ✓% #» r rj.,, » n. 7 "AH* vanuuo turs. I he. Ihoes or flippers are flight, and unfit for much exercife. The drefs of the women differs little from that of the men, the chief diftimRion being the head-drtfs; that of the fair fex confifting of a bonnet like T U R [5 Turkey like an inverted bafket, formed of padeboard covered 11. with cloth of gold, with a veil extending to the eye- , Tur»mg- brows, while a fine handkerchief conceals the under part of the face. The perfonal cleanlinefs of both fexes is highly laudable ; but the European eye is not pleafed with the female cudom of ftaining the nails with a red tin&ure. The amusements of the Turks partake of their indolent apathy, if we except hunting, and thofe of a military deioription. To recline on an elegant car¬ pet, or in a hot feafon by the fide of a itream, and fmoke the delicate tobacco of Syria, may be regarded as their chief amufement. Chefs and draughts are favourite games; but thofe of chance are confidered as incompat¬ ible with ftridt morals. The coffee-houfes and baths furnifh other lources of amufement; and the bairam, or fdtival which follows their long lent, is a feaion of uni- * Tinker- veifal diffipation. * ton's Gao- It appears to be a miftaken notion, that the praftice graphy. 0f eating opium, to procure intoxication, is general a- mong the Turks. We are affured by a late traveller, that this praftice is cor.fined to a few individuals, who are regarded by the majority of their countrymen with as much contempt as drunkards are in the more polifhed focieties of Europe. Turkey. See Meleagris, Ornithology Index. TURMERIC. See Curcuma, Botany Index. TURNER, a fpecies of Brassica. See Botany In¬ dex ; and for the culture, fee AGRICULTURE Index. TuiiNEP-Bread. See Bread. Turnep-F/ij. See Chrysomela, Entomology Index. TURNING, the art of forming hard bodies, as wood, ivory, iron, into a round or oval fliape, by means of a machine called a lathe. This art was well known to the ancients, and feems to have been carried by them to a very great degree of perfe&ion ; at leaft, if we believe the tefiimony of Pliny and feveral other authors, who tell us, that thofe preci¬ ous vafes enriched with figures in half-relief, which Rill adorn our cabinets, were turned on the lathe. The art of turning is of confiderable importance, as it contributes efl'entially to the perfedtion of many other arts. The architedf ufes it for many ornaments, both within and without highly finifhed houfes. The ma- thematioian, the aftronomer, and the natural philofo- pher, have recourfe to it, not only to embellifh their infiruments, but alfo to give them the neceffary dimen- fion and precifion. In fhort, it is an art abfolutely ne- cefifary to the goldfmith, the watchmaker, the ioiner, the fmith. Turning is performed by the lathe, of which there are various kinds, and feveral infiruments, as gouges, chifels, drills, formers, ferew tales, ufed for cutting what is to be turned into its proper form as the lathe turns round. The following is a fimple kind of lathe (fig. i.), DXL ,n a’s the footflool, b the cord, c the frame of F the lathe, dd the puppets, e e the points,/the fpanging- S‘ ‘ tree. The lathe fhould be fixed in a place very well light¬ ed ; it fhould be immoveable, and neither too high nor too 1ow\ The puppets fhould neither be fo low as to oblige the workman to fioop in order to fee his work properly, nor fo high that the little chips, which he is continually driving off. fhould come into his eyes. The piece to be turned fhould be rounded (if it be i ] T U R wood) before it be put on the lathe, either with a fmall Turning. ^ hatchet made for the purpofe, or with a plane, or with v a file, fixing it in a vice, and fhaving it down till it is everywhere almoft of an equal thicknefs, and leaving it a little bigger than it is in.ended to be when finiihcdoiF. Before putting it on the lathe, it is alfo neceflary to find the centres of its two end furfaces, and that they ihould be exactly oppofite to each other, that when the points of the puppets are applied to them, and the piece is turned round, no fide may belly out more than another. To find thefe two centres, lay the piece of wood to be turned upon a plank ; open a pair of compaffes to almoft half the thickneis of the piece ; fix one of the legs in the plank, and let the point of the other touch one of the ends of the piece, brought into the fame plane with the plank on which the conipaflfes is fixed and very near the fixed leg. Defcribe four arches on that end at equal diilances from each other at the circumference of the end, but interfering one another within ; the point of interfe£lian is the centre of the end. In the fame man¬ ner mult the centre of the other end be found. After finding the two centres, make a fimall hole at each of them, into which infert the points of the puppets, and 1 fix the piece fo firmly as not to be fbaken out, and yet loofe enough to turn round without difficulty. The piece being thus fixed, it is neceffary in the next place to adjull the cord, by making it pafs twice round the piece, and in fuch a manner that the two ends of the cord, both that which is fixed to the fpang and to the foot-board, come off on the fide on which the turner Hands, that the piece may move againfl the edge of the cutting-tool and be turned. If the lathe be moved by a wffieel, the manner of adjufling the cord needs no di- rerions. If the workman does not choofe to be at the trouble to find the two centres of the piece in the manner de- feribed above, let him lay, as nearly as he can, the cen¬ tre of one end upon the point of the left hand puppet^ and then let him puffi forward the right hand puppet, linking it with a mallet till its point is as near as he can in the centre of the other end of the piece ; and then fixing the right hand puppet by a gentle blow of the mallet on the key, let him turn round the piece to fee by the eye if the centres have been properly found. If any part of it bellies out, let him ftrike that part gently with the mallet till it goes properly \ then let him ftrike one of the puppets pretty fmartly to drive the points in¬ to the piece, and afterwards fix the puppet by linking the key. If the wToikman cannot judge by the eye whether the piece be turning properly round its centres or not, he ffiould apply gently the point of an inftru- ment called a triangular graver, leaning it on the rejl, and it will ma:k by a line the place where the piece is out of its centre •, and by linking upon this line with a mallet, the piece can eafily be placed properly. The rejl, of which we have juft fpoken, ought to be placed upon the tw'o arms of the lathe, and fixed with ferews as near the piece as the workman pleafes. The piece being fixed between the two points of the puppets (or, as they are called in Scotland, the heads'), the cord adjuiled, and the refi fixed as near the work as poffibie without touching it ; the workman is now to take i gouge (fig. 2. in which a is the mouth and b thepj^ 7 handle) of a proper fize in his left hand, and hold it by 61 the handle a little inclined, keeping the back of the hand T U R , Tlim’”2’, hand lowcrmoft. With his right hand, the back of ' which is to be turned upwards, he is to grafp it as near the end as poflible on this fide of the rejlthen leaning the gouge on the rejl, he is to prefent the edge of it a little higher than the horizontal diameter of the piece, fo as to form a kind of tangent to its circumference; then putting the right foot on the foot-board, and turn¬ ing round the wheel, and holding the gouge firmly on the rejl, the piece will be cut neatly. In the fame man¬ ner are’the chifels, formers, and other inftruments to be ufed, taking care that the wood be cut equally, and that the inftrument be not pulhed improperly, fometimes ftronger than at others \ and taking care alfo that the inftrument ufed do not follow the work, but that it be kept firmly in the hand without yielding. The young turner ought to endeavour to acquire the management of the gouge and the chilel, which are the inftruments by far the moft frequently ufed, and the moft neceffary in this art: by them, almoft entirely, are the foft woods turned; for as for hard woods and other things, as box, ebony, horn, ivory, and the me¬ tals, they are hardly ever turned except by Jhaving off. In that cafe gravers are to be ufed with fquare, round, 3) 4> or triangular mouths (fig. 3, 4, 50* They ihould be an^ held horizontally while applied to the wood, and not obliquely as directed for the gouge and the chifel. After the work is completely turned, it is next to be polifhed } and this cannot be done with the inftruments hitherto mentioned. Soft woods, as pear-tree, hazel, maple, ought to be poliftied with fhark-fkin or Dutch rufhes. There are different fpecies of fharks 5 fome of which have a grayifh, others a reddifh {kin. Shark-fkin is always the better to be a good deal ufed ; at firft it is too rough for poliftiing. 'I he Dutch-rujh (equifetum hyemale), which grows in moift places among moun¬ tains, and is a native of Scotland. The oldeft plants are the beft. Before ufing them they fhould be moif- tened a little, otherwiftf' they break in pieces almoft im¬ mediately, and render it exceedingly difficult to polifh with them. They are particularly proper for fmoothing the hard woods, as box, lignum vitae, ebony, &c. Af¬ ter having cleaned up the piece w'ell, it fhould be rub¬ bed gently either with wax or olive-oil, then wiped clean and rubbed with its own rafpings or wfith a cloth a little worn. Ivory, horn, lilver, and brafs, are polifh¬ ed with pumice-ftone finely pounded and put upon lea¬ ther or a linen cloth a little moiftened : with this the piece is rubbed as it ttirns round in the lathe j and to prevent any dirt from adhering to any part of it, every now and then it is rubbed gently wTith a fmall brufh dipt in water. To polifh very finely, the wmrkmen make ufe of tripoli, a particular kind of earth, and afterwards of putty or calx of tin. Iron and fteel are polifhed with very fine powder of emery j this is mixed with oil, and put between two pieces of very tender wTood, and then the iron is rubbed with it. Tin and filver are polifhed with a burnifher and that kind of red ftone called in France fanguine dune. They may be polifhed alfo with putty, putting it dry into fhamoy-fkin, or wfith the palm of the hand. To fucceed in turning iron, it is neceflary to have a lathe exceedingly ftrong in all its parts, and exceeding¬ ly well fixed. The puppets fhould be fhort, and the rejl well fixed very near the work : the back of the rejl T U R fhould be two or three lines lower than the iron to be Turning, turned. e—y-—™ The lathe and other inftruments being prepared, it is neceffary to determine the length and thicknefs of the iron to be turned according to the defign which is to be executed, and to make a model of it in wood a little thicker than it ought to be : Then one exactly like this is to be forged of the belt iron that can be procured v that is to fay, it muft not be new, but w7ell prepared and well beaten wdth hammers ^ it muft have no flaws, nor cracks, nor pimples. New7 iron, which has not been well beaten, often contains round drops of caft iron, called by the workmen grains, which blunt the edges of the gouges, chifels, and other inftruments ufed for cutting, break them, or make them Aide. The iron being forged according to the model, it fhould be annealed, that is, heated red hot and allowed to cool flowly on the coals till the fire go out of itfelf. Some people, to fbften the iron, cover it over with clay and allow it to cool. The iron cylinder being thus made, it is next to be put upon the lathe, finding the centres as formerly direded, and boring a fmall hole in them that the iron may not efcape from the points. The points fhould be oiled from time to time to pre¬ vent their being exceflively heated and fpoiled 'while the iron is turning. A crotchet is then to be applied to the iron to be turned, a little above its centre, pretty gently, and by this means the inequalities of the cylinder will be taken off. Other inftruments are then to be applied to mold the iron according to the model 5 and whenever any of them grow hot, they are to be plunged into a bafon of water lying befide the wmrkman. If the iron, after being properly turned, is to be bored like a gun- barrel, one of the puppets is to be removed and another fubftituted in its place, having a fquare hole through it, into wdiich the collar of the iron is to be fixed firmly, fo as not to fhake •, then borers are to be applied, like thofe which lockfmiths ufe to bore keys j and beginning with a fmall one, and afterwards taking larger ones, the hole is to be made as wide and deep as neceffary j great care muft be taken to hold the borers firm on the rjl, otherwife there is danger of not boring the hole ftraight. The borer muft be withdrawn from time to time to oil it and to clean the hole. Since it is difficult to make a hole quite round with borers alone, it is neceffary to have alfo an inftrument a good deal fmaller than the hole, one of the fides of which is fharp, very well tem¬ pered, and a little hollow in the middle. This inftru¬ ment being fixed in a pretty long handle, is to be ap¬ plied with fteadinefs to the inner furface of the hole, and it will entirely remove every inequality that may have been there before its application. To cut a ferew upon the cylinder, fome perfons ufe an inftrument confifting principally of a female ferew •, but this is rather an improper inftrument j for if one preffes too violently, or inclines it ever fo little to the right or left, he runs the greateft rifk of fpoiling the ferew. To avoid this danger, fome ufe it only to trace out the lines of the ferew, and afterw ards finilh it with a file. But the following is a much better way. Take a tap for making a female ferew, the threads of which have been cut very accurately, and exaflly of the fize of the ferew which you want *, and having put it in the opening which you have traced in the collar of the [ 5*2 1 I T r B IsI I N G-. Tlate 1) X T. . f \ tub. [5 Turning, axis on which the fcrew is to be cut, folder it with tin, ''' l'a!-araraoniac, and rolin, as exaclly correfponding to the axis as poJible. Take then a puppet with a hole cut into a correfponding female fcretv, into which the male fcrew is to be put. The axis on which the lerew is to be cut mufl be placed exaftly horizontally between the two puppets. The rejl is then to be brought as near as poffible to the place where the fcrew is to be cut, and a fmall hollow ihould be cut in that part of it which is exactly oppofite to the place where the fcrew is to be cut, to hold your inftrument firmly and prevent it from fhaking. The inftrument with which the fcrew is to be cut ftiould be very {harp, and its point ftiould make an angle of 6o° with the fcrew to be cut ; and if you wifh the fcrew to be cut very deep, it ftiould make an angle a little larger. The lathe being now put in •motion, the tap fixed at the end of the axis will move gradually through the female fcrew in the puppet; and your inftrument in the mean time will trace a fimilar male fcrew on the axis fixed in the lathe. Many per- fons, after having in this manner drawn the outlines of the fcrew, finilh it with a fcrew'-tale of three teeth cor¬ responding exactly to the fize of the fcrew, or with a triangular file ; but this laft method is rather improper. For turning ovals, a lathe of fomewhat a different conftruffion is ufed. The axis or fpindle, having on it the pulley over which the band-cord paffes for turning the lathe, is fixed between the two puppets fo as to turn round eafily : one end of it paffes through one of the puppets, and to it is firmly fixed a circular plate of brafs, fo that it turns round along with the fpindle. Upon this plate two brazen fegments of circles are fatt¬ ened, the circumferences of, which correfpond to the circumference of the plate : their chords are parallel, and equally diftant from the centre of the plate, fo that they leave a dittance between them. They have a groove in each of them : in thefe grooves another plate is placed wftiich exa&ly fills up the fpace between the two grooves, but is ihorter than the diameter of the larger circular plate on which it is laid. This plate is made to Hide in the grooves. To its centre is fixed a fhort fpindle, on which the piece of wood to be turned is fixed. When the lathe is fet a going, the circular plate moves round, and carries the piece along with it; the plate of brafs on which the piece is fixed being fixed loofely in the grooves already defcribed, Aides down a little every time that the grooves become perpendicular to the floor (and there are particular contrivances to prevent it from Aiding down too far) ; and by thefe two motions combined, the circular one of the large plate, and the ftraight one of the fmall, the circumference of the piece of wood to be turned neceffarily defcribes an oval ; and gouges or other tools being applied in the ufual manner fupported on the reft, it is cut into an oval accordingly. The fmall plate may be made to Hide either more or lefs in the grooves ; and by this con¬ trivance the tranfverfe diameter of the oval, or rather ellipfe, may be made longer or Ihorter at pleafure. 1. The method of moulding boxes of fhell and horn. In the firft place, form a proper mould, which muft con- fift of two pieces, viz. of a circle about half an inch thick, which fhould Hope a little in order to draw out the moulded fhell the more eafily ; and a ring fitted to the outfide of the circle, fo that both together make the ftiape of a box. Thefe two pieces being adjufted, it is Vol. XX. Part II. l3 1 TUB neceffary to round the fhell to be moulded of fuch a fize Turamg-. that, when moulded, it will be a little higher than the ring of the mould, that there may be no deficiency. 1 he mould is then to be put into a prtfs on a plate of iron, exactly under the fcrew of the prefs; put then the ftrell upon the circle of the mould, fb that its centre alfo is exactly oppoftte to the fcrew of the prefs : then take a piece of wood formed into a truncated cone, and not fo thick as the diameter of the circle of the mould nor fo deep as the ring : then put a plate of iron above the cone, and fcrew down the prefs gently and cautioufly till the whole is well fixed : then plunge the whole into a cauldron of boiling water placed above a fire. In 8 or 10 minutes the fhell or horn will begin to Yoften ; fcrevv the prefs a little firmer that the wooden cone may fi.rk into the foifened lliell : repeat tins from time to time till the cone is quite funk in the mould ; then take out the prefs and plunge it into cold water. When it is cold, take the box now formed out of the mould, and put into the infide of rt a new mould of tin exaftly of the form you wifh the infide of the box to be ; do the fame with the outfide, put it again into the prefs and plunge it into boiling water ; fcrew the prefs gradually till the box receive the defired form. 2. Method of preparing green wood fo that it will not fplit in the turning.—Cut the wood into pieces of a pro¬ per fize, put them into a veffel full of potafh ley. Boil them about an hour ; take the cauldron from the fire, allow the ley to cool; and take out the wood and dry it in the lhade. 3. Method of giving an ebony-blach to hard and fine woods.—After forming the wood into the deftined figure, rub it with aquafortis a little diluted. Small threads of wood will rife in the drying, which you will rub off with pumice-ftone. Repeat this procefs again, and then rub the wood with the following compofition • Put into a glazed earthen veffel a pint of ftrong vinegar, two ounces of fine iron-filings, and half a pound of pounded galls, and allow them to infufe for three or four hours on hot cinders. At the end of this time augment the fire, and pour into the veffel four ounces of copperas, and a chopin of water having half an ounce of borax and as much indigo diffolved in it ; and make the whole boil till a froth rifes. Rub feveral layers of diis upon the wood; and when it is dry, polirh it with leather, on w7hich you have put a little tripoli. 4. Method of giving, to plum-tree the colour of brazil tuW.—Slake lime with urine, and bedaub the wood over with it while it is hot : allow it to dry ; then take off the coat of lime and rub it with fhamoy ftdn well osled. Or, fteep the wood in w'ater, having a quan¬ tity of alum diilolved in it: then, having allowed brazil wood to diffolve in water five or fix hours, fteep the wood in it, kept lukewarm during a night; and when it is dry, rub it, as before direbled, with ftiamoy ikin well oiled. 5- Method of giving a fine black colour to wood Steep the wood for two or three days in lukewarm water in which a little alum has been diffolved ; then put a handful of logwood, cut fmall, into a pint of wa¬ ter, and boil it down to lefs than half a pint. If you then add a little indigo, the colour will be more beauti¬ ful. Spread a layer of this liquor quite hot on the wood with a pencil, which wall give it a violet colour, 3 T When T U R [ 51 " 'um'ng, Wlien it is dry, fpread on another layer j dry it again iurnftone.^ an(j gjve jt a ; then boil verdegrife at difcretion in v its own vinegar, and fpread a layer of it on the wood : when it is dry, rub it with a brufli, and then with oiled Ihamoy ikin. This gives a fine black, and imitates per- feftly the colour of ebony. 6. Method of cleaning and whitening bones before vftig them.—Having taken off with a faw the utelefs ends of the bones, make a ftrong ley of alhes and quick¬ lime, and into a pailful of this ley put four ounces of alum, and boil the bones in it for an hour $ then take the veffel containing the ley off the fire, and let it cool j then take out the bones and dry them in the fhade. 7. Method offoldering ffjells.—Clean the two fides of the {hells which you with to join together ; then, having joined them, wrap them up in linen folded double and well moiftened j then heat two plates of iron pretty hot that they may keep their heat for fome time j and putting the {hells rolled up between them under a prefs, which you mull ferew very tight, leave them there till the whole is cold, and they will be folder- ed. If you do not fucceed the firlt time, repeat the procefs. 8. Method of moulding fbells.—Put fix pints of wTater into a kettle ; add to it an ounce of olive or other oil; make the water boil j then put in your {hell, and it will grow foft. Take it out and put it into a mould under a prefs, and it will take the figure you want. This mull be done quickly •, for if the {hell cool ever fo little, the procefs will fail. It will not require much preffure. 9. Method of tinging bones and ivory red.—Boil fhavings of Icarlet in water. When it begins to boil, throw in a quarter of a pound of afhes made from the dregs of wine, which will extradl the colour : then throw in a little rock alum to clear it, and pafs the wa¬ ter through a linen cloth. Steep the ivory or bone in aquafortis, and put it into the water. If you wifh to leave white fpots, cover the places deftined for them with wax. 10. To tinge ivory black.—Steep the ivory during five or fix days in water of galls with alhes made with dried dregs of wine and arfenic ; then give it two or three layers of the fame black wdth which plum-tree is blackened, in order to imitate ebony. Or, diffolve frlver in aquafortis, and put into it a little rofe-water. Rub the ivory with this, and allow it to dry in the fun. 11. Method of hardening wood to make pulleys.—Af¬ ter finilhing the pulley, boil it feven or eight minutes in olive oil, and it will become as hard as copper. 12. To male Chinefe varnifh.—Take of gum lac in grains four ounces j put it into a ftrong bottle with a pound of good fpirit of wine, and add about the bulk of a hazel nut of camphor. Allow them to mix in fummer in the fun, or in winter on hot embers for ,34 hours, ftirking the bottle from time to time. Pafs the whole through a fine cloth, and throw aw’ay what remains upon it. Then let it fettle for 24 hours, and ou wall find a clear part in the upper part of the ottle, which you muff feparate gently, and put into another vial, and the remains will ferve for the 'firft layers. TURNSJONE. See Tringa, Ornithology In- dex. 4 1 T U S TURPENTINE, a tranfparent vifeous fubftance,Turpentiae flowing either naturally or by incifion from feveral refi- ,li nous trees; as the terebinthus, pine, larch, fir, &c. See , ru‘':u!y- , Pinus, Botany Index. See alio Chemistry and Ma~ v ter 1 a Medica Index. Oil of Turpentine. See Chemistry and Mate¬ ria Medica Index. TURPETH, the cortical part of the root of a fpe- cies of convolvulus. See Materia Medica Index. TURQUOISE, is the tooth of an animal penetrated with copper ere. TURRITIS, Tower-mustard j a genus of plants belonging to the clafs tetradynamia j and in the natural fyftem ranging under the 39th order, Siliquofce. See Botany Index. TURTLE. See Testudo, Erfetology Index. Tup.TLE-Dove. See Columea, Ornithology In¬ dex. TUSCAN order, in ArchiteSlure. See Archi¬ tecture, N° 42. Tuscan Earth, a yellotvilh kind of bole ftrund in many parts of Italy, and particularly about Florence, where there is a ftratum eight or ten feet thick, at the depth of five or fix feet from the furface. It is fuppofed to have an aftringent property. TUSCANY, a duchy of Italy, which makes part of the ancient Hetruria, and, excepting fome detached part®, is encompafled by a part of the Mediterranean, called here the Tufcan Sea ; the ecclefiaftical {fate j the duchy of Modena ; and the republic of Lucca j its ex¬ tent from north to fouth being about 116 Englilh miles, and from eaft to weft about 80. Though fome parts of it are mountainous, yet both the hills and dales are covered with vines, olives, citron, lemon, and orange trees, &c. The mountains yield alfo copper, iron, alum, &c. and {bme of the fineft marble. Here is allb plenty of corn, rice, faffron, ho¬ ney, wax, wrool, flax, hemp, with mineral waters, rich paiture, falt-pits, fulphur, alabafter, calcedony, lapis lazuli, borax, amethyfts, carnelians, jafpers, cryftals, and black Hate. In fome places the elms and alhes yield manna. The principal river in Tufcany is the Arno, which has its fource in the Apennine mountains, and falls in¬ to the fea below Pifa. There are feme other fmaller rivers. This duchy fell under the dominion of the Romans about 455 years before Chrift. The Oftrogoths poffel- fed themfelves of it in the fifth century, and after them the Lombards, who were expelled by Charlemagne anno 800 ; in confequence of which it became fubjeft to the German emperors, who appointed governors over it. At laft the cities of Floience, Pifa, Sienna, and fome others, during the contentions between the pope and the emperor, and their refpe&ive adherents, the Guelphs and Gibbelines, withdrew themfelves from the dominion of both, and erebted themfelves into feparate commonwealths. In that of Floience, John de Medi- cis, a popular nobleman, fo infinuated himfelf into the favour of his countrymen, that they invefled him with fovereign power. Pope Pius V. conferred the title of grand duhe on Cofmo de Medicis anno 1570, in whole family the duchy continued until the death of Gallon de Medicis, who died anno 1737. The duchy was then transferred to the duke of Lorrain, afterwards the em¬ peror T Y M [ 5 peror Francis I. in lieu of the duchy of Lorrain, which, by the peace of 1736, was given to King Slaniflaus du¬ ring his life, and then was to be annexed to France. Leopold, the fecond fon of Francis I. and afterwards emperor of Germany, fucceeded to this duchy. It is now enjoyed by Leopold’s fecond fon, brother to the prefent emperor of Germany, Francis II. The grand duke’s annual revenues are computed at about 500,000!. fterling, arifing chiefly from the tenths of all eltates that are fold or alienated, and the ground-rents of the houfes in Leghorn, and the duties on alrnoft all manner of provilions. Tufcany now forms part of the kingdom of Italy iubjeft to France. 1LJSK, or Torsk. See Gadus, Ichthyology Index. 1USSILAGO, Colt’s-Foot j a genus of plants belonging to the clafs of fyngcnefia 5 and in the natural fyflem ranging under the 49 th order, Combofita. See Botany Index. TUTENAG, an alloy of zinc. See Chemistry Index. TUTOR, in the civil law, is one chofen to look to the perfons and eflate of children left by their fathers and mothers in their minoritv. The different kinds of tutonj eftablifhed among the Romans, and die powers and dudes of tutors, are deferibed in Inji. Leg. j. tom. xiii. left. 1. and 2. to which the reader is referred. See alfo the article Guardian.—For the nature and effe&s of tutory in the Scotch law, which is founded on that of the Romans, fee Scots Law, Part III. Se