irv 'j'. AS u EDINBURGH, 20th AugusM803. The folloxving Works are Published Periodically BY ARCHIBALD CONSTABLE & CO. EDINBURGH, AND CONSTABLE, HUNTER, PARK, & HUNTER, 10, LUDGATE STREET, LONDON. I. The EDINBURGH REVIEW, or CRITICAL JOUR- NAL, from its commencement, October 1802, to July 1809, Twenty-eight Numbers. 11. 2s. ; or done up in 14 Vol. boards, 11. 9s. Published Quarterly. II. The FARMER’S MAGAZINE, a periodical work, publish¬ ed quarterly, exclusively devoted to Agriculture and Rural Affairs, for the Years 1800, 1801, 1802, 1808, 1804, 1805, 1806, 1807, 1808, 36 Numbers, (and Supplement to 1803). 4/. 3s.} or in 9 Volumes in boards, 4/. 7s. 6d. The establishment of a Board for promoting agriculture and internal improvement brought husbandry into fashion, and directed public attention to an art which, before that period, had been un¬ dervalued and neglected. From this change of public sentiment, the Proprietors of the Farmer’s Magazine were encouraged to bring forward a periodical work which both contained interesting discus¬ sions upon agricultural subjects, and furnished select and important information respecting the state of markets, produce of crops, rate of rents, and value of labour, in almost every district of the island. The design, at least the latter part of it, was new, therefore was not car¬ ried into execution till the assistance of numerous respectable agri¬ culturists, both in Scotland and in England, was sought for and ob¬ tained ; and to the active and steady exertions of these friends, may be attributed the uncommon and unprecedented success of the work since its commencement—a success far beyond that of any agricul¬ tural publication hitherto attempted in this, or in any other country. In the volumes of the Farmer’s Magazine already published, may be found regular essays or dissertations upon every agricultural sub¬ ject which can be mentioned, together with an immense number of hints or observations, all calculated for the improvement of agricul¬ ture, and the benefit of those connected with it. What is of great importance to husbandmen, information is given in a plain and'prac- tical manner, neither clouded by theory, nor enveloped in technical terms. That eminent writer on husbandry, the Rev. Mr Harte, in his Treatise on Agriculture, says, “ The plain practical author pays his little contingent toRie republic of knowledge with a bill of un¬ stamped real bullion ; whilst the vaip-glorious man of science throws down an heap of glittering counters, which are gold to the eye, but lead to the touchstone. ” III. The EDINBURGH MEDICAL and SURGICAL JOURNAL, for 1805, 1806, 1807, 1808, exhibiting a concise view of the latest and most important discoveries in Medicine, Sur¬ gery, and Pharmacy, (published quarterly), 16 Numbers, 2/. 8s. ; or any single Number, 3s. Also Nos. 17. 18. and 19. 3s. each. *** The object of the Edinburgh Medical and Surgical Jour¬ nal is the improvement of Medicine in all its branches, by the com¬ bined efforts of the Editors, and of their numerous and respectable correspondents. It affords to the profession at large an opportunity of recording, and of disseminating, very quickly and very widely, the knowledge of the remarkable facts which may occur in their prac¬ tice, and of the theoretical opinions which may be the result of their observations ; while the Editors endeavour, by a critical but candid analysis of the recent publications in the various departments of me¬ dicine, to make works of merit quickly known to their numerous read¬ ers, and to extract and condense whatever is most valuable in rare or expensive publications. After the experience of four years, the Editors have the satisfac¬ tion of finding the patronage with which they have been encouraged, progressively increasing. The Fourth Volume is enriched by com¬ munications from Doctors Alley, Bostock, Cheyne, Chisholm, Clarke, Corkindale, Dickson, Duncan, sen. and jun., Kellie, Paterson, Ruttei, Tavarez, Thackeray, Vetch, Wilson, and Wright; and Messrs Ai- noldi, Barlow, A. Burns, Cullen, Ellis, Fuller, Gibb, Hill, Jenkinson, Lawrence, Machel, Maunoir, Noble, Quarrier, Soden, and Wood. IV. The SCOTS MAGAZINE, from its commencement in the year 1739 to 1808 inclusive, 70 Volumes, new and neatly bound } also odd Numbers and Volumes to complete sets. The Scots Magazine was begun in January 1739, a few years after the first publication of the Gentleman’s Magazine, and has ever since contmued to be the standard work of the kind in Scotland. Few pe¬ riodical publications have been held in higher estimation ; and the pre¬ sent Editors have the satisfaction to reflect, that no pains have been spared by them to support and to raise its character, and that their efforts have been rewarded by the approbation of the Public. They have not rested satisfied with those voluntary communications, which have been liberally communicated to them, from persons often of the first distinction in Scotish literature. They have, besides, exerted themselves to the utmost in collecting from all quarters, whatever could contribute to the information and amusement of the Public. The Biography of eminent persons deceased, has always formed an interesting department of periodical works. This the Editors have not overlooked ; but have studied, to the utmost of their power, to let no eminent man depart, without some such tribute to his me¬ mory. Antiquities are a subject replete with amusement, often with infor- ihation, and peculiarly suited to the taste of the present age. Scot¬ land, too, is rich in them; and the connexions and opportunities of the Editors have enabled them, and they trust will enable them, to present their readers with a constant succession of curious articles in this department. Although, from the number of their communications, the Editors would find little difficulty in filling all their pages with original mat¬ ter ; yet this method, however easy for themselves, wrould, in many cases, be little to the advantage of their readers. It has appeared more eligible to insert only such as possessed superior merit in point of subject or manner ; and, instead of the others, to introduce inte¬ resting extracts from rare or valuable works, which are not accessible to the generality of readers ; and, particularly, translations from au¬ thors in foreign languages, which have not appeared in an English dress. From connexions which they have recently established, "they hope to be able greatly to enlarge their command of foreign works for this latter purpose. A few pages are appropriated to Poetry. The Scots Magazine has been the means of introducing to public notice several of the most po¬ pular Scotish poets, by whose communications it is still enriched. In regard to Intelligence, both foreign and domestic, no periodical work has maintained a higher reputation than the Scots Magazine. During the long period through which it has been continued, it has always held the first rank as a work of reference. The present Edi¬ tors hav'e omitted nothing which could tend to support this reputa¬ tion. A larger portion of their pages has been appropriated to this object than in any other magazine now published ; and maps and plans are introduced, wherever they seem likely to be useful, in il¬ lustrating military operations, or important political events. To every number is prefixed a view and. description of some re¬ markable Scotish edifice, either such as is interesting from its anti¬ quity, or an object of curiosity from its recent erection; and is pub¬ lished regularly on the first day of every month. D. WiLLISON, riUNTER, EDINBURGH.J Works Published by ARCHIBALD CONSTABLE & CO. Edinburgh, AND CONSTABLE, HUNTER, PARK, & HUNTER, London. I. An INQUIRY into the PRACTICAL MERITS of the SYSTEM for die GOVERNMENT of INDIA, under the Su¬ perintendance of the BOARD of CONTROUL. By the Earl of Lauderdale. 8vo. 7s. 6d. boards. II. A SERIES OF DISCOURSES ON THE PRINCIPLES OF RELIGIOUS BELIEF, as connected with Human Happi¬ ness and Improvement. By the Rev. R. Morehead, A. M. of Baliol College, Oxford, Junior Minister of the Episcopal Chapel, Cowgate, Edinburgh. Second Edition. 9s. boards. *** “ It is the singular and unaffected benevolence of manner— the tone of genuine goodness and conciliating candour* so unlilce the contemptuous arrogance of vulgar theologians, that forms the chief charm of the volume before us ; and induces us to point it out to the attention of the public, as eminently calculated to fix the principles of the young and careless, and to improve the charity and mend the hearts of readers of every description. ”—Edinburgh Review, No. xxvii. ^ III. OBSERVATIONS on FUNGUS HASMATODES, or SOFT CANCER, in several of the most important Organs of the Human Body •, containing also a Comparative View of the Struc¬ ture of Fungus Hsematodes and Cancer, with Cases and Dissec¬ tions. By James Wardrop, F. R. S. E. Fellow of the Royal Col¬ lege of Surgeons, and one of the Surgeons of the Public Dispen¬ sary of Edinburgh. Illustrated by Eleven Plates. 12s. boards. ^ few copies of this work have been printed in Royal 8vo, with proof impressions of the plates coloured. 1/. Is. boards. IV. ESSAYS on the MORBID ANATOMY of the HU¬ MAN EYE, of which the various morbid appearances are illus¬ trated by Coloured Engravings, by Meadows, Medland, Maddocks, Heath, &c. after Drawings by Mr Syme. In One Volume Royal 8vo. 1/. Is. boards. V. A DISSERTATION on the NUMBERS of MANKIND, in Antient and Modern times. By Robert Wallace, D. D. late one of the Ministers of Edinburgh. Second Edition, revised and corrected by George Wallace, Esq. Advocate. Octavo. 9s. boards. *** The first edition of the above work was published in the year 1753, and is often referred to by Mr Mai thus. VI. NEW THEORY OF THE FORMATION OF VEINS ; with its application to the Art of working Mines. By Abraham Gotti,eb Werner, Counsellor of the Mines of Saxony, Professor of Mineralogy, and of the Art of Working Mines at Freyberg, &c. Translated from the German. To which is added, an Ap¬ pendix, containing Notes illustrative of the subject. By Charles Anderson, M. D. Fellow of the Royal College of Surgeons, Member of the Chirurgical Society, of the Wernerian Natural History Society, &c. One Volume 8vo, 9s. boards. VII. The VILLA GARDEN DIRECTORY, or MONTH- -LY INDEX of WORK to be done in Town and Villa Gardens, Parterres, &c. ; with Hints on the Treatment of Plants and Mowers kept in the Green-Room, the Lobby, and the Drawing Room. By Walter Nicol, Designer of Gardens, &c. and Author of “The Forcing, Fruit, and Kitchen-Gardener, ” “ The Practical Planter, ” &c. Foolscap 8vo. 7s. 6d. '*** It is believed there is no book of gardening on the plan of this work. It is intended as an assistant to gentlemen whose business ne¬ cessarily confines them to the chamber and to the counting-room, who seek health and recreation at their villas, and to those who take upon themselves the management of their own gardens and parterres. ^ VIII. A LETTER addressed to JOHN CARTWRIGHT, Esq. Chairman of the Committee at the Crown and Anchor, on the subject of Parliamentary Reform. By the Earl of Selkirk. The Second Edition. Is. IX. AN ALPHABETICAL LIST of the NAMES of MI¬ NERALS at present most familiar in the English, French, and German languages, with Tables of Analyses. In one vol. 8vo. 5s. in boards. X. THE PLOUGH-WRIGHT’S ASSISTANT; being a New Practical Treatise on the Plough, and on various other important Implements made use of in Agriculture. By Andrew Gray, Author of “ The Experienced Mid-Wright. ” Royal Oc¬ tavo, yr ice Ibr. hoards. Containing Engravings of the Old Scots Plough—the Plough with a Convex twisted Mould-board—the Plough with a Concave twisted Mould-board—the Chain Plough —the Double or Two-Furrow Plough—of Harrows in general— the Break Harrow—the Common Harrow—a Machine whereby Land may be Harrowed in a Wet Season—the Roller—the Drain or Mole Plough—Plan, or Bird’s-eye View of a Drill Machine— Plan, or Bird’s-eye View of a Drill Machine with Indented Cylin¬ ders—the Cultivator, or Horse-hoe—a sowing Machine—of Wheels in general—of Cart-wheels-—of Carts or Carriages in ge¬ neral—of Placing the Bushes into the Wheel—of the Method of finding the Dish of a'Wheel—of the Axle-bed—of Contracting the Wheels before—of Wheel-carriages used in Husbandry- Plan, Elevation, and Section of a Thrashing Machine. XL The EXPERIENCED MILL-WRIGHT ; or a Treatise on the Construction of some of the most useful Machines, with the latest Improvements ; to which is prefixed, a short account of the general Principles of Mechanics, and of the Mechanical Powers. By Andrew Gray, Mill-Wright. Second Edition, 4to. with 44 Engravings. 21. 2s. half-bound. XII. ELEMENTS of MECHANICAL PHILOSOPHY, be¬ ing the substance of a Course of Lectures on that Science. By John Robison, LL. D. Professor of Natural Philosophy in the University of Edinburgh. Volume first, large 8vo. with 22 cop¬ perplates. \l. is. boards. XIII. A TRACT on MONASTIC ANTIQUITIES, with some account of a Recent Search for the Remains of the Kings Interred in, the Abbey of Dunfermline. By John Graham Dal yell, Esq. With Specimens of the Chartidary of Dunferm¬ line fnely engraved. 8vo. 9s. boards. XIV. The PASTORAL or LYRIC MUSE of SCOTLAND, a Poem, descriptive of the united influence of our national Poetry and Music, in softening the Passions, and civilizing the Manners of our feudal Ancestors on the Borders. By FIector Macneill, Esq. 4to. 7s. 6d. boards. XV. MEMOIRS of CAPTAIN GEORGE CARLETON, an English Officer, who served in the Wars against France and Spain, containing an account of the Earl of Peterborough, and other General Officers, Admirals, &c. Octavo. 12s. boards. *** While the eyes of die public are turned with hope and expect¬ ance towards the regeneration of the Spanish kingdom, all informa¬ tion respecting the character of the people and state of the country, particularly in a military point of view, must be highly acceptable. The Memoirs of Carleton were written during that memorable war, in which the Catalonian Insurgents, supported by an auxiliary Bri¬ tish Force, drove the French from Madrid, and forced them to re¬ cross the Pyrenees; when it was, as now, the common cry, in the streets of the Spanish capital, “ Paz con la Inglaterra, y con todo el mundo la guerra. ” It is the work of an eyewitness and actor in the scenes he re¬ cords; and was esteemed by the late Dr Johnson to contain the most authentic account of the campaigns of the gallant Earl of Peter¬ borough. WORKS PUBLISHED BY ARCHIBALD CONSTABLE & CO. XVI. The BATTLE of FLODDEN-FIELD, a Poem of the Sixteenth Century ; with the various Readings of the differ¬ ent Copies, Historical Notes, a Glossary, and an Appendix, con¬ taining Ancient Poems and Historical Matter, relative to the E- vent. By Henry Weber, Esq. Embellished with Three En¬ gravings. 8vo. Handsomely printed. 15s. boards. A very few in Royal Paper, \l. 7s. 6d. boards. * * The antient Poem of Flodden-Field having become extremely fcarce, is now, for the firft time, pnblifhed in an authentic form, the text being eftablifhed by the collation of the different manuferipts and printed copies. Copious notes are fubjoin- ed, as alfd an Appendix, containing numerous antient poems relating to the battle and its confequences, together with the minute accounts of the mod creditable Englifn hiftorians. The engravings of the two ftandards carried by the Earls of Huntly and Marifchall, and the fword and dagger of King James IV., are added as appropriate embellilhments. The whole, it is hoped, will be found an interefting commentary to ah event, which has latterly become fo univerfally popular, by the publication of Mr Scott’s Marmion. XVII. The POOR MAN’S SABBATH, with other POEMS. By John Struthers. Third Edition. Foolscap 8vo. 5s. bds. XVIII. A TREATISE on SCROFULA. By James Rus¬ sell, Fellow of the Royal College of Surgeons, Professor of Cli¬ nical Surgery in the University of Edinburgh. 8vo. 5s. sewed. XIX. HISTORY OF THE UNIVERSITY of EDIN¬ BURGH, from 1580 to 164-6. By Thomas Crawford, A. M. Professor of Mathematics in the College of Edinburgh in the year 164-6. To which is prefixed, the Charter granted to the College by King James, anno 1582. 8vo. 7s. 6d. sewed. *** Of this interefling tradt only One Hundred Copies have been printed for fale. XX. RESUI^T of an INQUIRY into the Nature and Causes of the Blight, the Rust, and the Mildew, v/hich have particu¬ larly affected the Crops of Wheat on the Borders of England and Scotland; with some Observations on the Culture of Spring Wheat. By Sir John Sinclair, Bart. M.P. &c. 8vo. 4-s. sewed. XXL MEMOIRS of ROBERT CARY, Earl of Monmouth, written by himself. Published from an original MS. in the cus¬ tody of the Earl of Corke and Orrery ; to which is added, Frag- menta Regalia, being a History of Queen Elizabeth’s Favour¬ ites, by Sir Robert Naunton ; with explanatory Annotations. Handsomely printed in Octavo. 10s. 6d. boards. A few Co¬ pies on Royal Paper, price \l. 5s. boards. *.* The Memoirs of Cary were firft publiihed from the original Manufcript by the*Earl of Corke and Orrery. They contain an interefting account of fome im¬ portant tranfadlions in Elizabeth’s reign, and throw particular light upon the perfonal character of the Queen. To the prefent edition have been added additional explana¬ tory Notes, particularly referring to Border Matters; and, as a fuitable,companion to theie Memoirs, the Fragmenta Rtgalia of Sir Robert Naunton has alfo been reprinted. XXII. The WHOLE WORKS of Henry Mackenzie, Esq. revised and corrected by the Author ; with the addition of various Pieces never before published. Most beautifully printed in Eight Vol. Post 8vo, with a Portrait of the Author. 3/. 3s. boards. *** This Edition, hefides being publifhed under the careful infpeftion and review of the Author, contains feveral hitherto unpubiiPned works, particularly a Tragedy and a Comedy, in v/hich it is believed the Public will be intererted. Among the al¬ ready publifhed pieces, is included a Pamphlet publilhid in the year 1790, the Hif- tory of the Proceedings of the Parliament 1784, that Parliament in which Mr Pitt laid the foundation of all thofc meafures to which the country has imputed the ppuer which Great Britain exercifed, under his aufpices, of refilling the tyrannous encroach¬ ment of Buonaparte, fo fatal to the red of Europe. It adds a double intered to this publication, when we are informed, in a note by the Author, that- it was anxioufly- revifed and corredted hy the hand of Mr Pi'.t himfelt. XXIIL The ADVENTURES of ROBERT DRURY, dur¬ ing fifteen years captivity in the Island of Madagascar ; containing a Description of that Island ; an account of its Produce, Manu¬ factures, and Commerce ; with an account of the Manners and Customs, Wars, Religion, and Civil Policy of the Inhabitants ; to which is added, a Vocabulary of the Madagascar. Language. Written by himself, and now carefully revised and corrected from the original copy. With two Engravings. 8vo. 8s. boards. %* “ Among the numerous relations of voyages and travels, which combine fo much inftru&ion with delight, the adventures of Robert Drury will be found one of the rooft interefting and amufing; for the wprk is rvot that of one who paffed rapidly through the feenes which he deferibes, but tire experience of a long feries <.f years'Ipent in cap¬ tivity. Indeed, the author was become fo naturalized, that he found much difficulty in regaining his native language. The narration of the numerous deftructiyc wars, and the furpriftng incidents and viciffitudes of fortune which his unfortunate condi¬ tion induced, together with the deferiptions of the cuftoms, the religion, and the pro- dudtions of the country, cannot fail highly to gratify every reader. The whole is de¬ livered in an artlefs dyle, which enhances the intereft we feel for the author, as we are more immediately introduced to his duration of hfe, and more habituated, to his own modes of thinking. ” XXIV. A SERMON preached in the Episcopal Chapel, Cow- gate, Edinburgh, November 16, 1806, the day after the Funeral of Sir WILLIAM FORBES, of Pitsligo, Bart. By Archibald Alison, LL. B. F. R. S. Lond. and Edin., Prebendary of Sarum, See. &c. &c. and Senior Minister of that Chapel. 4-to, 2s. 6d. and 8vo, Is. sewed. XXV. ACCOUNT of the LIFE and WRITINGS of j AMES BRUCE of Kinnaird, Esq. F. R. S. Author of Travels to^dis- cover the Source of the Nile, in the Years 1/68, 1769, 1/70, 1771, 1772, and 1773. By A. Murray, F. A. S. E. and Secretary for Foreign Correspondence. Handsomely printed in Royal 4-to, with 22 beautiful Engravings by Heath. 2/. 12s. 6d. boards. *„* This w-ork, being publilhed in Quarto, forms a mod appropriate Supplement to the Firft Edition of Bruce’s Travels; for, belides the Life, it contains much im¬ portant Correfpondence between the Traveller and many of the firfl Literary Charac¬ ters in Europe, as w-ell as illuftrations and teftimonies in favour of the Authenticity of his Travels to Difcover the Source of the Nile. XXVI. QUEEN HOO-HALL, a Legendary Romance, inter¬ spersed with several original and beautiful Ballads ; and ANCI¬ ENT TIMES, a Drama ; both illustrative of the Domestic Man¬ ners and Amusements of the Fifteenth Century. _ By the late Jo¬ seph Strutt, author of “ Rural Sports and Pastimes of the Peo¬ ple of England, ” &c. In Four neatly printed Volumes, small bvo. Price 18s. in boards. * * « We have perufed, with great pleafure, the interefting pages of this work, which contains a lively and well detailed pi&ure of antient cuftoms, related with all the fimplkity of native genius. "—Monthly Mufeum, July 1808. Works in the Press, and preparing for Publication. I. 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 Uordonstoun, 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 prefented not only with an accurate genealogical hifbry of the antient Houfe of Sutherland, but alfo with a minute detail of the principal tranf- aftions which occurred during a period of nearly 600 years, particularly in the coun¬ ties of Sutherland and Caithnefs, and the Highlands of Scotland in general. The hif- tory of thefe parts, it is prefumed, will receive more elucidation from this work than from any which the public is at prefent poffefied of. The whole has been carefully tranferibed by the kind permiffion of the Marchionefs of .Stafford, from the original nianufeript preferred at Durrobin Caftle. An Appendix will be added, containing an inventory of writs of the Earldom, and the work will be illustrated by foveral en¬ gravings. II. The WORKS of GAWIN DOUGLAS, Bishop of Dun- keld, with Historical and Critical Dissertations on his Life and "Writings, Notes and a Glossary. By the Right lion. Sylvester (Douglas) Lord Glenbervie. 4 vol. 8vo. Elegantly printed. *** The whole works of Gawin Douglas, confiding of his Iranflation of Virgil’s JEneid, the Palace of Honour,dind King Hart, are now, for the firfl time, collected into one edition. Two Diffcrtations, the one on the Family of Douglas, the other on the Poet’s Life and Writings, will be prefixed, and copious notes added. The text of Ruddiman’s edition of the TEneid has been collated with the following- five manuferipts; viz. two in the library of the Uniycrfity of Edinburgh, one in that of the Faculty of Advocates, a fourth in the pofTtffion of the Marquis of Bath at Long- leet, and the fifth at Lambeth Palace. The excellent Gloflary of Ruddiman is made the bafis of that in the prelint work, but confiderably enlarged, and extended to the other poems. III. The DRAMATIC WORKS of John Ford ; with an Introduction and explanatory Notes. By Henry Weber, Esq. In Two Vol. 8vo. WORKS IN THE PRESS, AND PREPARING FOR PUBLICATION. IV. The PEERAGE of SCOTLAND; containing an 4 His¬ torical and Genealogical Account of the Nobility of that King¬ dom, from their Origin to the present Generation.’ Collected from the Public Records, and Antient Chartularies of this Nation, the Charters, and other Writings of the Nobility, and the Works of our best Historians. By Sir Robert Douglas of Glenbervie, Bart. Continued to the present time by J. P. Wood, Esq. Hand¬ somely printed in 2 vol. Folio, with the'Arms of each Family beau¬ tifully engraven. XII. METRICAL ROMANCES of the Thirteenth, Four¬ teenth, and Fifteenth Centuries. Published from Antient Manu¬ scripts, and illustrated by an Introduction, Notes, and a Glossary. By Henry Weber, Esq. In Three Volumes crown octavo. ‘ Of all manner of minf rales, . ' Andjefours that tellen tales, Both of •weeping and of game, And of all that longeth unto fame. ' CflAUCER. V* The prefent publication is intended to comprehend the mod valuable of thofe Romances, which have not yet been fubmitted to the public.' The Life of Alexander attributed by Warton to Adam Davie, and ftrongly recommended by him for nubli- * * \ e r- • 1 ™ n . anwuuLcu uy vvaiion to Aaam uavie, and Urongly recommended bv him for nnM; ■Pi ft t A fe(r Cop'es,are Pr" d °n, arg,e Paper’ forrrmT two fl'p(,'T Volumes, with ! cation, will form the firft article;*and will be followed by Richard cZrdeLion which" ^ii ti imprdlions of the Plates; and as the number printed is very limited, Noblemen j befidcs its very confiderable poetical merit, mud excite a^drong national intered* and and Gentlemen who wifh to fecitre Copies, are refpettfully requeded to leave their by others, feladed either for the beauty of the tale, or feme circumdances rendering names, either with Archibald Constable & Co. Edinburah. or with Consta- them curious: amnno-wbicb ^ -n L r , . & names, eithei with A.rchibald Constable & Co. Edinburgh, or with Consta ble, Hunter, Park, & Hunter, io, Ludgate-Strcet, Loncjon, where Specimens of the woi k may now be feen. V. LEI 1ERS cf the late ANNA SEWARD, writfejn be¬ tween the Tears t/SI and 180,, 5 vcl. post bv'O, with Portraits and other Plates. VI. A SYSTEM of SURGERY. By J. Russell, F. R. S. E. Fellow of the Royal College of Surgeons, one of the Surgeons to the Royal Infiimary, and Professor of Clinical Surgery in the University of Edinburgh. 4 vol. 8vo. VIL ILLUSTRATIONS of the HU ETONIAN THEORY. By John Playfair, Professor of Natural Philosophy in the Uni¬ versity of Edinburgh, F. R. S. London, and Secretary to the Royal Society, Edinburgh. Second Edition, with Additions. 1 vol. 4to, with Engravings. Y III. CALEDONIA, or an Account, Historical and Topo- graphical, or North Britain, from the most antient to the present times. By George Chalmers, Esq. F. R. S. Vol. II. 4to. V Thc fi| d volume of the above work, publilhed lad year, contains the Antient Hi dory of North Britain. The fecond volume, which will appear in the courfe of 1809, will detail, after an Introdudory Chapter of 26 Sections, the local Hidory of its ieveral Shires, in a-correlattve fequence; beginning with Roxburgh, the mod fouthern dire, and proceeding fuccdlively, to Berwick, Haddington, E'dinburgh, Linlithgow Peebles, Selkirk, Dumfries, Kirkcudbright, Wigton, and perhaps Ayrlhire: And the local Hidory of each dire will be given in eight didimd feftions; —1 Of its Name • 2 Of its Situation and Extent; 3. Of its Natural Objefts; 4. of its Antiquities- e’ Of its Edablidment as a Shire; 6 Of its Civil Hidory; 7. Of its Agriculture, Manu- faOures, ! rade; 8. Of its Ecclftafical Hidory ; the Account of each Shire concluding with a Supplemental State, which contains, in a Tabular form, the Names of the fevc- ral Parides, and the number of their Miniders 5 their Extent and Population in I75J> I79T» and 1801; with the Miniders’Stipends in 1755 and 1708 and their Patrons; forming, what Scotland does not now podefs, a fort of Liber Regis This mod intereding work will be completed by the publication of two other vo¬ lumes. Ehe third vfrill contain the local hidory and defeription of the remaining counties, on the plan dated above. The fourth volume will confid of a Topograph! cal Dictionary, containing whatever is intcrefting relative to all places and oMods of any importance m this part of the United Kingdom. This volume will be preceded by an Historical View of the different Languages fpoken in Scotland them curiousj among which a few Comical Romances will be found. To the Intro- duftion, the Editor, at the requed-of feveral genifemen mod anxious for the publi¬ cation, has fubjoined a fummary account of thc German early Poetry and Romance- a fubjoft of high intered, but as yet entirely unknown to this nation, and but little cultivated on the Continent, ff the prefent publication Ihould meet with the encou¬ ragement which the importance of this fpecies of compofition in the Hidory of Eng- hih Poetry deferves, a continuation, compriling thofe excluded from this feleftiorl on account of its limited extent, will he publifhed. * XHE A TREATISE on the DISEASES and MANAGE- MEN I of SHEEP, with introductory Remarks on their Anato¬ mical Structure ; and an Appendix, containing Documents, exhi¬ biting the Value of the Merino Breed, and their Progress in Scot¬ land. By Sir George Stewart Mackenzie of°CouJ, Bart 1 vol. 8vo. XUv. SHIPWRECKS and DISASTEPBS at SEA, according to the most Authentic Accounts, Ancient and Modern. 3 vol. 8vo! IX. The ENGLISH AbSOP, a Collection of Fables, Antient and Modern, in Verse, translated, imitated, and original. By Sir Brooke Boothby, Bart. 2 vol. beautifully printed. Post 8vo. X- I he HISTORY of SCOTLAND, by Robert Lindsay of Pitscottie. Edited from Antient and Authentic Manuscripts, by John Graham Dalyell, Esq. 1 vol. 8vo, handsomely print- etl, with a 1 brtrait of Iving James V. from an original Picture. ' XT. The GARDENER’S KALENDAR, or MONTHLY DIRECTORY of Operations in every Branch of HORTICUL- In 1 vo1- 8vo* BY Walter Nicol, Author of ‘ The Villa Garden Directory, ’ ‘ The Forcing, Fruit, or Kitchen Gar¬ dener,'’—« The Practical Planter, ’ &c. V The Kalendar will be preceded by a DifTertation on the Situations proper for Gardens and Orchards ; on Soils, and how to improve them ; on Manures and their application ; and on the Rotation of Crops [t will exhibit the neweft and mofl approved methods of cultivating all kinds of culinary Vegetables, Fruits, Shrubs, and 1 FUwers.the Management of Hot-boufcs of every defeription. Hot-walls, Flued Fits, ann Hflr-hens ? thf* r* r . r. *T^5 k<^ e^‘tec^ ^7 Walter Scott, Esq. with a Life of the Author, Notes Critical and Illustrative, &c. &c. Nineteen Volumes Octavo, handsomely printed, with a few co¬ pies on Royal Paper. CJ* The Prefent edition of this incomparable Englilh Claffic is offlred to the pub¬ ic on a plan different from that adopted by former editors. In the Life of the Au- • u t0 C°lIate an<1 combine thc various information which has been !ohn\ny Mr1Shte.rulan’. Lord 0rrfJD Dr Delany, Mr Pilkington, Dean Swift, Dr J nfon, and others, into one aiffintf: and comprehenffve narrative ; which it is Xadh m3f ?r7 nf'th.er 3 libf' or apol°Sy for Swift, nor a colloftion from the pleadings of thofe who have written either; but a plain, impartial, and conneaed biographical narrative By the favour of diffinguiihed friends in Ireland, the Editor hopes to obtain confide rah le light upon fome paiTages in the Dean’s life, which have ™rf°hPeT eXedch'S bl0Sraphei's- In preparing the text and notes, no labour or cxpenle has been fpared to procure original information. The Tale of a Tub for example, is iliuftrated with the marginal notes of the learned Bentley, tranferibed IT "|an“fcrlpt jottings on his own copy. Although neither long nor numerous, they offer fome curious elucidations of the author, and afford a lingular infhnce of the equanimity with which the fatire even of Swift was borne by the venerable fcho- ar againft whom it was io unadvifedly levelled. Some preliminary critical obferva- tions are offered on the various literary productions of the Dean of St PatrickV and niece**h Vp a'?atll’’'s Uj1 anc<:dotes accompany his political treatifes. All ’thofe pi ces which, though hitherto admitted into Swift’s works, are pofitively afeertained l&zzzz r sr Spr urjrPoVi'gL™"' “'"P'eK 'h,'' th0fe °f Ia" rcars' The wo* will NY I. RESEARCHES into the ORIGIN and AFFTNTTV nf tfTfr' TP™? I-ANGUAGE^B^Sf Vobme Qifa’rto. ' e‘ary fpr ^°reign One *** Tbe'immediate objea of this w’ork is, to illu(Irate the earfo ftot-- uT»" oL’X GrtfSf' ^i,,Cipl“- ’ TI’'C,liEht *“3: form .o ,he wholo of claflic philology ; exhibit, J ,fZficTc( thf precet'H? which the mind invents and improves articulate fueerh • and u . , piocels by of the origin of the mod antioft European natio^^^^ conrfe of invefligation depend, not on conieHure hut ’ „ , a,Ce.r^lned 1IJ th= every European language with thofe to which it is’-refneftivelv ip1^”^11 3 the operative Gardener, and ,o the fciehUBc ^ j ^ n"^" - TraXVfto'y/r D. willison, printer, Edinburgh.] . ' t ’ / ® I773> publiflied lad year (i808.) year (1808.] PROJECTILES. be =r —. Moreover, the times in which the fame ve- ^ ^? ^mie number* ■It 1S a nui»ber or units, of time, 401 2a locity rvill be extinguiflied by different forces, afting uniformly, - re inverfely as the forces, and gravity would extinguifh the velocity i in the time —fin thefe mea- § fures) to—, . Therefore we have the following 2a proportion —(rrR) : ^ : 2 c, and 2 c is equal to E, the time in which the velocity i will be extin- guiihed by the uniform a&ion of the rcfiftance compe¬ tent to this velocity. The velocity ! would in this cafe be extinguilhed af¬ ter a motion uniformly retarded, in which the fpace de- fcribed is one half of what would be uniformly defcribed during the fame time with the conftant velocity i. Therefore the fpace thus defcribed by a motion which begins with the velocity I, and is uniformly retarded by the refinance competent to this velocity, is equal to the height through which this body muff fall in vacuo in or¬ der to acquire its terminal velocity in air. All thefe circumftances may be conceived in a man¬ ner which, to fome readers, will be more familiar and palpable. The terminal velocity is that where the re- fiftance of the air balances and is equal to the weight of the body. The refiftance of the air to any particular body is as the fquare of the velocity ; therefore let R be the whole refiftance to the body moving with the velo-~ city i, and r the refillanceto its motion wdth the termi¬ nal velocity u; we muff have r=rRx«*, and this muff be = W the weight. Therefore, to obtain the terminal velocity, divide the weight by the refiffance to the velo¬ city l, and the quotient is the fquare of the terminal W velocity, or ——: And this is a very expeditious me¬ thod of determining it, if R be previoufly known. Then the common theorems give a, the fall neceffary for producing this velocity in vgcuo , and the time of the fall and eu—ia, <=: the fpace uniformly g J defcribed with the velocity u during the time of the fall, or its equal, the time of the extinftion by the uniform aftion of the refiffance r ; and, fince r extinguilhes it in the time e, R, which is times fmaller, wall extinguilh it in the time «V, and R will extinguifh the velocity i, which is u times lefs than u, in the time u e, that is, in the time 2a; and the body, moving uniformly during the time 2 ay — E, with the velocity x, will defcribe the fpace 2a ; and, if the body begin to move with the velocity i, and be uniformly oppofed by the refiftance R, it will be brought to reft wdien it has defcribed the fpace. a ; and the fpace in which the refiftance to the velocity, i wall extinguifti that velocity by its urfiform action, is equal to the height tlwough wThich that body muft. fall/» •x/tfcz/o in order to acquire its terminal velo¬ city in air. And thus every thing is regulated by the tirne E in which the velocity I is extinguifhed by the uniform adtion of the correfponding refiftance, or by 2 a, which is the fpace uniformly defcribed during this time, with the velocity i. And E and 2 a muft be expreffed Vol. XVII, Part II. or of length. Having ascertained thefe leading circumftances for an The coin¬ unit of velocity, weight, and bulk, we proceed to de-Panfon duce the fimilar circumftances for any other magnitude j rrijt*e^ene* and, to avoid unneceffary complications, we (hail always^1' ljppo:e the bodies to be fpneres, differing only in dia¬ meter and dcnlity. ^1‘irft, then, let the velocity be increafed in the ratio of i to v. The reffftance will now be ~ r. E 2a and The extinguififing time will be 7 ^ v ' ' v e v—2 a; fo that the rule is general, that the fpace along which any velocity will be extinguiftied by' the uniform action of the correfponding refiftance, is equal to the height neceffary for communicating the terminal velocity to that body by gravity. For e Ter>’nearly’ = v* vz dz pounds- We may take an example. A ball of caff iron weigh¬ ing 12 pounds, is 4! inches in diameter. Suppofe this ball to move at the rate of 25-A feet in a fecond (the reafon of this choice will appear afterwards). The height wffiich will produce this velocity in a falling body is 94 feet. The area of its great circle is 0.11044 feet, or ToWon °f one foot. Suppofe water to be 840 times heavier than air, the weight of the air incumbent on this great circle, and 94 feet high, is 0.081151 pounds: half of this is 0.0405755 or or nearly ^ of a pound. This fhould be the refiftance of the air to this motion of the ball. In all matters of phyfical difcuffion, it is prudent to v 32. confront every theoretical conclufion with experiment.ofexperxl This is particularly neceffary in the prefent inftance, be-ment. caufe the theory on which this propofition is founded is extremely uncertain. Newton fpeaks of it with the moft cautious diffidence, dnd fecures the juftnefs of the conclufions by the conditions which he affumes in his inveftigation. He defcribes with the greateft precifion the ftate of the fluid in which the body muft move, fo as that the demonftrations may be ftridf, and leaves it to others to pronounce whether this is the real conftitu- tion of our atmofphere. It muft be granted that it is not; and that many other fuppofitions have been intro¬ duced by his commentators and followers, in order to fuit his inveftigation (for rve muft affert that little or nothing has been added to it) to the circumftances of the cafe. Newton himfelf, therefore, attempted to compare his Nekton’s proportions with experiment. Some were made byexperi- dropping balls from the dome of St Paul’s cathedral 5 ments. and all thefe ftiowed as great a coincidence with his theory as they did with each other ; but the irregulari¬ ties P R O J £ tics were too great to allow hina to fay with precifion 'vhat was the refiftance. It appeared to follow the pro¬ portion of the fquares of the velocities with fufficient ex- adtnefs J and though he could not fay that the refiftance was equal to the weight of the column of air having the height neceffary for communicating the velocity, it was always equal to a determinate part of it; and might be ftated rr n a, n being a number to be fixed by nume¬ rous experiments. One great fource of uncertainty in his experiments feems to have efcaped his obfervation : the air in that dome is almoft always in a ftate of motion. In the fum- mer feafon there is a very fenfible current of air down¬ wards, and frequently in winter it is upwards: and this current bears a very great proportion to the velocity of the defcents. Sir Ifaac takes no notice of this. He made another fet of experiments with pendulums j and has pointed out feme very curious and unexpected circumftances of their motions in a refilling medium. .There is hardly any part of his noble work in which his addrefs, his patience, and his aftoniftiing penetration, appear in greater luftre. It requires the utmoft intenfe- nefs of thought to follow him in thefe difquifitions; and we cannot enter on the fubjefl at prefent : fome notice will be taken of thefe experiments in the article RESIST* JNCE of Fluids. Their refults were much more uni¬ form, and confirmed his general theory ; and, as we have faid above, it has been acquiefced in by the firft 4I mathematicians of Europe. Inutility of But the deductions from this theory were fo inconfift- the theory ent with the obferved motions of military projeCtileSj in praftice. when the velocities are prodigious, that no application could be made which could be of any fervice for deter¬ mining the path and motion of cannon Ihot and bombs ; and although Mr John Bernoulli gave, in i^iS, a molt elegant determination of the trajectory and motion of a various b°(iy projected in a fluid which refills in the duplicate mathemati- r^t^° t^e velodties (a problem which even Newton cian>, Sec. did not attempt), it has remained a dead letter. Mr Benjamin Robins, equally eminent for phyfical fcience and mathematical genius, was the firft who fufpeCted the true caufe of the imperfeCtion of the ufually received theories ; and in 1737 he publilhed a fmall trad, in which he fliowed clearly, that even the Newtonian theo¬ ry of refiftance mult caufe a Cannon ball, difeharged with a full allotment of powder, to deviate farther from the parabola, in which it wmuld move in vacuo, than the parabola deviates from a ftraight line. But he farther afierted, on the authority of good reafoning, that in fuch great velocities the refiftance mult be much greater than this theory afiigns; becaufe, befides the refiftance arifing from the inertia of the air which is put in motion by the ball, there mult be a refiftance arifing from a condenfa- tion of the air on the anterior furface of the ball, and a farefaCtion behind it: and there mult be a third refilt- ance, arifing from the ftatical prelfure of the air on its anterior part, when the motion is fo fwift that there is a vacuum behind. Even thefe caufes of difagreement with the theory had been foreleen and mentioned by Newton (fee the Scholium to prop. 37. book ii. Princip.); but the lubjeCt feems to have been little attended to. The eminent mathematicians had few opportunities of making experiments ; and the profefltonal men, who were in the service of princes, and had their countenance and aid in 403 42 The at¬ tempts of Various C T I L E S. this matter, were generally too deficient in mathemati¬ cal knowdedge to make a proper ufe of their opportuni¬ ties. The numerous and fplendid volumes which thele gentlemen have been enabled to publifh by the patro¬ nage of fovereigns are little more than prolix extenfions of the fimple theory of Galileo. Some of them, how7- eyer, fuch as St Remy, Antonini, and Le Blond, have given moft valuable collections of experiments, ready for the ufe of the profound mathematician. 43 Twro or three years after this firft publication, Mr9bfervd" Robins hit upon that ingenious method of meafuring ^0:?s. the great velocities of military projeCliles, which has ' handed down his name to pofterity with great honour, and reiift- And having afeertained thele velocities, he difcoveredar.ce, the prodigious refiftance of the air, by obferving the diminution of velocity which it occafioned. This made him anxious to examine w!hat was the real refiftance to any velocity whatever, in order to afeertain what wras the law of its variation ; and he was equally fortunate in this attempt. His method of meafuring the refift¬ ance has been fully deferibed in the article Gunnery, N° 9, &c. It appears (Robins’s Math. Works, vol. i. page 205.) that a fphere of 4E inches in diameter, moving at the rate of 25^- feet in a fecond, fultained a refiltance of 0»°49I4 pounds, or °f a pound. This is a greater refiftance than that of the Newtonian theory, which gave m the proportion of 1000 to 1211, or very nearly in the proportion of five to fix in fmall numbers. And wre may adopt as a rule in all mo¬ derate velocities, that the refiftance to a fphere is equal to ,^5- of the xveight of a column of air having the great circle of the fphere for its bafe, and for its alti¬ tude the height through which a heavy body mult fall in vacuo to acquire the velocity of projection. This experiment is peculiarly valuable, becaufe the ball is precifely the fize of a 12 pound fliot of call iron; and its accuracy may be depended on. There is but one fource of error. The whirling motion mult have occafioned fome whirl in the air, wThich would continue till the ball again pafied through the fame point of its revolution. The refiftance obferved is therefore pro¬ bably fomewhat lefs than the true refiftance to the velo¬ city of 25-j- feet, becaufe it was exerted in a relative ve¬ locity which w7as lefs than this, and is, in faCt, the re¬ fiftance competent to this relative and fmaller velocity. —Accordingly, Mr Smeaton, a moft fagacious natu- and on\fr ralift, places great confidence in the obfervations of aRoufear.d Mr Roufe of Leicefterfliire, wTho meafured the refiftance Bond a.' by the effeCt of the wind on a plane properly expofed to it. . He does not tell us in w’hat wray the velocity of the wind was afeertained ; but our deference for his great penetration and experience difpofes us to believe that this point Xvas well determined. The refiftance ob¬ ferved by Mr Roufe exceeds that refulting from Mr , 45 Robins’s experiments nearly in the proportion of 7 to 10. T^e>, d'fFer Chevalier de Borda made experiments fimilar to thofe mefi con- of Mr Robins, and his refults exceed thofe of Ro- clulions. ~ bins in the proportion of 5 to 6. Thefe differences are fo confiderable/ that we are at a lofs wdiat meafure to abide .by. It is much to be regretted, that in a fub- ject fo interefting both to the philofopher and the man of the wmrld, experiments have not been multipli¬ ed. Nothing would tend fo much to perfeft the fcience 3 E 2 of 404 PROJECTILES. of gunnery j and indeed till this be done, all the labours of mathematicians are of no avail. Their inveftigationg mutt remain an unintelligible cipher, till this key be Supplied. It is to be hoped that Dr Charles Hutton of Woolwich, \<’ho has fo ably extended Mr Robins’s Examination of the Initial Velocities of Military Pro- jettiles, will be encouraged to proceed to this part of the fubjeft. We thould with to fee, in the firft place, a numerous fet of experiments for afcertaining the re¬ finances in moderate velocities } and, in order to avoid all error from the retilxance and inertia of the machine, which is neceflarily blended with the retitlance of the ball, in Mr Robins’s form of the experiment, and is fepa- sated with great uncertainty and ritk of error, we would recommend a form of experiment fomewhat dif- , ferent. A new form Let ax*s anc^ arra which carries the ball be con- of experi. nedded with wheelwork, by which it can be put in mo¬ ment re- ticn, and gradually accelerated. Let the ball be fo commend- conneQe(j with a bent fpring, that this fhall gradually comprefs it as the reflftance increafes, and leave a mark of the degree of compreflion ; and let all this part of the apparatus be fcreened from the air except the ball. The velocity will be determined precifely by the revolutions of the arm, and the refiftance by the compreffion of the fpring. The belt method would be to let this part of the apparatus be made to fide along the revolving arm, fo that the ball can be made to delcribe larger and lar¬ ger circles. An intelligent mechanician will eafily con¬ trive an apparatus of this kind, held at any diitance from the axis by a cord, which pailes over a pulley in the axis itfelf, and is then brought along a perforation in the axis, and comes out at its extremity, where it is fitted with a fwivel, to prevent it from fnapping by be¬ ing twilled. Now let the machine be put in motion. The centrifugal force of the ball and apparatus will caure it to fly out as far as it is allowed by the cord ; and if the whole is put in motion by connedling it with fotne mill, the velocity may be moll accurately afcer- tained. It may alfo be fitted with a bell and hammer like Gravefande’s machine for meafuring centrifugal, forces. Now by gradually veering oflf more cord, the dilfance from the centre, and confequently the velocity and refiftance inc; eafe, till the hammer is difengaged and llrikes the bell. Another great advantage of this form of the experi¬ ment is, that the refiftance to very great velocities may be thus examined, which was impoflible in Mr Robins’s way. This is the great defideratum, that we may learn in what proportion of the velocities the refiftances in- creafe. In the fame manner, an apparatus, confifting of Dr Lynd’s Anemometer, defcribed in the article Pneuma¬ tics, N° 311, &c. might be whirled round with pro¬ digious rapidity, and the fluid on it might be made clammy, which would leave a mark at its greateft ele¬ vation, and thus difcover the refiftance of the air to ra¬ pid notions. Nay, we are of opinion that the refiftance to very rapid motions may be meafured dire&ly in the conduit pipe of fome of the great cylinder bellows employed in blaft furnaces: the velocity of the air in this pipe is afcertained by the capacity of the cylinder and the ftrokes of the pifton. VVc think it our duty to point out to fuch as have the opportunities of trying them methods w'hich promife accurate refults for afcertaining this molt defirable point. We are the more puzzled what meafure to abide by, , 47 becaufe Mr Robins himfelf, in his Practical Propofi- tions, does not make ufe of the refult of his own expe-experi- riments, but takes a much lower meafure. We muftments as content ourfelves, however, with this experimental mea-J^1 rn0^: fine, becaufe it is as yet the only one of which any ac-t ‘ bf c!e~ 1 • J r J J pended on* count can be given, or well-founded opinion formed. Therefore, in order to apply our formulae, wre mult 48 reduce this experiment, which was made on a ball of APPJled to 4 s inches diameter, moving wuth the velocity of 25-]- ^ormu~ feet per fecond, to what would be the refiftance to a ball of one inch, having the velocity 1 foot. This will evidently give us R——being diminilhed in 4T X 25*2 the duplicate ratio of the diameter and velocity. This gives us R—0,00000381973 pounds, or .3‘^I973_ 0£ ICOOOOO a pound. The logarithm is 4,38204. The refiftance here determined is the fame whatever fubltance the ball be of; but the retardation occafioned by it will depend on the proportion of the refiftance to the vis infda of the ball; that is, to its quantity of motion. This in fimilar velocities and diameters is as the denfity of the ball. The balls uled in military fervice are of call; iron or of lead, whofe Ipecific gravities are 7,207 and 11,37 nearly, water being 1. There is confiderable variety in caft iron, and this denfity is about the medium, Thefe data will give us For Iron. For Lead. W, or weight of a ball 1 inch in diameter - - lbs. 0.13648 0.21333 Log. of W - - 9.13309 9-333IO E" - 1116" 6 1761".6 Log- of E - 3.04790 3.24591 u. or terminal velocity - 180.02 a-z Log- 27653 2.37553 a, or producing height S5^-3 880.8 Thefe numbers are of frequent ufe in all queftions on this fubjedf. Mr Robins gives an expeditious rule for readily find¬ ing a, which he calls F (fee the article Gunnery), by which it is made 900 feet for a caft iron ball of an inch diameter. Rut no theory of refiftance which he pro- fefles to ufe will make this height necelfary for produ¬ cing the terminal velocity. His F therefore is an em- pirical quantity, analogous indeed to the producing height, but accommodated to his theory of the trajec¬ tory of cannon-fhot, which he promifed to publifti, but did not live to execute. We need not be very anxious about this ; for all our quantities change in the fame proportion with R, and need only a corre£ticn by a multiplier or divifor, when R ftiall be accurately efta- bliftied. We may illuftrate the ufe of thefe formulae by an ex¬ ample or two. 1. Then, to find the refiftance to a 24 pound ball 49 moving with the velocity of 1670 feet in a fecond,^xa‘T‘P!f^ which is nearly the velocity communicated by i61bs.° 1 eu u*k-' of powder. The diameter is 5,603 inches. PROJECTILES. Log. R Log. d* Log. 1670* + 4.58204 + M9674 +6.44548 2.52426 40 L°g- 3344lbs•='* But it is found, by unequivocal experiments on the retardation of fuch a motion, that it is 504 lbs. This is owing to the caufes often mentioned, the additional refinance to great velocities, arifing from the condenfa- tion of the air, and from its preiTure into the vacuum left by the ball. 2. Required the terminal velocity of this ball ? Log. R - - +4.58204 Log, d* Log. reuft. to veloc. 1 Log. W Diff. of a and b, — log a* Log. 447.4 ~u + 1.49674 6.07878 zz a 1.38021 —b 5-3°143 2.65071 5° Table of teiminal velocity according to Newton As the terminal velocity ?/, and its producing height <7, enter into all computations of military projectiles, we have inferted the following Table for the ufual fizes to Newti n cannon^bot5 computed both by the Newtonian the- and Robins. 017 refidance, and by the refiftances obferved in Ro¬ bins’s experiments. 2 3 4 6 9 12 18 24 32 Newton. Robin' Term. Vel 289.9 324-9 348.2 3 6 43 390.8 418.1 438.6 469-3 492-4 C12.6 54°-5 Perm. Ve’. 2626.4 329^-5 3788.2 4I7°-3 4472.7 5463-5 6010.6 6883.3 7576-3 8024.8 9I29-9 263.4 295.2 316.4 33i-9 355-i 379-9 398-5 426.5 447.4 465.8 49M 2168.6 2723-5 3127.9 3442.6 394°-7 4511.2 4962.9 5683-5 6255.7 6780.4 7538-3 D’am. Inch. I.94 2- 45 2.80 3.08 3- 52 4.04 4- 45 5- °9 5.61 6.21 6- 75 Mr Mul- hdr Muller, in his writings on this fubjeft, gives a ler’s theory much fmaller meafure of refiftance, and confequently a altogether much greater terminal velocity : but his theory is a enoneous. miftake from beginning to end (See his Supplement to his Treatife of Artillery art. 150, &c.) In art. 148.be aftumes an algebraic expreffion for a principle of mecha¬ nical argument } and from its confequence draws erro¬ neous conclufions. He makes the refidance of a cylin¬ der one-third lefs than Newton fuppofes it ; and his rea- fbn is falfe. New'ton’s meafure is demondrated bv his commentators Le Seur and Jaquier to be even a little too fmall, upon his own principles, (Not. 277 Prop. 36. B. II.) Mr Muller then, without any feeming reafon, introduces a new principle, wdrich he makes the chief /import of his theory, in oppofition to the theories of o her mathematicians. The principle is falfe, and even abfurd, as we /hall have occafion to fhow by and by. In confequence, however, of this principle, he is ena¬ bled to compare the refults with many experiments, and the agreement is very flattering. But we (hall foon fee that little dependence can be had on fuch comparifons. We notice thefe things here, becaufe Mr Muller being head ot the artillery Ichool in Britain, his publications have become a fort of text-books. We are miferably deficient in works on this fubjeft, and mult have re- courle to the foreign writers. We now proceed to confider thefe motions through The mo- their whole courfe : and we /hall firft confider thenJas tions con- aftefted by the refidance only 5 then we /hall confider ddered the perpendicular afcents and defcents of heavy bodies t!irough through the air; and, laftly, their motion in a curvili-°Ie neal traje&ory, when projefted obliquely. This muft be done by the help of the abftrufer parts of fluxionary mathematics. To make it more perfpicuous, we /hall, by way oi introduction, confider the /imply relilted rec¬ tilineal motions geometrically, in the manner of Sir Ifaac Newton. As we advance, w e fhall quit this track, and profecute it algebraically, having by this time ac¬ quired di/lindt ideas of the algebraic quantities. ^ \7e muft keep in mind the fundamental theorems of Pre'iminary- varied motions. ©bferva- 1. i he momentary variation of the velocity is pro-tl0nS‘ portional to the force and the moment of time jointly, and may therefore be renrefented by ^±zv—ft, w'here v is the momentary increment or decrement of the velo. cby *’,/the accelerating or retarding force, and} the moment or increment of the time t. 2. The momentary variation of the fquare of the ve¬ locity is as the force, and as the increment or decrement of the fpace jointly 5 and may be reprefented by v j, ~fs The firft propofition is familiarly known. The fecond is the 39th of Newton’s Principia, B. I. It is 54 demonftrated in the article Optics, and is the moft ex-The mo- tenfively ufeful propofition in mechanics. asaf- Thefe things being premifed, let the ftraight line^fl^ AC (fig. 5.) reprefent the initial velocity V, and letonly. CO, perpendicular to AC, be the time in which this Fig. 5, velocity would be extingui/hed by the uniform a61ion 0/ the refiftance. Draw through the point A an equi¬ lateral hyperbola AeB, having OF, OCD for its af- fymptotes; then let the time of the reflfted motion be reprefented by the line CB, C being the firft inftant of the motion. If there be drawn perpendicular ordinates * e-> gfi LB, &c. to the hyperbola, they will be pro¬ portional to the velocities of the body at the inftants D, &c. and the hyperbolic areas AC x. e, ACgfy ACDB, &c. will be proportional to the fpaces defcrib- ed during the times Cx, CCB, &c. For, fuppofe the time divided into an indefinite num¬ ber of fmall and equal moments, C n 7 7 i then DO : CO=m : //, and DC : CO~in-*-h : //, and m-~n tn—n rr„ _ DL— CO, or t — e . iheretore any velo- nn city is reduced to one half in the time in rvliich the ini¬ tial reliftance would have extinguilhed it by its uniform adtion. 55 Thus may the chief circumftances of this motion be An^tne^ determined by means of the hyperbola, the ordinates and abfciflie exhibiting the relations of the times anding this velocities, and the areas exhibiting the relations of both motion, to the fpaces defcribed. But we may render the con¬ ception of thefe circumftances infinitely more eafy and Ample, by exprefling them all by lines, inftead of this combination of lines and furfaces. We lhall accom- plifti this pUrpofe by conftrudting another curve LKP, having the line MIA, parallel to OD for its abfcifla, and of fuch a nature, that if the ordinates to the hyper¬ bola AC, /£-, BD, &c. be produced till they cut this curve in L,/>, #, K, &c. and the abfciffa in L, g, /z, 5, &c. the ordinates g />, Jin, J K, &c. may be pro¬ portional to the hyperbolic areas e A. C x, f A. Cgi § A c K. Let us examine what kind of curve this will be. Make 0C:0.*i~0k : then Hamilton’s Co* hies, IV. 14. Cor.), the areas AC k e,e xgf are equal : therefore drawing p s, n t perpendicular to OM, we lhall have (by the aflumed nature of the curve Lp K), M j- = j / j and if the abfciffa OD be divided into any number of fmall parts in geometrical progreflion (rec¬ koning the commencement of them all from O), the axis V i of this curve will be divided by its ordinates into the fame number of equal parts 5 and this curve will have its ordinates LM, ps, nt, &c. in geometri¬ cal progreflion, and its abfeiflae in arithmetrical progref¬ lion. Alfo, let KN, MV touch the curve in K and L, and let OC be fuppofed to be to Oc, as OD to Od, and therefore Cc to Dz/ as OC to OD ; and let thefe lines Cc, Dr/ be indefinitely fmall 5 then (by the nature of the curve) L 0 is equal to K r : for the areas a AC rq Z>BDr/ are in this cafe equal. Alfo hoh Xo kr, as LM to KI, becaufe cC : r/D~CO : DO : Therefore IN : IK r K : IK : ML — rk 01 ML: MV —0 / : 0 L and IN : MN = r K : 0 L. That is, the fubtangent IN, or MV, is of the fame mag¬ nitude, or is a conftant quantity in every part of the curve. Laftly, the fubtangent IN, correfponding to the point K of the curve, is to the ordinate K £ as the redtangle BDOG or ACOF to the parabolic area BDCA. For let fg Jin be air ordinate very near to BD ^ K j and let Jin cut the curve in n, and the ordinate KI irt q ; then we have K? : y*=:KI : IN, or D^ : y « —DO : IN ; but BD : AC=CO: DOj therefore BD . D ^ : AC , q n — CO : IN. Therefore the fum of all the rectangles BD.Djf is to the fum of all the reClangles AC. qn, as CO to IN j but but the fum of the re&angles ED . D ^ is the fpace ACDB j and, becaufe AC is given, the fum of the re£t- angles AC.qn is the reftangle of AC and the fum of all the lines qti ; that is, the reftangle of AC and RL : therefore the fpace ACDB : AC . RLrrCO : IN, and ACDB x IN=AC . CO • RL j and therefore IN : RL =AC . CO : ACDB. Hence it follows that QL exprefles the area BVA, and in general, that the part of the line parallel to OM, which lies between the tangent KN and the curve L/>K, expreffes the correfponding area of the hyperbola which lies without the reflangle BDOG. And now, by the help of this curve, we have an eafy way of convincing and computing the motion of a body through the air. For the fubtai»gent of our curve now reprefents twice the height through which the ball mull fall in vacuo, in order to acquire the terminal velocity ; and therefore ferves for a fcale on which to meafure all the other reprcfentatives of the motion. The whole ^ut ^ remains to make another obfervation on the reduced to curve L /> K, which will fave us all the trouble of a Ample graphical operations, and reduce the whole to a very anthmeti- fimple arithmetical computation, It is of fuch a na- —ture, that when MI is conlidered as the abfcilTa, and is divided into a number of equal parts, and ordinates are drawn from the points of divifion, the ordinates are a feries of lines in geometrical progreffion, or are conti¬ nual proportionals. Whatever is the ratio between the firlt and fecond ordinate, there is the fame between the fecond and third, between the third and fourth, and fo on 5 therefore the number of parts into which the ab- Iciffa is divided is the number of thefe equal ratios which is contained in the ratio of the iirll ordinate to the lalt : For this reafon, this curve has got the name of the logijiic or logarithmic curve ; and it is of immenfe ufe in the modern mathematics, giving us the folution of many problems in the molt Ample and expeditious manner, on which the genius of the ancient mathema¬ ticians had been exercifed in vain. Few of our readers are ignorant, that the numbers called logaritk?ns are of equal utility in arithmetical operations, enabling us not only to folve common arithmetical problems with altonifhing difpatch, but alfo to folve others which are quite inacceflible in any other way. Logarithms are no¬ thing more than the numerical meafures of the abfciffa of this curve, correfponding to ordinates, which are meafured on the fame or any other fcale by the natural numbers ; that is, if ML ^ be divided into equal parts, and from the points of divilion lines be drawn parallel to MI, cutting the curve L /> K, and from the points of interfeftion ordinates be drawn to MI, thefe will divide MI into portions, which are in the fame proportion to the ordinates that the logarithms bear to their natural numbers. In conftru&ing this curve we were limited to no par¬ ticular length of the line LR, which reprefented the fpace ACDB ; and all that we had to take care of was, that when OC, Ok, Og were taken in geometrical pro- greflion, M r, M £ fhould be in arithmetical progreflion. The abfciffae having ordinates equal tops, tit, &c. might have been twice as long, as is fliown in the dotted curve which is drawn through L. All the lines which ferve to meafure the hyperbolic fpaces would then have been doubled. But NI would alfo have been doubled, and PROJECTILES. our proportions would have Rill held good j becaufe this fabtangent is the fcale of meafurement of our figure, as L or 2 a is the fcale of meafurement for the motions. Since then we have tables of logarithms calculated for every number, we may make ufe of them infiead of this geometrical figure, which Rill requires confi- derable tiouble to fuit it to every cafe. There are two fets of logarithmic tables in common ufe. One is call¬ ed a table of hyperbolic or natural logarithms. It is luited to fuch a curve as is drawn in the figure, where the fubtangent is equal to that ordinate r v which cor- refponds to the fide O of the fquare Oinferted be¬ tween the hyperbola and its aflymptotes. This fquare is the unit of furface, by which the hyperbolic areas are expreffed ; its fide is the unit of length, by which the lines belonging to the hyperbola are exprelfed j r t/ — L or the unit ot numbers to which the logarithms are fmted, and then IN is alfo i. Now the fquare (ttOa. being unity, the area BA CD will be fome number j 5T O being alfo unity, OD is fome number : Call it *. Then, by the nature of the hyperbola, OB : O tt =z *■6 : DB : That is, x : i = i : —, f0 that DB is —. x x , Now calling ~D d x, the area BD db, which is the fluxion (ultimately) of the hyperbolic area, is —. Now . ■v in the curve Ly^K, MI has the fame ratio to NI that BA CD has to OaOjt : I herefore, if there be a fcale of which NI is the unit, the number on this fcale cor¬ refponding to MI has the fame ratio to i which the number meafuring BACD has to I j and I r,'which correfponds to BD db, is the fluxion (ultimately) of MI: I herefore, if MI be called the logarithm of x, x . v~is properly reprefented by the fluxion of ML In fliort, the line MI is divided precifely as the line of numbers on a Gunter’s fcale, which is therefore a fine of logarithms ; and the numbers called logarithms are jjufl the lengths of the different parts of this line meafured on a fcale of equal parts. Therefore, when we meet with fuch an expreflion as — viz. the fluxion x of a quantity divided by the quantity itfelf, wTe confider it as the fluxion of the logarithm of that quantity, be¬ caufe it is really fo wThen the quantity is a number j and it is therefore flri&ly true that the fluent of - is the hy- x J perbolic logarithm of x. Certain reafons of convenience have given life to ano¬ ther fet of logarithms ; thefe are fluted to a lo^iftic curve whofe fubtangent is only rVoVorr of the ordmate t v, which is equal to the fide of the hyperbolic fquarey and wdrich is affumed for the unit of number. We fliall fuit our applications of the preceding invefligation to both thefe, and fhall firfl ufe the common logarithms whofe fubtangent is 0,43429. The whole fubjeft will be befl illuflrated by taking 57 an example of the different queflions w'hich may be pro- Muftrated pofed. by exam- 407 Recolleft that the reflangle ACOF is — 2a, or —, or S' E. pies. 4oS PROJECTILES. E, for a ball of cad-iron one inch diameter, and if it , * u*d has the diameter d, it is , or lad, or Ed. S I. It mav be required to determine what will be the fpace defcribed in a given time / by a ball fetting out with a given velocity V, and what will be its velocity v at the end of that time. Here we have NI : MT—ACOF : BDCA •, now NI is the fubtangent of the logiftic curve } MI is the difference between the logarithms of OD and OC ; that is, the difference between the logarithms of e-j-S and e; ACOF is lad, or FjL, 0r Ed. S Therefore by common logarithms 0,43429 : log. eJpt—log. e—iad : S,rr fpace defcribed, e or 0,43429 • — and S. log. lad °543429 Xlog. lad: S, eJrl e-\-t by hyperbolic logarithms 'a—iad X l°g- Let the ball be a 12 pounder, and the initial velocity be 1600 feet, and the time 20 feconds. We muft firft find e, which is 2 ^ ^ V Therefore, log. la - - ^ (4> 5) log. V. (i6oo) Log. of $",03,=e And e-f-t is 23"o3, of which the log. is from w’hich take the log. of e + 3-°323^ + 0.6S321 — 3.20415 0.48145 1.36229 0.48145 remains the log. of This muft be confidered as a common number by which we are to multiply . 0.43429 Therefore add the logarithms oi lad -}- 3.68557 . e -J-/ log. -i- - + 9-9449° log. 0.43429 9.63778 3.99269 Log. S, 9833 feet For the final velocity, OD : OC=AC : BD, or e-p : e=V : v. 23",03 : 3",03m 600 : 2104,—^. The ball has therefore gone 3278 yards, and its ve¬ locity is reduced from 1600 to 210. It may be agreeable to the reader to fee the gradual progrefs of the ball during fome feconds of its motion. T. S. Diff. V. Biff. *383 2456 3336 4080 4725 6" 5294 1073 880 744 645 569 1203 964 804 690 604 537 397 239 160 114 86 67 The firft column is the time of the motion, the fecond is the fpace deferred, the third is the differences of the 3 fpaces, fhowing the motion during each fucceflive fe¬ cond ; the fourth column is the velocity at the end of the time t; and the laft column is the differences of ve¬ locity, fhowing its diminution in each fucceflive fecond. We fee that at the diftance of 1000 yards the velocity is reduced to one half, and at the diftance of lefs than a mile it is reduced to one-third. II. It may be required to determine the diftance at which the initial velocity V is reduced to any other quantity v. This quetlion is folved in the very fame manner, by fubftituting the logarithms of V and v for thofe of e-j-t and e; for AC : BD—OD : OC, and . AC OD . V , e+t therefore log. 3^3= log- or log- ~ = log- -7-' Thus it is required to determine the diftance in which the velocity 1780 of a 24 pound ball (which is the me¬ dium velocity of fuch a ball difeharged with 16 pounds of powder) will be reduced to 1500. Here d is 5.68, and therefore the loga¬ rithm of 1 a d is V Log. —zr 0.07433, of which the log is Log. 0.43429 +3.78671 + 8.87x16 —9.63778 3.02009 of a fe- Log. 1047,3 feet, or 349 yards This redudlion will be produced in about -g- cond. III. Another queftion may be to determine the time which a ball, beginning to move with a certain veloci¬ ty, employs in pafling over a given fpace, and the dimi¬ nution of velocity wdiich it fuftains from the refiftance of the air. We may proceed thus : log. ——zr/. Then to log. lad\ 8=0,43429 0.88084 e-\-t add log. e, and we obtain log. e+/, and from Then to find v, fay which if we take e wTe have t. e-\-t: e=y • v. We fliall conclude thefe examples by applying this App]jcat;on laft rule to Mr Robins’s experiment on a roulket bullet 0f an expe- of of an inch in diameter, which had its velocity re- riment of duced from 1670 to 1425 by pafling through 100 feet Mr R°biri-S* of air. This we do in order to difeover the refiftance WS S which it fuftained, and compare it with the refiftance to Works, a velocity of 1 foot per fecond. vol. i. p. We muft firft afeertain the firft term of our analogy. I3S' The ball w^as of lead, and therefore 2 a muft be multi¬ plied by d and by m, which exprefles the ratio of the denfity of lead to that of caft-iron. d is 0.75, and m is 11.37 -= 1.577. Therefore log. la 3.03236 7.21 9.87506 0.19782 Log. ladtn 3.10524 and ladtnz=. 1274.2. £ f Now 1274.2 : ioorro.43429 : 0.03408zzlog. 'l. f! d 7H • • But e——-——=0.763, and its logarithm = 9.88352, which, added to 0.03408, gives 9.91666, which is the log. of e+/, =0.825, from which take e, and there remains 59 Recapitu¬ lation.] 62 PROJECTILES. remains l=, o".o6l, or of a fecond, for the time IOOO of paffage. Now, to find the remaining velocity, fay 82c: .763=1670 : 1544, But m Mr Robins’s experiment the remaining veloci¬ ty^ was only 1425, the ball having loft 245 5 whereas by this compulation it ftiould have loft only 126. It ap¬ pears, therefore, that the refiftance is double of what it would have been if the refiftance increafed in the dupli¬ cate proportion of the velocity. Mr Robins fays it is nearly triple. But he fuppofes the refiftance to flow mo¬ tions much fmaller than his own experiment, fo often mentioned, fully warrants. The time e, in which the refiftance of the air would extinguifli the velocity is o" 763. Gravity, or the weight of the bullet, would have done it in l^7° or c 2/' • 32 ’ ’ therefore the refiftance is ~ ^ - times, or nearly 68 times its weight, by this theory, or 5.97 pounds. If we cal¬ culate from Mr Robins’s experiment, we muft fay log. —; O.43429 =r 100 : *> V, which will be 630.23, and and •^J^-Sives 'dS for the proportion of the refiftance to the weight, and makes the refiftance 12.07 pounds, fully double of the other. It is to be obferved, that with this velocity, which greatly exceeds that with which the air can rufti into a void, there muft be a ftatical preffiire of the atmo- fphere equal to 6± pounds. This will make up the dif¬ ference, and allows us to conclude that the refiftance arifing folely from the motion communicated to the air follows very nearly the duplicate proportion of the velo¬ city. # The next experiment, with a velocity of 1690 feet gives a refiftance equal to 157 times the weight of the’ hullet, and this bears a much greater proportion to the former than 16902 does to 1670% which fhows, that al¬ though thefe experiments clearly demonftrate a prodigi¬ ous augmentation of refiftance, yet they are by no means fufceptible of the precifion which is neceffary for difco- vering the law of this augmentation, or for a good foun¬ dation of pra&ical rules; apd it is ftill greatly to be wiflied that a more accurate mode of inveftigation could be difcovered. Thus we have explained, in great detail, the princi¬ ples and the procefs of calculation for the Ample cafe of the motion of proje&iles through the air. The learn¬ ed reader will think that we have been unreafonably prolix, and that the whole might have been comprifed m lefs room, by taking the algebraic method. We ac¬ knowledge that it might have been done even in a few lines. But we have obferved, and our obfervation has been confirmed by perfons well verfed in fuch fubjedls, that in all cafes where the fluxionary procefs introduces the fluxion of a logarithm, there is a great want of di- ftinfl ideas to accompany the hand and eye. The folu- tion comes out by a fort of magic or legerdemain, cannot tell either .how or why. We therefore thought it our duty to furnilh the reader wdth diftinft conceptions of the things and quantities treated of. For this reafon after fhowing, in Sir Ilaac Newton’s manner, how the* fpaces defcribed in the retarded motion of a proieaile Vol. XVII. Part II. V J c 409 followed the proportion of the hyperbolic areas, we (hewed the nature of another curve, where lines could be found which increafe in the very fame manner as the path of the proje&ile increafes ; fo that a point deferr¬ ing^ the abfeifla MI of this curve moves precifely as the proje&ile does.. Then, difeovering that this line is the fame with the line of logarithms on a Gunter’s fcale, w^e (hewed how the logarithm of a number really reprefents the path or fpace defcribed by the proje&ile. Havmg thus, we hope, enabled the reader to conceive diftm&ly the quantities employed, w^e (hall leave the geometrical method, and profecute the reft of the fub- jedt in a more compendious manner. We are, in the next place, to confider the perpendi-Of thf per- cu ar afeents and defeents of heavy projedliles, where pendicular the refiftance of the air is combined with the adlion ofafcents of gravity : and we (hall begin with the defeents. ^ “7 pro“ Let a,, as before, be the terminal velocity, and g theJCL *tS* accelerating power of gravity : When the body moves with the velocity «, the refiftance is equal to g ; and in every other velocity v, we muft have u* : v*=g . g —, =rf for the refiftance to that velocity. In the defeent the body is urged by gravity g, and oppofed by the refiftance ~~~ : therefore the remaining acce¬ lerating force, which we (hall call / is p- -g 0r u1 ’ g lr g y* g(u* U* ’ U1 ’ Now the fundamental theorem for varied motions is /' ’ . • w u7" s — u v, and s = —, — — x f S -, and s = u% X* 62 is 14850, and =r 680,34 u2 . . : L. -, or, which is ftill more conveni- -, that is, equal to , M X 2^ S _ ^ 7^* ent for us, — the logarithm of a certain number: therefore having found the natural number correfponding to the fradlion M X conplcier it as a logarithm, and take out the number correfponding to it 1 call this n. Then, fince n is equal to —-— have n u ■ n v2 and nu2 — u2 — u v2, or 72 = a* X « — v, and v2 72* X n — 1 To expedite all the computations on this fubjeft, it will be convenient to have multipliers ready computed for M X2g, and its half, viz. 27,794, whofe log. is - 1.44396 and 13,897 - - - 1.14293 But v may be found much more expeditloufly by , . , ^ obferving that */ —— is the fecant of an arch of a circle whofe radius is a, and whofe fine is v, or whofe radius is unity and fine : therefore, confi- dering the above fra&ion as a logarithmic fecant, look for it in the tables, and then take the fine of the arc of which this is the fecant, and multiply it by u j the pro- du£l is the velocity required. We fhall take an example of a ball whofe terminal velocity is 689^ feet, and afcertain its velocity after a fall of 1848 feet. Here, &*_:475200 an(j[ l0g. . =25.67688 u =26893- - - - '2.83844 £=32 - - - i‘S0SlS 8 = 1848 - - - 3.26670 Then log. 27,794 - - + 1-44396 log. S - - - + 3.26670 log. u1 _ . . — 5.67688 Log. of 0,10809 = log. n - 9-°3378 ©,10809 is the logarithm of 1,2826 = 77, and n—1 = 0,2826, and U= 323>6% - ^ % and v — 323,6. In like manner, 0,054045 (which is half of 0,10809) will be found to be the logarithmic fecant of 28°, w7hofe fine 0,46947 multiplied by 689^ gives 324 for the ve¬ locity. The procefs of this folution fuggefts a very perfpicu- ous manner of conceiving the law of defcent j and it may be thus exprefled : M is to the logarithm of the fecant of an arch whofe fine is—, and radius 1, as 227 is to the height through u which the body muft fall in order to acquire the veloci¬ ty v. Thus, to take the fame example. 0,46947, which is the fine of 28°. The logarithmic fecant of this arch is 0,05407. Now M or 0,43429 ; 0,05407 = 14850 : 1848, the height wanted. 2. Required the velocity acquired by the body by falling 1848 feet. Say 14850 : 1848 = 0,43429 : 0,05407. Look for this number among the logarith¬ mic lecants. It will be found at 28°, of which the lo¬ garithmic fine is - - - 9.67161 Add to this the log. of 72 - - 2.83844 The fum . - - 2.51005 is the logarithm of 323,62, the velocity required. We may obferve, from thefe lb]utions, that the ac¬ quired velocity continually approaches to, but never equals, the terminal velocity. For it is always expref- fed by the fine of an arch of which the terminal veloci- ty is the radius. We cannot help taking notice here £rroneous of a very ftrange affertion of Mr Muller, late profeflbr a tier non of of mathematics and direclor of the royal academy at Muiler^ Woolwich. He maintains, in his Treatife on Gunnery, his Treatife of Fluxions, and in many of his numerous works* that a body cannot poffibly move through the air with a greater velocity than this 5 and he makes this a fundamental principle, on which he eftablilhes a theo¬ ry of motion in a refilling medium, which he afferts with great confidence to be the only jull theory 5 fay¬ ing, that all the inveftigations of Bernoulli, Euler, Ro¬ bins, Simpfon, and others, are erroneous. We ufe this ftrong exprefiion, becaufe, in his criticifms on the works of thofe celebrated mathematicians, he lays afide good manners, and taxes them not only with ignorance, but with dilhonelty } faying, for inftance, that it required no fmall dexterity in Robins to confirm by his experi¬ ments a theory founded on falfe principles 5 and that Thomas Simpfon, in attempting to conceal his obliga¬ tions to him for fome valuable propofiticns, by chan¬ ging their form, had ignorantly fallen into grofs errors. Nothing can be more palpably abfurd than this affer- tion of Mr Muller. A blown bladder will have but a fmall terminal velocity 5 and when moving with this ve¬ locity, or one very near it, there can be no doubt that it w-ill be made to move much r.sifter by a fmart ftroke. Were the affertion true, it would be impoffible for a portion of air to be put into motion through the reft, for its terminal velocity is nothing. Yet this author makes this affertion a principle of argument, faying, that it is impoffible that a ball can iffue from the mouth of a cannon with a greater velocity than this; and that Robins and others are grofsly miftaken, when they give them velocities three or four times greater, and refin¬ ances which are 10 or 20 times greater than is pcfiible 5 and by thus compenfating his fmall velocities by ftill fmaller refiftances, he confirms his theory by many ex¬ periments adduced in fupport of the others. No rea- fon whatever can be given for the afferlion. New-ton, or perhaps Huygens, was the firft wrho obferved that there was a limit to the velocity which gravity could communicate to a body j and this limit was found by his commentators to be a term to which it was vaftly convenient to refer all its other motions. It therefore became PROJECTILES. became an object of attention *, and Mr Muller, through inadvertency, or want of difcernment, has fallen into this miftake, and with that arrogance and felf-conceit which mark all his writings, has made this miftake a fundamental principle, becaufe it led him to eftablifti a novel fet of doctrines on this fubjeft. He was fretted at the faperior knowledge and talents of Mr Simpfon, his inferior in the academy, and was guilty of feveral mean attempts to hurt his reputation. But they wer^e 62 unfuccefsful. Motion of We might proceed to confider the motion of a body a J.0*3/ ^r°’ Proje£ted downwards. While the velocity of projeftion downwards t^an termina^ velocity, the motion is deter¬ mined by what we have already faid : for we mull com¬ pute the height neceflary for acquiring this velocity in the air, and fuppofe the motion to have begun there. But if the velocity of projection be greater, this method fails. We pafs it over (though not in the leaft more difficult than what has gone before), becaufe it is of mere curiofity, and never occurs in any interefting cafe. We may juft obferve, that fince the motion is fwifter than the terminal velocity, the refiftance muft be great¬ er than the weight, and the motion will be retarded. The very fame procefs will give us for the fpace defcrib- and L yu-Cv A fu4-v —> or ™ V — is always an abftracl U -y' M " u—v number, multiplying this time. We may illuftrate this rule by the fame example. In what time will the body acquire the velocity 323,62 ? Here + v re 10x2,96, u—v — 36$>1* } therefore /u-\-v A V —!—~0,22I 22, u 21 U- /»542- , and — (in feet and feconds) is $ Now, for greater perfpicuity, convert the u equation Mg u—v into a proportion 5 thus edS=:—XL V being the velocity of «3 Relation between the time of defeent and fpace deferibed, fcc. g V—u‘ projeclion, greater than u. Now as this fpace evident¬ ly increafes continually (becaufe the body always falls), but does not become infinite in any finite time, the frac- . V1— tion — does not become infinite ; that is, v* does —u1 7 not become equal to : therefore although the veloci¬ ty V is continually diminiihed, it never becomes fo fmall as u. Therefore a is a limit of diminution as well as of augmentation. We muft now afeertain the relation between the time of the defeent and the fpace deferibed, or the velocity acquired. For this purpofe we may ufe the other fun¬ damental propofition of varied motions f t~v, which, in the prefent cafe, becomes — — _T !u-\-v u M : A v —- : U and we have 0,43429 : 0,22122 = 21", 542 : 10",973, the time required. This is by far the molt diftind! way of conceiving the fubjeft j and we fhould always keep in mind that the numbers or fymbols which we call logarithms are really parts of the, line MI in the figure of the logiftic curve, and that the motion of a point in this line is pre- cifely fimilar to that of the body. The Marquis Po- leni, in a differtation publilhed at Padua in 1725, has with great ingenuity ccnftrudled logarithmics fuited to all the cafes which can occur. Herman, in his Phoro- nomia, has borrowed much of Poleni’s methods, but has oofeured them by an affedlation of language geometri-. cally precife, but involving the very obfeure notion of abftrabt ratios. t-=zv : therefore t 2T v g u1— u uv 1* ’ ~ £ x zP— -, and t This flu- , u / u A-v u yore t——xLv , g u—v M^ u—v ent needs no conftant quantity to complete it, or rather Crco ; for t muft: be rro when V—O. This will evi¬ dently be the cafe : for then L s/ is Lv —= u—v u L 1, =0. 41 It is eafy to fee that V ^is the cotangent of the \ complement of an arch, whofe radius is t, and whofe fine is -: For let KC (fig. 6.) be —and BErr'y; then KD—zz-f-'1’? ar|d DAzzzz—v. Join KB and BA, and draw CG parallel to KB. Now’ GA is the tangent of \ BA, complement of HB. Then, by fimilarity of triangles, GA : AC — AB : BK, = ; v^DKcr^/zz—v : antl ^j^(=cotan. . u x f'-'1- . > therefore look for — among the na- g J zzJ—v!‘ u Fig. 6. Now (art. Fluxions) f-^L.=Ls/^±v. There- tUral r,neS’ °r f°r loS- J an,onS the and take the logarithmic cotangent of the half comple¬ ment of the correfponding arch. This, confidered as a common number, will be the fecond term of our pro¬ portion. This is a ffiorter procefs than the former. By reverfing this proportion we get the velocity cor¬ refponding to a given time. .To compare this defeent of 1848 feet in the airpalIof with the fall, of the body zzz vacuo during the fame body°ii] time, fay 21 ",542* : io//,973j=:i848 : 1926,6, whichairIcomPa” makes a difference of 79 feet. But how does this quantity X * yEt %nify a time ? Obferve, that in whatever numbers, or by what¬ ever units of fpace and time, u and g are expreffed, — expreffes the number of units of time in which the ve- s . . locity u is communicated or extinguished by gravity j Cor. r. The time in which the body acquires the velocity u by falling through the air, is to the time of acquiring the fame velocity by falling in vacuo, as u. !u-\-v 1 eft with that of one in vacuoi L V zz—« to v : for it would acquire, this velocity in 3 F 2 vacua 412 65 Time of the afcent of a body projected perpendi¬ cularly. P R O J E C vacuo during the time and it acquires it in the air in S ■t . u-\-v the time -L v —-—. g u—v 2. The velocity which the body acquires by falling through the air in the time -T, is to the ve- g u—v locity which it would acquire in vacuo during the fame time, as v to //L u—v For the velocity which it would acquire in vacuo during the time - Ju+v mull; be a L u^v 2M^j- uz 4-V: is — ; we mall have a zr and vzz TILES. v Here — will be found the tangent of 30.48J, the lo¬ garithmic fecant of which is 0,06606. This, multi- plied by gives 2259 feet for the height. It would have rifen 2640 feet in a void. Suppofe this body to fall down again. We can Velocity of compare the velocity of projection with the velocity projection with which it again reaches the ground. The alcent comPared 0 0 with that with which ^ „ which it reaches u the ground. 66 and defeent are equal: therefore J- -f-V* multiplies the conltant faftor in the afcent, is equal to (becaufe in any time J: — the velocity vo is acquired.) & In the next place, let a body, whofe terminal velo¬ city is u, be projeCled perpendicularly upwards, with any velocity V. It is required to determine the height to which it afeends, fo as to have any remaining velo¬ city v, and the time of its afcent j as alfo the height and time in which its whole motion will be extin- guifhed. # We have now —— for the expreflion of f; for both gravity and refiftance aft now in the fame di¬ rection, and retard the motion of the afeending body : a, r <§■("*+^s) ’ • , • a* vv therefore — 5 sz=.— vv% and rrr x -, the multiplier in the defeent. The firft is u —Vs the fecant of an arch whofe tangent is V j the other is the fecant of an arch w'hofe fine is v. Thefe fecants are equal, or the arches are the fame j therefore the ve¬ locity of projection is to the final returning velocity as the tangent to the fine, or as the radius to the cofine of the arch. Thus fuppofe the body projected with the terminal velocity, or V=:w; then ?/:=—^=.. If V ~ 689, ^=487. We mult in the lalt place afeertain the relation of the fpace and the time. Tir gitf + V*') • • • U* V Here ^— 1~—v, and / = X , =r ux •’ g * u'-l-v1’ and s=~~xf -|-C, — xL'v/“i+^ + g •S u -\-v* g ' C (fee art. Fluxions). This mult be =0 at the be¬ ginning of the motion, that is, when v~Y, that is, XLVu2-{-V*C—o, orC=— XL ^u2^-vz and g g if /— . — the complete fluent will be s ——XL v ux — T VlF+v* )= —vT g J u^ + v2’ M ^ Let h be the greatelt height to which the body will if rife. Then s — h when v ~ 0 ; and /i zr — X g f is 4. v2 u* , L V — > = X a V - a ♦ We have u* M j1- w AmW* nur r 2Mgs * >theicfore ^ v^+v1/ - ~ur~ Therefore let n be the number whofe common logarithm -f Va u uv . ■ “ X —,—; and t g ux -\~vx —« r 4- vx 4- C. Now (art. Fluxions) f is an arch w?hofe tangent u2 -\-v — — and radius 1 ; therefore t—— — x arc. tan. —-4-C. u g This mult be zz 0 when vz g :V, or C- g X arc. tan. and the complete flu* —The quan- u‘ ' u2-\-v2' n —u2; and thus -we obtain the relation of s and ■u, as in the cafe of defeents: but wre obtain it Itill eafier by ob- ferving that u2 4-Vz is the fecant of an arch whofe radius is «, and whofe tangent is V, and that tju2 -\-v2 is the fecant of another arch of the fame circle, whofe tangent is v. Let the fame ball be projected upwards with the ve¬ locity 411,05 feet per fecond. Required the whole height to which it will rife ? V « V - = 0, and C=- X arc. tan. — “ g g u ( V ent is / zz — x ( arc. tan. arc. tan. g_ \ « tities within the brackets exprefs a portion of the arch of a circle whofe radius is unity ; and are therefore ab- ftraft numbers, multiplying -, which we have Ihown to ^g be the number of units of time in which a heavy body falls in vacuo from the height <7, or in which it acquires the velocity //. We learn from this expreflion of the time, that how-T. ^ ever great the velocity of projeftion, and the height af^nUi- to which this body will rife, may be, the time of its mited. afcent is limited. It never can exceed the time of fal¬ ling from the height a in vacuo in a greater proportion than that of a quadrantal arch to the radius, nearly the proportion of 8 to 5. A 24 pound iron ball cannot continue riling above 14 feconds, even if the refiftance to quick motions did not increafe fafter than the fquare of the velocity. It probably will attain its greateft height in lefs than 12 feconds, let its velocity be ever fo great. *» In the preceding example of the whole afcent, v—o, and 68 This time compared in bodies proje&ed in air and in vacuo. Fig. 6. 69 Neceffity of further experi¬ ments. P R O J E and the time -X arc. tan. —, or-arc. 30°. 48'. g » g Now 30°.48'=i848', and the radius 1 contains 3438 j therefore the arch = =0, C376; and - = 21", C4. 3438 g Therefore/r=2i'',54 X 0,5376,= 11",58, or nearly ii| feconds. The body would have rifen to the fame height in a void in io|; feconds. Cor. 1. The time in which a body, ~projected in the air wdth any velocity V, will attain its greateft height, is to that in wdiich it would attain its greateft height m vacuo, as the arch whofe tangent expreffes the velocity is to the tangent 5 for the time of the afcent in the air u . V is — x arch; the time of the afcent in vacuo is —. Now g g , V u - is = tan. and V= # x tan. and - = - x tan. u . g g It is evident, by infpe&ing fig. 6. that the arch AI is to the tangent AG as the fedtor ICA to the tri¬ angle GCA j .therefore the time of attaining the great¬ eft height in the air is to that of attaining the greateft height in vacuo (the velocities of proje&ion being the fame), as the circular feftor to the correfponding tri¬ angle. If therefore a body be proje&ed upwards with the terminal velocity, the time of its afcent will be to the time of acquiring this velocity in vacuo as the area of a circle to the area of the circumfcribed fquare. 2. The height H to which a body wall rife in a void, is to the height h to which it would rife through the air wrhen projected with the fame velocity V as M*V* to t/1 X * ——— : for the height to which it will rife in • V3 vacuo is —, and the height to which it rifes in the air is 2g . 6 413 _{_ V2 therefore H V* «* /u1 -f V2 U* /«2_LV2 M7 V —T—-> =V ;M =v* u1 -f- V2 M X A ^ _ M-V2 : u1 X A —^ . Therefore if the body be projected with its terminal velocity, fo that V=a, the height to which it will rife in the air is of the height to which it will rife 43429 5 in vacuo. or — in round numbers. 7 We have been thus particular in treating of the per¬ pendicular afcents and defcents of heavy bodies through the air, in order that the reader may conceive diftinftly the quantities which he is thus combining in his algebraic operations, and may fee their conneftion in nature wdth each other. We (hall alfo find that, in the prefent ftate of our mathematical knowledge, this fimple ftate of the cafe contains almoft all that wre can determine with any confidence. On this account it were to be wiftied that the profeflional gentlemen would make many experi¬ ments on thefe motions. There is no way that pro- mifes fo much for aflifting us in forming accurate no- C T I L E S. tions of the air’s refiftance. Mr Robins’s method with the pendulum is impracticable with great ftiot; and the experiments which have been generally reforted to for this purpofe, viz. the ranges of ihot and (hells on a ho¬ rizontal plane, are fo complicated in themfelves, that the utmoft mathematical (kill is neceffary for making any inferences from them; and they are fubjeCt to fuch irregularities, that they may be brought to fupport al¬ moft any theory whatever on this fubjeCt. But the per¬ pendicular flights are affeCted by nothing but the initial * velocity and the refiftance of the air ; and a confiderable deviation from their intended direction does not caufe any fenfible error in the confequences which wre may draw from them for our purpofe. But we muft now proceed to the general problem, of ob- to determine the motion of a body projected in any di- lique pro- reCtion, and with any velocity. Our readers wall be-je<^10n* lieve beforehand that this muft be a difficult fubjeCt, wdien they fee thfe fimpleft cafes of reCtilineal motion abundantly abftrufe : it is indeed fo difficult, that Sir 7r Ifaac Newton has not given a folution of it, and has This pro¬ thought himfelf well employed in making feveral appro- ^em not ximations, in which the fertility of his genius appears ^non7 in great luftre. In the tenth and fubfequent propofi- tions of the fecond book of the Principia, he (hows what ftate of denfity in the air wall comport with the motion of a body in any curve wffiatever : and then, by apply¬ ing this difeovery to feveral curves which have fome fi- milarity to the path of a projeCtile, he finds one which is not very different from what we may fuppofe to ob¬ tain in our atmofphere. But even this approximation wTas involved in fuch intricate calculations, that it feemed impoflible to make any ufe of it. In the fecond edition of the Principia, publiffied in 1713, Newton correfts fome miftakes which he had committed in the firft, and car¬ ries his approximations much farther, but (till does not attempt a direCt inveftigation of the path which a body will deferibe in our atmofphere. This is fomewhat fur- prifing. In prop. 14. &c. he (hows how a body, actu¬ ated by a centripetal force, in a medium of a denfity varying according to certain laws, will deferibe an ec¬ centric fpiral, of which he affigns the properties, and the law of defeription. Had he fuppofed the denfity conftant, and the difference between the greateft and lead diftances from the centre of centripetal force ex¬ ceedingly fmall in comparifon with the diftances them¬ felves, his fpiral would have coincided with the path of a projeCtile in the air of uniform denfity, and the fteps of his inveftigation would have led him immediately to the complete folution of the problem. For this is the real ftate of the cafe. A heavy body is not aCted on by equal and parallel gravity, but by a gravity inverfely proportional to the fquare of the diftance from the centre of the earth, and in lines tending to that centre nearly ; and it was with the view of fimplifying the inveftigation, that mathematicians have adopted the other hypothefis. Soon after the publication of this fecond edition ofojfp^ the Principia, the difpute about the invention of the among fluxionary calculus became very violent, and the great and promoters of that calculus upon the continent were in tore‘£n the habit of propofing difficult problems to exercife the tidans^' talents of the mathematician. Challenges of this kind frequently pafled between the Britifli and foreigners. Dir 4H PROJECTILES. Dr Keill of Oxford had keenly efpoufed the claim of Sir Ifaac Newton to this invention, and had engaged in a very acrimonious altercation with the celebrated John Bernoulli of Bade. Bernoulli had publilhed in the Aftn F.ruditorum Lipjice an inveftigation of the law of forces, by which a body moving in a refilling medium might defcribe any propofed curve, reducing the whole to the llmplell geometry. This is perhaps the molt elegant fpecimen -which he has given of his great talents. Dr Keill propofed to him the particular problem of the trajectory and motion of a body moving through the air, as one of the molt difficult. Bernoulli very foon folved the problem in a way much more general than it bad been propofed, viz. without any limitation either of the law of reliitance, the law of the centripetal force, or the law of denfity, provided only that they were regular, and capable of being expreiTed algebraically. Dr Brook Taylor, the celebrated author of the Method of Incre¬ ments, folved it at the fame time, in the limited form in which it was propofed. Other authors lince that time have given other folutions. But they are all (as indeed they mull be) the fame in fubftance wuth Ber¬ noulli’s. Indeed they are all (Bernoulli’s not excepted) the fame with Newton’s firft approximations, modified by the fieps introduced into the inveftigation of the fpiral motions mentioned above ; and we Hill think it molt ftrange that Sir Ifaac did not perceive that the •variation of curvature, which he introduced in that in- velfigation, made the wffiole difference between his ap¬ proximations and the complete foiulion. This wTe ffiall point out as wTe go along. And \vt now proceed to the Bernoulli’s problem itfelf, of which we ffiall give Bernoulli’s folu- lolution. tion, reftriCted to the cafe of uniform denfity and a re- fiftance proportional to the fquare of the velocity. This folution is more fimple and perfpicuous than any that has fince appeared. Problem. To determine the trajeClory, and all the circumftances of the motion of a body projected ■Jog- 7- through the air from A (fig. 7.) in the direftion AB, and refilled in the duplicate ratio of the velocity. Let the arch AM be put rr £, the time of defcribing it /, the abfciffa APrr^, the ordinate PM =r y. Let the velocity in the point M=w, and let MNzz-z, be defcribed in the moment t; let r be the refill ance of the air, g the force of gravity, meafured by the ve¬ locity winch it will generate in a fecond ; and let a be the height through which a heavy body mull fall in va¬ cuo to acquire the velocity which would render the refillance of the air equal to its gravity : fo that we have r — becaufe, for any velocity u, and producing tP height h, we have g—~y. in Let M m touch the curve in M ; draw the ordinate jftN m, and draw7 M 0, N « perpendicular to N/> and M wl Then we have MNrrs, and Mo=«, alfo mo is ultimately — y and M m is ultimately — MN or 53. Laltly, let us fuppofe * to be a conlfant quantity, the ‘ttffion of elementary ordinates being fuppofed equidiftant. gravity in The aflion of gravity during the time t mav be a given meafured by m N, which is half the fpace which it tune. „ 1 would caufe the body to defcribe uniformly in the time t with the velocity which it generates in that time. Let this be refolved into «N, by which it defle&s the body into a curvilineal path, and tnn, by which it retards the afeent and accelerates the defeent of the body along the tangent. The refinance of the air afts folely in retard¬ ing the motion, both in afeending and defeending, and has no defleftive tendency. The whole adlion of gra¬ vity then is to it5 accelerating or retarding tendency as m N to m A, or (by fimilarity of triangles) as m M to mo. Ot cz?L\ y — g \ and the whole retardation in 2; pry the afeent wall be r-|- The fame fluxionary fymbol z will exprefs the retardation during the defeent, becaufe in the defeent the ordinates decreafe, and ^ is a negative quantity. The diminution of velocity is — v. This is propor¬ tional to the retarding force and to the time of its adlion jointly, and therefore — v = r-j- f- X t; but the time /is as the fpace 2; divided by the velocity v; therefore rz+gy x —, = — * — v — r X - ind vv • • v* % • rz—gy — —— gy. Becaufe 772N is the deflexion by gravity, it is as the force ^ and the fquare of the time t jointly (the momentary action being held as uniform). We have therefore 772N, or —y—gtz. (Obferve that 772 N is in fa£t only the half of — y ; but g being twice the fall of a heavy body in a fecond, we have — y itrift- ly equal to p-P). But t*—^- : therefore — w— JUL vz v'- P •• • and v*zz and — v* y = g z*. The fluxion of —y this equation is — vz y — Ivy v — 2gz z ; but, be¬ caufe 2; : y = mM : m 0, — mN : mn, —y: 25, we have 2; z—yy. Therefore 2gy y— 2g % —v'y— 2vy vy and — 2 v v y = vzy, — 2gy ij, and —~ • ty* 'll * -f-i • vv — —i- —gy. But we have already —■ v v — 2y •gy; therefore y v* z and finally V 2a y a y ox ay =z z y, for the fluxionary equation of the curve. If we put this into the form of a proportion, we Relation have 22 : 2 = y.y. Now7 this evidently eftabliflies a re- theTength lation between the length of the curve and its variation of the of curvature ; and between the curve itfelf and its evo- ' UIve luta, which are the very circumftances introduced by Newton curvature. P R O J E Newton into his invefligatxon of the fpiral motions. And the equation-fL—iL ih evidently an equation conneft- a y ed with the logarithmic curve and the logarithmic fpiral. But we muft endeavour to reduce it to a lower order of fluxions, betore we can eftablith a relation between ss, x, and y. Let p exprefs the ratio of y to a?, that is, let /> be =: ?/ • • # # 4-, ox p x ~ y. It is evident that this expreffes the x inclination of the tangent at M to the horizon, and that p is the tangent of this inclination, radius being unity. Or it may be confldered merely as a number, multiply¬ ing a?, fo as to make \l~y. We now have rr />3 w3, and fince :z2 ~ w3-f-we have z3 zr xl -{- ^3»3, rr l +/>J X and % — xsji /j3. Moreover, becaufe we have fuppofed the abfcifla x to increafe uniformly, and therefore x to be conftant, We have y — x p, andy — x p. Now let q exprefs the ratio of p to jc, that is, make ~ ~ q, or q x — p, x This gives us « y rr p, and x2 q — x p, — y. By thefe fubftitutions our former equation ay ~ % y changes to a x2 q — x ^7 i -f pz \ x p, ox a y —p kJx and, taking the fluent on both Tides, we have a q —J p sji+/>2+C, C being the conftant quantity required for completing the fluent according to the li¬ miting conditions of the cafe. Now x — -71, and 7. — q . q ap f'TZr, Therefore x p s/1 +Pt\ + C " J ^v'x-f^J-l-C Alfc, fince y — p x, — ~, we have y rr q f app p \!1 +/,:!| ~f* c Alfo z — x sji -f-pl ~ ap J i-f^3 ^n/i+^I+C The values of #, y, z, give us — C aP -f f p i -r/'i + C f "p __ f ap'p ■£ pp •f* b k.! 14- />3i + C’ ^ •f' p i ^ 1 + P2\ + ^^1 a J7+p\p _ f ps/i+p* f = f as/y-\-pYp pJ1 4- ’Z' j, v/i4-/,2l 4-c’'_ ^P v/H^l4-C The procefs therefore of defcribing the traje£lory is, xjl. To find q in terms of p by the area of the curve whofe abfciffa is p and the ordinate is sj\ -j-/>3* C T I L E S. ' 4r5 2d, We get x by the area of another curve whofe. abfciffa is p, and the ordinate is 3d, We get y by the area of a third curve whofe ab¬ fciffa is />, and the ordinate is <1 The problem of the trajectory is therefore complete¬ ly folved, becaufe we have determined the ordinate, ab¬ fciffa, and arch of the curve for any given nofition of ^ ^ ns tangent. It now only remains to compute the mag-pUte niLudes of thefe ordinates and abfciffse, or to draw them magnitude by a geometiical conftruction. But in this confifts theot thf: ordt- difficulty. The areas of thefe curves, which exprefs theIiaj:e ^.rid lengths of x and y, can neither be computed nor exhi-*3 CU ‘ bited geometrically, by'any accurate method yet difeo- vered, and we muft content ourfelves with approxima¬ tions. Thefe render the defeription of the trajeftory ex¬ ceedingly difficult and tedious, fo that little advantage has as yet been derived from the knowledge we have got of its properties. It will however greatly aftift our con¬ ception of the fubject to proceed forne length in this conftru&ion ; for it muft be acknowledged that very fewr diftindt notions accompany a mere algebraic opera¬ tion, efpecially if in any degree complicated, which we confefs is the cafe in the prefent queifion. Let B m NR (fig. 8.) be an equilateral hyperbola, ofIT which B is the vertex, BA the femitranfverfe axis, ‘ which wre (hall affume for the unity of length. Let AV be the femiconjugate axis — BA, — unity, and AS the aflymptote, bifefting the right angle BAY. Let PN, p n be two ordinates to the conjugate axis, exceedingly near to each other. Join BP, AN, and draw' B/3, Nv perpendicular to the affymptote, and BC parallel to AP. It is wrell known that BP is equal to NP. Therefore PN3 — BA1 + AP3. Now fince BA — i, if we make AP —/) of our formulae, PN is >^/i -f-/;3, and P/> is = />, and the area BAPNB = f P sj 1 -\-pl \ '■ That is to fay, the number^ p i-}-/>3 (for it is a number) has the fame proportion to unity of number that the area BAPNB has to BCVA, the unit of furface. This area confifts of two parts, the triangle APN, and the hyperbolic fe&or ABN. APN = \ AP x PN, — teAZi, and the hyperbolic feflor ABNrrBNA, which is equivalent to the hyperbolic logarithm of the number reprefented by A sr when A /3 is unity. There¬ fore it is equal to i the logarithm of p -j_ VV-J../.) ’% Hence we fee by the bye that p •s/1 -|-/)3 err p V^i 4~/ji 4- 4 hyperbolic logarithm p -\-\/\ -{-/./• Now let AMD be another curve, ftich that its ordi¬ nates V««, PD, &c. may be proportional to the areas AB m V, ABNP, and may ha'vT the fame proportion to AB, the unity of length, which thefe areas have to ABCV, the unity of iiirface. Then VM : VC err" Vm BA : YXBA, and PD : P^ ere PNBA : VCBA, &c. Thefe ordinates will now re prefent p 1+7* with reference to a linear unit, as the areas to the hyperbola reprefented it in reference to a Ihjjerficiai unit. Again, 4t6 PROJECTILES. Fig. 7. Fig. S. Again, in every ordinate make PD : P 5 = P £ : PO, and thus we obtain a reciprocal to PD, or to T, or equivalent to f —1 This J * p \ +/>* X •A/ will evidently be -r-, and PO op will be and the area ap a contained between the lines AF, AW, and the curve GEOH, and eut off by the ordinate PO, will reprefent x a Laftly, make PO : PQnAV : AP, = 1 : /> j and then P£) will reprefent and the areai- ALEQP will reprefent a But we muft here obferve, that the fluents exprefled by thefe different areas require what is called the cor- reElion to accommodate them to the circumftances of the cafe. It is not indifferent from what ordinate we begin to reckon the areas. This depends on the initial dire&ion of the projectile, and that point of the abfcif- fa AP muff be taken for the commencement of all the areas which gives a value of p fuited to the initial di¬ rection. Thus, if the projection has been made from A (fig. 7.) at an elevation of 450, the ratio of the fluxions x and y is that of equality ; and therefore the point E of fig. 8. where the two curves interfeCt and have a common ordinate, evidently correfponds to this condition. The ordinate EV pafles through V, fo that AV ox p— AB, zz: 1, =z tangent 450, as the cafe re¬ quires. The values of x and of y correfponding to any other point of the trajeftory, fuch as that which has AP for the tangent of the angle which it makes with the horizon, are now to be had by computing the areas VEOP, VEQP. Another curve might have been added, of which the ordinates would exhibit the fluxions of the arch of the trajeClory z ^1 ^ and of which the area And this would have p x/ i+/>1 17 Confequen- ces of knowing the form ef the tra¬ jectory. defcribe fimilar trajectories if the velocities are in the fubduplicate ratio of the diameters. This we (hall find 78 to be of confiderable practical importance. But let usTodeter- now proceed to determine the velocity in the different m‘ne .t*ie. points of the trajeCtory, and the time of defcribing its fe- j-0° veral portions. points. Recoiled, therefore, that t)* =z —~—, and that 2* 2 . = ar*! -f- p* and y — x p. This gives v'z —gx 1 +/>* Therefore v* X 1 +/>* _ p \/ 1 -f-/1 + c and v^JzzU. ±JL, = V a \/—S\/1 + /,i p /JI+/I + C Alfo t was found zz: —, zz x s/ '+P* _ P s/i 4- />* qv If we now fubftitute for v its value juft found, we obtain t =r ——, P \/ a and t =fj- \/ a sj —g' /> v/l+/>1+C 79 would exhibit the arch itfelf. been very eafy, for it is » z= .. . P s/1 ~\rp1 i + C, which is evidently the fluxion of the hyperbolic loga¬ rithm of P\/l+P'\- But it is needlefs, fince 2 zz x >y/i -f-/)1, and we have already got x. It is only in- creafing PO in the ratio of BA to BP. And thus we have brought the inveftigation of this pro¬ blem a confiderable length, having afcertained the form of the trajedory. This is furely done when the ratio of the arch, abfcifs, and ordinate, and the pofition of its tan¬ gent, is determined in every point. But it is ftill very far from a fcdution, and much remains to be done before we can make any pradical application of it. The only general confequence that we can deduce from the premi- fes is, that in every cafe where the refiftance in any point bears the fame proportion to the force of gravity, the trajedory will be fimilar. Therefore, two balls, of the fame denfity, projeded in the fame diredion, will 4 The greateft difficulty ftill remains, viz. the accom- ulty modating thefe formulae, which appear abundantly lim- ^cact';m‘ pie, to the particular cafes. It would feem at firft ^ pf fight, that all trajedories are fimilar 5 fince the ratio ofj^ to par- the fluxions of the ordinate and abfciffa correfponding to ticular any particular angle of inclination to the horizon feemscafes- the fame in them all: but a due attention to what has been hitherto faid on the fubjed will ffiow us that we have as yet only been able to afcertain the velocity in the point of the trajedory, which has a certain inclina¬ tion to the horizon, indicated by the quantity />, and the time (reckoned from fome affigned beginning) when the projedile is in that point. To obtain abfolute meafures of thefe quantities, the term of commencement muft be fixed upon. This will be exprelfed by the conftant quantity C, which is affumed for completing the fluent oip 1 +p% which is the bafis of the whole conftrudion. We there found q~ 9P \/ 1 +PZ This fluent is in general q zz C+oZ’ pJ'^rP1 and the conftant quantity C is to be accommodated to fome circumftances of the cafe. Different authors have feleded different circumftances. Euler, thod the funpieit rig. 5. « x PROJECTI So Euler, in his Commentary on Robins, and in a differta- Euler’s me. t;on jn Memoirs of the Academy of Berlin publifh- thnrl , r . J r . ■r . ed in 1753, takes the vertex or the curve for the begin¬ ning of his ablciffa and ordinate. This is the limpleft method of any, for C muft then be fo chofen that the whole fluent may vanifli when/)—0, which is the cafe in the. vertex of the curve, where the tangent is parallel to the horizon. We flial! adopt this method. Therefore, let AP (fig. 9.) —v, PMzry, AM —2;. Put the quantity C which is introduced into the fluent 11 equal to -. It is plain that n mufl be a number ; for L e s. »/> \/1 -f- />* 417 fill: J n— height producing the velocity at N — and the *—P Sr it muft be homologous with /> 1 -f- />z, which is a number. For brevity’s fake let us exprefs the fluent of /> a/x -f/>* by the lingle letter P; and thus we ftiall P rPP have a X - / Afr’ y = “ xA+p-,a!=‘' And - - '—“Sll + P) X . _ _ Now the n 4- P « -j- P height h neceffary for communicating any velocity v is __4£(i±A) 2^(«+P) : i p gJ \/ •j-g (I-[-/>»). « + /’ And laftly, Thefe fluents, being all taken fo as to vanifli at the vertex, where the computation commences, and where p\s — 0 (the tangent being parallel to the horizon), we obtain in this cafe h — — — and n — —. n 2>i 2h Hence rve fee that the circumftance which modifies all the curves, diftinguifhing them from each other, is the velocity (or rather its fquare) in the highelt point of the curve. For h being determined for any body whofe terminal velocity is u, n is alfo determined ; and this is the modifying circumftance. Confidering it geo¬ metrically, it is the area which muft be cut off from the area DMAP of fig. 8. in order to determine the ordinates of the other cuives. We muft farther remark, that the values now given relate only to that part of the area where the body is defcending from the vertex. This is evident ; for, in order that y may increafe as we recede from the vertex, its fluxion muft be taken in the oppofite fenfe to what it was in our inveftigation. There we fuppofed y to in¬ creafe as the body afcended, and then to diminifh during the defcent; and therefore the fluxion of y was firft po- fitive and then negative. The fame equations, however, will ferve for the afccnding branch CNA of the curve, only changing the fign of P } for if we confider y as decreafing during Hence we learn by the bye, that in no part of theRermrk- afcending branch can the inclination of the tangent be^lcpio- fuch that P fhall be greater than n ; and that if ,ve flip-1>erty of tlie pofe P equal to n in any point of the curve, the velo-f^paorv. city in that point will be infinite. That is to fay, there ‘ ' is a certain aflignable elevation of the tangent which cannot be exceeded in a curve which has this elocity in the vertex. The belt way for forming a conception of this circumftance in the nature of the curve, is to invert the motion, and fuppofe an accelerating force, equal and oppofite to the refiftance, to acl on the body in conjunftion with gravity. It muft defcribe the fame curve, and this branch ANC muft have an affymptote LO, which has this limiting pofition of the tangent. For, as the body defcends in this curve, its velocity increafes to infinity by the joint aclion of gravity and this accelerating force, and yet the tangent never ap¬ proaches fo near the perpendicular pofition as to make P—This remarkable property of the curve wras known to Newton, as appears by his approximations, which all lead him to cuives of a hyperbolic form, ha¬ ying one aflymptote inclined to the horizon. Indeed it is pretty obvious: For the refiftance increafing fafter than the velocity, there is no velocity of projeilion fo great but that the curve will come to deviate fo from the tangent, that in a finite time it will become pa¬ rallel to the horizon. Were the refiftance proportional to the velocity, then an infinite velocity would produce a redilineal motion, or rather a defledion from it lefs than any that can be afligned. We now fee that the particular form and magnitude on what- of this trajedory depends on two circumftances, a and Its form and n. <7 affeds chiefly the magnitude. Another eircum- ma^niuide fiance might indeed be taken in, viz. the diminution ofdePends- the accelerating force of gravity by the fiatical efted of the air’s gravity. But, as w e have already obferved, this is too trifling to be attended to in military projediles. y — was made equal to />. Therefore the ra- x >• dius of curvature, determined by the ordinary me- tfindc tc ^ C1+/,z) (v/1+/)Z) * j , r x . thods, is 7 *, and, becaufe ~ is * Simpfon's P P Fluxions, — ~pp f°r ^ie defcending branch of the curve, the" 6S’ radius of curvature at M is ^, and, tf-f-P the afcent, we muft confider q as exprefling —and in the afcending branch at N, it is ———- ^ ^ nges of a gun by theory, but the theory by the range of the gun. Now the variety and irregularity of all the experiments which are appealed to are fo great, and the acknowledged difference between the refinance to flow and fwift motions is alfo fo great, that there is hardly any fuppofition which can he made concerning the refiilance, that will not agree in its re- fults with many of thofe experiments. 1c appears from the experiments of Dr Hutton of Woolwich, in 1784, 1*785, and 1786, that the (hots frequently deviated to the right or left of their intended track 200, 300, and fometimes 400 yards. This deviation was quite acci¬ dental and anomalous, and there can be no doubt but that the fliot deviated from its intended and fuppofed elevation as much as it deviated from the intended ver¬ tical plane, and this without any opportunity of mea- furing or difeovering the deviation. Now, when we have the wdrole range from one to three to choofe among for our meafiu-e of refiflartce, it is evident that the con¬ firmations which have been drawn from the ranges of fliot are but feeble arguments for the truth of any opi¬ nion. Mr Robins finds his meafures fully confirmed by the experiments at Metz and at Minorca. Mr Muller finds the fame. Yet Mr Robins’s meafure both of the initial velocity and of the refiilance are at leafl treble of Mr Muller’s j but by compenfation they give the fame refults. The Chevalier Borda, a very expert mathematician, has adduced the very fame experiments in fupport of his theory, in which he abides by the Newtonian meafure of the refiftance, which is about -5- of Mr Robins’s, and about | of Muller’s. What are we to conclude from ail this ? Simply this, that we have hardly any knowledge of the air’s refift¬ ance, and that even the folution given of this problem has not as yet greatly increafed it. Our knowledge con- lifts only in thofe experiments, and mathematicians are attempting to patch up fome notion of the motion of a body in a refilling medium, which fhall tally with them. There is another effential deleft in the conditions af¬ firmed in the folution. The denfity of the air is fup¬ pofed uniform \ whereas wTe are certain that it is lefs by one-fifth or one-fixth towards the vertex of the curve, in many cafes which frequently occur, than it is at the beginning and end of the flight. This is ano¬ ther latitude given to authors in their affumptions of the air’s refiftance. The Chevalier de Borda has, with tonfiderable ingenuity, accommodated his inveftigation to tills circumftance, by dividing the trajedlory into portions, and, without much trouble, has made one equation anfwer them all, We are difpofed to think that his folution of the problem (in the Memoirs of the Academy of Paris for 1769) correfponds better with the phyfical circumftances of the cafe than any other. But this procefs is there delivered in too concife a man¬ ner to be intelligible to a perfon not nerfeclly familiar with ail the refources of modern analyfis. We there¬ fore preferred John Bernoulli’s, became it is elementary and rigorous. 91 After all, the practical artillerift rnuft rely chiefly on Necetiity of the records of experiments contained in the books of practice at the academies, or thofe made in a more pub-U lie manner. Even a perledl theory of the air’s refift¬ ance can do him little lervice, unlefs the force of gun¬ powder were uniform. This is far from being the cafe even in the fame powder. A few hours of a damp day will make a greater difference than occurs in any theo¬ ry ; and, in fervice, it is only by trial that every thing is performed. If the firft ftiell fall very much ihort of the mark, a little more powder is added ; and, in cannon¬ ading, the correction is made by varying the elevation. We hope to be forgiven by the eminent mathemati¬ cians for thefe obfervations on their theories. They by no means proceed from any difrefpect for their labours. We are hot ignorant of the almoft infuperable difficul¬ ty of the talk, and we admire the ingenuity with which fome of them have contrived to introduce into their ana¬ lyfis reafonable fubftituiions for thofe terms which would render the equations intractable. But we mull Hill fay, upon their own authority, that thefe are but inge¬ nious gueffes, and that experiment is the touchftone by which they mould, thefe fubllitutions 5 and when they have found a coincidence, they have no motive to make any alteration. Now, when we have fuch a latitude for our meafure of the air’s- refiilance,- that we may take if. of any value, from one to three, it is no w'onder that compenfations of errors ftiould produce a coincidence ; but where is the coincidence ? The theorift fuppofes the ball to fet out with a certain velocity, and his theory gives a certain range : and this range agrees with obfer- vation—but how ? Who knows the velocity of the bail in the experiment ? This is concluded from a theory in¬ comparably more uncertain than that of the motion in a refilling medium. The experiments of Mr Robins and Dr Hutton ftrow, in the molt incontrovertible manner, that the refiilance to a motion exceeding 1100 feet in a feconcl, is almoft three times greater than in the duplicate ratio to the re¬ fiftance to moderate velocities. Euler’s tranflator, in his comparifon of the author’s trajeflories with experi¬ ment fuppofes it to be no greater. Yet the coincidence is very great. -The fame may be faid of the Chevalier de Borda’s. Nay, the fame may be faid of Mr Ro¬ bins’s own practical rules : for he makes his F, which correfponds to our almoft double of what thefe au¬ thors do, and yet his rules are confirmed by practice. Our obfervations are therefore well founded. But it mull not be inferred from all this, that the yhe'theory phyfical theory is of no ufe to the praflical artillerift. is ftill of It plainly {hows him the impropriety of giving the pro- fome ufe in jeciile an enormous velocity. This velocity is of no ef Plaice, fe£t after 200 or 330 yards at fartheft, becaufe u it to rapidly reduced by the prodigious refiftance of the air. Mr Robins has deduced feveral practical maxims of the greateft importance from what we already know of this ful ft eft, and wftiich could hardly have been even conjec¬ tured without this knowledge. See Gunnery. And 422 PROJECTILES. 93 And it mud: dill 4e acknowledged, that this branch hrou"hT cT Phyfical ^c'ence highly interefting to the philofo- fjreater per- i nor Should we defpair of carrying it to greater teetion. perfection. The defeits arife almott entirely from our ignorance of the law of variation of the air’s refiitance. Experiments may be contrived much more conducive to our information here than thofe commonly relorted to. The oblique flights of projeftiles are, as we have feen, of very complicated inveftigation, and ill fitted for initrudling us; but numerous and well contrived expe¬ riments on the perpendicular afeents are of great fim- plicity, being affected by nothing but the air’s refin¬ ance. To make them inftrudfive, we think that the following plan might be purfued. Let a let of expe¬ riments be premifed for afeertaining the initial veloci¬ ties. Then let fhells be difeharged perpendicularly with great varieties of denfity. and velocity, and let no¬ thing be attended to but the height and the time •, even a confiderable deviation from the perpendicular will not alfefl either of thefe circumftances, and the effect of this circumflance can eafily be computed. The height can be afeertained with fufficient precifion for very va¬ luable information by their light or fmoke. It is evi¬ dent that thefe experiments will give direB informa¬ tion of the air’s retarding force j and every experiment gives us two meafures, viz. the afeent and defeent: and the comparifon of the times of afeent and defeent, com¬ bined with the obferved height in one experiment made with a great initial velocity, will give us more informa¬ tion concerning the air's refiflance than 50 ranges. If rve Ihould fuppofe the refiflance as the fquare of the ve¬ locity, this comparifon will give in each experiment an exaft determination of the initial and final velocities, which no other method can give us. Thefe, with ex¬ periments on the time of horizontal flights, with known initial velocities, will give us more inftruftion on this head than any thing that has yet been done; and till fomething of this kind is carefully done, we prefume to fay that the motion of bodies in a refilling medium will remain in the hands of the mathematicians as a matter of curious {peculation. In the mean time, the rules which Mr Robins has delivered in his Gunnery are very fimple and eafy in their ufe, and feem to come as near the truth as any we have met with. He has not informed us upon what principles they are founded, and we are difpofed to think that they are rather em¬ pirical than fcientific. But we profefs great deference for his abilities and penetration, and doubt not but that he had framed them by means of as fcientific a difeuf- fion as his knowledge of this new and difficult fuhjedl 94 enabled him to give it. Tables cal- We lhall conclude this article, by giving two or three th^rece" ';a^es’ cornPut-e(l from the principles effablifhed above, ding1 fain- an<^ which ferve to bring into one point of view' the piples. chief circumftances of the motion in a refilling medium. Although the refult of much calculation, as any perfon who confiders the fubjeft will readily fee, they muft not be confidered as offering any very accurate refults; or that, in comparifon with one or two experiments, the differen¬ ces ffiall not be confiderable. Let any perfon perufe the publithed regifters of experiment? which have been made with every attention, and he will fee fuch enormous irre¬ gularities, that all expectations of perfeft agreement with them muft ceafe. In the experiments at Woolwich in J 7 3 which were continued for feveraldays, not only do 3 the experiments of one day differ among themfelves, but the meqn of all the experiments of one day differs from the mean of all the experiments of another no lefs than one fourth of the whole. The experiments in which the greateft regularity ipay be expeCled, are thofe made with great elevations. When the elevation is fmall, the range is more affeCled by a change of velocity, and ftill more by any deviation from the fuppofed or intended di¬ rection of the {hot. The firft table ftiorvs the diftance rn yards to wffiich a ball projected with the velocity 1600 will go, while its velocity is reduced one-tenth, and the diftance at which it drops 16 feet from the line of its direction. This table is calculated by the reftfbnce obferved in Mr Robins’s experiments. The firft column is the weight of the ball in pounds. The feco>d column remains the fame whatever be the initial velocity j but the third co¬ lumn depends on the velocity. It is here given for the velocity which is very ufual in military fervice, and its ufe is to affift us in dire Clin? the gun to the mark.—■ If the mark at which a ball of 24 pounds is directed is 474 yards diftant, the axis of the piece muft be pointed 16 feet higher than the mark. Thefe defieCtions from the line of direction are neatly as the fquares of the diftances. The next table contains the ranges in yards of a 2 pound fliot, proieCted at an elevation cf 450, with the different velocities in feet per fecond, expreffed in the firit column. The fecond column contains the diftances to which the ball would go in vacuo in a horizontal plane ; and the third contains the diftances to which it. will go through the air. The fourth column is added, to ff’.ow the height to which it rifes in the air ; and the fifth fliows the ranges correCted for the diminution of the air’s denfity as the bullet afeends, and may therefore be called the correBed range. I. 200 400 600 800 ICOO I 200 I4OO I60O 1800 2000 2200 24OO 2(500 2800 3000 3200 II. 416 1664 3740 6649 IO3OO 14961 20364 26597 4r559 50286 59846 III. 349 1121 1812 2373 2845 3259 3640 3950 4235 4494 4720 4917 5106 5293 5455 IV. V. 106 33 8 606 866 1138 13'78 1606 1814 1992 2168 2348 2460 2630 2762 2862 3 60 11 ;o i859 2435 2919 3343 3734 4050 4345 46x0 4842 5°44 5238 543° 5596 5732 The 'St#'* y, o 42 3; PRO J E The initial velocities caft never be puflied as far as Jfeoftbe we have calculated for in this table 5 but we mean it latt table, for a table of more extenfive ufe than appears at firit fight. Recolleft, that while the proportion of the ve¬ locity at the vertex to the terminal velocity remains the fame, the curves will be fimilar : therefore, it the initial velocities are as the fquare-roots of the diameters of the balls, they will defcribe fimilar curves, and the ranges ■will be as the diameters of the balls. Therefore^ to have the range of a 1 2 pound (hot, if f rojedled at an elevation of 45, with the velocity 1 500 ; fuppofe the diameter of the 1 2 pounder to be d, and that of the 24 pounder D j and let the velocities be v and V : Then fay, s/d \ ,J!5 — x 500, to a fourth proportional V. If the 24 pounder be projefted with the velocity V, it will defcribe a curve fimilar to that defcribed by the 1 2 pounder, having the initial velocity 1 500. Therefore find (by interpolation) the range of the 24 pounder, having the initial velocity V. Call this R. Then D : or axis DA, is the fcale of the initial.velocities in feet per fecond, meafured on a fcale of 400 equal parts in Relation of an inch. The ordinates to the curve ACG exprefs the1*16 ‘hff6- yards of the range on a fcale containing 800 yards in [■p^YoTt* an inch. The ordinates to the curve Axy exprefs (by the fame fcale) the height to which the ball rifes in the air. The ordinate BC (drawn through the point of the abfeiffa which cerrefponds to the initial velocity 2000) is divided in the points 4, 9, 12, x 8, 24, 32, 42, in the ratio of the diameters ofcannon-fhot of different weights ^ and the fame ordinate is produced on the other fide of the axis, till BO be equal to BA ; and then BO is divided in the fubduplicate ratio of the fame diameters. Lines are drawn from the point A, and from any point D of the abfeiffa, to thefe divifions. We fee diftinftly by this figure how the effeCt of the initial velocity gradually diminifhes, and that in very great velocities the range is very little increafed by its augmentation. The dotted curve APQR, (hows what the ranges in vacuo would be. By this figure may the problems be folved. Thus, to find the range of the 12 pounder, with the initial velocity 1500. Set off 15CO from B to F ; draw FH parallel to the axis, meeting the line i2Ain H; draw the ordinate HK ; draw KL parallel to the axis, meet¬ ing 24 B in L •, draw the ordinate LM, cutting 12 B in N. MN is the range required. If curves, fuch as ACG, were laid down in the fame manner for other elevations, all the problems might be folved with great difpatch, and with much more accu¬ racy than the theory by which the curves are drawn can pretend to. Note, that Jig. 10. as given on P/ate CCCCXLII. is one-Jui/f lefs than the fcale according to which it is defcribed; but the prafiical mathematician xvill find no difficulty in drawing the figure on the enlargedficale to f jrrefipond to the dej'cription. PROJECTION OF THE SPHERE. Siereogra. -pIIE PROJECTION of tlie SPHERE IS il peifpeftlve phic Pro- l peprefentation of the circles on the fur 1 ace of the jedtion of p ! anci ;s vanou(ly denominated according to the the Sphere, pofltJons 0f the eye and plane of projeffton. There are three principal kinds of projection •, the fiereographic, the orthographic, and gnomic. In the ftereoeraohic proje&ion the eye is fuppofed to be placed on the furface of the fphere ; in the orthographic it is fuopofed to be at an infinite diftance 5 and in the gno¬ mic projeflion the eye is placed at the centre of t. e fphere. Other kinds of projeftion are, the globular, Mercator"1 s, ficenographic, &c. for which fee the c-.rtmles Geography, Navigation, Perspective, &c. Definitions. 1. The plane upon which the circles of the fphere are deferibed, is called the p ane ofi projection, qx the primitive circle. The pole of this circle is the pole Stereogra- of projection, and the place of the eye is the projecting nhic Pro- point. _ ' . 2. The line ofimeafiures of any circle of the fphere is ttK P Kre ^ that diameter of the primitive, produced indefinitely, which paffes through the centre of the projected circle. Axiom. The projection, or reprefentation of any point, is where the (freight line drawn from it to the pro¬ jecting point interfeCls the plane of projection. SECTION I. Ofi the Stcresgraphic Projection of the Sphere. In the fiereographic projection of the fphere, the eye m PROJECTION OF Stereo.;ra- eye is placed on the flirface cf the fphere in the pole oi J.hir Fro- (_he great circle upon which the fphere is to be projeft- the S°b>rc' ° hhe projedlion of the hemifphere oppofile to the ,tu r('f-ye falls within the primi'.ive, to which the projection is generally limited*, it, however, may be extended to the ether hemifphere, or that wherein the eye is placed, the projeftion of which falls without the primitive. As ail circles in this projection are projected either into circles or ftraight lines, which are ealily dcoribed, it is therefore more generally underftood, and by many ■preferred to the other projections. Proposition I. Theorem I. THE SPHERE. Sedion I. But if the circle MN (fig. 2.) be not parallel to the Suneogra- primitive circle ED, let the great circle ABCD, paf- ! fing through the projecting point, cut it at right angles tJJie Sphere, in the diameter MN, and the primitive in the diameter ——v ■ _/ BD. Through M, in the plane of the,great circle, let Fig. a. MF be drawn parallel to BD ; let AM, AN be joined, and meet BD in m, n. J hen, becaufe AB, AD are quadrants, and BD, MF parallel, the arch AM is equal to AF, and the angle AMF or A mn is equal to ANM. Hence the conic lurface delcribed by the revolution of AM about the circle MN is cut by the primitive in a fubcontrary pofition j therefore the lection is in this cafe likevvife a circle. Every great circle which paffes through the projecting point is projected into a ftraight line palling through the centre of the primitive*, and every arch of it, reckoned from the other pole of the primitive, is pro¬ jected into its femitangent. ccccxliii. Let ABCD (fig. i.) be a great circle palling through Fig. i. A, C, the poles of the primitive, and interfering it in the line of common feClion BED, E being the centre of the fphere. From A, the projecting point, let there be drawn ftraight lines AP, AM, AN, AO, to any number of points P, M, N, Q, in the circle Ar>CD : thefe lines will interfeCt BED, which is in the fame plane with them. Let them meet it in the points /*, w, «, q; then/>, m, n, q, are the projections of P, M, N, : hence the whole circle ABCD is projected into the Itraight line BED, palling through the centre of the primitive. Again, becaufe the pole C is projected into E, and the point M into m \ therefore the arch CM is project¬ ed into the ftraight line E m, which is the femitan¬ gent of the arch CM to the radius AE. In like man¬ ner, the arch CP is projected into its femitangent, E />, &c. Corollaries. 1. Each of the quadrants contiguous to the project¬ ing point is projected into an indefinite ftraight line, and each of thole that are remote into a radius of the primitive. 2. Every fmall circle which paffes through the pro¬ jecting point is projected into that ftraight line which is its common feCtion with the primitive. 3. Every ftraight line in the plane of the primitive, and produced indefinitely, is the projection of fome circle on the fphere paffing through the projecting point. 4. The projection of any point in the furface of the fphere, is diftant from the centre of the primitive, by the femitangent of the diftance of that point from the pole oppofite to the projecting point. Proposition II. Theorem II. Every circle on the fphere which does not pafs through the projecting point is projected into a circle. If the given circle be parallel !o the primitive, then a ftraight line drawn from the projecting point to any point in the circumference, and made to revolve about the circle, will deferihe the furface of a cone *, which being cut by the plane of projection para-b-i : o the bafe, the feCtion will be a circle.- See CONIC-Sethons. 2 Corollaries. 1. The centres and poles of all circles parallel to the primitive have their projection in its centre. 2. rJ he centre and poles of every circle inclined to the primitive have their projections in the line oi mea- fures. 3. All projected great circles cut the primitive in two points diametrically oppofite ; and every circle in the plane of projection, which paftes through the extre¬ mities of a diameter of the primitive, or through the projections of twm points that are diametr r ally oppo¬ fite on the fphere, is the projection of fome great circle. 4. A tangent to any circle of the fphere, which does not pafs through the projecting point, is projected into a tangent to that circle’s projection 5 alfo, the circular projections of tangent circles touch one another. 5. The extremities of the diameter, on the line of meafures of any projected circle, are diftant from the centre of the primitive by the femitangents of the leaft and greateft diftances of the circle on the fphere, from the pole oppofite to the projecting point. 6. The extremities of the diameter, on the line of meafures of any projected great circle, are diftant from the centre of the primitive by the tangent and cotan¬ gent of half the great circle's inclination to the primi¬ tive. 7. The radius of any projeCted circle is equal to half the fum, or half the difference of the femitangents of the leaft and greateft diftances of the circle from the pole oppofite to the projeCling point, according as that pole is within or without the given circle. Proposition III. Theorem III. An angle formed by two tangents at the fame point in the furface of the fphere, is equal to the angle formed by their projeClions. Let EG I and GH (fig. 3.) be the tw*o tangents, Fig. 3. and A the projecting point*, let the plane AGE cut the fphere in the circle AGE, and the primitive in the line BML. Alfo, let MN be the line of common fec- tion of the p1ane AGH with the primitive : then the angle FGH=LMN If the plane FGH be parallel to the primitive BLD, the propofition is manifeft. If not, through any point K in AG produced, let the plant FKPi, parallel to the primitive, be extended to meet FCH : • the line FH. Then, fcecaufi* the plane AGF meets t. e iv o parallel planes BED, FKH, the lines of common feCtion LM, FK are parallel 5 there- Section I. PROJECTION OF THE SPHERE. Stereogra- fore the angle AMLrrAKF. But fince A is the 'edlion of poIe t^e chords, and confequently the arches tJhe Sphere. ^ are ecluah and the arch AEG is the fum of ’ v*—w the arches AL, BG ; hence the angle AML is equal loan angle at the circumference Banding upon AG, and therefore equal to AGI or FGK ; confequently the angle FGKizrFKG, and the fide FG=:FK. In like manner HG—HK : hence the triangles GHF, KHF are equal, and the angle FGH—FKHzzLMN. 4-5 rraNHGrrNCG: hence ENC=INE + INC~NCG Stereogra- -f-INC—a right angle; and therefore NC is a tan-. Pietro, gent to the primitive at N ; but the arch ND is the^f s^ere difiance of the lefs circle from its neareft pole TV . . hence NC is the tangent, and EC the fecant of the difiance of the lefs circle from its pole to the radius of the primitive. Proposition VI. Theorem VI. Corollaries. 1. An angle contained by any two circles of the fphere is equal to the angle formed by theiij projec¬ tions. For the tangents to thefe circles on the fphere are projected into ftraight lines, which either coincide with, or are tangents to, their projections on the primi¬ tive. 2. An angle contained by any two circles of the fphere is equal to the angle formed by the radii of their projedfion? at the point of interfe&ion. Proposition IV. Theorem IV. The centre of a prqjedled great circle is diftant from the centre of the primitive ; the tangent of the incli¬ nation of the great circle to the primitive, and its ra¬ dius, is the fecant of its inclination. Fig. 4. Let MNG (fig. 4.) be the projedlion of a great circle, meeting the primitive in the extremities of the diameter MN, and let the diameter BD, perpendicular to MN, meet the projedlion in F, G. Bifedl FG in H, and join NH. Then, becaufe any angle contained by two circles of the fphere is equal to the angle formed by the radii of their projections at the point of interfec- tion; therefore the angle contained by the propofed great circle and the primitive is equal to the angle ENH, of which EH is the tangent, and NH the fe¬ cant, to the radius of the primitive. The projeftion of the poles of any circle, inclined to the primitive, are, in the line of meafures, difiant from the centre of the primitive, the tangent, and cotan¬ gent, of half its inclination. Let MN (fig. 6.) be a great circle perpendicular topiT. <5. the primitive ABCP), and A the projedting point; then P, p are the poles of MN, and of all its parallels w n, &c. Let AP, A p meet the diameter BD in F /; which will therefore be the projected poles of MN and its parallels. The angle BEM is the inclination of the circle MEN, and its parallels, to the primitive : and becaufe BC and MP are quadrants, and MC common to both; therefore PC —BM: and lienee PEC is alfo the inclination of MN and its parallels. Now EF is the tangent of EAF, or of half the angle PEC the in¬ clination; and E/is the tangent of the angle EA f; but EA /"is the complement of EAF, hence EyHs the cotangent of half the inclination. Corollaries. 1. The projedtion of that pole which L nearefi to the projedting point is without the primitive, and the pro¬ jedtion of the other within. 2. The projedted centre of any circle is always be¬ tween the projedtion of its neareft pole and the centre of the primitive ; and the projedted centres of all circles are contained between their projedted poles. Corollaries. 1. All circles which pafs through the points M, N are the projedtions of great circles, and have their cen¬ tres m the line BG; and all circles which pafs through the pofiiis F, G, are the projedtions of great circles, and have their centres in the line HI, perpendicular to BG. 2. If NF, NH be continued to meet tbe primitive in L, F ; then BE is the meafure of the great circle’s in¬ clination to the primitive; and MT—2BL. Proposition V. Theorem V. The centre of projedtion of a lefs circle perpendicular to the primitive, is diftant from the centre of the primi¬ tive, the fecant of the diftance of the lefs circle from its neareft pole ; and the radius of projedtion is the tangent of that diftance. Fig. 5. Let MN (fig. 5.) be the given lefs circle perpendi¬ cular to the primitive, and A the projedling point. Draw AM, AN to meet the diameter BD produced in G and H ; then GH is the projedted diameter of the lefs circle : bifea GH in C, and C will be its centre ; join NE, NC. Then becaufe AE, NI are parallel, the angle INEzrNEA ; but NEA=2NMA Vol. XVIL Part II. Proposition VII. Theorem VII. Equal arches of any two great circles of the fphere will be intercepted between twro other circles drawn on the fphere thraugh the remote poles of thofe great circles. Let AGB, CFD (fig. y.) be two great circles of the„. fphere, whofe remote poles are E, P ; through which draw the great circle PE EC, and lefs circle PGE, in- terfedting the great circles AGB, CFD, in the points B, G,and D, F ; then the arch BG is equal to the arch DF. Becaufe E is the pole of the circle AGB, and P the pole of CFD, therefore the arches EB, PD are equal : and fince BD is common to both, hence the arch ED is equal to the arch PB. For the fame reafon, the arches EF, PG are equal ; but the angle DEF is equal to the angle BPG : hence thefe triangles are equal, and therefore the arch DF is equal to the arch BG. Proposition VIII. Theorem VIII. If from either pole of a projedted great circle, two ftraight lines be drawn to meet the primitive and the pro¬ jedtion, they will intercept fimilar arches of thefe circles. 3 H On 426 PROJECTION OF THE SPHERE. Seflion L Stereogra- On the plane of prcje&lon AGB (fig. 7.) let the phk Fro- great circle CFD be projehted into c f d, and its pole P the*"Sphere into/>; through f) draw the ftraight lines/) d,pf, then w—— y—.are the arches GR,/d limilar. Since /> d lies both in the plane AGB and APBE, it is in their common fe&ion, and the point B is alfo in their common leblion ; therefore p d paffes through the point B. In like manner it may be Ihown that the line p f paffes through G. Now the points D, F are projected into d,f: hence the arches FD,y d are li¬ milar ; but GB is equal to FD, therefore the inter¬ cepted arch of the primitive GB is fimilar to the pro¬ jected arch f d. Corollary. Hence, if from the angular point of a projected fphe- rical angle two ftraight lines. be drawn through the projected poles of the containing lides, the intercepted arch of the primitive will be the meafure of the fpheri- cal angle. Proposition IX. Problem I. To defcribe the projection of a great circle through two given points in the plane of the primitive. Let P and B be given points, and C the centre of the primitive. Fig. 8. 1. When one point P (fig. 8.) is the centre of the primitive, a diameter drawn through the given points will be the great circle required. Fig. 9. 2. When one point P (fig. 9.) is in the circumfe¬ rence of the primitive. Through P draw the diameter PD ; and an oblique circle defcribed through the three points P, B, D, will be the projeClion of the required great circle. 3. When the given points are neither in the centre nor circumference of the primitive. Through either of Fig. 10. the given points P (fig. 10.) draw the diameter ED, and at right angles thereto draw the diameter FG. From F through P draw the ftraight line FPH, meet¬ ing the circumference in H : draw the diameter HI, and draw the ftraight line FIK, meeting ED produced in D j then an arch, terminated by the circumference, being defcribed through the three points, P, B, K, will be the great circle. Proposition X. Problem II. To defcribe the reprefentation of a great circle about any given point as a pole. Let P be the given pole, and C the centre of the pri¬ mitive. 1. When P (fig. 8.) is in the centre of the primitive, then the primitive will be the great circle required. jj. 2. When the pole P (fig. 11.) is in the circumfe¬ rence of the primitive. Through P draw the diameter PE, and the diameter AB drawn at right angles to PE will be the projected great circle required. 3. When the given pole is neither in the centre nor circumference of the primitive. Though the pole P Plate j draw the diameter AB, and draw the diame- ccccxi.iv. ^ej. perpendicular to AB ; through E and P draw the ftraight line EPF, meeting the circumference in F. Make FG equal to FD) through E and G draw the ftraight line EGH, meeting the diameter AB produ- Stereogra- ced °if neceffary in H 5 then from the centre H, with P1*1/ Pro- the radius FIE, defcribe the oblique circle DIE, and it^ will be the projeftion of the great circle required. t -t Or, make DK equal to FA } join EK, which inter- fects the diameter AB in I j then through the three points, D, I, E, defcribe the oblique circle DIE. Proposition XL Problem III. To find the poles of a great circle. 1. When the given great circle is the primitive, its centre is the pole. 2. To find the pole of the right circle ACB (fig. 11.) Draw the diameter PE perpendicular to the given circle AB ; and its extremities P, E are the poles of the circle ACB. 3. To find the pole of the oblique circle DEF (fig. Fig. 13. 13.) Join DF, and perpendicular thereto draw the diameter AB, cutting the given oblique circle DEF in E. Draw the ftraight line FEG, meeting the cir¬ cumference in G. Make GI, GH, each equal to AD j then FI being joined, cuts the diameter AB in P, the lower pole ; through F and H draw the ftraight line FH />, meeting the diameter AB produced in />, which will be the oppofite or exterior pole. Proposition XII. Problem IV. To defcribe a lefs circle about any given point as a pol*, and at any given diftance from that pole. 1. When the pole of the lefs circle is in the centre of the primitive j then from the centre of the primitive, with the femitangent of the diftance of the given circle from its pole, defcribe a circle, and it will be the pro- jeftion of the lefs circle required. 2. If the given pole is in the circumference of the primitive, from C (fig. 14.), the centre of the primitive, p- fet off CE the fecant of the diftance of the lefs circle from its pole P ; then from the centre E, with the tan¬ gent of the given diftance, defcribe a circle, and it will be the lefs' circle required. Or, make PG, PF each equal to the chord of the diftance of the lefs circle from its pole. Through B, G, draw the ftraight line BGD meeting CP produced in D : bifedl GD in H, and draw HE perpendicular to GD 5 and meeting PD in E, then E is the centre of the lefs circle. 3. When the given pole is neither in the centre nor circumference of the primitive. Through P (fig. 15.), the given pole, and C the centre of the primitive, drawF’g- I5* the diameter AB, and draw the diameter DE perpen¬ dicular to AB } join EP, and produce it to meet the primitive in p; make p F,/> G, each equal to the chord of the diftance of the lefs circle from its pole ; join EF which interfefts the diameter AB in H ; from E through G draw the ftraight line EG I, meeting the diameter AB produced in I} bifeft HI in K : Then a circle de¬ fcribed from the centre K, at the diftance KH or KI, will be the projeftion of the lefs circle. Proposition XIII. Problem V. To find the poles of a given lefs circle. The poles of a lefs circle are alfo thofe of its parallel great Se&ion I. Stereogra- great circle. _ If therefore the parallel great circle be phic Pro. given, then its poles being found by Prob. III. will be the Sphe0re.thofc of tlle lefs circle- Sut if the parallel great circle be not given, let HMIN (fig. 15.) be the" given lefs Fig. 15. circle. Through its centre, and C the centre of the pri¬ mitive, draw the line of meafufes IAHB j and draw the diameter DE perpendicular to it, alfo draw the ftraight line EHF meeting the primitive in F ; make F /> equal to the chord of the diftance of the lefs circle from its pole join E and its interfeftion P with the diame¬ ter AB is the interior pole. Draw the diameter /> CL through E and L, draw E L q meeting the diameter AB produced in q •, then q is the external pole. Or thus : Join El interfering the primitive in G; join alfo EH, and produce it to meet the primitive in F j bifer the arch GF in p ; from E to ^ draw the ftraight line EP />, and P is the pole of the given lefs circle. PROJECTION OF THE SPHERE. 427 line of chords will give the meafure of the arch DE of Sfereogra- flip' mxr#an 1 (*0 t*-/-»1 rj phic Pt'O— je<5Hon of Problem VIII. the given lefs circle. Proposition XVI. To meafure any fphericai angle. 1. If the angle is at the centre of the primitive, it is meafured as a plane angle. 2. When the angular point is in the circumference of the primitive 5 let A (fig. 19.) be the angular point, r^f and ABE an oblique circle inclined to the primitive. Through P, the pole of ABE, draw the line APp meet¬ ing the circumference in p : then the arch E /> is the meafure of the angle BAD, and the arch AF p is the meafure of its fupplement BAF : alfo /> F is the mea¬ fure of the angle BAG, and p ED that of its fupple¬ ment. Proposition XIV. Problem VI. To meafure any arch of a great circle. ^ 1. Arches of the primitive are meafured on the line of chords. 2. Right circles are meafured on the line of femi- tangents, beginning at the centre of the primitive. Thus, the meafure of the portion AC (fig. 16 ) of the right circle DE, is found by applying it to the line of femi- tangents. The meafure of the arch DB is found by fubtrafting that of BC from 900 : the meafure of the arch AF, lying partly on each fide of the centre, is ob¬ tained by adding the meafures of AC and CF. Laftly, J o meafure the part AB, which is neither terminated at the centre or circumference of the primitive, apply CA to the line of femitangents ; then CB, and the difference between the meafures of thefe arches, will be that of AB. Or thus : Draw the diameter GH perpendicular to DE j then from either extremity, as D, of this diame¬ ter, draw lines through the extremities of the arch in¬ tended to be meafured ; and the intercepted portion of the primitive applied to the line of chords will give the xneafure of the required arch. Thus IK applied to the line of chords will give the meafure of AB. 3. To meafure an arch of an oblique circle : draw lines from its pole through the extremities of the arch to meet the primitive, then the intercepted portion of the primitive applied to the line of chords will give the Fi«- 17. mea^ure of the arch of the oblique circle. Thus, let " ’ AB (%• i7-)> be an arch of an oblique circle to be meafured, and P its pole •, from P draw the lines PAD, PBE meeting the primitive in B and E ; then the arch DE applied to the line of chords will give the meafure of the arch of the oblique circle AB. 3. If the angular point is neither at the centre nor circumference of the primitive. Let A (fig. 20.) ber-.^ . the angular point, and DAH, or GAF, the angle toH^ be meafured, P the pole of the oblique circle DAF, and p the pole of GAH : then from A, through the points P draw the ftraight lines APM, A/> N, and the arch MN will be the meafure of the angle DAH; and the fupplement of MN will be the meafure of the angle HAF or DAG. Proposition XVII. Probl£m IX. To draw a great circle perpendicular to a projefted great circle, and through a point given in it. Find the pole of the given circle, then a great circle defcribed through that pole and the given point will be perpendicular to the given circle. Hence if the given circle be the primitive, then a diameter drawn through the given point will be the required perpendicular. If the given circle is a right one, draw a diameter at right angles to it} then though the extremities of this dia¬ meter and the given point defcribe an oblique circle, and it will be perpendicular to that given. If the given circle is inclined to the primitive, let it be reprefented by BAD (fig. 2i.), whofe pole is P, and let A be the point through which the perpendicular is to be drawn : ^ 216 then, by Prob. I. defcribe a great circle through the points P and A, and it will be perpendicular to the ob¬ lique circle BAD. Proposition XVIII. Problem X. Through a point in a proje&ed great circle, to defcribe another great circle to make a given angle with the former, provided the meafure of the given angle is not lefs than the diftance between the given point and circle. Proposition XV. Problem VIL To meafure any arch of a lefs circle. Fig. 18. Let DEG (fig. 18.) be the given lefs circle, and DE the arch to be meafured : find its internal pole P } and defcribe the circle AFI parallel to the primitive, and whofe diftance from the projecting point may be equal to the diftance of the given lefs circle from its pole P: then join PD, PE, which produce to meet the parallel circle in A and F. Now AF applied to a Let the given circle be the primitive, and let A (fig 19.) be the angular point. Draw the diameters AE, DF perpendicular to each other ; and make the angle CAG equal to that given, or make CG equal to the tangent of the given angle then from the centre G, with&the diftance GC, defcribe the oblique circle ABE, and it will make with the primitive an angle equal to that given. If the given circle be a right one, let it be APB (fig. 22.) and let P be the given point. Draw the diameter Fia- 2a 3H2 GH ® 428 .St.ereog:r.- phic t-'ro- jetftion of the Sphere. '23* PROJECTION OF THE SPHERE. Se6aon TL GH perpcnJicHiar Lo AB j join GP, and produce k to a; make J:I b equal to twice A a : and G b being join¬ ed interfecls AB in C. Draw CD perpendicular to AB, and equal to the cotangent of the given angle to the radius PC ; or make the angle CPD equal to the com¬ plement of that given? then from the centre D, with the radius DP, deferibe the great circle FPE, and the angle APF, or BPE, will be equal to that given. If APB (fig. 23.) is an oblique circle. From the angular point P, draw the lines PG, PC through the centres of the primitive and given oblique circle. I hrough C, the centre of APB, draw G CD at right angles to PG 5 make the angle GPD equal to that given; and from the centre D, with the radius DP, deferibe the oblique circle FPE, and the angle APF, or BPF, will be equal to that propofed. about a as a pole, deferibe the great circle EDF, cut¬ ting the primitive and given circle in E and D, and it will be the great circle required. Scholium. Stereogra¬ phic Cro- jedtion of the Sphere. It will hence be an eafy matter to conftrudi; all the various fpherical triangles. The reader is, however, referred to the article Spherical TRIGONOME TR T, for the method of conftrufling them agreeably to thk pro¬ jection ; and alfo for the application to the refolution of problems of the fphere. For the method of projecting the fphere upon the plane of the meridian, and of the horizon, according to the itereographic projection, ice the article GEOGRAPHY. SECTION II. Propositiox XIX. Problem XL Any great circle cutting the primitive being given, to deferibe another great circle which (hall cut the gi¬ ven one in a propofed angle, and have a given arch intercepted between the primitive and given circles. Plate If the given circle be a right one, let it be reprefent- CCCcXLV ed by A PC (fig. 24.) ; and at right angles thereto draw F;S- the diameter BPM ; make the angle BPF equal to the complement of the given angle, and PE equal to the tangent of the given arch ; and from the centre of the primitive with the fecant of the fame arch deferibe the arch Gg. Through F draw EG parallel to AC, meet- ing Gg in G ; then from the centre G, \vith the tangent PF, deferibe an arch a 0, cutting APC in I, and join GI. Through G, and the centre P, draw the diameter FIK ; draw PL perpendicular to HK, and IL perpendicular to GI, meeting PL in L ; then L will be the centre of the circle HIK, which is that re¬ quired. But if the given great circle be inclined to the pri- j- mitive, let it be ADB (fig. 25.), and E its centre : D make the angle BDF equal to the complement of that given, and DF equal to the tangent of the given arch, as before. From P, the centre of the primitive, with the fecant of the fame arch, deferibe the arch G and from E, the centre of the oblique circle, with the ex¬ tent EF, deferibe an arch interfedfing G g in G. Now G being determined, the remaining part of the opera¬ tion is performed as before. When the given arch exceeds 90°, the tangent and fecant of its fupplement are to be applied on the line DF the contrary way, or towards the right; the former conflruflion being reckoned to the left. Profosition XX. Problem XII. Any great circle in the plane of projection being given, to deferibe another great circle, which (hall make gi¬ ven angles with the primitive and given circles. Jig. 26, Let ADC (fig. 26.) be the given circle, and its pole. About P the pole of the primitive, deferibe an arch m n, at the diilance of as many degrees as are in the angle which the required circle is to make with the pri¬ mitive. About Q the pole of the circle ADC, and at a dikance equal to the meafure of the angle which the required circle is to make with the given circle ADC, deferibe an arch 0 «, cutting m n in n. Then Of the Orthographic Projection of the Sphere. The orthographic projeflion of the fphere, is that in which the eye is placed in the axis of the plane of pro¬ jection, at an infinite diitance with refpedt to the dia¬ meter of the fphere; fo that at the fphere all the vifual rays are affirmed parallel, and therefore perpendicular to the plane of projection. Hence the orthographic projection of any point is where a perpendicular from that point meets the plane of projection : and the orthographic reprelentation of any objeCt is the figure formed by perpendiculars drawn from every point of the objeCt to the plane of pro¬ jection. This method of projection is ufed in the geometrical delineation of eclipfes, occultations, and tranfits. It is alfo particularly ufeful in various other projections, fuch as the analemma. See Geography, &c. Proposition I. Theorem I. Every ftraight line is projected into a flraight line. If the given line be parallel to the plane of projection, it is projected into an equal ftraight line ; but if it is inclined to the primitive, then the given ftraight line will be to its projection in the ratio of the radius to the cofine of inclination. Let AB (fig. 27.) be the plane of projection, and let CD be a ftraight line parallel thereto : from the ex¬ tremities C, D of the ftraight line CD, draw the lines CE, DF perpendicular to AB ; then by 3. of xi. of Fuel, the interfeCtion EF, of the plane CEFD, with the plane of projection, is a ftraight line : and becaufe the ftraight lines CD, EF are parallel, and alfo CE, DF ; therefore, by 34. of i. of Fuel, the oppofite fides are equal; hence the ftraight line CD, and its projec¬ tion EF, are equal. Again, let GH be the propofed ftraight line, inclined to the primitive ; then the lines GE, FIF being drawn perpendicular to AB, the inter¬ cepted portion EF will be the projection of GH. Through G draw GI parallel to AB, and the angle IGH will be equal to the inclination of the given line to the plane of projection. Now GH being the radius, GI, or its equal EF, will be the coftne of IGH ; hence the given line GH is to its projection EF as radius to the cofinc or inclination. FJg. 27. Corollaries. Section II. Orthogra- COROLLARIES. jeetion of *• A fli'aight line perpendicular to the plane of pro- the Sphere, jeflion is projefted into a point. v 2. Every flraight line in a plane parallel to the pri¬ mitive is projected into an equal and parallel ilraight line. 3. A plane angle parallel to the primitive is projected into an equal angle. 4. Any plane rectilineal figure parallel to the primi¬ tive is projected into an equal and fimilar figure. 5. The area of any rectilineal figure is to the area of its projection as radius to the cofine of its inclina¬ tion. Proposition II. Theorem II. Every great circle, perpendicular to the primitive, is prcjeCted into a diameter of the primitive ; and every arch ot it, reckoned from the pole of the primitive, is projected into its fine. PPiOJECTION OF THE SPHERE. 429 tance of the parallel circle from the primitive, or the Orthogra- fine of its diitance from the pole of the primitive. Phic.iJro'. jeCtion of Proposition IV. Theorem IV. thejsphere. An inclined circle is projected into an ellipfe, whofe tranfverfe axis is the diameter of the circle. 1. Let ELF (fig. 30.) be a great circle inclined to p;^ the prinaitive EEF, and EF their line of common fee- a J * tion. From the centre C, and any other point K, in EF, let the perpendicular CB, KI be drawn in the plane of the primitive, and CL, KN, in the plane of the great circle, meeting the circumference in L, N. Let LG, ND be perpendicular to CB, KI ; then G, D are the projections of L, N. And becaufe the tri¬ angles LCG, NKD are equiangular, CL*: CG*:: NK5: DK* : or EC* : CG* :: LKF : OK* : therefore the points G, D are in the curve of an ellipfe, of which. EF is the tranfverfe axis, and CG the lemiconjugate axis. Fig. 2S. Let BIT) ("fig. 28.) be the primitive, and ABCD a great circle perpendicular to it, pafljng through its poles A, C ; then the diameter BED, which is their line'of common feCHon, will be the projection of the circle ABCD. For if from any point, as G, in the circle ABC, a perpendicular GH fall upon BD, it will alfo be perpendicular to the plane of the primitive : therefore H is the projection of G. Hence the whole circle is projected into BD, and any arch AG into EH equal to G1 its fine. Corollaries. 1. Every arch of a great circle, reckoned from its in- terfeCtion with the primitive, is projected into its verfed fine. 2. Every lefs circle perpendicular to the primitive is projected into its line of common feCtion with the pri¬ mitive, which is alfo its own diameter 3 and every arch of the femicircle above the primitive, recksned from the middle point, is projected into its fine. 3. Every diameter of the primitive is the projection of a great circle ; and every chord the projection of a lels circle. 4. A fpherical angle at the pole of the primitive is projected into an equal angle. Proposition III. Theorem III. A circle parallel to the primitive is projected into a circle equal to itfelf, and concentric with the primi¬ tive. Let the lefs circle FIG (fig. 29.) be parallel to the l lS-29- plane of the primitive END. The ftraight line HE, which joins their centres, is perpendicular to the primi¬ tive } therefore E is the projection of H. Let any radii HI and IN perpendicular to the primitive be drawn. Then IN, FIE being parallel, are in the fame plane 5 therefore IH, NE, the lines of common feCtian of the plane IE, with two parallel planes, are parallel ; and the figure IHEN is a parallelogram. Hence NE — IH, and coniequentiy ITG is projected into an equal circle KNL, whofe centre is E. Corollary. • The radius of the projection is the cpfine of the dif- Corollaries. 1. In a projected great circle, the femiconjugate axis is the cofine of the inclination of the great circle to the primitive. 2. Perpendiculars to the tranfverfe axis intercept correfponding arches of the projection and the primi¬ tive. 3. The eccentricity of the projection is the fine of the inclination of the great circle to the primitive. Cafe 2. Let AQB (fig. 31.) be a lefs circle, incli-p- ned to the primitive, and let the great circle LBM, per- a’ pendicular to both, interfeCt them in the lines AB, LM. From the centre Q, and any other point N in the dia~ meter AB, let the perpendiculars TOP, N£), be drawn in the plane of the lefs circle, to meet its circumference in T, P, Q. Alfo, from the points A, N, O, B, let AG, NI, OC, BH, be drawn perpendicular to LM j and from P>.& draw PE, QD, TF, perpendicular to the primitive ; then G, I, C, H, E, D, F, are the projections of thefe points, Becaufe OP is perpendicu¬ lar to LMB, and OC, PE, being perpendicular to the primitive, are in the fame plane, the plane COPE is per¬ pendicular to LBM. But the primitive is perpendicular to LBM 5 therefore the common feCHon EC is perpen¬ dicular to LBM, and to LM. Flence CP is a parallelo¬ gram, and EC — OP. In like manner, FC, DI, are proved perpendicular to LM, and equal to OT, NQ. Thus ECF is a ftraight line, and equal to the diameter PT. Let QJi, DK be parallel to AB, LM; then HO = NQ DI =r KC, and PR >< RT zr EK X Kh. But AO : CG : : NO : Cl ; therefore AOJ • CG* : : OR* : DK* : and ECJ : CG* : ; EKF ; DK*. Corollaries. 1. The tranfverfe axis is to the conjugate as radius to the cofine of the circle’s inclination to the primitive. 2. Half the tranfverfe axis is the cofme of half the fum of the greateft and leaft diftances of the lefs circle from the primitive. 3. The extremities of the conjugate axis are in the line of meafures, diftant from the centre of the primitive by the cofines of the greateft and leaft diftanccs of the l.efs circle from the primitive. 4? if, PROJECTION OF THE SPHERE. SeOion II. 4. If from the extremities of the conjugate axis of any elliptical projection perpendiculars be drawn (in the fame direction if the circle do not interfeft the primi¬ tive, but if othervvife in oppofite directions), they will interfeCt an arch of the primitive, whofe chord is equal to the diameter of the circle. Proposition V. Theorem V. The projected poles of an inclined circle are in its line of meafures diftant from the centre of the primitive the fine of the inclination of the circle to the pri¬ mitive. Let A BCD (fig. 32.) be a great circle, perpendicu¬ lar both to the primitive and the inclined circle, and interfeCting them in the diameters AC, MN. Then ABCD paffes through the poles of the inclined circle ; let thefe be P, ; and let P/>, Qjq, be perpendicular to AC ; />, q are the projected poles } and it is evident that /> O fine of BP, or MA, the inclination. Corollaries. 1. The centre of the primitive, the centre of the pro- lection, the projected poles, and the extremities of the conjugate axis, are all in one and the fame ftraight line. 2. The diftance of the centre of projection from the centre of the primitive, is to the cofine of the dittance of the circle from its own pole, as the fine of the cir¬ cle’s inclination to the primitive is to the radius. Proposition VI. Problem I. To defcribe the projection of a circle perpendicular to the primitive, and whofe diftance from its pole is equal to a given quantity. Let PA p B (fig. 33.) be the primitive circle, and P, p the poles of the right circle to be projected. Then if the circle to be projected is a great circle, draw the diameter AB at right angles to the axis P/>, and it will be that required. But if the required pro¬ jection is that of a lefs circle, make PE, PF each equal to the chord of the diftance of the lefs circle from its pole •, join EF, and it will be the projection of the lefs circle required. Proposition VII. Problem II. Through a given point in the plane of the primitive to defcribe the projection of a great circle, having a given inclination to the primitive. 1. When the given inclination is equal to a right an¬ gle, a ftraight line drawn through the centre of the primitive, and the given point, will be the projection re¬ quired. 2. When the given inclination is lefs than a right angle, and the given point in the circumference of the primitive. Let R (fig. 34.) be a point given in the circumference of the primitive, through which it is re¬ quired to draw the projection of a great circle, inclined to the primitive in an angle meafured by the arch QP of the primitive. Through the given point R draw the diameter PCS, and draw GC^ at right angles to it. Make the arch 4 GV of the primitive equal to QP, and draw VA at Orthogra- right angles to GC j and in Gj-, towards the oppofite t'ro' parts of C, take CB equal to AC j then, with the the Sphere greater axis RS, and lels axis AB, defcrib& an ellipfe, ^ ^ ‘t and it will be the projection of the oblique circle re¬ quired. 3. When the diftance of the given point from the primitive is equal to the cofme of the given inclination. Every thing remaining as in the preceding cafe j let A be the given point, and AC the cofine of an arch GV, equal to the given arch QP; then drawing the diameter RCS at right angles to ACB, the ellipfe de- fcribed with the given axis RS, AB will be the projec¬ tion of the inclined circle. 4. When the diftance of the given point from the centre of the primitive is lefs than the femidiameter of the primitive, but greater than the cofine of the given in¬ clination. Let D be the given point, through which draw the diameter IC i; and at the point D draw QL perpen¬ dicular to DC meeting the primitive in L ) alfo draw LK, making with LD the angle DLK equal to the complement of the given inclination. Let LK meet DC in K ; then will DK be lefs than DC. On DC as^^er 03 a diameter defcribe a circle, and make DH equal to^^j DK ; through H draw a diameter of the primitive RCS, and defcribe an ellipfe through the points R, D, S, and it will be the proje&ion of the inclined circle. Proposition VIII. Problem III. Through two given points in the plane of the primi¬ tive to defcribe the projeftion of a great circle. 1. If the two given points and the centre of the pri¬ mitive be in the fame ftraight line, then a diameter of the primitive being drawn through thefe points will be the projeftion of the great circle required. 2. When the two given points are not in the fame ftraght line with the centre of the primitive •, and one of them is in the circumference of the primitive. Let DR (fig. 34.) be the two given points, of which R is in the circumference of the primitive. Draw the diameters RCS, and GC g, FDH perpendicular to it, meeting the primitive in G^F. Divide GC, £ C, in A, B, in the fame proportion as FH is divided in D j and defcribe the ellipfe whofe axes are RS, AB, and centre C ; and it will be the projection required. 3. When the given points are within the primitive, and not in the fame ftraight line with its centre. Let D, E (fig. 35.) be the two given points *,Fig. 35. through C the centre of the primitive draw the ftraight lines ID, KEfj draw DL perpendicular to If, and EO perpendicular to K k, meeting the primitive in L, O. Through E, and towards the fame parts of C, draw EP parallel to DC, and in magnitude a fourth proportional to LD, DC, OE. Draw the diameter CP meeting the primitive in R, S, and defcribe an el¬ lipfe through the points D and R, or S, and it will alfo pafs through E. This ellipfe will be the projection of the propofed inclined circle. Proposition IX. Problem IV. To defcribe the projection of a lefs circle parallel to the primitive, its diftance from the pole of the primitive being given. From Sedticn II. PROJECTION OF THE SPHERE. Orthogra- From the pole of the primitive, with the fine of the ^edionof Siven diftance of the circle from its pole, defcribe a the Sphere. c^rc^e» an^ ^ will be the proje£tion of the given lefs 43* circle. Proposition X. Problem V. About a given point as a projefted pole to defcribe the projedtion of an inclined circle, whofe diftance from its pole is given. Fig. 36, Let P (fig. 36.) be the given projefted pole, through which draw the diameter and draw the diameter H b perpendicular thereto. From P draw PL per¬ pendicular to GP meeting the circumference in L j through which draw the diameter L /. Make LT, LK each equal to the chord of the diftance of the lefs circle from its pole, and join TK, which interfedls L /, in Q. From the points T, Q, K, draw the lines -FA, QS, KB, perpendicular to G^j and make OR, OS, each equal to or QX. Then an ellipfe defcribed through the points A, S, B, R will be the projedlion of the propofed lefs circle. Proposition XL Problem VI. To find the poles of a given projedled circle. 1. If the projedfted circle be parallel to the primitive, the centre of the primitive will be its pole. 2. If the circle be perpendicular to the primitive, then the extremities of a diameter of the primitive drawn at right angles to the ftraight line reprefenting the projedled circle, will be the poles of that circle. 3. When the projedled circle is inclined to the pri¬ mitive. p;g. 3^. Let ARBS (fig. 36, 37,) be the elliptical projection of any oblique circle; through the centre of which, and C the centre of the primitive, draw the line of mea- fures CBA, meeting the ellipfe in B, A ; and the pri¬ mitive in G,£-. Draw CH, BK, AT perpendicular to G g, meeting the primitive in H, K, T. Bifeft the arch KT in L, and draw LP perpendicular to G ; then P will be the projected pole of the circle, of which ARBS is the projection. Proposition XII. Problem VII. intercepted portion BF of the primitive wall be the Orthogra- meafure of the given arch DE of the lefs circle DEH. PIi;c.i>ro*. 3. If the given lefs circle, of which an arch is to be meaiured, is perpendicular to the primitive. f Let ADEB (fig. 40.) be the lefs circle, of whichFig. 40. the meafure of the arch DE is required. Through C, the centre of the primitive, draw the line of meafures Mm, and from the interfeCtion O of the given right circle, and the line of meafures, with the radius OA, or OB, defcribe the femicircle AFGB ; through the points D, E, draw the lines DF, EG parallel to the line of meafures, and the arch FG will be the meafure of DE, to the radius AO. In order to find a fimilar arch in the circumference of the primitive, join OF, OG, and at the centre C of the primitive, make the angle mCH equal to FOG, and the arch mM to the radius Cm will be the meafure of the arch DE. 4. When the great projection is of a lefs circle incli¬ ned to the primitive. Let RDS (fig. 41.) be the projeftion of a lefs circle pig. ^ inclined to the primitive, and DE a portion of that cir¬ cle to be meafured. Through O the centre of the pro- jecled circle, and C the centre of the primitive, draw the line of meafures Mm; and from the centre O, with the radius OR, or OS, defcribe the femicircle RGFS ; through the points D, E draw the lines DF, EG parallel to the line of meafures, and FG will be the meafure of the arch DE to the radius OR, or OS. Join OF, OG, and make the angle mCH equal to hOG, and the arch ?n H of the primitive will be the meafure of the arch DE of the inclined circle RDS. The converfe of this propofition, namely, to cut off an arch from a given projected circle equal to a given arch of the primitive, is obvious. The above operation would be greatly (hortened by ufing the line of fines in the feflor. It feems unneceffary to infill farther on this projec¬ tion, efpecially as the reader will fee the application of it to the projection of the fphere on the planes of the Meridian, Equator, and Horizon, in the article Geo¬ graphy $ and to the delineation of Ec/ipfes in the arti¬ cle Astronomy. The Analemma, Plate CCXXXV. in the article Geography, is alfo according to this projec¬ tion j and the method of applying it to the folution of aftronomical problems is there exemplified. To meafure any portion of a projected circle, and con- verfely. 1. When the given projection is that of a great cir¬ cle. Fig. 38. Let ADBE (fig. 38.) be the given great circle, either perpendicular or inclined to the primitive, of which the portion DE is to be meafured, and let M m be the line of meafures of the given circle. Through the points D, E, draw the lines EG, DF parallel to M m; and the arch FG of the primitive will be the meafure of the arch DE of the great circle, and con- verfely. 2. When the projection is that of a lefs circle paral- P^ate lei to the primitive. ccccxlvi. Let DE (fig. 39.) be the portion to be meafured, 39* of the dels circle DEH parallel to the primitive. From the centre C draw the lines CD, CE, and produce them to meet the primitive in the points B, F. Then the SECTION III. Of the Gnomonic ProjeGion of the Sphere. In this projection the eye is in the centre of the fphere, and.the plane of projection touches the fphere in a given point parallel to a given circle. It is named gnomonic, on account of its being the foundation of di¬ alling : the plane of projection may alfo reprefent the plane ot. a dial, whofe centre being the projeted pole the femiaxis of the fphere will be the ftile or gnomon of the dial. As the. projection of great circles is reprefented by ftraight lines, and lefs circles parallel to the plane of projetion are projected into concentric circles : there¬ fore many problems of the fphere are very eafily refol- ved. Other problems, however, become more intricate on account of fome of the circles being projected into el- lipfes, parabolas, and hyperbolas. Brofositioit 43 2 Gnomonic Proiefticn of the Sphere. PROJECTION OF Proposition I. Theorem I. Every great circle is projected into a ftraight line per¬ pendicular to the line of meafures •, and whofe diftance from the circle is equal to the cotangent of its incli¬ nation, or to the tangent of its neareft diftance from the pole of the projection. THE SPHERE. Section III. Gnoinonic Corollary. projedlion If a circle be parallel to the plane of projection, and Sphere. 45 degrees from the pole, it is projected into a circle u—v. . ■,.< equal to a great circle of the fphere j and therefore may be confidered as the primitive circle, and its radius the radius of projection. *'-S-43> Let Bx\D (fig. 42.) be the given circle,'and let the circle CBED be perpendicular to BAD, and to the plane of projection 5 whofe interfeCtion CF with this laft plane will be the line of meaiures. Now fince the circle CBED is perpendicular both to the given circle BAD and to the plane of projection, the com¬ mon fection of the two laft planes produced will there¬ fore be perpendicular to the plane of the circle CBED produced, and confequently to the line of meafures : hence the given circle will be projected into that fec¬ tion ; that is, into a ftraight line palling through &, / the focus of (he ellipfe, hyperbola, or parabola 5 then HKrz' — for the ellipfe H £ — : — for the hyperbola j and f n being drawm perpendicular to AE f l — n E-j-Fjf . for the parabola. Proposition V. Theorem V. Let the plane TW (fig. 44.) be perpendicular to theFig. 44. plane of projection TV, and BCD a great circle of the fphere in the plane TW. Let the great circle BED be projected into the Itraght line b e k. Draw CQS perpendicular to b h, and C m parallel to it and equal to CA, and make QS equal to Qy/z; then any aftgle QS t is the meafure of the arch Q t of the projected circle. Let the circle PI (fig. 42.) be parallel to the plane GF, then the equal arches PC, Cl are projected into the equal tangents GC, CH *, and therefore C the point of contaCt and pole of the circle PI and of the projec¬ tion, is the centre of the reprefentation G, H. Join AQ : then becaufe C m is equal to CA, the angle QC m equal to QCA, each being a right angle, and the fide QC common to both triangles •, therefore O m, or its equal QS, is equal QA. Again, fince the plane ACQ is perpendicular to the plane TV, and b Q to Se&lon III. PROJECTION OF Gnomonic to the interfe&ion CQ ; therefore ^ Q is perpendicular ^t'lhe011 an^ * ^encej fmce AQ^ and QS are Sphere, equal, all the angles at S cut the line £ in the fame u—/ points as the equal angles at A. But by the angles at A the circle BED is projedted into the line b Q. Therefore the angles at S are the meafures of the parts of the projected circle b and S is the dividing centre thereof. THE SPHERE. Corollary. Hence, if from the projected pole of any circle a perpendicular be erefted to the line of meafures, it will cut off a quadrant from the reprefentation of that circle. Proposition VIII. Theorem VIII. 4J3 Gnomonic Prcjedtion of the Sphere. Corollaries. 1. Any great circle £ is projedled into a line of tangents to the radius SQ. 2. If the circle b C pafs through the centre of pro- jedtion, then the projedting point A is the dividing cen¬ tre thereof, and C is the tangent of its correfpondent arch CB to CA the radius of projedtion. Proposition VI. Theorem VI. Fig. 44. Let the parallel circle GLH (fig. 44.) be as far from the pole of projedtion C as the circle FNI is from its pole ; and let the diftance of the poles C, P be bifedt- ed by the radius AO : and draw b AD perpendicular to AO ; then any ftraight line b Qt drawn through b will cut off the arches h /, F n equal to each other in the reprefentations of thefe equal circles in the plane of projedtion. Let the projedtions of the lefs circles be defcribed. Then, becaufe BD is perpendicular to AO, the arches BO, DO are equal •, but fince the lefs circles are equally diftant each from its refpedtive pole, therefore the arches FO, OH are equal 5 and hence the arch BF is equal to the arch DH. For the fame reafon the arches BN, DL are equal ; and the angle FBN is equal to the angle LDH 3 therefore, on the fphere, the arches FN, HL are equal. And fince the great circle BNLD is projedted into the ftraight line bQ n I. &c. therefore n is the projedlion of N, and / that of L ; hence/«, h /, the projections of FN, HL refpedtively, are equal. Proposition VII. Theorem VII. Fig. 45. If F/? d, h/g, (fig. 45.) be the projedtions of two equal circles, whereof one is as far from its pole P as the other from its pole C, which is the centre of projec¬ tion 3 and if the diftance of the projedted poles C,/> be divided in 0, fo that the degrees in Co, op he equal, and the perpendicular 0 S be eredted to the line of meafures g h. Then the line p n,C l drawn from the poles C, p, through any point () in the line 0 S, will cut off the arches F n, h l equal to each other, and to the angle QC/>. The great circle A 0 perpendicular to the plane of the primitive is projedted into the ftraight line 0 S perpendi¬ cular to g h, by Prop. i. cor. 3. Let £) be the projec¬ tion of q ; and fince p £), CQ are ftraight lines, they are therefore the reprefentations of the arches P y, C y of great circles. Now fince P y C is an ifofceles fpherical triangle, the angles PCQ, CPQ are therefore equal 3 and hence the arches P y, C y produced will cut off equal arches from the given circles FI, GH, whofe re¬ prefentations ¥ n, hi are therefore equal : and fince the angle QC/> is the meafure of the arch h /, it is alfo the meafure of its equal F 77. Vol. XVII. Part II. Let ¥ nh (fig. 45.) be the projection of any circle FI,Fig.45* and p the projedfion of its pole P. If be the cotangent of CAP, and g B perpendicular to the line of meafures g C, let CAP be bifedted by A 0, and the line 0 B drawn to any point B, and alfop B cutting ¥ nk m d; then the angle ^ 0 B is the mea- fures of the arch F d. The arch PG is a quadrant, and the angle g 0 PA -J-0 APzzg AC <9 APrr^ AC -j- CA o=g Ao; therefore g Az=g 0 ; confequently 0 is the dividing cen¬ tre of ^ B, the reprefentation of GA 3 and hence, by Prop. v. the angle ^ 0 B is the meafure of^B. But fince pg reprefents a quadrant, therefore p is the pole of ^B 3 and hence the great circle/x/B pafling through the pole of the circles g B and F n will cut off equal arches in both, that is, F d—g B z= angle ^ 0 B. Corollary. The angle ^oB is the meafure of the angle gp¥>. lor the triangle gp¥> reprefents a triangle on the fphere, wherein the arch which g B reprefents is equal to the angle which the angle/> reprefents 3 becaufe £/> is a quadrant: therefore ^ 0 B is the meafure of both. Proposition IX. Problem I. To draw a great circle through a given point, and whofe diftance from the pole of projedlion is equal to a given quantity. Let ADB ("fig. 46.) be the projedHon, C its pole or Fig. 46. centre, and P the point through which a great circle is to be drawn : through the points P, C draw the ftraight line PC A, and draw1 CE perpendicular to it: make the angle CAE equal to the given diftance of the circle from the pole of projedHon C 5 and from the centre C, with the radius CE, deicribe the circle EFG : through P draw the ftraight line PIK, touching the circle EFG in I, and it will be the projedlion of the great circle re¬ quired. Proposition X. Problem II. To draw a great circle perpendicular to a great circle which paffes through the pole of projedHon, and at a " given dirtance from that pole. _ Let ADB (fig. 46.) be the primitive, and Cl the given circle : draw CL perpendicular to Cl, and make the angle CLI equal to the given diftance : then the ftraight line KP, drawn through I parallel to CL, will be the required projedlion. Proposition XL Problem III. At a given point in a projected great circle, to draw ano¬ ther great circle to make a given angle with the for¬ mer 3 and, converfely, to meafure the angle contained between two great circles. Let P (fig. 47.) be the given point in the given great Fig. 47. 3 I circle 434 PROJECTION OF THE SPHERE. Section III. Cnomonic circle PE, and C the centre of the primitive : through points P, C draw the ftraight line PCG ; and draw Sphere. t^e ra(iius of the primitive CA perpendicular thereto ", V—y—> join PA; to which draw AG perpendicular: through G draw BGD at right angles to GP, meeting PB in B j bifeft the angle CAP by the ftraight line AO ", join BO, and make the angle BOD equal to that given j then DP being joined, the, angle BPD will be that requir¬ ed. If the meafure of the rngle BPD be required, from the points B, D draw the lines BO, DO, and the angle BOD is the meafure of BPD. Proposition XII. Problem IV. To defcribe the projection of a lefs circle parallel to the plane of projection, and at a given diftance from its pole. one half of « : then with the vertex and focus k, de- Gnomonic fcribe the parabola f for the projection of the given cir- Projection cleFE. ®ftthe ophere. Proposition XV. Problem VII. v— J To find the pole of a given projected circle. Let DMF (fig. 50.) be the given projected circle Fig. 50. wdiofe line of meafures is DF, and C the centre of pro¬ jection •, from C draw the radius of projection CA, per¬ pendicular to the line of meafures, and A will be the projecting point : join AD, AF, and bifedt the angle DAF by the ftraight line AP j hence P is the pole. If the given projedtion be an hyperbola, the angle /"AG (fig. 49.)) bifefted, will give its pole in the line of meafures j and in a parabola, the angley’AE bifedted will give its pole. Proposition XVI. Problem VIII. Fig. 46. Let x\DB (fig. 46.) be the primitive, and C its cen¬ tre : fet the diftance of the circle from its pole, from B to H, and from FI to D j and draw the ftraight line AED, interfering CE perpendicular to EC, in the point E : with the radius CE defcribe the circle EFG, and it is the projeftion required. Proposition XIII. Problem V. To draw a lefs circle perpendicular to the plane of pro- PJate jeaion- ^7' Let C (fig. 48.) be the centre of projection, and TI b ^ ‘ a great circle parallel to the propofed lefs circle : at C make the angles ICN, TCO each equal to the diftance of the lefs circle from its parallel great circle TI j let CL be the radius of projection, and from the extremity L draw LM perpendicular thereto j make CV equal to LM ; or CF equal to CM : then with the vertex V and aiTymptotes CN, CO defcribe the hyperbola W VK f ; or, focus F and CV defcribe the hyperbola, and it will be the perpendicular circle deferibed. Proposition XIV. Problem VI. To defcribe the projection of a lefs circle inclined to the plane of projection. Draw the line of meafures p (fig. 49.) 5 and at C, the Fig. 49. centre of projection, drawr CA perpendicular to dp, and equal to the radius of projection : with the centre A, and radium AC, defcribe the circle DCFG 5 and draw KAE parallel to dp: then take the greateft and lealt diftances of the circle from the pole of projection, and fet them from C to D and F refpeCtively, for the circle DF 5 and from A, the projecting point, draw the ftraight lines AF/j and AD d; then df will be the traniverfe axis of the el- lipfe : but if D fall beyond the line RE, as at G, then from G draw the line GAD d, and df \s the tranfverfe axis of an hyperbola : and if the point D fall in the line RE, as at E, then the line AE wall not meet the line of meafures, and the circle wall be projected into a parabola whofe vertex is f: bifeCt ^yin H, the centre, and for the ellipfe take half the difference of the lines A.d, Af which laid from H will give K the focus: for the hy¬ perbola, half the fum of Ad, Af being laid from H, will, give I its focus : then wath the tranfverfe axis y/j and focus K, or k, defcribe the ellipfe ^ My or hyper¬ bola y^w, which will be the projection of the inclined circle : for the parabola, make EQ equal to Fy and drawy« perpendicular to AQ_, and make fk equal to To meafure any portion of a projected great circle, or to lay off' any number of degrees thereon. Let EP (fig. 51.) be the great circle, and IP a por- ^r. tion thereof to be meafured : draw ICD perpendicular to IP ; let C be the centre, and CB the radius of projection, with which defcribe the circle EBD j make IA equal to IB ", then A is the dividing centre of EP j hence AP being joined, the angle IAP is the meafure of the arch IP. Or, if IAP be made equal to any given angle, then IP is the correfpondent arch of the projection. Proposition XVII. Problem IX. To meafurc any arch of a projected lefs circle, or to lay off any number of degrees on a given projected lefs cir¬ cle. Let Fn (fig. 52.) be the given lefs circle, and P its pole : from the centre of projection C draw7 CA perpen-5Z* dicular to the line of meafures GH, and equal to the ra¬ dius of projection •, join AP, and bifeCt the angle CAP by the ftraight line AO, to which draw7 AD perpendicu¬ lar : defcribe the circle G / H, as tar diftant from the pole of projection C as the given circle is from its pole P •, and through any given point n, in the projected cir¬ cle F n, draw7 D « /, then H / is the meafure of the arch F n. Or let the meafure be laid from H to /, and the line D/joined w7ill cut off F « equal thereto. Proposition XVIII. Problem X. To deferibe the gnomonic projection of a fpherical triangle, when three tides are given j and to find the meafures of either of its angles. Let ABC (fig. 53.) be a fpherical triangle whofe pig 53. three tides are given: draw the radius CD (fig. 54.) Fig. perpendicular to the diameter of the primitive EF; and 6 at the point D make the angles CDA, CDG, ADI, equal refpeCtively to the tides AC, BC, AB, of the fpherieal triangle ABC (fig. 530’ hues DA, DG interfeCting the diameter EF, produced if neceffary in the points A and G : make DI equal to DG ; then from the centre C, with the radius CG, defcribe an arch ; and from A, with the diftance AI, defcribe ano¬ ther arch, interfeCting the former in B j join AB, CB, and ACB wall be the projection of the fpherical tri¬ angle (fig. 53.) and the reCtilineal angle ACB is the meafure of the fpherical angle ACB (fig. 53-)• Proposition Section III. PROJECTION OF THE SPHERE. I'rojcdion Proposition XIX. Problem XI. Sphere. ^iie three angles of a fpherical triangle being given, to t v projecl it, and to find the meafures of the lides. Fig. 55. -k6*- 55’) the fpherical triangle of which the angles are given : conftruft another fpherical triangle EFG, whofe fides are the fupplements of the given angles of the triangle ABC ; and with the fides of this fup- plemental triangle defcribe the gnomonic projeftion, &c. as before. It may be obferved, that the fupnlemental triangle El'G has alfo a fupplemental part EF^,* and when the fides GE, GF, which are fubftituted in place of the angles A, B, are obtufe, their fupplements E, ^ F are to be ufed in the gnomonic projedlion of the tri¬ angle. Proposition XX. Problem XII. Given two fides, and the included angle of a fpheri¬ cal triangle, to defcribe the gnomonic projedtion of that triangle, and to find the meafures of the other parts. Fig. 56. the fides AC, CB, and the angle ACB (fig. J3-)> be given •, make the angles CDA, CDG (fig. 56.) equal refpedlively to the fides AC, CB (fig. 530 ? ah° make the angle ACB (fig. 56.) equal to the fpherical angle ACB (fig. 53.), and CB equal to CG, and ABC will be the projedlion of the fpherical triangle. ^ To find the meafure of the fide AB : from C draw CL perpendicular to AB, and CM parallel thereto, .meeting the circumference of the primitive in M 5 make LX equal to LM; join AN, BN, and the angle ANB will be the meafure of the fide AB. To find the meafure of either of the fpherical angles, as BAC : from D draw DK perpendicular to AD, and make KH equal to KD : from K draw KI per¬ pendicular to CK, and let AB produced meet KI in I) and join HI : then the redtilineal angle KHI is the meafure of the fpherical angle BAC. By proceeding in a fimilar manner, the meafure of the other angle will be found. Proposition XXL Problem XIII. Two angles and the intermediate fide given, to defcribe the gnomonic projedlion of the triangle; and to find the meafures of the remaining parts. Let the angles CAB, ACB, and the fide AC of the fpherical triangle ABC (fig. 53.), be given : make the angle CDA (fig. 56.) equal to the meafure of the given fide AC (fig. 53.) 5 and the angle ACB (fig. 56.) equal to the angle ACB (fig. 53.) j produce AC to H, draw DK perpendicular to AD, and make KH equal to KD j draw KI perpendicular to CK, and make the angle KHI equal to the fpherical angle CA B : from I, the interfedlion of KI, HI, to A draw IA, and let it in- terfedl CB in B, and ACB will be the gnomonic pro- jedlion of the fpherical triangle ACB (fig. 53.). The unknown parts of this triangle may be meafured by laft problem. Proposition XXII. Problem XIV. Two fides of a fpherical triangle, and an angle oppo- fite to one of them given, to dqfcribe the projedtion of the triangle; and to find the meafure of the re- Gnomonic mainyrg parts. Projedtion Let tlie fides AC, CB, and the angle BAC of the Sphere, fpheiical triangle ABC (fig. 33.) be given : make the ^ angles CDA, CDG (fig. 56.) equal refpedKvely to the meafures of the given fides AC, BC : draw DK perpendicular to AD, make KH equal to DK, and the angle KHI equal to the given fpherical angle BAC : draw the perpendicular KI, meeting HI in I; j°in -A I; and from the centre C, with the diftance CG, defcribe the arch GB, meeting AI in B, join CB, and ABC will be the redlilineal projedlion of the fpherical triangle ABC (fig. 53.) and the meafures of the unknown parts of the triangle may be found as before. Proposition XXIII. Problem XV. Given two angles, and a fide oppofite to one of them, to defcribe the gnomonic projedtion of the triangle, and to find the meafures of the other parts. Let the angles A, B, and the fide BC of the tri¬ angle ABC (fig. 53.) be given : let the fupplemental triangle EFE be formed, in which the angles E, F, G, are the fupplements of the fides BC, C A, AB, refpedlive- ly, and the fides EF, EG, GE, the fupplemenls of the angles C, A, B. Now at the centre C (fig. 36.) make the angles CDA, CDK equal to the meafures of the fides GE, GF refpedlively, being the fupple¬ ments of the angles B and A $ and let the lines DA, DK interfedl the diameter of the primitive EF in the points A and K: draw DG perpendicular to AD, make GH equal to DG, and at the point H make the angle GHI equal to the angle E, or to its fupplement; and let El, perpendicular to CH, meet HI in I, and join AI: then from the centre C, with the diftance CG, defcribe an arch interfering AI in B •, join CB, and ABC will be the gnomonic projedtion of the gi¬ ven triangle ABC (fig. 33.): the fupplement of the angle ACB (fig. 36.) is the meafure of the fide AB, the* meafures of the other parts are found as before. Jt has already been obferved, that this method of pro- jedlion has, for the moft part, been applied to dialling only. However from the preceding propofitions, it ap¬ pears that all the common problems of the fphere may be more eafily refolved by this than by either of the pre¬ ceding methods of projedlion; and the facility with which thefe problems are refolved by this method has given it the preference in dialling. It may not per¬ haps be arnifs, in this place, to give a brief illuftration of it in this particular branch of fcience. In an horizontal dial, the centre of projedlion Z Fig. 57. (% 57*) reprefents the zenith of the place for which the dial is to be conftrudled ; ZA the perpendicular height of the ftyle : the angle ZPA, equal to the given latitude, determines the diftance ZP of the zenith from the pole; and AP the edge of the ftyle, which by its fhadow gives the hour: the angle ZAP, equal alfo to the latitude, gives the diftance of the equator EQ from the zenith : let E a be equal to EA, and a will be the dividing point of the equator. Hence if the angles E a I, E zr II, &c. E a XI, E a X, &c. be made equal t0 I5e>j 30°> &c*tbe equator will be divided into hours} 3 I 2 and 4.36 PROJECTION OF THE SPHERE. Section III. Gnomonic and lines drawn from P to tliefe points of divifion will ^fthfi011 ^ ^our fines* Sphere. ^ t^e e^^er vertical, or inclined to the hori- u—-y^j zon, then the point Z will be the zenith of that place whole horizon is parallel to the plane of the dial: ZE wdll be that latitude of the place ; and the hours on the former dial will now be changed into others, by a quan¬ tity equal to the difference of longitude between the given place and that for which the dial is to be conftru&ed. Thus, if it is noon when the fhadow of the ftyle falls on the line P X, then the difference of meridians is the angle E « X, or 30°. Hence, wdien a dial is to be conftrucfed upon a given plane, either perpendicular or inclined to the horizon, the declination and inclination of that place muff be previoully found. In an ereft diredt fouth dial, its zenith Z is the fouth point of the horizon, ZP is the diffance of this point from the pole, and ZE its diftance from the equa¬ tor. If the dial is directed to the north, Z reprefents the north point of the horizon 5 PZ the diftance of Z from the pole under the horizon ; and ZE the elevation of the equator above the horizon. If the dial is an ereft eaft or weft dial, the zenith Z is the eaft or weft points of the horizon accordingly, and the pole P is at an infinite diftance, for the angle ZAP is a right angle; and therefore the line AP will not meet the meridian PZ. The line ZA produced is Gnomonic the equator, and is divided into hours by lines perpendi- Projection cular to it. ot t^ie If the plane of the dial is parallel to the equator, its t p ^ere’ . zenith Z coincides with one of the poles of the equa¬ tor P 5 and hence the hour lines of this dial are formed by drawing lines from the point Z, containing angles equal to 150. In the preceding methods of proje&ion of the fphere, equal portions ef a great circle on the fphere are re- prefented by unequal portions in the plane of projec¬ tion, and this inequality increafes with the diftance from the centre of projection. Hence, in projections of the earth, thofe places towards the circumference of the projection are very much diftorted. In order to avoid this inconveniency, M. de la Hire * propofed, that the # 77^ a, eye fhould be placed in the axis produced at the di- VAcademic ftance of the fine of 450 beyond the pole: In this cafe R°yal des arches of the fphere and their projections are very near-*^'170r- ly proportional to each other. Hence in a map of the earth agreeable to this conftruCtion, the axis, inftead oigraphy. being divided into a line of femitangents, is divided equally, in like manner as the circumference. The map of the world is conftruCted agreeable to this method of projection. PRO Projection PROJECTION, in Perfpeflive, denotes the ap- Prolate Pearance> or reprefentation of an objeCt on the perfpec- . , tive plane. The projection of a point is a point through which an optic ray paffes from the objective point through the plane to the eye } or it is the point wherein the plane cuts the optic ray. And hence may be eafily conceived what is meant by the projection of a line, a plane, or a folid. PROJECTION, in Alchemy, the calling of a certain imaginary powder, called powder of projection, into a crucible, or other veffel, full of fome prepared metal, or other matter 5 which is to be hereby prefently tranf- muted into gold. Powder of PROJECTION, or of the philofophers ftone, is a powder fuppofed to have the virtue of changing any quantity of an imperfeCt metal, as copper or lead, into a more perfeCt one, as filver or gold, by the admixture of a little quantity thereof. ^ The mark to wdiich alchemifts directed all their en¬ deavours, was to difcover this pow'der of projection. See Philosophers Stone, and Chemistry, Hi/lory of PROJEC CURE, in Architecture, the outjetting and prominency, or embofiing, which the mouldings and other members have beyond the naked w’all, co¬ lumn, &c. PROLAPSUS, in Surgery, a prolapfion or falling out of any part of the body from its natural fituation : thus we fay, prolapfus intefini, “ a prolapfion of the in- teftine,” &c. See Surgery. PROLATE, in Geometry, an epithet applied to a fpheroid produced by the revolution of a femi-ellipfis about its larger diameter, See Spheroid. PRO PROLEGOMENA, in Philology, certain prepara- Prolego- tory obfervations or difcourfes prefixed to a book, &c. mena containing fomething neceffary for the reader to be ap- II. prifed of, to enable him the better to underftand the, Pro_llfic* book, or to enter deeper into the fcience, &c. PROLEPSIS, a figure in Rhetoric, by which we an¬ ticipate or prevent what might be objected by the adver- fary. See Oratory, N° 80. PROLEPTIC, an epithet applied to a periodical dif- eafe wdiich anticipates, or wLofe paroxyfm returns fooner and fooner every time j as is frequently the cafe in agues. PROLIFER flos, (proles, “ an offspring 5” and fero, “ to bear) 5” a prolific flower, or a fiower wLicb from its own fubftance produces another; a Angular de¬ gree of luxuriance, to which full flmvers are chiefly in- cident. See Botany. PROLIFIC, fomething that has the qualities necef¬ fary for generating. The prolific powers of fome individuals among man¬ kind are very extraordinary.—Inftances have been found where children, to the number of fix, feven, eight, nine, and fometimes fixteen, have been brought forth after one pregnancy. The wife of Emmanuel Gago, a la¬ bourer near Valladolid, was delivered, the 14th of June 1779, of five girls, the two firft of whom were bap¬ tized : the other three were bom in an hour after; two of them were baptized 5 but the laft, when it came into the world, had every appearance of death. The cele¬ brated Tarfin was brought to bed in the feventh month of her pregnancy, at Argenteuil near Paris, 17th July 1779, of three boys, each 14 inches and a half long, and of a girl 13 inches: they were all four baptized, but did not live 24 hours. The IROJKOTION of the ftEHEiiE . 'T®' 4k Hate CCOCXUJi. ' -> ✓ -s . / Plate eccc xur. i \ fepHiEiu: M-atc CCCCXTiV NT aJ IB C | / C- \ >' 3 /] - ; i\ / m \ j k: i r1/ / ... ( . * Pk on p c tic > Moitiie Sphilkt I’l.ite CCCJdXIA’I Mate CX’CCX ,r/2si. 1 K U < r j . A T?i \ w -X 7Z V Tv^x t' > I PRO [ 437 ] PRO Prolific The public papers for the month of June 1779 thefe expectations might roufe indignation, and be fol- Promii'e, Proimfe mac^e menti°n one Maria Ruiz, of the diftrict of lowed by confequences injurious to the perfon, the cha- u-—v—^ _ ' Lucena in Andalufia, who was fucceflively delivered of rafter, or intereft, of him who made it—it becomes a 2-t 16 boys, without any girls; and feven of them were matter of prudence in the promifer to keep his word.comes^o ftill alive on the 17th of Auguft thereafter. The fol- And farther, as a certain degree of confidence is found be binding, lowing, though a recent faft, is almoft incredible: In neceflary to the very exiftence of civil fociety, and as the year 1755, a Mufcovite peafant, named James others may have afted on the faith of his promife, it is Kyrl°ffi an an(^ perform the promife in a fenfe of his own Prometheus, in Ancient AJlronomy, was the name of without fatisfying the reafonable hopes of the promifee. a conftellation of the northern hemilphere, now called When the daughter of Tarpeius bargained with Ta- Promife Hercules, Engonajin. See ASTRONOMY. tius to betray the citadel for what he and his Sabines defined. PROMISE, inordinary cafes, is a declaration of fome wore on their left hands, meaning their rings and their intention to be put in execution ; but in morals is a fo- golden bracelets, Tatius probably performed his pro- lemn affeveration by which one pledges his veracity that mife in the way w'hich he intended, wdien he caufed her he fliall perform, or caufe to be performed, the thing to be buried under their Ihields, wdiich they carried alfo which he mentions. on their left hands. But who w ill fay that here were not As inch a declaration excites expeftations in the treachery and a dilhonourable abufe of that confidence minds of thofe to whom it is made; and as to fruftrate which had been repofed in him ? It PRO f 43& ] PRO is not bind¬ ing. Promife. It mud therefore be obvious, that the import of a u,—y——j promjpe^ w}iere its meaning is difputed, is not to be de1- In doubtful termined by the fenfe of the promifer nor by the expec- r ales the tations of the promifee j and if it was faid that the obli- interpreta- gation of a promife arofe from thofe expeftations which turn of nei- jla^ ra;feci by it, the affertion now muft be limited be ^tufted expedfations which were intentionally raifed by the promifer, or thofe which to his knowledge the pro¬ mifee was induced to entertain in confequence of that declaration which had been made to him. Should there flill be a doubt about wdrat expeftations were intention¬ ally raifed, and what ihould have been reafonably enter¬ tained, recourfe muft be had to the judgement of thole who are allowed to be perfons of candour, and who are acquainted with the charafters of the men, and with 5 thofe circumftances in which the promife was made. Cafes where The following are fome of the cafes in which a pro- a promife mife is not binding. As the obligation to perform the promife arifes from thofe expectations which are inten¬ tionally raifed by the promifer j it is plain that no pro¬ mife can be binding before acceptance, before the pro¬ mife has been communicated to the promifee, and be¬ fore he has entertained hopes of its performance. The cafe is limilar where a promife is releafed, that is, where the performance is difpenfed with by the promilee, and 7 where he entertains no expectations on account of any When it is thing than the promifer has laid to him. Should a third releafed by perf0n entertain hopes on account of the promife, he is Jee proim' to cherilh thefe hopes at his own hazard, having no en¬ couragement from the promifer to do fo : yet if this per- fon has been warranted to hope by the promifee, the pro¬ mifee has renounced his privilege of releating the pro¬ mife, and along with the promifer becomes bound for its 8 performance. Where its A promife is not binding where the performance is perform- unlawful *, and the performance is unlawful where it is ance is un- contrary to former promifes, or to any moral and reli- la-.vfuh gious precept, which from the beginning to the end of time is of perpetual and unalterable obligation. Thus no man is bound by his promife to give to me wThat he has already promifed to another ; and no man is bound by his promife to blafpheme God, to commit murder, or to criminate the innocent. Such promifes are un¬ lawfully made, and cannot be otherwife than unlawful¬ ly performed. Some have even carried their fcruples fo far as to doubt, whether any promife unlawfully made, can be doubts have lawfully performed. Should a man, during the lifetime aruen. ]-qs wjfe> happen to promife marriage to another, fuch -a man (they fay) by the Chriftian religion has already committed adultery in his heart *, and Ihould he after¬ wards become a widower, be is not bound, and he even ought not, to fulfil his engagements, as this would be putting his criminal intention into execution. This fpe- cies of reafoning, we muft confefs, is to us unintelligi¬ ble.—As the wife is dead, what now fhould prevent tne man from marrying the objeCt of his affeClions ? Why, fay the cafuifts, he already is under a promife to marry her, and his promife was made at a time when it ftiould not have been made. It is true, the performance, con- fidered by itfelf, is oppofed by no law human or divine *, but then it originated in what was wrong ; and however much the Supi-eme Being and the bulk of the creation may be out of the fecret, we have difeovered by the in¬ genious j,logic of cafuiftry, that evil can never fpring 2 0 A cafe where out of good, nor good out of evil j but that the means Promife. and the end, the motive and the action, are always of the *' fame complexion in morals. 10 When a promife is made, the particular circumftances Error'e.cm? in which it is to be deemed obligatory are fometimes l)romiles‘ mentioned. “ I promife (for inftance) to lend my friend 200 pounds within three days, provided a certain cre¬ ditor which I name do not make a demand on me before that time. In other cafes no circumftance is forefeen by the promifer to prevent the fulfilling of his engage¬ ment and hence we have erroneous promifes, which proceed on the fuppofition that things are true, poffible, and lawful, which are not fo. An erroneous promife, which proceeds on the falfe reprefentation of the pro¬ milee, is not binding. A London gentleman lately purchafed an eftate in the fouth of England at a public fale, believing the defeription which he faw in the newfpapers, and which likewife was given by the au&ioueer, to be true j but finding afterwards that the eftate nowife correfponded to the defeription, the law freed him from his engage¬ ment, becaufe the feller had evidently been guilty of a breach of promife in not fatisfying thofe expe&ations which he had intentionally and even ftudioufiy excited in the buyers. An erroneous promife, whofe performance is impof- A promife fible, is not binding. Before the conclulion of the not binding late war a planter of Tobago promifed to fend to hisw^entlie friend in England 1 2 hogftieads pf fugar from the next IsYm year’s produce of bis eftale j but before that time To- pofiible, bago fell into the hands of the French, and the Weft Indian found it impoflible to anfwer the expectations of his friend in England. J2 An. erroneous promife, whofe performance is unlaw- nor when ful, or, to fpeak more precifely, whofe performance is lt ls unlaw- contrary to a prior promife, or to any moral or reli-fu^ gious obligation, is not binding. A father, believing the accounts from abroad of his fon’s death, foon af¬ ter bequeathes his fortune to his nephew : but the fon, the report of whofe death had been falfe, returns home, and the father is releafed from the promife to his nephew, becaufe it was contrary to a prior promife, which he had tacitly come under to his fon. This prior promife wras implied in the whole of the father’s con- duft, and was exprefled in figns as emphatic and as unequivocal as thofe of language. It had all the ef- feCl too of the moft folemn promife on the fon, who, to his father’s knowledge, was induced in confequence of this promife to entertain the moft fanguine hopes of fucceeding to his father, if he furvired. The world likewife could bear teftimony that thefe expectations were not raftily cherifhed. He was brought into exif- tence by means of his father, who was thereby under- ftood to love him affectionately •, he was uihered in¬ to fociety as the reprefentative of his family, and was therefore fuppofed to be the heir of its wealth. Religion itfelf fupported his pretenfions, pronouncing the father worfe than an infidel who negleCts to fliow that atten¬ tion to his children which the world naturally expeCts from a parent.—That the father’s promife was not re¬ leafed from the mere circumftance that the miftake was known to his nephew the promifee, will appear plain from the following circumftance. Suppofe the father a landed proprietor, that the leafe of one of his farms has expired, and that he has long been expeCting to PRO [ 439 refufed, fion grant a Promife. to let it at 200l.; fuppofe that this fum is ' and that he agrees with the prefent tenant to new leafe ?t 150!-—the obligation here to perform 'his promife is not diffolved by an after offer of 200!., though the tenant knew that 200I. had been expend¬ ed, and that only from defpairing of that fum his landlord had granted the new leafe at 150I.; the pro¬ mife is binding, becaufe the performance is every way lawful, contrary to no prior engagement, and oppofed to no principle in morals. The law of the land, were the proprietor reluftant, would enforce the obligation, and exacd obedience in the tone of authority 5 becaufe breaches of faith, were they permitted in fuch cafes, would deftroy all confidence, and annihilate the bonds of focial union : Men live and profper but in mutual trull 5 A confidence of one another’s truth. Oroonoko. . 13 Util ity no criterion The great difficulty which many have to encounter in determining when erroneous promifes ought or ought judgeot t0 not to k'ffib arifes from their proceeding on a prin- tiie validity whole confequences they do not feem to be al- ofpromifes ways aware. There is feldom, they perceive, a virtu¬ ous aflion that is not attended with fbrne happy effects 5 and it will, perhaps, be generally allowed, that the com¬ parative merit of fimilar virtues may fafely be ellimated by their utility : But to make utility, as fome do, the criterion of virtue, and pronounce an adlion vicious or virtuous merely on account of thofe confequences which they fee may flow from it, is a dangerous maxim. Evil has often fprung out of good, and good out of evil ; and good and evil have frequently fprung from the fame ac- . . I4. This prin¬ ciple would give a fane- tion to vice and falfe- hcod. tion. In Mandeville’s Hive, That root of evil Avarice, That damn’d ill-natur’d baneful vice,. Was Have to Prodigality, That noble fin •, whilft Luxury Employ’d a million of the poor, And odious Pride a million more. Envy itfelf and Vanity Vvere minillers of Induftry : That darling folly, Ficklenefs, In diet, furniture, and drefs, That flrange ridiculous vice, was made The very wheel that turn’d the trade. The defeription here is not altogether falfey and thefe indeed may be fome of the confequences that flow from avarice, luxury, pride, vanity, and envy : but thefe are not all.—To fee at once all the confequences that fpring from an aflion, the good and the bad, the par¬ ticular and general, the immediate and remote, would require fometimes the forefight of Ornnifcience, and at all times a knowledge fuperior to what is human. In the Fable of (he Bees, the author’s objeft was to fliow that private vices are public benefits 5 and he therefore was naturally led by his argument to confider only fuch confequences of vice as favoured his hypothefis. He xvanted candour. And that artifice which runs through his Fable happens to remind us, that while the remote and the general effebls of an aflion may not be feen, the particular and immediate, which fall within our no¬ tice, are apt to be viewed through tire medium of paf- ] PRO interefl, or opinion. For thefe reafons, it appears Promife. furprifing how any perfon fhould ever imagine that the —v— obligation to perform a promife (hould depend entirely upon the ideas which the promiler apprehended of its utility. 1 he belt 1'efutation of fuch an opinion are the Angu¬ lar conclufions to which it leads. j 5 A late writer on political juftice, who appears to t'l>e confe- have embraced it, gets into realoning not very common. rlliences In a part of his lyitem he looks on morals as an article of trade: virtue and vice, in his Chapter of Promifes, are but antiquated terms tor profit and lofs j and right and abiurd. and wrong are ufed to exprefs what is beneficial and what is hurtful, in his apprehenfion, to himfelf and the community.—-With refpedt to veracity, thofe “ rational and intelligent beings,” by whom he withes the affairs' of the world to be carried on, may, while they , aft as rational and intelligent, break or perform their promifes at pleafure. He thinks it “ effential to various circum- ftances of human intercourfe, that we fliould be known to beflow a Heady attention upon the quantities of con¬ venience or inconvenience, of good or evil, that might arife to others from our conduft.” After this atten¬ tion, the difappointment of the promifee is not to be minded, though the expeftations excited by thefe “ ra¬ tional and intelligent beings” may have “ altered the na¬ ture of his fituation, and engaged him in undertakings from which he would otherwile have abftained.” What the promifer takes to be the general utility and the fit- nefs of things is to be his guide. And a breach of promife will be attended with the following advantages: “ The promifee, and all other men, will be taught to depend more upon their own exertions, and lels upon the affiftance of others, which caprice may refufe or juftice withhold. He and all others will be taught to acquire fuch merit, and to engage in fuch purfuits, as (hall oblige any honeft man to come to their fuccour if they ftiould Hand in need of affiflance.” This breach of promife, with a view to the general utility, will, lb far from being criminal, form a part of that refolute execution of juftice which would in a thoufand ways increafe the independence, the energies, and the virtue of mankind L” * Godwin's Such are the views which determined this author to Inquiry confider “ the validity of promifes” as “ inconfiflent r^nce,n'l7’g with juftice,” and as “ foreign to general good.” From y.1,:?;™1 one, however, who relies with fo much confidence onbockiii’.- the promifer, it would certainly be defirable to know, chap* 3* whether the perfon, who violates his faith for the pub- x6 lie utility, is always to be candid. Where, breach of A private faith promotes his-own inlereft, ought he alone to de- ’“dwidual cide on the validity of his promife ? or where promifes!!<1S nor’/’lu are broken tor the general good, is he to be guided byhisfehemes his own vifionary Ichemesof utility? Is he to aft as of utility on . truftee for the public without any delegated power ? ^ public, and ftiall the community fubmit to his decifions without fo much as putting the queftion, Who hath made thee a ruler over us ? When a writer thus deviates fo far from the path of reafon, it is natural to alk, what was the ignis fatuus that milled him ? In the prefent cafe it is pretty obvious. Being fomething of opinion with the celebrated Turgot f, that romances are the only f See Note, books in which moral principles are treated in an im-hook bb partial manner, this gentleman, in his Chapter ofcns!i3- ^ Promifes, feems to have borrowed a part of his morality » from.. PRO [ 440 Promile, from the doggerels of Butler j and having adopted, though from different motives, the political principles of Sir Hudibras’s fquire, that obedience to civil go¬ vernment is not due becaufe it is promifed, he has come to exaftly the fame concluffon with refpedl to the ob¬ ligation of keeping one’s word. But Ralph has rea- foned with more ingenuity; and has fliown not only that the public good, but the glory of the Lord, may be fometimes promoted by a breach of faith. The faints are God¬ win’s ra¬ tional and intelligent teings. I? Views of utility an unfafe guide in morals. The faints, * whom oaths and vows oblige, Know little of their privilege •, Farther, I mean, than carrying on Some felf-advantage of their own : For if the dev’l, to ferve his turn, Can tell truth, why the faints ftrould fcorn, When it ferves theirs, to fwear and lie, I think there’s little reafon why : Fife h’ has a greater pow’r than they, Which ’twere impiety to fay : W’ are not commanded to forbear, Indefinitely, at all to fwear j But to fwear idly, and in vain, Without felfintereft and gain ; For breaking of an oath and lying Is but a kind of felf-denying, A faint-like virtue j and from hence Some have broke oaths by Providence : Some, to the glory of the Lord, Perjur’d themlelves and broke their word — For faints may do the fame thing by The fpirit, in fincerity, Which other men are tempted to, And at the devil’s inftance do. Hudibras, Canto II. Here are new views of utility j which, were they to be confidered as of any weight, would increafe the dif¬ ficulty of determining when an erroneous promile ought to be kept. But fliould views of utility be laid afide, and ffiould it be made an invariable rule that truth is on no account to be violated, that deceit is never to be praftifed, and that moral obligations are not to be diffblved for the profped! of any phyfical advantage ; thofe doubts which arife concerning the validity of erroneous pro- mifes will foon difappear. Difagreeable perhaps and ridiculous confequences may fometimes arife to a few individuals from an honeft and confcientious adherence to their promife ; but will any aflert that the general good, t/iat burden of the fong, will ever be endangered by too much veracity ? So numerous inconveniences arife daily from the re¬ gular operation of thofe great phyfical laws, which are under the immediate direftion of Providence, that thofe philofophers who have adopted the principle of utility, and are much furprifed to fee the univerfe fo aukwardly planned for the eafe and comfort of them and their fpe- cies, have been under the neceffity of imputing many events in nature to the malignity of fome evil indepen¬ dent being ; or of allowing that things have degenera¬ ted fince they firft came from the hands of the Crea¬ tor, and that they muff now be exceedingly altered from what they had been when He chofe to pronounce them all very good. Thus, abfurdity or impiety muff; l ] PRO always be the confequence of judging of the vice Promife. and virtue of an a6tion by its utility, and of eftimat- ''“"“’'v ing its utility by our limited views and erroneous con¬ ceptions. As for extorted promifes, it is curious to obferve how this queftion ftrould always be ftarted, whether or not they ought to be kept ? and another queftion ftrould feldom be thought of, whether or not they ought lS to be made ? Fortitude was one of the cardinal virtues, Extorted among the ancients ; and is deemed of fuch importance pronrifes. in the Chriftian fyftem, that the fearful are clafied with the unbelievers, and are thought unworthy of the fa¬ vour of the Deity, as being incapable of fupporting thofe trials to which heaven expofes the faithful as the trueft ^ teft of Chriftian virtue.—If a perfon flrould want the Whether neceflary fortitude to be virtuous, it will be a poor ex-binding or cufe for his bafenefs, that he has added deceit to hisnot‘ cowardice : and furely it is not the bufinefs of morality, when it has found him guilty of one crime, to grant him a difpenfation for committing two. The laws of jurifprudence, it will readily be allowed, cannot favour the claims of the promifee ; becaufe they ought never to lend their fupport to oppreffion and violence. But their acquittal, ftrould he violate his faith, will by no means vindicate the charafter of the promifer. Their acquitting a woman from the charge of adultery, goes a fhort way in reftoring the fair reputation of her innocence. Let jurifprudence decide as it will, the man of honour and the generous patriot can never be brought to re- fpeft the perfon who, ftruck vrith a panic, could betray either himfelf or his friends. The magnanimous fpirits who could die for the truth will view with contempt his pitiful deceit. Thofe unfortunate men who may fuffer from that very diftruft which the breach of his faith has begotten, will always deteft him as a traitor and enemy ; and heaven itfelf cannot be fuppofed to re¬ ward that foldier who deferts her caufe, and relinquifties the poll which ftie has afligned him, at the fight of dan- ger. If we once begin to accommodate morality to the difpofitions and humours of mankind, it is hard to fay where this fpecies of complaifance will end. The de¬ grees of timidity are fo various, and fome tempers by nature fo yielding, that repeated importunity or an ear¬ ned: requeft will extort a promife. 2Q A young lady was frequently prefied by her dying q-he laws hufband to grant him a promife that Ihe would not of morality marry after his death. For fome time (he was able to are not to refill with becoming fpirit his abfurd requeft ; but upon be accom¬ modated to nterefts of ot a fecond lover, andraan^‘n^' his declaring oftener than once that he could not other-^ jiu_ wife die in peace, Ihe complied and promifed. I 00 mours and young, however, for this effort of continence, {he after wrards liftened to the addreffes found her heart infenfibly engaged before Ihe adverted to the impropriety of a new attachment. But propo- fals of marriage could fcarcely fail to remind her of her promife and awaken her fcruples. Thefe llte foon com¬ municated to her lover, with her firm refolution to re¬ main a widow, if the contrary meafure, which Ihe great¬ ly preferred, and on which her earthly happinefs depended, were not approved by fome fpiritual coun- fellor. Upon this declaration it was agreed to take the advice of their own minifter, who was an eminent diffenting clergyman PRO [44 Promife. clergyman in the diocefe of Oxford : but this gentle- ■,~l man, unwilling to decide in a matter of fuch importance, propofed to refer it to Dr Seeker, who was then bifhop of that fee. This prelate too declined to give any judg¬ ment in the cafe j but, as was his way, muttered up a number of arguments on each fide of the queftion, and committed them to a letter, which a learned gentleman of our acquaintance had feme time ago an opportunity of feeing in manufeript. If the fentiments to which the bithop was inclined could have been inferred from his ftatement of argu¬ ments, he feemed to think that the promife was binding. In our opinion, he ought to have given a pofitive deci- fion. It was no matter whether the promife was ex¬ torted or not : the promile was made; and the queftion was now, whether or not wras the performance lawful ? That it was lawful appears evident. The lady was un¬ der a moral obligation to remain a widow 5 and no moral obligation, fo far as we know, required her to marry. To be fruitful and multiply, indeed, is declared in Scripture, and is found, to the woful experience of many, to be one of the general laws of our nature. But of all thofe laws intended by nature to regulate the con- ducl of inferior intelligences, the moral,which were meant to be checks and corredlors of thofe abufes to which the phyfical are apt to be carried, are certainly the moft Moral laws facred and obligatory. To procreate his fpecies, a man fuperior to is not then to be guilty of adultery, or of fornication, or to liften to the lewd calls of incontinency. St Paul’s ligation. obfervation, that it is better to marry than burn, can¬ not be allowed in this inftance to have much weight. He has not defined what degree of amorous inflamma¬ tion conftitutes burning, nor in what cafes this burning would be a fufficient warrant for marrying. In the prefent inftance he does not even confider marriage as a duty j he compares it with burning, and thinks it on¬ ly the leaft of the two evils. Not that marriage is evil of itfelf ^ for he that marrieth doth well: but there are circumftances in which it would be inconvenient to mar¬ ry, and in which he that marrieth not is faid to do bet¬ ter. But if thofe inconveniences be reafons fufficient to deter from marrying, is that perfon to be held excufable who, in order to gratify an animal paffion, fomewhat refined, fhould violate an oath, and trample on a facred moral obligation ? The young lady might indeed declare that her earth¬ ly happinefs was at an end if ffie were not permitted to marry again : but what circumftance prevented her from marrying ? It was not the opinion of her own paftor, or the bilhop of Oxford : the truth is, it was certain fcruples of her orvn, which being unable of her- felf to overcome, ffie had pioufiy folicited the affiftance of others. It is certainly a misfortune that a devotion¬ al and amorous turn ftrould always be fo clofely con- nefled in the females. Both, however, cannot always be indulged. Who will fay, that the motive is rational which inclines one to cheriffi a paffion which confcience difapproves ? The virtue of continency might indeed have borne hard on this lady’s conftitution, and in her way to immortal happinefs might have formed a gate fo ftrait and narrow as it might be difficult for her to pafs through : but after all, her cafe was not harder than that of nuns, who take the vows of perpetual chaftity, and endure fufferings of a fimilar nature, and in fome inftances Vol. XVII. Part II. 1 ] PRO even perhaps greater than hers ; yet doing it cheerfully, Promite- from the fuppofition that the Omnifcient is well acquaint- o II ed with the nature of the great facrifice which they ‘ roriS^‘oe'j make, and that after death he will ftudy to requite them, and bellow on them fomelhing like an equivalent, which in their opinion can fcarcely be lefs than a happinefs in heaven as ample as their withes and as lulling as their fouls. Every promife, therefore, which is not releafed, nor fraudulently obtained by the promifee, is to be held bind¬ ing if the performance be lawful and poffible. 22 The Chriftian cannot, and a man of honour willA promife fcarcely venture to reject this maxim, that a gcod man0* a fimil?r ought not to change though he i’wear to his hurt. a limple promife and a promiffory oath are not very dif- '' ferent in point, of obligation. Moft people know, and where any moral duty is concerned, they ought parti¬ cularly to refledt, that this world is governed by an Al¬ mighty Being, who knows all things, who lives always, and who is juft to reward and to puniffi. The perfon who makes a promiflbry oath does it avowedly under an immediate fenfe of thefe truths; the perfon who makes a fimple promife, though he certainly ought, yet may not reftedl on thefe at the time. The former, when he violates his oath, exhibits, only to outward appearance, a greater contempt of the Divine power, knowledge, and juftice, than he who violates a fimple promife under an impreffion of the fame truths. To Him who knows the fecrels of the heart, the breach of the promife muft appear as criminal as the breach of the oath. See Assumpsit and Oath. PROMONTORY, in Geography, a high point of land or rock projecting into the fea; the extremity of which towards the fea is called a cape or headland. See Geography Index. PROMPTER, in the drama, an officer pofted be¬ hind the feenes, whole bufineis it is to watch attentively the adlors fpeaking on the ftage, in order to fugged and put them forward when at a ftand, to corredt them when amifs, &c. in their parts. PROMULGATED, of Promulged, fomething publifhed or proclaimed, and generally applied to a law, to denote the publiftung or proclaiming it to the people. PiiONAOS, in the ancient agriculture, a porch to a church, palace, or other fpacious building. Sec the article Porch. PRONATION, among anatomifts. The radius of the arm has two kinds of motion, the one called pro- nation, the other fuptnation. Pronation is that where¬ by the palm of the hand is turned downwards ; and fu- pination, the oppofite motion thereto, is that whereby the back of the hand is turned downwards. The pe¬ culiar mufcles whereby pronation is performed, are call¬ ed pronatores, as thofe by which fupination is performed are termed fupinatorcs. See Anatomy, Table of the Mufcles, and Plates. PRONG-hoe, in huffiandry, a term ufed to exprefs an inftrument ufed to hoe or break the ground near and among the roots of plants. The ordinary contrivance of the hoe is very defe&ive, it being only made for feraping on the furface ; but the great ufe of hoeing being to break and open the ground, Sefide the killing of the weeds, which the ancients, and many among us, have thought the only ufe of the hoe, 3 K this PRO [ 442 ] PRO Prong-hoe this dull and blunt inftrument is by no means calculated _ il . for the purpofes it is to ferve. The proncr-hoe confiits of tion. ^wo hooked points ol fix or feven inches long, and when - firuck into the ground wall ttir and remove it the fame depth as the plough does, and thus anfwer both the ends ol cutting up the weeds and opening the land. It is ufe- ful even in the horfe-hoeing hufbandry, becaufe the hoe- plough can only come within three or four inches of the rows of the corn, turnips, and the like ; whereas this in- ftrument may be ufed afterwards, and with it the land may be railed and ftirred even to the very ftalk of the plant. See Agriculture. PRONOUN, Pronomen, in Grammar, a declinable part of fpeech, which being put inftead of a noun, points out fome perfon or thing. See Grammar. PRONUNCIATION, in Grammar, the manner of articulating or founding the wmrds of a language. Pronunciation makes the moft difficult part of written grammar •, in regard that a book expreffing itfelf to the eyes, in a matter that wholly concerns the ears, feems next akin to that of teaching the blind to diftinguilh co¬ lours : hence it is that there is no part lb defeftive in grammar as that of pronunciation, as the writer has fre¬ quently no term whereby to give the reader an idea of the found he wmuld exprefs j for want of a proper term, therefore, he fubftitutes a vicious and precarious one. To give a juft idea of the pronunciation of a language, it feems neceflary to fix as nearly as poffible all the feve- ral founds employed in the pronunciation of that lan¬ guage. Cicero tells us, that the pronunciation under¬ went feveral changes among the Romans : and indeed it is more precarious in the living languages, being, as Du Eos tells us, fubfervient to faflrion in thefe. The French language is clogged wfith a difficulty in pronunciation from wffiich moft others are free 5 and it confifts in this, that moft of their wTords have twro different pronuncia¬ tions, the one in common profe, the other in verfe. As to the pronunciatiqn of the Engliftr language, the ingenious Mr Martin, in his Spelling-Book of Arts and Sciences, lays down the following rules : 1. The final (e) lengthens the found of the foregoing vowTel; as in can, cane; rob, robe; tun, tune, &c. 2. The final (e), in words ending in re, is founded before the r like u ; as majjacre, maJJ'a-cur ; lucre, lu cur, &c. 3. The Latin diphthongs te, ce, are founded like e; as /Etna, Etna, ceconomy, eco¬ nomy, &c. : but at the end of the words oe founds like 0; as in toe, foe, &c. 4. Alfo the Engliffi improper diph¬ thongs, ea, eo, eu, ue, found only the e and u ; as tea or te ; feoffee or feffce ; due or du ; true or tru, &c. though fometimes eo and ea are pronounced like ce, as in people, fear, near, &c. 5. Sometimes the diphthong {ie ) is pronounced like e in ceiling, like ee in field, and, at the end of wmrds, always like y, as in lie, &c. 5 and uft thou art, and to dull thou fhalt return.” Had our firft parents been thus left, they mult have looked upon themielves as rejected by their Maker, delivered up to trouble and forrow in the world, and as having no hope in any other. With fuch impreflions on their minds they could have retained no fenfe of religion j for reli¬ gion, when^ unaccompanied by hope, is a ftate of frenzy and diftraction . yet it is certain that they could have no hope from any thing exprefsly recorded by Mofes, ex¬ cept what they might draw from this fentence paffed on their deceiver.. Let us then endeavour to afcertain what confolation it could afford them. At that awful juncture, they muff have been fenfible that their fall was the vi&ory of the ferpent, whom by- experience they had found to be an enemy to God and to man. It could not therefore but be fome comfort to them to hear this enemy firrt condemned, and to fee that, however lie had prevailed againft them, he had gained no viftory over their Maker. By his condem¬ nation they were lecured from thinking that there was any malignant being equal to the Creator in power and dominion j an opinion which, through the prevalency of evil, gained ground in after times, and was deftruaive of all true religion. The belief of God’s fupreme do¬ minion being thus preferved, it was ftill neceffary to give them luch hopes as might induce them to love as -veil as to fear him j and thefe they could not but con¬ ceive when they heard from the mouth of their Creator and Judge, that the ferpent’s viaory was not complete even over themfelves ; that they and their pofterity mould be enabled to conteff his empire j and that though they were to fuffer much in the ftruggle, they tliould yet finally prevail, bruile the ferpent’s head, and deliver themfelves from his power and dominion. . This prophecy therefore was to our firft parents a light. Ihining in a dark . place. All that they could certainly conclude from it was, that their cafe was not defpeiate that fome remedy, fome deliverance from the evil they were under, would in time appear ; but when or where, or by what means they were to be delivered, they could not poffibly underftand, unlefs the matter was further revealed to them, as probably it was at the infti- tution of facnfice (See Sacrifice). Obfcure, how¬ ever, ^as this promife or prophecy was,, it ferved after the fall as a foundation for religion, and truft and con¬ fidence towards God in hopes of deliverance in time from the evils of difobedience : and this appears to have been the foie purpofe for which it was given, and not, Prophe cy> 1 45o j PRO .viil put enmity as fome wsll-raeaning though weak advocates for Clirif- tianity have imagined, as a prediclion pointing diretlly to the crofs of Chrill. As this prophecy, was the firft, fo is it the only con- fiderable one in which we have any concern from the creation to the days of Noah. It was proportioned to the then wants and neceflities of the world, and was the grand charter of God’s mercy after the fall. Nature had no certain help for finners; her rights were loft with ner innocence. It was therefore neceffary either to deftroy the offenders, or to raife them to a capacity of falvation, by given them fuch hopes as might ena¬ ble them to exercife a reafonable religion. So far the light of this prophecy extended. By what means God intended to work their falvation, he did not exprefsly declare : and who has a right to complain that he did not, or to prefcribe to him rules in difpenfing his mercy to the children of men ? Upon the hopes of mercy which this prophecy gives The curfe in very general terms, mankind refted till the birth of removed Noah. At that period anew propliecy was delivered ^jern tfie by Lamech, who foretels that his fon ftiould comfortsrouncl' them concerning the work and toil of their hands, “ becaufe of the earth which the Lord had curfedy We are to remember that the curfe pronounced upon the earth was part of the fentence paffed upon our firft pa¬ rents ; and when that part was remitted, if it ever was remitted, mankind would acquire new and more lively hopes that in God’s good time they {hould be freed from the whole. But it has been Ihcwn by Bilhop Sherlock*, * u/e and that this declaration, of Lamech’s was a predi&ion, that Intent of during the life of his fon the curfe fhould be taken off Prophecy. from the earth : and the fame prelate has proved with great perfpicuity, and in the moft fatisfaiftory manner, that this happy revolution actually took place after the Hood. The limits prefcribed to an article of this kind will not permit us even to abridge his arguments. We ftrall only obferve, that the truth of his conclufion is manifeft from the very words of fcripture; for when God informs Noah of his defign to deftroy the world, he adds, “ But with thee will I eftablilh my covenant and as foon as the deluge was over, he declared that he “ would not again curfe the ground any more for man’s fake 5 but that while the earth Ihould remain, feed time and harveft, and cold and heat, and fummer and winter, and day and night, Ihould not ceafe.” From this laft declaration it is apparent that a curfe had been on the earth, and that feed-time and harveft; had often failed j that the curfe was now taken off; and that in confe- quence of this covenant, as it is called, with Noah and his feed and with every living creature, mankind Ihould not henceforth be fubje&ed to toil fo fevere and fo gene¬ rally fruitlefs. 0 It may feem furprifing perhaps to fome, that after foA future great a revolution in the world as the deluge made,life not God fhould fay nothing to the remnant of mankind ofthen espli* the punifhments and rewards of another life, but fhould make a new covenant with them relating merely to fruit- C ful feafons and the bleffings of the earth. But in the fcriptures we fee plainly a gradual working of provi¬ dence towards the redemption of the world from the curfe of the fall; that the temporal bleflings were firft reftored as an earneft and pledge of better things to follow ; and that the covenant given to Noah had, ftriaiy fpeaking, nothing to do with the hopes of futuri- PRO Prophecy, ty, wlucli were referved to be the matter of another “V—■*'' covenant, in another age, and to be revealed by him, whofe province it was to “ bring life and immortality to light through the gorpel.” But if Noah and his forefathers expected deliverance from the whole curfe of the fall, the aftual deliverance from one part of it was a very good pledge of a further deliverance to be ex¬ pelled in time. Man himlelf was curfed as well as the ground ; he was doomed to dull : and fruitful feafons are but a fmall relief, compared to the greatnefs of his lofs. But when fruitful feafons came, and one part of the curfe was evidently abated, it gave great aflurance that the other fhould not laft for ever, but that by fome means, ftill unknown to them, they fliould be freed from the wrhole, and finally bruife the ferpent’s head, who, at the deluge, had fo feverely bruifed man’s heel. Upon this affurance mankind relied for fome genera¬ tions, and praftifed, as we have every reafon to believe, a rational wmrlhip to the one God of the univerfe. At laft, howTever, idolatry was by fome means or other in¬ troduced (fee Polytheism), and fpread fo univerfally through the world, that true religion would in all pro¬ bability have entirely failed, had not God vilibly inter- pofed to preferve fuch a fenfe of it as w^as necelfary for the accomplifhment of his great defign to reftore man¬ kind. This he did by calling Abraham from amidft his idolatrous kindred, and renewing to him the word of prophecy : “ Get thee out of thy country (faid he), and from thy kindred, and from thy father’s houfe, unto a land that I will fhew thee. And I wall make of thee a great nation, and I will blefs thee and make thy name great; and thou (halt be a blefiing. And I wall blefs them that blefs thee, and curfe him that curfeth thee ; and in thee lhall all the families of the earth be bleffed.” Thefe magnificent promifes are feveral times repeated to the father of the faithful with additional cir- cumftances of great importance, fuch as, “ that he fhould be multiplied exceedingly •, that he fhould be a father of many nations ; that kings fhould come out of him and above all, that God would eftablifh an everlafling Covencnit with him and his feed, to give him and them all the land of Canaan for an everlafling pojfeffion, and to be their Gody Upon fuch of thefe promifes as relate to tempo¬ ral bleftings we need not dwell. They are much of the fame nature with thofe which had been given be¬ fore to Lamech, Noah, Shem, and Japheth; and all the wmrld knows how amply and literally they have been fulfilled. There was however fo little probability in nature of their accomplifhment at the time wftien they were made, that we find the patriarch afking “ Where- f Genefis ^7 he fhould hnoivf that he fhould inherit fuch an ex- Xv. 8. &c. tent of country ?” And as die promifes that he fhould f 451 1 P R O *3 Promife to Abraham. inherit it were meant to be a foundation for religion Prophecy* and confidence in God, a miraculous fign was given him ' '' V"—*■' that they came indeed from the fpirit of truth. This removed from his mind every doubt, and made him give the fulleft credit, not only to them, but alfo to that other promife, “ that in his feed fhould all the nations of the earth be bleffed.” What diftincl notion he had of this blefting, or in what manner he hoped it fliould be effected, we cannot pretend to fay. “ But that he underftood it to be a pronufe of reftoring mankind, and delivering them from the remaining curfe of the fall, there can be no doubt. He knew that death had entered by fin •, he knew that God had promifed viclory and redemption to the feed of the woman. Upon the hopes of this reftoration the religion of his anceftors was founded ; and when God, from whom this blefling on all men veas expe&ed, did exprefsly promife a blefling on all men, and in this pro¬ mife founded his everlafting covenant—what could Abra¬ ham elfe expedl but the completion in his feed of that ancient promife and prophecy concerning the viclory to be obtained by the woman’s feed ? The curfe of the ground ivas expiated in the flood, and the eartli reftored with a blefling, which was the foundation of the tempo¬ ral covenant with Noah ; a large {hare of which God exprefsly grants to Abraham and his pofterity particu¬ larly, together with a promife to bring, by their means, a new and further blefling upon the whole race of men. If we lay thefe things to heart, we cannot fuppofe that lefs could be expedted from the new promife or prophe¬ cy given to Abraham than a deliverance from that part of the curfe ftill remaining on men : Z)a/? thou art, and to dujl thou /halt return. In virtue of this covenant A- braham and his pofterity had reafon to expedl that the time would come when man fhould be called from his dull again. For this expeclation they had his affurance who gave the covenant, that he would be their God for ever. Well might bur Saviour then tell the fens of Abraham, that even Mofes at the bufti fliowed the re- furredlion of the dead, when he called the Lord the God of Abraham, and the God of Ifaac, and the God of Jacob*.” * sher- Thefe promifes made to Abraham were renewed to^ock’- life Ifaac and Jacob ^ to the laft of whom it was revealed,hntenl not only that all the nations of the earth fliould be Prolhe' bleffed in his feed, but that the blefling fliould fpring ^ from his fon Judah. It is, however, by no means evi- rr j^ac dent that any one of thofe patriarchs knew precifely by an(i jacob, what means (a) the Curfe of the fall was to be entirely removed, and all men called from their dull again. It was enough that they were convinced of the fa6l in ge¬ neral terms, fince fuch conviftion was a fufficient foun¬ dation of a rational religion ; and the defeendants of A- braham had no other foundation upon •which to reft 3 L 2 their (a) This they certainly could not know from the promifes exprefled in the very general terms in which thev are recorded in the book of Genefis. It is, however, not improbable that thofe promifes, as they immediately re¬ ceived them, were Conceived in terms more precife and particular *, and, at all events, Dr Warburton has proved to the full convi£lion of every man who is not a determined unbeliever, that Abraham was commanded to facrifice his fon Ifaac, not only as a trial of his obedience, but alfo that God might give him what he earneftly defired a feenical reprefentaticn of the means by which mankind were to be redeemed from death. The learned writer thinks, and his reafoning compels us to think with him, that to this tranfaftion our Saviour alludes when he fays ** Your father Abraham rejoiced to fee my day, and he faw it and was glads” 15 T he iavr or Mofes and the fuc- ceeding prophets. PRO [45 Pro^iecy. their hopes, and pay a cheerful worfhip to the God of their fathers, till the giving of the law to Mofes. Then indeed they were incorporated into a fociety with muni¬ cipal laws of their own, and placed under a theocratic government; the temporal promiies made to their fa¬ thers were amply fulfilled ; religion was maintained a- mong them by rewards and puniihments equally diftri- buted in this world (fee Theology) : and a fines of prophets fucceeding one another pointed out with great¬ er and greater ciearneis, as the fulnels of time approach¬ ed, the perfon wb-3-was to redeem mankind from the power of death by what means he was to work that great redemption, and at what precife period he was to make his appearance in the world. By thefe fuperna- tural interpofitions of divine providence, the principles of pure theilm and the practice of true religion were preserved among the children of Ifrael, when all other nations were funk in the grofleil idolatry, and wallowed in the molt abominable vices ; when the far-famed E- gyptians, Greeks, and womans, fell down with adoration to flocks and Itones and the vileft reptiles; and when 16 Were all intended to keep alive a fenfe of religion.. '1 The pro¬ phecies to be confider ed ip con- netfhon, they E d no well-grounded hope of another life, and were in fa£t without God in the world. From this fhort deduction,.we think ourfelves intitled to conclude, that the primary ufe and intent of prophe¬ cy, under the various difpenlations of the Old Tefta- ment, was not, as is too often fuppofed, to eftabliih the divine million of Jefus Chrift, but to keep alive in the m.nds of thoie to whom it was given, a fenfe of reli¬ gion, and a hope of future deliverance from the curie of the falT It was, in the expreflive language of St Peter, “ a light that (hone in a dark place, unto which men did well to take heed until'the day dawned and the day- flar arofe in their hearts.” But though this was cer¬ tainly the original intent of prophecy (for Chrift, had he never been foretold, would have proved himfeif to be the fbn of God with power by his aftonifhing mi¬ racles, and his refurrection from the dead), yet it can¬ not be denied, that a long feries of prophecies, given in different and far diftant ages, and having all their completion in the life, death, and refurreffion, of.Telus concur very forcibly with the evidence of miracles to prove that he was the feed of the woman ordained to bruife the head of the ferpent, and reftore man to his forfeited inheritance. To the Jews the force of this evidence mull have been equal, if not fuperior, to that of miracles themfelves; and therefore we find the A- poftles and firft preachers of the gofpel, in their ad- dreffes to them, conftantly appealing to the law and the prophets, whilft they urged upon the Gentiles the evi¬ dence of miracles. In order to form a right judgement of the argument for the truth of Chnftiaiuty drawn from the fure word of.prophecy, we muft not confider the prophecies given in the Old I eft ament as fo many prediSlions only inde¬ pendent of each other ; for if we do, we fhall totally lofe light of the purpofe for which they were originally gi¬ ven, and fhall never be able to fatisfy ourfelves when confronted by the obje&ions of unbelievers. It is eafy for men of leifure and tolerable parts to find difficulties in particular prediffions, and in the application of them made by writers, who lived many hundred years ap'o, and who had many ancient books and records of the Jewifh church, from which they drew many palfages, and perhaps fome prophecies j which books and records 2 ] PRO we have not to enable us to underftand, and to juftify Prophecy, their applications. But it is not fo eafy a matter to x—■■■' fnow, or to perfuade the world to believe, that a chain of prophecies reaching through leveral thoufand years, delivered at different times, yet manifeftly fubfervient to one and the fame adminiftration of providence from beginning to end, is the effe& of art and contrivance and religious fraud. In examining the feveral prophe¬ cies recorded in the Old Teftament, we are not to fup- pofe that each of them exprefsly pointed out and clear¬ ly characterized Jefus Chrift. Had they done fo, in- ftead of being a fupport to religion in general, the pur¬ pofe for which they were originally intended, they would have had a very different effeCt, by making thofe to whom they were given repine at being placed under difpenfations- fo very inferior to that of the gofpel. We are. therefore to inquire only whether all the notices, which, in general and often metaphorical’ terms, God gave to the fathers of his intended falvation, are perfeCT- ly anfwered by the coming of Chrift ; and we fhall find that nothing has been promifed with refpeCl to that fub- jecl which has not been performed in the ampleft man¬ ner. If we examine the prophecies in this manner, we fhall find that there is not one of them, which the Apofiles have applied to the Meftfah, that is not appli¬ cable in a rational and important fenfe to fomething in the birth, fife, preaching, death, refurreClion, and afeen- flon of Jefus of Nazareth ; that as applied to him they are all confiftent w ith each other ; and that thouuh home few of them may be applied without abfurdity to perfons and events under the Jewifh difpenfation, Chrift is the only perfon that ever exifted in whom they all meet as in a centre. In the limits preferibed us, it is impofiible that we ftiould enter upon a particular proof of this pofition. It has been proved by numberlefs wri¬ ters, and, with refpecl to the moft important prophecies, by none with greater fuccefs than Bifhop Sherlock in his Ufe and Intent of Prophecy in the feveral ages of the World ; a work which we recommend to our read¬ ers as one of the moft valuable on the fubjeCl m our own or any other language. But admitting that it wmuld have been improper, for Objection the reafons already hinted at, to have given a clear and train the precife defeription of Chrift, and the Chriftian difpenfa-ubbunty tion, to men who were ordained to live under difpen-,,f P10ijhe- fations lefs perfeft, howq it may be a/ked, comes it toCy’ pafs that many of the prophecies applied by the writers of the gofpel to our Saviour and his aftions are ftill dark and obfeure, and fo far from belonging evidently to him and to him only, that it requires much learning and fa- gacity to fhowr even now' the conneftion between fome prophecies and the events ? T f. In anfwer to thefe queftions, the learned prelate juft Ar.bvtrtd. referred to obferves, “That the obfeurity of prophecy does not arife from hence, that it is a relation or deferip¬ tion of fomething ; for it is as eafy to (peak of things future plainly, and intelligibly, as it is of things part or prefent, It is not, therefore, of the nature of prophecy to be obfeure ; for it may eafily be made, when he wdio gives it thinks fit, as plain as hiflory. On the other fide, a figurative and dark defeription of a future event will be figurative and dark ftill when the event happens; and confequently will have all the ob¬ feurity of a figurative and dark defeription as well after as before the event. The prophet Ifaiah deferibes the peace ) PRO [ 453 ] PRO Prcphfcy, peace of Chrift’s kingdom in the following manner : "-y—‘ The wolf dull dwell with the lamb, and the leopard (hall lie down with the kid, and the calf and the young lion, and the fading,‘together, and a little child ihall lead them.’ Nobody, fome modern Jews excepted, ever underftood this literally ; nor can it now be lite¬ rally applied to the ftate of the gofpel. It was and is capable of different interpretations : it may mean tem¬ poral peace, or that internal and fpiritual peace—that tranquillity of mind, which lets a man at peace with God, himfelf, and the world. But whatever the true meaning is, this prophecy does no more obtrude one determinate fenfe upon the mind fince the coming of Chrift than it did before. But then we fay, the Hate of the gofpel rvas very properly prefigured in this de- fcription, and is as properly prefigured in a hundred more of the like kind •, and fince they all agree in a fair application to the ftate of the gofpcd, we ftrongly con¬ clude, that this Hale wras the thing foretold under fuch expredions. So that the argument from prophecy for the truth of ChriRianity does not reit on this, that the event has neceffarily limited and afcertained the parti- oular fenfe and meaning of every prophecy •, but in this, that every prophecy has in a proper fenfe been completed by tire coming of ChriH. It is abfurd, therefore, to expedf clear and evident conviftion from every fingle prophecy applied to ChriH j the evidence muR arife from a viewr and comparifon of all together.” It is doubtlefs a great mi flake to fuppofe that prophecy was intended folely or chiefly for their fakes in wmofe time the events predicted are to happen. What great occa- fion is there to lay in fo long beforehand the evidence of prophecy to convince men of things that are to hap¬ pen in their own times ; the truth of which they may, if they pleafe, learn from their own fenfes ? Yet fome people are apt to talk as if they thought the truth of the events predidled depended very much on the evi¬ dence of prophecy : they fpeak, for inflance, as if they imagined the certainty and reality of our Saviour's re- furrecRion were much concerned in the clearnefs of the prophecies relating to that great and w’onderxul event, and feem to think that they are confuting the truth of his refurreRion when they are pointing out the abfurdi- ty of the prophecies relating to it. But can any thing be more abfurd ? For what ground or pretence is there to inquire whether the prophecies foretelling that the Mefliah fhould die and rife again do truly belong to Chrifl, unlefs rve are firR fatisfied that ChriR died and rofe again ? The part which unbelievers ought to take in this queRion, if they would make any ufe of prophecy, fhould be, to fhowT from the prophets that Chrifl was neceffarily to rife from the dead; and then to prove that in faR Jefus never did rife. Here would be a plain confequence. But if they like not this method, they ought to let the prophecies alone ; for if ChnR did not rife, there is no harm done though the prophets have not foretold it. And if they allow the relurreRion of ChriR, what do they gain by difcrediting the prophets ? The event will be what it is, let the prophecies be what they will. Thefe confiderations fliow how far the gofpel is necef¬ farily concerned in prophetical evidence, and how clear the prophecies fhould be. ChriR claims to be the per- fqn foretold in the law and the prophets j and as truth muR ever be confiflent with itfelf, this claim muR be Prophecy, true as well as all others. This is the part then to be —'•v—--' tried on the evidence of prophecy : Is ChriR that per- fon defcribed and foretold under the Old Teftament or not? Whether all the prophecies relating to him be plain or not plain, it matters little ; the fingle queRion is, Are there enough plain to fliow us that ChriR is the perfon foretold under the Old Teftament ? If there be, we are at an end of our inquiry, and want no farther’ help from prophecy ; efpecially fince we have feen the day dawn and enjoyed the marvellous light of the gofpel of God. 2o But fo unreafonable are unbelievers, that whilft fome Objections of them objeR to the obfcurity of the prophecies, from the others have rejeRed them altogether on account of their clearnel’s, pretending that they are hiltories and not prediRions. The prophecies againft which this objec¬ tion has been chiefly urged are thofe of Daniel, which were fiift called in quettion by the famous Porphyry, lie affirmed that they were not compofed by Daniel, whofe name they bear, but by fome author who lived in Judea about the time of Autiochus Epiphanes , becaufe all to that time contained true hiftory, but that all the faRs beyond that were manifeftly falfe. 2I This method of oppofing the prophecies, as a father anfwereT of the church rightly obferves, is the flrongeft teftimo- ny of their truth : for they are fo exaRly fulfilled, that to infidels the prophet feemed not to have foretold things future, but to have related things paft. To an infidel of this age, if he has the fame ability and know¬ ledge of hiftory that Porphyry had, all the fubfequent prophecies of Daniel, except thofe which are Rill ful¬ filling, would appear to be hiftory and not prophecy ; from vvhat for it entirely overthrows the notion of their being has bappen- written in the days of Antiochus Epiphanes, or of theec' fltice Maccabees, and eftablifhes the credit of Daniel as a pro- tfie 0hFc' phet beyond contradiRion, that there are feveral of^p. thofe prophecies which have been fulfilled fince that pe¬ riod as well as before ; nay, that there are prophecies of Daniel which are fulfilling at this very time in the world. Our limits will not permit us to enter into the objec¬ tions which have been made to this prophet by the au¬ thor of The Literal Scheme of Prophecy coufidered ; nor is there occafion that we fliould enter into them. They have been all examined and completely anfuered by Bifhop Chandler in his Vindication of his Defence of Chriftianity, by Mr Samuel Chandler in his Vindica-1 tion of the Antiquity and Authority of Daniel’s Prophe¬ cies, and by Bifhop Newton in his excellent Differla-^ ^ ^ ^ tions on the Prophecies. To thefe authors we refer thep,cqs 0f\he reader; and ihall conclude the prefent article with aprtfentagc. view of fome prophecies given in very remote ages, which are in this age receiving their accomplifhment. Of thefe the firft is that of Noah concerning the fer- vitude of the pofterity of Canaan. In the greater part of original manufcripts, and in our verfion of the holy fcriptures, this prophecy is thus expreffed : “ Curfed be Canaan; a fervant of fervants fhall he be unto his brethren but in the Arabic verfion, and in fome co¬ pies of the Septuagint, it is, “ Curfed be Ham the fa¬ ther of Canaan ; a fervant of fervants fhall he be to his brethren.” Whether the curfe was really pronounced upon Ham, which we think moft probable, or only uo- on his fon Canaan, we fhall find the prediRion remark¬ ably PRO [ 454 iProphacy. ably fulfilled, not barely ages after the book of Genefis v was very generally known, but alio at this very day. It is needlefs to inform any man who has but looked into the Old Teftament, that when the ancient patri¬ archs pxonounced either a curfe or a blefling upon any of their fons, they meant to declare the future fortunes, not Ox that fon individually, but of his defcendants as a tribe or a nation. Let us keep this in mind, and pro¬ ceed to compare with Noah’s prophecy jirjl the fortunes of the defcendants of Canaan, the fourth fon of Ham, and then the fortunes of the pofterity of Ham by his other fons. With the fate of the Canaanites every reader is ac¬ quainted. They were conquered by Jofhua feveral cen¬ turies after the delivery of this prophecy j and fuch of them as were not exterminated were by him and Solo¬ mon reduced to a date of the lowed fervitude to the If- raelites, the poderity of Shem the brother of Ham. The Greeks and Romans, too, who were the delcendants of Japheth, not only fubdued Syria and Paledine, but alfo purfued and conquered fuch of the Canaanites as were anywhere. remaining, as for indance the Tyrians and Caithaginians, of whom the former were ruined by A- lexander and the Grecians, and the latter by Scipio and the Romans. Nor did the effefts of the curfe dop there. The miferable remainder of that devoted people have been ever fmce (laves to a foreign yoke 5 fird to the Saracens who are defcended from Shem, and afterwards to the Turks who are defcended from Japheth j and un¬ der the Turkifh dominion they groan at this day. If we take the prophecy as it dands in the Arabic crlion, its accomph(hment is dill more remarkable. The whole continent of Africa was peopled principally by the poderity of Ham. And for how many ages have the better paits of that country lain under the dominion fird of the Romans, then of the Saracens, and now of the lurks? In what wickednefs, ignorance, barbarity, Havery, and mifery, live mod of its inhabitants ? and of the poor negroes how many thoufands are every year (old and bought like beads in the market, and conveyed from one quarter of the world to do the work of beads in another; to the full accomplidiment indeed of the prophecy, but to the lading difgrace of thofe who are from the love of gain the indruments of fulfilling it. (Nothing can be more complete than the execution of tne ^fentence^ as well upon Ham as upon Canaan *, and the hardied infidel will not dare to fay that it was pro¬ nounced after the event. I he next prophecy which we (hall notice is that of Abraham concerning the multitude of his defcendants •, which every one knows is dill fulfilled in the Jews even in their difperfed (late, and therefore cannot have been given after the event of which it fpeaks. . fame kind are the feveral prophecies concern¬ ing Khmael; of which fome have been fulfilled, and others are at prefent fulfilling in the mod adonifliing manner. Of tVnc \ \ . •. r . ^ ] PRO manner. Of this fon of Abraham it was foretold, that “ Jould be a wild man ; that his hand diould be againd every man, and every man’s hand againd him : that he (hould dwell in the prefence of all his brethren : that he diould be multiplied exceedingly, beget twelve princes, and become a great nation.” ' The facred hif- torian -who records thefe prophecies adds, that “ God was with the lad, and he grew, and dwelt in the wilder- nefs, and became an archer.” To (how how fully and literally all thefe prophecies Prophecy, have been accomplidied, would require more room than ^ we have to bellow j and to the reader of hidory the la¬ bour would be (uperfluous. We (hall therefore only re- qued the unbeliever to attend to the hidory of the Arabs, the undoubted defcendants of Idimael j and ta fay how it comes to pafs, that though they have been lobbers by land and pirates by lea for time immemorial, though their hands have been againft every man, and every man’s hand againd them, they always have dwelt, and at this day dwell, in the prefence of their brethren^ a free and independent people. It cannot be pretended that no attempt has ever been made to conquer them ; for the greated conquerors in the world have all in their turns attempted it: but though fome of them made great progrefs, not one was ever crowned with fuccefs. It cannot be pretended that the inaccediblenefi of their country has been their protedlion ; for their country has been often penetrated, though it never was entirely fubdued. When in all human probability they have been on the brink of ruin, they wxre fignally and pro¬ videntially delivered. Alexander was preparing an ex¬ pedition againd them, when he was cut off in the (lower of his age. Pompey was in the career of his conqueds when urgent affairs called him elfewhere. Ailius Gal¬ los had penetrated far into their country, when a fatal difeafe dedroyed great numbers of his men, and oblio-ed him to return. Trajan befieged their capital city, but was defeated by thunder and lightning and whirlwinds. Severus befieged the fame city twice, and was twice re¬ pelled from before it. The Turks, though they w'ere able to wred from them their foreign conqueds, have been fo little able to fubdue the Arabs themfelves, or even to redrain their depredations, that they are obliged to pay them a fort of annual tribute for the fafe paffage of the pilgrims who go to Mecca to pay their devotions. On thefe fads w^e diall not exclaim. He who is not druck upon comparing the fimple hidory of this Angular people with the prophecies fo long ago delivered of them and their great ancedor, whofe love of liberty is compa¬ red to that of the wild afs, would rife wholly unmoved from our exclamations. A fourth prophecy of this kind, which cannot be al- The leged to have been uttered after the event, is the denun- perLn If ciation <)f Moles againd the children of Ifrael in cafe of the Jews their difobedience ; which is fo literally fulfilled, that '5,ainIy even at this moment it appears rather a hidory of theforetold* prefent date of the Jews, than a remote prediftion of their apodafy and punidiment. “ And the Lord diall fcatter thee among all people from the one end of the earth even unto the other. And among thefe nations dialt thou find no eafe, neither (hall the foie of thy foot have red ; but the Lord (hall give thee there a tremb¬ ling heart and failing of eyes, and forrow of mind. And thy life (hall hang in doubt before thee ; and thou (halt fear day and night, and (halt have none affurance of thy life,” (Deut. xxviii. 64, 65, 66.). “ And thou dialt become an adonifhment, a proverb, and a bye-word among all nations, whither the Lord (hall lead vou.” (Deut. xxviii. 37.). ' _ Similar to this denunciation, but attended with fome circumdances dill more wonderful, is the following pre- diftion of the prophet Hofea: “ The children of Ifrael (hall abide many days without a king, and without a prince, and without a facrifice, and without an image, and PRO [ 455 Prophecy, and without an ephod, and without teraphim. After- v "' wards (hall the children of Ifrael return, and feek the Lord their God, and David their king; and fhall fear the Lord and his goodnefs in the latter days (b).” In this paffage we find the ftate of the Jews for the laft 1700 years clearly and diftin&ly defcribed with all its circumftances. From the time that they rejefted their Meffiah all things began to work towards the deftruc* tion of their politics both civil and religious •, and with¬ in a few years from his death, their city, temple, and government, were utterly ruined ; and they themielves not carried into a gentle captivity, to enjoy their laws, and live under governors of their own, as they did in Babylon, but they were fold like beads in a market, and became Haves in the drifted fenfe j and from that day to this have had neither prince nor chief among them. Nor will any one of them ever be able, after all their pretences, to prove his defcent from Aaron, or to fay with certainty whether he is of the tribe of Judah or of the tribe of Levi, till he fhall difcover that un- knowm country where never mankind dwelt, and where the apocryphal Efdras has placed their brethren of the ten tribes. This being the cafe, it is impodible they can have either an altar, or a facrifice, or a priedhood, according to the inditution of Mofes, but are evidently an outcad people living under laws which cannot be ful¬ filled. The caufe of this deplorable condition is likewife af- figned with the fame perfpicuity : They are fcattered over the face of the earth, becaufe they do not acknow¬ ledge Chrid for the Mediah ; becaufe they do not fub- mit to their own king, the true David. In the prophe¬ tic writings the name of David is frequently given to the Mediah, who was to defcend from that prince. Thus Ezekiel, fpeaking of the kingdom of Chrid, fays, 44 I wall fet up one Shepherd over them, and he (hall feed them, even my fervant David ; he diall feed them, and he (hall be their drepherd.” And Jeremiah fays, 44 They diall ferve the Lord their God, and David their king, whom I will raife up unto them.” That in thefe places, as w^ell as in the padage under condderation, the Mediah is meant, is undeniable; for David the fon of Jede w^as dead long before any of the three prophets was born'; and by none of them it is faid, “ afterwards David their king diall come again but 44 afterwards the children of Ifrael Jhall return to David their king,” they (hall recover from their blind infatua¬ tion, and feek him whom they have not yet knowm. By their not receiving Jefus for their Chrid, they have forfeited all claim to the divine favour, and are, of con- fequence, “ without a king, and without a chief, and without a facrifice, and without an altar, and without a priedhood.” The time, however, will come, when they diall re¬ turn and feek “ the Lord their God and David their king;” when they diall tremble before him w'hom their fathers crucified, and honour the fon even as they ho- 25 and the caufe of it. 26 Their re turn alfo foretold. ] PRO iiour the father. That this part of the prophecy will Prophecy* in time be as completely fulfilled as the other has been L ■ J may be confidently expefted from the wonderful prefer- vation of the Jews for fo many ages. Scattered as they a) e over the whole earth, and haled as they are by all nations, it might naturally be thought, that in procefs of time they would have coalefced with their conquer¬ ors, and have been ultimately abforbed and annihilated by their union, fo that no trace of them diould now have remained ; yet the faft is, that, difperfed as they have ever fince been over the whole face of the globe, they have never, in a fingle indance, in any country, lod their religious or natural didinftions ; and. they are now generally fuppofed to be as numerous as they were under the reigns of David and Solomon. This is contrary to all hi dory, and all experience of the courfe of human affairs in fimilar cafes ; it has been boldly and juftly ftyled a Handing miracle. Within 1000 or 1200'years back, a great variety of extraordinary and important re¬ volutions have taken place among the nations of Eu¬ rope. In the fouthern part of this iiland the Britons were conquered by the Saxons, the Saxons by the Danes,, and the Danes and Saxons by the Normans ; but in a fevy centuries thefe oppofite and hodile nations were con- folidated into one indidinguifliable mafs. Italy, about the fame time that Britain was fubdued by the Saxons, wras conquered by the Goths and Vandals : and it is not eafy to conceive a more driking contrad than that which fub- fided between the polifhed inhabitants of that delightful country and their favage invaders ; and yet how foon did all didinftton ceafe between them ! In France, the Roman colonies gradually adimilated wfith the ancient Gauls; and in Spain, though the Moors continued for feveral ages, and till their final expulfion, a didinft people, yet after they w^ere once reduced to a date of fubjeftion, their numbers very fenfibly diminifhed ; and fuch of them as were differed to remain after their lad overthrow^ have been long fince fo blended with the Spa¬ niards that they cannot now be didinguidied. But with regard to the Jews, the wonder is, that though they do not in any country where they are fettled bear any pro¬ portion to the natural inhabitants, though they are uni- verfally reduced to a date of the fowled fubjeftion, and even expofed to hatred, contempt, and perfecution ; yet in no indance does there feem to be the lead appearance or probability of their numbers being diminifhed, in no indance do they difcover any decay of attachment to their religious principles. Whence then comes it that this people alone, who, having no form of government or a republic anywhere fubfiding, are without the means by which other people are kept united and didinft, diould dill be preferved amongd fo many different nations ? How comes it, when they have been thus fcattered in¬ to fo many didant corners, like dud which cannot be perceived, that they fhould dill fo long furvive the dif- folution of their own date, as well as that of fo many others? To thefe quedions the anfwer is obvious: They are (b) Such is our trandation of this remarkable prophecy ; but the Greek verfion of the Seventy has it, per¬ haps more properly, thus: “ The children of Ifrael fhall abide many days without a king, and without a chief, and without a facrifice, and without an altar, and without a priedhood, and without a prophecies. Afier- wards,’ &c. c/ PRO [ 456 ] PRO piOphecy, Prophet. 27 Of prophe¬ cies re- fpedling the Chii- Itian church. are prcfeived, that, as a nation, “ they may return and feek the Lord their God and David their king, and fear the Lord and his goodnefs in the latter days.” - We might here fubjoin many prophecies both from the Old and the New Teftament, and efpecially from the writings of St Paul and St John, which fo clearly deferibe the various fortunes of the Chriftian church, her progrels to that fiate of general corruption under which lire was funk three centuries ago, and her gradual reftoration to her primitive purity, th.it they cannot be fuppofed to proceed from the cunning craftinefs of men, or to have been written after the events of which they fpeak. To do juftice to thefe, however, would require a volume, and many excellent volumes have been writ¬ ten upon them. The reader who wifhes for fatisfaftion on fo interefting a fubjeft will do well to confult the writings of Mr Mede and Sir Ifaac Newton, together with Bifhop Newton’s DilTertations, and the Sermons of Hurd, Halifax, and Bagot, preached at Warburton’s lecture. We lhall only obferve, that one of the ableft: reafoners that Great Britain ever produced, after having paid the clofeft attention to the prediftions of the New Teftament, hath been bold enough to put the truth of revealed religion itfelf upon the reality of that prophetic fpirit which foretold the defolation of Chrift’s church and kingdom by antichrift. “ If (fays he), IN THE days of St Paul and St John, there was any foot- ftep of fuch a fort of power as this in the world j or if there had BEEN any fuch power in the world ; or if there was then any appearance or probability that could make it enter into the heart of man to imagine that there EVER could BE any fuch kind of power in the world, much lefs in the temple or church of God; and if there be not NOW fuch a power aftually and con- fpicuoufly exercifed in the world; and if any pifture of this power. DRAWN AFTER THE EVENT, can now de¬ feribe it more plainly and exactly than it was originally deferibed in the words of the prophecy—then may it, with feme degree of plaufibility, be fuggefted, that the prophecies are nothing more than enthufiaftic imagina¬ tions.” Upon the whole, we conclude with Bifhop Sherlock, that the various prophecies recorded in the Holy Scrip¬ tures were given, not to enable man to forefee with clearnefs future events, but to fupport the feveral dif- penfations of religion under which they were refpedfive- ly promirlgated. The principal prophecies recorded in the Old Teftament led mankind to hope for a complete deliverance from the curfe of the fall ; and therefore tended to fill their minds with gratitude, and to enforce a cheerful obedience to that God who in the midft of judgement lemembereth mercy. The prophecies, whe¬ ther in the Old or New Teftament, that pourtray the prefent Irate of the Jews, and the various fortunes of the Chriftian church, as they are daily fulfilling in the pre- lenee of all men, are the ftrongeft pofiible proof of the divinity of our holy religion, and fupply to us in the latter days the place of miracles, by which it was at firft eftablifhed. PROPHET, in general, a perfon who foretels future events; but is particularly applied to fuch infpired per- fons among the Jews as were commiflkmed by God to declare his will and purpofes to that people. Among the canonical books of the Old Teftament we have the writings of 16 prophets, four of whom are denominated 2 the greater prophets, viz. Ifaiah, Jeremiah, Ezekiel, and Prophet Daniel; fo called from the length and extent of their li writings, which exceed thofe of the others, viz. Hofea, 1 i0F0rt'0r>« Joel, Amos, Obadiah, Jonah, Micah, Nahum, Habak- ^ "* kuk, Haggai, Zechariah, and Malachi, who are called the lefer prophets, from the ftiortnefs of their writings. The Jews do not place Daniel among the prophets, be- caufe, they fay, he lived the life of a courtier rather than that of a prophet. An account of the feveral writings of the prophets may be feen each under it a particular head. See the article Isaiah, &c. Sons of the P ROPUFTS, in feripture hiftory, an appel¬ lation given to young men who were educated in the fchools or colleges under a proper mafter, wjio was commonly, if not always, an infpired prophet, in the knowledge of religion and in facred roufic, and thus were qualified to be public preachers; which feems to have been part of the bulinefs of the prophets on the Sabbath days and feftivals. It is probable that God generally chofe the prophets," whom he infpired, out of thefe fchools. See Prophecy. PROPITIATION, in Theology, a facrifice offered to God to afluage his wrath and render him propitious. Among the Jews there were both ordinary and public facrifices, as holocaufts, &c. offered by way of thar.kf- giving; and extraordinary ones, oft’ered by particular perfons guihy of any crime, by way of propitiation. The Romifh church believe the mafs to be a faerifice of propitiation for the living and the dead. The re¬ formed churches allow of no propitiation but that one offered by Jefus Chrift on the crofs. See Sacrifice. PROPITIATORY, any thing rendering God pro¬ pitious ; as we fay propitiatory facrifices, in contradi- ftin61 ion to facrifices which were euchari/lical. Among the Jews the propitiatory was the cover or lid of the ark of the covenant ; which was lined both within and withoutfide with plates of gold, infomuch that there was no wood to be feen. This propitiatoiy was a type or figure of Chrift, whom St Paul calls the propitiatory ordained from all ages. See Ark of the Covenant. PROPOLIS, the name of a certain fubftance more tenacious than wax, with which the bees Hop up all the holes or cracks in the fide of their hives. See Bee, N° 13. PROPONTIS, or sea of Marmora, a part of the Mediterranean, dividing Europe from Alia ; it has the Hellefpont or canal of the Dardanelles to the fouth- weft, whereby it communicates with the Archipelago, and the ancient Bofphorus of Thrace, or ftrait of Conftantinople to the north-eaft, communicating with the Black or Euxine fea. It has- two caftles : that on the Alia fide is on a cape, where formerly flood a tem¬ ple of Jupiter. The caftle of Europe is on an oppo- fite cape, and had anciently a temple of Serapis. It is 120 miles long, and in fome places upwards of 40 miles broad. PROPORTION, the identity or fimilitude of two ratios. Plence quantities that have the fame ratio be¬ tween them are faid to be proportional ; e. gr. if A be to B as C to D, or 8 be to 4 as 30 to 15 ; A, B, C, D, and 8, 4, 30, and 15, are faid to be in proportion, or are limply called proportionals. Proportion is frequent¬ ly confounded with ratio ; yet have the two in reality very different ideas, which ought by all means to be diftinguilhed. Ratio is properly the relation or habi¬ tude PRO [ 457 ] P R O Proportion, tude of two things, which determines the quantity of * one from the quantity of another, without the interven¬ tion of any third : thus we fay the ratio of 5 and 10 is 2, the ratio of 12 and 24 is 2. Proportion is the fame- r.cfs or likenefs of two fuch relations *, thus the relations between 5 and 10 and 12 and 24 being the fame, or equal, the four terms are laid to be in proportion. Hence ratio exifts between two numbers, but propor¬ tion requires at lead three. Proportion, in fine, is the habitude or relation of two ratios when compared toge¬ ther *, as ratio is of two quantities. See Algebra, A- ritumetic and Geometry. Arithmetical and Geometrical P ROPORZION. See Pro¬ gression. Inordinate PROPORTJON, is where the order of the terms compared is dhturbed or irregular. As, for ex¬ ample, in two ranks of numbers, three in each rank, viz. in one rank, - - 2, 3, 9, and in the other, - - 8, 24, 36, which are proportional, the former to the latter, Tout in a different order, viz. - 2 : 3 : : 24 : 35, and - - - - 3 : 9 : : 8 : 24, then ; calling out the mean terms in each rank it is con¬ cluded that - - 2 : 9 : : 8 : 36, that is, the fivlt is to the third in the firil rank, as the fir ft is to the third in the fecond rank. Harmonica/ or Mafical PROPORTION, is a kind of numeral proportion formed thus : of three numbers, il the firft be to the third as the difference of the firft and fecond to the difference of the fecond and third j the three numbers are in harmonical proportion. Thus 2, 3, 6, are harmonical, becaufe 2 : 6 : : 1 : 3. So alfo four numbers are harmonical, when the firft is to the fourth as the difference of the firft and fecond to the difference of the third and fourth. Thus 24, 16, 12, 9, are harmonical, becaufe 24 : 9 : : 8 : 3. By continuing the proportional terms in the firft cafe, there arifes an harmonical progreftlon or fe- ries. 1. If three or four numbers in harmonical propor¬ tion be multiplied or divided by the fame number 5 the produffs or quotients will alfo be in harmonical pro¬ portion : thus, if 6, 8, 1 2, which are harmonical, be divided by 2, the quotients 3, 4, 6, are alro harmoni¬ cal ; and reciprocally the produffs by 2, v.z. 6, 8, 1 2. 2. To find an harmonical mean between two num¬ bers given ; divide double the produff of the two num¬ bers by their fum, the quotient is the mean required ; thus fuppofe 3 and 6 the extremes, the produff of thefe is 18, which doubled gives 36 ; this divided by 9 (the fum of 3 and 6) gives the quotient 4. Whence 3, 4, 6, are harmonical. 3. 'bo find a third harmonical proportion to two numbers given. Call one of them the firft term, and the other the fecond ; multiply them together, and divide t!ie pro¬ duff by the number remaining after the lecond is fub- traffed from double the firft •, the quotient is a third harmonical proportional: thus, fuppofe the given terms 3, 4, their produff 12 divided by 2 (the remainder af¬ ter 4 is taken from 6, the double of the firft), the quo¬ tient is 6, the harmonical third fought. 4. To find a fourth harmonical proportion to three terms given •, multiply the firft into the third, and di- Vql. XVII. Part II. vide the product by the number remaining after the Proportion- middle or fecond is fubtra6led from double the firft ; II. the quotient is a third harmonical proportion } thus fup- ^ 10P0iui0n-, poling the numbers 9, 12, 16, a fourth will be found by the rule to be 24. 5* If there be four numbers difpofed in order, where¬ of one extreme and the two middle terms are in arith¬ metical proportion j and the fame middle terms with the other extreme are in harmonical proportion ; the lour are in geometrical proportion •, as here 2 : 3 : : 4 : 6, which are geometrical^ whereof 2, 3, 4, are arith¬ metical, and 3, 4, 6, are harmonical. 6. If betwixt any two numbers you put an arithme¬ tical mean, and alfo an harmonical one, the four will be in geometrical proportion : thus betwixt 2 and 6 an arithmetical mean is 4, and a harmonical one 3 } and the four 2 : 3 : : 4 : 6, are geometrical. We have this notable difference between the three kinds of proportion, arithmetical, harmonical, and geo¬ metrical ; that from any given number we can raife a continued arithmetical feries increafing in infinitum, but not decreafmg : the harmonical is decreafable in infini¬ te m, but not increafable \ the geometrical is both. Proportion, or Rule of Three. See Arithmetic. Reciprocal PROPORTION. See Reciprocal. Proportion is alfo ufed for the relation between unequal things of the fame kind, whereby their feveral parts correfpond to each other with an equal augmenta¬ tion or diminution. Thus, in reducing a figure into little, or in enlarging it, care is taken to obferve an equal diminution or en¬ largement, through all its parts : fo that if one line, e. gr. be contraffed by one-third of its length, all the reft fhall be contraffed in the fame proportion. Proportion, in ArcluleSlure, denotes the iuft mag¬ nitude of the members of each part of a building, and the relation of the feveral parts to the whole 5 e. gr. of the dimenfions of a column, &c. with regard to the or- donnance of the whole building. One of the greatell differences among architeffs, M. Perrault obferves, is in the proportion of the heights .of entablatures with refpeff to the thicknefs of the columns, to which they are always to be accommo¬ dated. In effcff, there is fcarcely any work, either of the an¬ cients or modern'!, wherein this proportion is not dif¬ ferent ; fome entablatures are even near twice as high as others :—yet it is certain this proportion ought of all others to be molt regulated ; none being of greater im¬ portance, as there is none in which a defect is fooner feen, nor any in which it is more (hocking. Compafi of PROPORTION, a name by which the French, and after them fome Englifh, authors call the Sector. PROPORTIONAL, relating to proportion. Thus we fay, proportional compaffes, parts, feales, fpirals, &c. Proportionals, in Geometry, are quantities, either linear or numeral, which bear the fame ratio or relation to each other. PROPOSITION, in Logic, part of an argument wherein fome quality, either negative or pofitive, is at¬ tributed to a fubjeff. Proposition, in Mathematics, is either fome truth advanced and (hown to be fuch by demonftration, or fpme operation propofed and its folution Ihown. If the 3 M propofitioK PRO •Propofition propofition be deduced from feveral theoretical defini Profe ^ons comPared together, it is called a theorem ; if from u—a praxis, or feries of operations, it is called a problem. See the articles Theorem and Problem. Proposition, in Oratory. See Oratory, N° 28. 124. Proposition, in Poetry, the firft part of a poem, wherein the author propoies briefly, and in general, what he is to fay in the body of his work. It tliould comprehend only the matter of the poem, that is, the action and perfons that add. Horace prefcribes modefty and fimplicity in the propofition, and would not have the poet promife too much, nor raife in the reader too great ideas of what he is going to relate. PROPREFECT, among the Romans, the prefeft’s lieutenant, or an officer whom the prefedl of the pre- torium commifTioned to do part of his duty in his place. PROPRETOR, a Roman magilfrate, who, having difcharged the office of pretor at home, was fent into a province to command there with his former pretorial authority. It wras alfo an appellation given to thofe who, without having been pretors at Rome, were fent extraordinarily into the provinces to adminifter juffice with the authority of pretors. PROPRIETOR, or Proprietary, is he who pof- feffes any thing as his own in the utmofi degree. Such monks were called proprietary as had referved goods and effe6ls to themfelves, notwithffanding their formal re¬ nunciation of all at the time of their profeffion. They are frequently mentioned in the Monaji. Anglic. &c. and were to be very feverely dealt with ; to be excom¬ municated, deprived of burial, &c. Monachi proprieta- rii excommunicentur ab abbotibus : et,Ji in morte propri¬ etor ius inventus fierit, ccclc/ia/lica car eat febultura. &c. Addit. ad Matt. Par. PRO RATA, in commerce, a term fometimes ufed by merchants for in proportion ; as, each perfon mull reap the profit or fuftain the lofs, pro rata to his interefl, that is, in proportion to his flock. PROROGATION, the aft of prolonging, adjourn¬ ing, or putting off, to another time. The difference be- between a prorogation and an adjournment of parlia¬ ment is, that by prorogation the feffion is ended, and fuch bills as paffed in either houfe, or both houfes, and had not the royal affent, mull at the next affembly be¬ gin again. PROSCRIPTION, a publication made in the name of the chief or leader of a party, whereby he promifes a reward to any one who fhall bring him the head of one of his enemies. Sylla and Marius by turns profcribed each others ad¬ herents.—Under the triumvirate great part of the befl and braveft of the Romans fell by profcription. The term took its rife from the praftice of writing down a lift of the perfons names, and polling it in pub¬ lic 5 from pro and fcribo “ I write.” PROSE, the natural language of mankind, loofe and unconfined by poetical meafures, rhymes, &c. In which fenfe it Hands oppofed to verfe. There is, however, a fpecies of profe which is meafu- red, fuch as that in which epitaphs and other infcrip- tions are generally written ; and indeed every man who has formed for himfelf a flyle writes in uniform periods regularly recurring. It has been much difputed whe- [ 45s ] PRO ther a poem can be written in profe. We enter not into that difpute, as we have faid enough on the fubjeft elfe- where. See Novel. The word profe comes from the Latin prof a, which fome will have derived from the Hebrew poras, which fignifies expendit: others deduce it from the Latin pror- fa, ofprorfus, “ going forwards by way of oppofi- tion to verfa, or “ turning backwards,” as is neceffary in writing. PROSECUTION, in the criminal lawn The next flep towards the punifhment of offenders after Commit¬ ment, is their profecution, or the manner of their for¬ mal accufation. And this, in the Englifh law, is either upon a previous finding of the faft by an inquefl or grand jury ; or without fuch previous finding. The former wjay is either by Presentment or In¬ dictment. See thefe articles. The remaining methods of profecution are without any previous finding by a jury, to fix the authoritative ft amp of verifimilitude upon the accufation. One of thefe, by the common law, was when a thief was taken with the mainour, that is, with the thing ftolen upon him, in manu. For he might, wEen fo detefted, fla¬ grante deliEio, be brought into court, arraigned, and tried, without indiftment : as by the Danifh law he might be taken and hanged upon the fpot without ac¬ cufation or trial. But this proceeding w^as taken away by feveral ftatutes in the reign of Edward III. though in Scotland a fimilar procefs remains to this day. So that the only fpecies of proceeding at the fuit of the king, without a previous indiftment or prefentment by a grand jury, now feems to be that of Information j which fee. Thefe are all the methods of profecution at the fuit of the king. There yet remains another, w'hich is merely at the fuit of the fubjeft, and is called an Ap¬ peal. See that article. But of all the methods of profecution, that by indift¬ ment is the moft general. See Indictment. PROSECUTOR, in law, he that purfues a caufe in another’s name. PROSELYTE, a new convert to fome religion or religious feft. PROSERPINACA, a genus of plants belonging to the triandria clafs, and in the natural method ranking- under the 15th order, Inundatce. See Botany Index. PROSERPINE, in fabulous hiftory, the daughter of Jupiter and Ceres, w-as carried off by Pluto as fhe w7as gathering flowers with her companions. Ceres, difconfolate for the lofs of her daughter, after having long fought her, heard where fhe was, and intreated Jupiter to let her return from hell. This requeft Ju¬ piter granted, on condition ftie had tafted nothing in Pluto’s dominions. Ceres therefore went to fetch her j but w'hen her daughter wras preparing to return, Afca- laphus gave information that he had feen Proferpine eat fome grains of a pomegranate flie had gathered in Plu¬ to’s garden j on which £he was fentenced to continue in Tartarus in quality of Pluto’s fpoufe, and the queen of thofe gloomy regions: but to mitigate the grief of Ce¬ res for her difappointment, Jupiter granted that her daughter fhould only fpend fix months together in hell wdth her hufband, and the other fix on earth with her mother. Some mythologifts imagine that the latter part of the fable Piofe II Proferpine. FRO t 459 ] PRO Profeuche fable alludes lo the corn, which muft remain all the tl winter hid in the earth, in order to fprout forth in the Ptixagoras. (prjjng? anci proc[uce the harveft. PROSEUCHE, in antiquity, properly fignities praij- €t'; but it is taken for the places of prayer of the Jews, and was pretty near the fame as their fynagogues. But the fynagogues were originally in the cities, and were covered places : whereas, for the mod part, the pro- feuches were out of the cities, and on the banks of ri¬ vers j having no covering, except perhaps the fhade of fome trees or covered galleries. The word is Greek, TTgos-eti^n, prayer. PROSEAMBANOMENE, the name of a mufical note in the Greek fyltem. As the two tetrachords of the Greeks were conjunc¬ tive, or, in other words, as the higheft note of the firft ferved likewife for the lowed note of the fecond, it is plain that a complete o£lave could not be formed. To remedy this deficiency, therefore, one note beneath the lowed tetrachord wyas added, as an oftave to the high- ed of the lad tetrachord. Thus, if we fuppofe the fird to have begun on B, the lad mud have ended upon A, to which one note fubjoined immediately beneath the lowed B in the diatonic order mud have formed an oftave. This note was called projlambanomene. But it appears from authors who have fcrutinized antiquity Burney's with fome diligence, and perhaps with as much fuccefs Hiflory of as the data upon which they proceeded could produce, Mufic. that the names of the notes in the Greek fydem, which r ‘ Llt‘ originally dgnified their natural Ration in the fcale of afcending or defcending founds, were afterwards ap¬ plied to# their pofitions in the lyre. Higher or lower, then, according to this application, did not fignify their degrees of acutenefs or gravity, but their higher or lower fituation upon this indrument. PROSODY, that part of grammar which treats of the quantities and accents of fyllables, and the manner of making verfes. The Englifh profody turns chiefly on two things, numbers and rhyme. See Poetry, n° 66—76. and Part HE PROSOPIS, in Botany, a genus of the monogy- nia order, belonging to the decandria clafs of plants. The calyx is hemifpherical and quadridentate $ the Rigma is Ample ; the legumen inflated and moncfper- mous. See Botany Index. PROSOPOPOEIA, a figure in oratory, whereby we raife qualities of things inanimate into perfons. See Oratory. PROSTATJE, in Anatomy, a gland, generally fup- pofed to be two feparate bodies, though in reality but one, fituated jud before the neck of the bladder, and furrounding the beginning of the urethra. See Ana- , TOMY Index. PROSTYLE, in ArchheBure, a range of columns in the front of a temple. PROTAGORAS, a famous Greek philofopher, was Enfield's born at Abdera. In his youth, bis poverty obliged Hi/lory of him to fubmit to the fervile office of frequently car- P/.’/lofophy, ij-ying logs of wood from the neighbouring fields to Abdera. It happened that as he was one day going on briikly towards the city under one of thefe loads, he was met by Democritus, who was particularly druck with the neatnefs and regularity of the bundle. Defi¬ ning him to dop and reft himfelf, Democritus exami¬ ned more clofely the ftruCture of the load, and found that Protagoras it was put together with mathematical exadtnefs j upon p which he alked the youth whether he himfelf had made 1 ^ . it up. Protagoras aflured him that he had ; and imme¬ diately taking it to pieces, with great eafe replaced every log in the fame exaft order as before. Democri¬ tus expreifed much admiration of his ingenuity ; and faid to him, “ Young man, follow me, and your talents ftiall be employed upon greater and better things.” The youth confented, and Democritus took him home, main ¬ tained him at his own expence* and taught him philo- fophy, which qualified him for the office of legiflator of the Thurians. He was more fubtle than folid in his reafonings; however he taught at Athens with great reputation, but was at length baniffied from thence for the impiety of his doftrines. He then travelled, and vi- fited the ifiands in the Mediterranean, where it is faid that he was the firft philofopher who taught for money. He died in a voyage to Sicily, in a very advanced age. He commonly reafoned by dilemmas, and left the mind in fufpenfe with refpeft to all the queflions he propofed. His moral principles w^ere adopted by Hobbes. (See Moral Philosophy). Plato wrote a dialogue againd him. He flouriffied 400 years B. C. PROTASIS, in the ancient drama, the fird part of a cOmic or tragic piece, wherein the feveral perfons are fliown, their charafters intimated, and the fubjeft of the piece propofed and entered upon. It might reach as far as our twro firft afts 5 and wffiere it ended the epitafis commenced. See the article Epi- tasis. PROTEA, the Silver-tree, a .genus of plants, be¬ longing to the tetrandria clafs •, and in the natural me¬ thod ranking under the 47th order, Atellatx. See Botany Index. PROTECTOR, a perfon who undertakes to Ihelter and defend the vTeak, helplefs, and diftrefled. Every Catholic nation, and every religious order, has a protestor redding at the court of Rome, -who is a car¬ dinal, and is called the cardinalproteBor. Protestor is alfo fometimes ufed for a regent of a king¬ dom, made choice of to govern it during the minority of a prince. Cromwell aflumed the title and quality of lord pro¬ teBor of the commonwealth of England. PROTESILAI TURRIS, the fepulchre of Protefi- laus, with a temple, at wdiich Alexander facrificed, (Arian) ; filuated at the fouth extremity of the Helle- fpont, near the Cherfonefus Thracia. Protefilaus was the fird Greek wffio landed on the coaft o. Troy, and the firft Greek flam by the Trojans, (Homer, Ovid). His wife Laodamia, to alluage her grief, begged the gods for a fight of his fhade ; and obtaining her requeft, ihe expired in his embraces, (Hyginus.) Protefilaus was alfo called Phylacidcs, from Phylace, a town of ThefTaly. PROTEST, in Law, is a call of witnefe, or an open affirmation that a perfon does, either not at all, or but conditionally, yield his confent to any a<51, or to the proceeding of any judge in a court in which his jurif- diftion is doubtful, or to anfwer upon his oath farther than he is bound by law. Any of the lords in parliament have a right to pro- teft their diflent to any bill pafled by a majority : wfliich proted is entered in form. This is faid to be a very 3 M 2 ancient P R O [ 400 1 PR O Proteft anc'enL finvSt'g'e. The commons have rtc right to pro- 11 teft. See Parliament. Protoyi.e-. PrqxssT, in Commerce, a fummons written by a no¬ tary-public to a merchant, banker, or the like, to accept Or .diicharge a bill of exchange drawn on him, after his having refufed either to accept or pay it. See Bll.L of Exchange. PROTESTANT, a name hr ft given in Germany to thofe who adhered to the doctrine ot Luther •, be- caufe in 1529 they protefted againft a decree of the emperor Charles V. and the diet of Spires ; declaring that they appealed to a general council. The fame name has alfo been given to thofe of the fentiments of Calvin ; and is now become a common denomination lor all thofe of the refeftmed churches. PROTEUS, in Heathen Mythology. See #’.GY?T, n° 6. PR OTH ON OT ARY, a term which properly lig- nities fr/l notary, and which was anciently the title of the principal notaries of the emperors of Conftanti- nople. Prothonotary, w’-h us, is ufed for an officer in the court of king’s bench and common pleas; the former of which courts has one, and the latter three. The prothonotary of the king’s bench records all civil ac¬ tions fued in that court, as the clerk of the crown-office does all criminal caufes. The pi-othoaetaries of the common pleas enter and enrol all declarations, plead¬ ings, affizes, judgements, and actions: they alfo make out all judicial writs, except writs of habeas corpus, and ffringes jurator, for which there is a particular office, called the habeas corpora office; they likewife enter re¬ cognizances acknowledged, and ail common recoveries 5 make exemplifications of records, &c. In the court of Rome there is a college of 1 2 pre¬ lates, called apfolicalprotkonotaries, empowered to re¬ ceive the laft wills of cardinals, to make all informa¬ tions and proceedings neceflary for the canonization of faints; and all fuch acts as are of great confequence to the Papacy : for which purpofe they have the right of ad million into all confiftories, whether public or half public. They alfo attend on the pope whenever he performs any extraordinary ceremony out of Rome. PROTO, a Greek term, frequently ufed in com- pofition of priority : thus proto-collum, in the ancient jurifprudence, fignifies the firft leaf of a book ; proto- martyr, the firft martyr ; proto-plaft, the firft man formed, &c. PROTOGENES', a celebrated ancient painter, was born at Caunas, a city of Caria. fubjeft to the Rhodians, and dourifhed 300 years before the birth of * our Saviour. He wras firft obliged to paint (hips for h’s livelihood •, but afterwTards acquired the higheft remr- *tation for hiftory-painting ; though Apelles blamed him for finifliing his pieces too highly, and not knowing when to have done. The fineft of his pictures was that of Jalifus, which is mentioned by feveral ancient authors, though none of them gave any dclcription of it. He worked feven years on this picture 5 during which time he lived entirely upon lupines and water, being of opinion that this light and fimple nouriffi- ment left him greater freedom of fancy. Apelles, on feeing this picture, rvas Itruck with fuch ,admiration, that he vTas unable to fpeak, or to find words fufficient io exprefs his idea of its beauty. It was this picture that laved the city of Rhodes when befieged by De- Protogene* metrius king of Macedon-, for being able to attack it ^ aor only on that fide where Protogenes worked, which he 1 ‘ 1 intended to burn, he chofe rather to abandon his -de- fign than to deftroy fo fine a piece. Pliny fays, that. Apelles afking him what price he had for his pictures, and Protogenes naming an inconfiderable fum, Apelles concerned at the injuttice done to the beauty of his produ'ftions, gave him 50 talents, about io,oool. for one picture only, declaring publicly that he would fell it for his own. 'i bis generofily made the Rho¬ dians fenfible of the merit of Protogenes ; and they were fo eager to purchafe the picture Apelles had bought, that they paid him a much greater price for it than he had given. PROT OTYPE, is the original or model after which a thing uras formed j but chiefly ufed for the patterns of things to be engraved, catt, &c. PROTRACTOR, an inftrument for laying down and meafuring angles upon paper with accuracy and difpatch ; and by which the uie of the line of chords is fuperfeded. This inftrument is varioufiy formed, as femicircular, rectangular, or circular ; and conftrucfted of different materials, as brafs, ivory, &c. It is necei- fary in laying down thofe furveys or other plans where angles are concerned. The retdangular prolraflor is conffrafted in form of a right-angled parallelogram, which, when applied to a cafe r,c mathematical inftruments, is fnbftiluted in place of the lemicircular protraftor and fcale of equal Plrte parts. Fig. 1. is a reprefentation ©f it: the manner ofccccxlviu ufing it is exaftly fimilar to that of the femicircular 1 ’S' I’ one. The circular protraftcr, as its name implies, is a complete circle, and is fuperior by far to either of the former, both in point of accuracy and difpatch, efpe- cially when feveral angles are to be formed at the fame point. The limb of this inffrument is divided into ^60 degrees, and each degree in force protractors is halved : it has a fubdividing fcale or vernier, by which an angle may be laid down or meafured to a fingle mi¬ nute. In the centre of the protraftor is a fine mark, which, when an angle is to be protracted r meafured, is to be laid upon the angular point, and o, or zero on the limb, upon the given line forming one fide of the angle. Fig. 2. reprefents a circular protraftor whofe limb is Fig- 2. divided as above deferibed, and the dividing fcale on the index, which moves round the limb of the protrac¬ tor on a conical centre, gives every minute ot a de¬ gree. That part of the index beyond the limb has a fteel point fixed at the end, in a direft line with the centre of the protraftor, and whofe ufe is to prick off the propofed angles. Fig. 3. is another circular protraftor, a little differ- Fig. 3- ently ccnftrufted from the former. The central point is formed by the interfeftion of two lines croffing each other at right angles, which are cut on a piece of glafs. The limb is divided into degrees and half degrees, ha¬ ving an index with a vernier graduated to count to a fingle minute, and is furnifhed with a tooth and pinion, by means of which the index is moved round by turn¬ ing a fmall nut. It has two pointers, one at each end of the index, furniffied with rprings for keeping them fufpended while they are bringing to any angle j and p n o r 4 ,5i ] pro Protra&or being brought, applying a finger to the top of the I! pointer, and preffing it down, pricks off the angle, proverb. 'p^ere js advantage in having two pointers, that all the bearings round a circuit may be laid or pricked oft, although the index traverfes but one half of the pro- tradfor. Fig. 4. Another circular protraftor, different from either of the former, is reprefented at fig. 4. The centre is alio formed by the interfedlioh of two lines at right angles to each other, which are cut on glafs, that all parallax may thereby be avoided. Ihe index is moved round by a tooth and pinion. ihe limb is divided into de¬ grees and half degrees, and fubdrvided to every minute by the vernier. The pointer may be fet at any conve¬ nient ditlance from the centre, as the focket which carries it moves upon the bar EL, and is fixed thereto by the nut ID, at right angles to the bar EC, and moveable with it. There is another bar EF : On this bar different fcales of equal parts are placed ; fo that by moving a fquare again!! the inner edge thereof, angles may be transferred to any ditlance within the limits, from the centre containing the lame number of degrees marked out by the index. It would indeed be fuperfiuous to deferibe any more of thefe circular protradlors, efpecially as the nttle al¬ terations in them depend very much upon the fancy of the art ill. Suffice it however to fay, that we have feen others frill differently coni!rafted, one of which we ihall briefly deferibe". The dhifions upon the limb of this inftrument are fimilar to thofe already de- feribei; but the index is a ftraight bat continued to fome confiderable diftance each way beyond the. limb of the inftrument, and has a vernier to fhow. minutes as ufual; a mark upon one cf the edges of the index al¬ ways coincides with the erntre of the in(1 rumen 1. In- flead, therefore, of pricking down the angle as in the formec, part of the line containing the angle may be drawn, which, although perhaps not. fo accurate as a point, is more confpicuous, and the line is eafily com¬ pleted upon removal of the protraftor. Ihe common dimenfions of the circular part of thefe inftrunients is from fix to ten inches diameter } and they are made of brafs. PROTUBERANCE, in Anatomy, is any eminence, whether natural or preternatural,that projects 01 advan¬ ces out beyond the reft. PROVEDITOR, an officer in feveral parts ot Italy, .particularly at Venice, who has the direftion ct matters relating to policy. PP.OVENCE, a province or government of I ranee bounded by Dauphine on the north, by Piedmont on the eaft, by the Mediterranean on the fouth, and by the river Rhone, which feparates. it from Languedoc, on the weft : it is about 1 00 miles long, and near as many broad. . . „ . , PRGVEXD, or Provender, originally fignified a kind of veffel containing the meafure of corn daily gi¬ ven to a horfe, or other beail ot labour, for Ins fuofift- ence; but is now generally ufed to figmfy the i.ood for cattle ; whatever it is. PROVERB, according to Camden, is a concife, witty, and wife fpeech, grounded upon experience, and for the moft part containing fome ufeful inftruc- Book of Proverbs, a canonical book of the Old Teftafnent, containing a part of the proverbs of Solo- ProverE mon the fon of David king of lirael. "i he firft 24 Providence. chapters are acknowledged to be the genuine wmrk of that prince ; the next five chapters are a collection of fe¬ veral of his proverbs made by order of King Hezekiah ; and the two laft Lem to have been added, though be¬ longing to different and unknown authors, Agur the. fon of Jakeh, and King Lemuel. In this excellent book are contained rules for the conduct of all conditions of life } for kings, courtiers,' mafters, fervants, fathers, mothers, children, &c. 1 PROVIDENCE, the iuperintenclence and care which Definition. God exercifes over creation. 2 That there exitls a divine providence, which attends belief of a to the affairs of this world, and direfts their courfe, hasPr0VK^n,ce been a received opinion among the human race in every country and in every period of hiitory. Every altar that is erefted, every prayer and every facrifice that is offered up, affords a proof of this belief. So fully have men been convinced of the fincerity of each other’s faith upon this fubjecl, that in one form, that of an appeal to the Divine Ruler of the world, by the folemnity of an oath, they have introduced it both into the moil ordi¬ nary and the moft important bufinefs cf life. ~ This univerfal conviction of men of all degrees ofExiftence knowledge, from the moft profound philofopher to theofprovi- rudeft barbarian, is probably to be traced to fome pri-^nc^V maeval tradition, never totally effaced from any nation 0]) £,jentj_ under heaven. The truth itfelf, however, is fufceptlble fic piinci- of the moft complete proof from principles of fcience. pies. If the world had a beginning, it may obvioufly have an end, and can be continued in exiflence only by the con- ftant energy of that power by which it was at firft crea¬ ted. He therefore who acknowledges a creation and denies a providence, involves himfelf in this palpable contradiction—“ that a fyftem, which of itfelf had not an original and momentary exiftence, may yet of itfelf have a perpetual exiftence ; or that a being which can¬ not of itfelf exift for a fecond of time, may yet, of it¬ felf, exift for thoufands of years!'’ Or fhouid we be fo complaifant, as for a moment to fuppofe, with certain theifts, ancient and modern, that the matter of the uni- verfe is felf-exiftent and eternal, and that the power of God was exerted, not in creating fubftances, but in. re¬ ducing the original matter from a iiate ot chaos into that beautiful order in which we tee it arranged } the conftant energy of providence muft ftill be aomitted as neceffary to preferve the forms and to continue the mo¬ tions which were originally impreffed upon the chaotic mafs. From late experiments it appears extremely doubtful whether any two atoms of the moft. folid body be in actual contaft ; and that they are not all in contact is certain. (See Metaphysics, N' ipb. and Op lies, N° 45, p. 185. Yet it requires a very confiderable de¬ gree of force to carry to a greater diftance from one another the parts of a ftone or of a bar of iron. By what power then are thefe parts kept contiguous i It cannot be by their own *, becaufe nothing can aft where it is not prefeni, and becaufe our bed philotophy. has long taught us that the atoms of matter are effentially inaftive. Again, it requires a very great degree of force to bring two bodies, however imall, into cppai ent contaft (fee Optics, ubifupra') ; and therefore it follows that they muft be kept afunder by fome foreign power. Everv attempt to folvc thefe phencmeiuw y the int.er- venrion. \ PRO [ Fiuvuler.ce, veiition of a fubtle fluid is vain ; for the queftidn recurs, what keeps the parts of the fluid itfelf contiguous, and yet feparated from each other? The cohefion therefore of the parts of matter* and that which is called their repullive power, demtmftrate, through the whole fyftem, the immediate energy of fomething which is not matter, and by which every bo¬ dy Imall and great is preferved in its proper fomn It has been elfewhere flrown [fee Metaphysics, Part II. chap. j. and MotiOH, N° iq, 20.), that the various motions which are regularly carried on through the uni- verfe, by which animals and Vegetables grow and decay, and by which we have day and night, fummer and win¬ ter, cannot be accoithted for by any laws of mere me- chanifm, but necefiarily imply the conftant agency of lomething which is itfelf diftin£t from matter. But the forms^ of bodies are preferved, and their natural mo¬ tions carried on, for purpofes obvioufly planned by Wif- dom. The power therefore which effecls. thefe things mull be combined with intelligence : but powTer and in¬ telligence preferving the order of the univerfe conftitute ail that is meant by *a general providence j which is therefore as certainly adminiflered as the fun daily rifes and lets, or as bodies are kept folid by what is terhled 4 cohefion and repulliou. Abliracted and metaphyfical as this reafoning may mins of appear* it is by no means peculiar to the philofophers of Hindoftan. Turope. Its force has been felt from time immemo- * Apiatic ”al ^ the Bramins of Hindoftan, who, as Sir William Refearihes, •'°nes informs us *, “ being unable to form a diftimft idea /ol. i. o biute matter independent of mind, or to conceive that the work of fupreme goodnefs was left a moment to itfelf, imagine that the Deity is ever prefcnt to his work, not in fubftance but in fpirit and in energy.” On this rational and fublime conception they have in- de^ built numberlefs abfurd fuperftitlons ; but their holding the opinion itfelf, fliows that they believe in the jcality of pi'ovidence upon philofophical principles: and what truth is there on which the mind of man has not ingrafted marks of its owrn weaknefs ? Few nations, however, except the ancient Greeks* have had philofophers equally fubtile with the Bramins of India ; and therefore though all mankind have in ge¬ neral agreed in the belief of a luperintfcnding Providence, they have in different ages and countries admitted that uPon different kinds of evidence, and formed very different notions concerning the mode in which the Di- s ' vine fuperintendence is exerted. While focieties are ftillinarude and linpoHlhed ftate, while individuals poffefs little fecurity and little leifure or the exertion of their rational powers, every impor¬ tant or fingular appearance in nature becomes an objeft of wonder or of terror. In this ftate of ignorance* men fee not the univerfe as it is, a great colledftion of connefted parts, all contributing to form one grand and beautiful yitem. Every appearance feems to ftand alone : they know that it muft have a caufe, but what that caufe is they are ignorant. The phenomena exhibited by nature are fo complicated and fo various, that it never occurs to them that it is poffible for one Being to govern the whole. Hence arofe the different fyftems of polytheifm that have appeared in the world. Nature was divided into different regions, and a particular invifible power was.afiigned to each department: one conduced the 'Earning chariot of the fun, another wielded the terrible 462 •Idea of pro vidence in rude ages. ] PRO thunderbolt, and others were employed in diflufing Providence^ plenty, and introducing the ufeful arts among men*.' * Thus, although the various fyftems of polytheifm in general acknowledged one Supreme Ruler, the father of gods and men, yet they at the fame time peopled not only the regions above, the air and the heavens, but they alio filled the ocean and the land, every grove, and every mountain, with aftive but invifible natures. ’Ha¬ ving arifen from the fame caufes, thefe fyftems of poly, theiim, which are fo many hypothefes concerning Divine providence, are all extremely fimilar * and we have ft very favourable fpecimen of them in the elegant my¬ thology of Greece and Rome, which gave to every re¬ gion of nature a guardian genius, and taught men in the deep receffes of the foreft, or in the windings of the ma- jeftic flood* to expeft the prefence of protefting and friendly powers. See Polytheism. , Notwithftanding this univerfal reception, in fome The doc- form or other, of the doftrine of a divine providence, trine has it has in every age met with fome opponents. The 0PP°* moft ancient of thefe were Democritus and Leucippus;r:ents in J hey denied the exiftence of a Deity^—afferted that all* m°fteVer^ things were mechanically neeeffary, and that thought^6’ and fenfe were only modifications of matter. This is atheifm in the ftrifteft fenfe, and the only form of it that lias ever been confiftently fupported. Epicurus followed upon the fame principles ; but he rendered the fyftem altogether abfurd, .by confefling the freedom of the human will. I o avoid the imputation of atheifm, he afferted the exiftence of God 5 but declared that he’ refided above the heavens, and interfered not in human affairs. One of his maxims was, that “ the bleffed and immortal Being neither hath any employment himfelf nor troubles himfelf with others.” Maximus Tyrius *’ * Max- jiiftly obferVes, that this is rather a defeription of a Tjr. Lif- Sardanapalus than of a Deity. And fome of the mo-fert- 2P- rahfts f of antiquity remarked, that they knew many d* men among themfelves poffeffed of aaive and generousi minds, whofe characters they valued more highly X^nNatwa that of Epicurus’s god. Some of the ancients alfo ap-•^>d’orz/w» pear to have entertained the following ftrange notion :lib’li' They acknowledged the exiftence of a Supreme and of many inferior deities 5 but at the fame time, they fop- pofed that there is a certain fate which rules over all and is fuperjor to the gods them lei Ves. See NeceSSITT in Pvfythology, The providence exerted by the Author of nature over his works is ufually divided into two branches : a general, referring to the management of the univerfe at large *, and a particular providence, chiefly regarding particular men. Upon the fir ft of thefe, in The Religion of Nature de- 7 hneated, the quell ion is ftated fomewhat in the follow- SSlce ing manner: The world may be faid to be governed * ' or at leaft cannot be fa?d to fludluate fortuitoufly, if there are laws or rules by which natural caufes acf • if the feveral phenomena in it fucceed regularly, and* in general the conftitution of things is preferved 5’ if there are rules obferved in the produdioh of herbs, trees and the like ; if the feveral kinds of animals are fonufhed with faculties proper to determine their a&ions in the different ftations which they hold in the general econo¬ my of the world 5 and laftly, if rational beings are ta¬ ken care of in fuch a manner as will at laft agree beft Wnu reafon. By the providence of God we ought to underftantl PRO [ 463 ] PRO 8 as it re- fpefts ina¬ nimate ob¬ jects, Providence, underftand his governing the world by fuch laws as thefe s ' ~'r" now mentioned : fo that if there are fuch, there mull be a Divine providence. With regard to inanimate objeBs, the cafe agrees pre- cifely with the above fuppofition. The whole of that univerfe which we fee around us is one magnificent and well regulated machine. The world that we inhabit is a large globe, which, conduced by an invifible power, flies with a rapidity of which we have no conception, through an extent of fpace which fets at defiance every power of fancy to embody it into any diitinft image. A large flaming orb Hands immoveable in the heavens } around which this, and other worlds of different magni¬ tudes, perform their perpetual revolutions. Hence arife the expe£led returns of day and night, and the regular diverfity of feafons. Upon theie great operations a thoufand other circumftances depend. Hence, for ex¬ ample, the vapours afcend from the ocean, meet above in clouds, and after being condenfed, defcend in (bowers to cover the earth with fertility and beauty. And thefe appearances are permanent and regular. During every age fince men have been placed upon the earth, this aftoniihing machine continued fteadily to perform its complicated operations. Nothing is left to chance. The fmalleft bodies are not lefs regular than the largeft, and obferve continually the fame rules of attraction, re- pulfion, &c. The apparent variations of nature pro¬ ceed only from different circumftances and combinations of things, acting all the while under their ancient laws. We ourfelves can calculate the effects of the laws of gravitation and of motion. We can render them fub- lervient to our own purpofes, with entire certainty of fuccefs if we only adhere to the rules eftabliihed by na¬ ture, that is to fay, by providence. Vegetables alfo live and flouriftr according to prefcri- bed methods. Each fort is produced from its proper feed ; has the fame texture of fibres, is at all times nourifhed by the fame kind of juices, digefted and pre¬ pared by the fame veffels. Trees and ihrubs receive annually their peculiar liveries, and bear their proper fruits : fo regular are they in this laft: refpecff, that every fpecies may be faid to have its profeflion or trade ap¬ pointed to it, by which it furnifhes a certain portion of manufacture, or of food, to fupply the wants of animals: being created for the purpofe of confumption, all ve¬ getables produce great quantities of feed to fupply the neceffary wafte. Here too, then, there is evidently a regulation by which the feveral orders are prefcrved, and the ends of them anfwered according to their firft: efta- blilhment. With regard to animals, they too, in ftructure of their form, are fubject to laws fimilar to thofe which govern the vegetable world. In the fentient part of their con- ffitution they are no lefs fubjecff to rule. The lion is al¬ ways fierce, the fox is crafty, and the hare is timid. Every fpecies retains from age to age its appointed place and character in the great family of nature. The various tribes are made and placed in fuch a manner as to find proper means of fupport and defence. Beafts, birds, fifties, and infecffs, are all poffeffed of organs and faculties adapted to their refpeflive circumftances, and opportunities of finding their proper food and prey. Man is fubjecft to the ordinary laws which other ma¬ terial and animal fubftances obey j but he is left more vegetable*. 10 animals, 11 and man at large in the determination of his aflions. Yet even Providence^ here things do not flueftuate at random. Individuals do "~v indeed rile and perifti according to fixed rules, and na¬ tions themfelves have only a temporary endurance. But the fpecies advances with a fteady progrels to in¬ tellectual improvement. This progrefs is often inter¬ rupted ; but it appears not to be lefs fure at the long- run than even the mechanical laws which govern the material part of our conftitution. Amidft the convul- fion of ftates and the ruin of empires, the ufeful arts, when once invented, are never loft. Thefe, in better times, render fubfiftence eafy, and give lei fure for reflec¬ tion and ftudy to a greater number of individuals. Tyre and Sidon have paffed away, Athens itfelf has be¬ come the prey of barbarians, and the profperity of ancient Egypt is departed, perhaps for ever ; but the ftiip, the plow, and the loom, remain, and have been perpetually improving. Thus every new convulfion of fociety does lefs mifehief than the laft j and it is hoped that by the afliftance of printing the moft poliflied arts and the moft refined fpeculations have now become im¬ mortal. The world is not then left in a ftate of confufion : it is reduced into order, and methodifed for ages to come5 the feveral fpecies of beingshaving their offices and provinces affigned them. Plants, animals, men, and nations, are in a ftate of continual change j but fuc- ceffors are appointed to relieve them, and to carry on the fcheme of Providence. r 2 But the great difficulty is, how to account fflr that Difficulty providence which is called particular : For rational be-0* account' ings, and free agents, are capable of doing and deferving well or ill ; and the fafety or danger, that happinefs or vidence.m unhappinefs of a man here, murt depend upon many things that feem fcarcely capable of being determined by Providence. Betides himfelf and his own conduct, he depends upon the conduct of other men; whofe actions, as we naturally fuppofe, cannot, confidently with their free will, be controuled for the advantage of another individual. The actions of numbers of men proceeding upon their private freedom, with different degrees of ability, as they crofs and impede, or diredtly oppofe each other, muft produce very different effects upon men of different characters, and thus in a ftrange manner embarrafs and entangle the general plan. And as to the courfe of nature, it may juftly be atked, is the force of gravitation to be fufpended till a good man pafs by an infirm building ? (See Prayer). Add to this, that fome circumftances appear abfolutely irrecon- cileable. The wind which carries one into port drives another back to fea j and the rains that are juft fuffi- cient upon the hills may drown the inhabitants of the valleys. In ftiort, may we expeft miracles ? or can there be a particular Providence that forefees and pre¬ pares for the feveral cafes of individuals, without force frequently committed upon the laws of nature and the freedom of intelligent agents ? In whatever way it is brought about, there is little No good doubt that fomething of this kind mufldke place. For argument as the Deity does direCt, as already mentioned, the great a£.ainft *ts and general progrefs of things in this world, he mullexiftence* alfo manage thofe of lefs importance. Nations are compofcd of individuals. The progrefs of individuals is the progrefs of the nation, and the greateft events ufually depend upon the hiftory and the moft trifling actions p 11 ■Prov.dtnce. actions of private perfons v———' cejve }10w the fapermtendence and management of all this can be brought about. But as the ways and the thoughts of the Omnipotent Spirit, whofe influence per¬ vades, and rules, and animates nature, referable not the limited operations of men^ we can only form conjec¬ tures concerning the means by which his government is conducted. i. In the firft place, then, it is not impohible that the O [ 464 ] PRO The difficulty is to con- Terrified by the gigantic bulk and mighty force of Go- Provitlerce 14 . The Deity -may eafily fore fee the adtioiis @f men; and may thence fit them for their fitua- tions in fife. 16 The pofli- bility of this exem¬ plified. Deity thould forefee the future actions of intelligent be¬ ings. Many of thefe actions depend upon the mecha- nifm of the material world, which was formed by himfelf, and mutt; be entirely known to him. Many men among ourfelves pcffefs much fagacity in difeerning the future actions of others, from attending to their known charac¬ ters, and the circumftances in which they are placed. If fuperior nature s do exilt, and minds more perfect than the human, they muft poflefs this penetration in a more eminent degree in proportion to the excellence of their intellectual powers. But if this difeernment be in God proportionable to his nature, as in lower beings it is • proportionable to theirs, it then becomes altogether unlimited, and the future actions of free agents are at once unlocked and expofed to his view. Add to this, that the Author of nature is well acquainted with the creatures that he has made •, he knows the me- chanifm of our bodies, the nature and extent.of our underftandings, and all the circumtlances by which we are furrounded. "With all thefe advantages, it is making no great ftretch to fuppofe him capable of difoernin-g the line of conduft which we will purfue; and this even fetting afide the infinity of his nature, to which a thoufand years are as one day, and fuppofing him to reafon from probabilities in the imperfeft manner that we do. 2. There is no impoffi'oiiity at leaf!, that men, whofe characters and actions are thus foreknown, may be in¬ troduced into the world in fuch times and places as that their acts and behaviour may not only -coincide with the general plan of things, but may alfo anfvver many private cafes. The celeitial bodies are fo placed that their jarring attraftions make out a fplendid lyilem. Why then may there not be in the Divine mind fome- thing like a projection of the future hi dory of mankind, as well as of the motions of the heavenly bodies r And why fhould it not be thought poffible for men, as well as for them, by fome fecret law, or rather by the ma¬ nagement of an unfeen power, to be brought into their places in fuch a manner as that, by the free ufe of their faculties, the conjunctions and oppofitions of their in- terefts and inclinations, the natural influence of their different degrees of talents, power, and wealth, they may confpire to make out the great fcheme of human affairs ? There is no abfurdity in this fuppofition : it is not beyond the power of an almighty and perfeCt Be¬ ing ; and it is worthy of him. Let us take from the Jewifli hiftory, as moft generally known, an example of what may be fuppofed to happen daily. It was the intention of providence to place David the fon of Jeffe upon the throne of the Hebrews. The country is in¬ vaded by a foreign enemy : the hoftile armies meet, and lie encamped upon oppofite mountains. A man comes forth from the army of the invaders, as was extremely common in thofe times, and defies the Hebrew hoft to fend.forth a champion to meet him in fingle combat. liah, no man would rifle the unequal conflief. David, who was too young to carry arms, had been fent to the camp with provifions for his brothers, and heard the challenge. In defence of his fleck he had killed fome bealls of prey in the wildernefs, and he was an excellent markfman with the fling. He thought it might pro¬ bably be as eafy to kill a man as a wild beail; at all events, he knew that a ftone well direfted would prove no lefs fatal to a giant than to a dwarf: he therefore refolved to try his {kill j and he tried it with fuccefs. Here no man’s free will was interrupted, and no miracle was accompliffied: Yet by this train of circumftances thus brought together, a foundation was laid for the fu¬ ture fortunes of the fon of jeffe, for the greatnefs of his country, and for accomplifhing the purpofes of Pro¬ vidence. According to Seneca, “ Hoc dico, fulmina non mitli a Jove, led fic omnia difpofita, ut ea etiam. quae ab illo non fiunt, tamen fine ratione non fiunt; quae illius eft.'—Nam etii Jupiter ilia nunc non facit, fecit ut fierent.”—I fay, that the lightning comes not direBly from the hand of Jove, but things are properly difpofed for the in direct execution of his will; for he acts not im¬ mediately, but by the intervention of means. 3. Laftly, it is not impoffiblc that many things may Secret in- be accompiiflied by fecret influence, upon the human Pierces oa mind, either by the Deity'himfelf, or by the intervention ^ of agents poffeffed of powers fuperior to thofe which from belong to us. “ For inftance, if the cafe fhculd require poffible. that a particular man be delivered from lome threaten¬ ing ruin, or from fome misfortune, which would certain¬ ly befal him if he fliould go fuch a way at fuch a time, as he intended : upon this occafion lome new reafons may be prefented to his mind why he fliould not the ci:oc* brought againd the opinion, that the world is governed ^uV(,°‘n„e by a Divine providence. 1 1. The fird of thefe is this, that the fydem of nature nom the contains many imperfections which it ought not to do if raperfec- it be the woik of a perfedlly wife and good Being. Totlons 01 na_ avoid the force of this objection, fome modern writersture’ have deferted the ground of fupreme and abfoiute g6od~ neis, which the ancient theids always occupied, and have alferted that the divine perfeftion confifts in unlimited power and uncontrouled lupremacy of will; that confe¬ quently the Deity does not always that which is bed, but merely what he himfelf pleafes •, and that for no other reafon but becaufe be wills to do fo. But this is no bet¬ ter than atheifm itfelf. For it is of no importance to us whether the univerfe is governed by blind fate or chance, that is to fay, by nothing at all j or whether it is govern¬ ed by(an arbitrary fovereignwdll that is directed by chance, or at lead by no principle of beneficence. ,r The true anfwer to this objection is, that no created anfwered. fydem can have every perfection, becaufe it mult necefih- rily be deditute of felf-exidence and independence ; and therefore if beings deditute of fome perfections be bet¬ ter than nothing, it wras wmrthy of infinite power and perfedt goodnefs to create fuch beings. In our prefent date, w7e mortals dand upon too low7 ground to take a commanding view of the whole frame of things. We can only reafon concerning what is unknown from the little that is within our reach. In that little, we can fee that wifdom and goodnefs reign ; that nature al¬ ways aims to produce perfection ; that many falutary effeCts refult even from the thunder and the dorm : and wre doubt not that a view' of the wdiole ItruCture of the univerfe would afford an additional triumph to the good¬ nefs and {kill of its great Architect. We fee a regular afeent in the fcale of beings from mere lifelefs matter up to man ; and the probability is, that the fcale continues to afeend as far above man in perfection as created beings can poffibly be raifed.— The foie purpofe of God in creating the world mud have been to produce happinefs : but this would be moll effeCtually done by creating, in the fird place, as many of the mod perfeCt clafs of beings as the fydem could contain ; and afterwards other claffes lefs and lefs per¬ feCt, till the whole univerfe Ihould be completely full. We do not politively affert fuch a fcheme of creation, 3 N Where (a) That fuch xvas the general belief of the Greeks in the days of Homer, is plain from that poet’s condantly introducing his deities into the narrative of his poems, and telling us that Minerva, or fome other god, altered the minds of his heroes. “ By this,” fays Plutarch, “ the poet does not mean to make God defray the wTill of man, but only move him to w7ill : nor does he miraculoufly produce the appetites themfelves in men, but only caufes fuch imaginations as are capable o£ exciting them.” PRO Providence. [ 466 ] PRO Where all muft full, or not coherent be j And all that rifes, rife in due degree, -vas actually in the divine Architeft’s intention ; but that it is poffible, Is fufficiently obvious. No man will pretend to lay, that this earth could afford a comfort¬ able fubliftence to a greater number of the human race, were all the inferior animals annihilated, than it could at prefent, fwarming as every element is with life.— Suppofe then, that as many men had been placed at firft upon the earth as it could poffibly fupport, and that matters had been fo conilituted, as that the num¬ ber Ihould never have been either increafed or diminish¬ ed 5 we beg leave to alk, whether, fmee there would have been evidently room for inferior animals, it would have been moft worthy of infinite goodnefs to leave the whole globe to men, or to introduce into it different orders of lefs perfeft beings, which, while they could not incom¬ mode this principal inhabitant, would each find plea- fure in its own exiftence ? To this queffion different anfwers cannot furely be given. Let the reader then extend his view, and confider the univerfe, which, how¬ ever vail, cannot be pofitively infinite, as one fyftem as much united as the feveral parts of this globe ; let him fuppofe that there were at firft created as many of the higheft order of beings as it could have contained had creation there ftopt; let him remember that happinefs in many different degrees is valuable •,—and he will not lurely think it any imputation on the goodnefs of God that there are in the univerfe many beings far from per- feflion. The moft imperfeft of thefe are by themfelves better than nothing ; and they all contribute to make tip a fyftem which, confidercd as a whole, we have every reafon to believe to be as perfedt as any thing not 22 felf-exiftent can poflibly be. Obje&ion 2. If the world is condudled by a benevolent provi- introduc ^ence5 ^ow cnme evil to be introduced into it ? This tion of evil has perplexed mankind in all ages. The an¬ cient Perfians refolved it, by affecting the exiftence of two gods, Oromafdes the author of good, and Arima- nius the author of evil. From them the Chriftian he¬ retics called Manichees borrowed their dodlrine of two oppofite co-eternal principles. Both the Platonifts and Stoics aferibed the origin of evil to the perverfenefs or imperfedlion of matter, which they thought the Deity could not alter : and Pythagoras imagined a ftate of pre-exiftence, in which the fouls of men had committed offences, for which they are here fuffering the punifli- ment. But thefe hypothefes are, fome of them impious, 23 and all unfatisfadlory. anfwered. Taking the expreffion in its moft extenfive fenfe, the evils to which the human race are expofed may be re¬ duced to pain, uneajinefs, difappointment of appetites, and death ; ot which not one could have been wholly pre¬ vented without occafioning greater evils, inconfiftent with the perfect goodnefs of the Creator. As long as we have folid bodies capable of motion, fupported by food, fubjeft to the influence of the almofphere, and divifible, they muft necefiarily be liable to diffolution or death : But if a man could fuffer death, or have his limbs bro¬ ken, without feeling pain, the human race had been long ago extmft. A fever is a ftate of the body in which the fluids are in great diforder. Felt we no uneafinefs from that diforder, we fhould have no inducement to pay the proper attention to our ftate, and ihould cer¬ tainly die unawares, without fufpecling ourfelves to be Providence, in danger ; whereas, under the prefent adminiftration of —v—^ divine providence, the pain and ficknefs of the difeafe compel us to have recourfe to the remedies proper for reftoring us to foundnefs and to health. Of the unea- fineffes to which we are liable, and which are not the ef- fe& of immediate pain, the greateft has been fometimes faid to arife from the apprehenfion of death, which conftantly flares us in the face, and frequently embitters all our pleafures even in the hour of perfeft health But this dread of death is implanted in our breafts for the very beft of purpofes. Had we no horror at the apprehenfion of death, we fhould be apt, whenever any misfortune befel us, to quit this world rafhly, and rufh unprepared into the prefence of our Judge : but the horror which attends our reftetftions on our own diffo¬ lution, arifing not from any apprehenfions of the pain of dying, but from our anxiety concerning our future ftate ot exiitence, tends ftrongly to make us aft, while we are here, in fuch a manner as to enfure our happinefs here¬ after. Add to this, that the fear of death is the great- eft fupport of human laws. We every day fee perfons breaking through all the regulations of fociety and good life, notwithftanding they know death to be the certain confequence, and feel all the horrors of it that are natural to man : and therefore were death divefted of thefe horrors, how infignificant wTould capital punifh- ments be as guardians of the law, and how infecure would individuals be in civil fociety ? _ With regard to the unavoidable misfortunes and an¬ xieties of our prefent ftate, fo far from being truly hurt¬ ful in themielves, they are proofs of divine beneficence. When we fee men difpleafed with their fituation, when we hear them complain of the difficulties, the miferies, and the cares of life, of the hardfhips which they have undergone, and the labours which ftill lie before them ; inftead of accounting them unfortunate, we ought to regard them as aftive beings, placed in the only fitua¬ tion that is fit for the improvement of their nature. 1 hat difeontent, thefe reftlefs wiffies to improve their condition, are fo many fine indications that their facul¬ ties will not languiffi. They who are in the leaft de¬ gree accuftomed to obferve the human charafter, know well the influence which plealhre and repofe have in en¬ feebling every manly principle, and how capable they are of attaching us even to a fordid and diflionourable exiftence. Happy indeed it is for the human race, that the number of thofe men is fmall whom providence has placed in fituations in which perfonal aftivity is unne- ceffary. By far the greater number are compelled to exert themfelves, to mix and to contend with their equals, in the race of fortune and of honour. It is thus that our powers are called forth, and that our nature reaches its higheft perfeftion. It is even perhaps a general truth, that they who have ft niggled with the greateft variety of hardlhips, as they always acquire the higheft energy of charafter, fo if they have retained their in¬ tegrity, and have not funk entirely in the conteft, fel- dom fail to fpend their remaining days refpeftable and happy, fuperior to paffion, and fecured from folly by the poffeffion of a wifdpm dearly earned. _ But the benefits of phyfical evils have been fet in a phyfis4al ftill ftronger light by a great matter of moral wifdom, evil the who was himfelf fubjeft to many of thofe evils. Thatcaufe of man moral Sood'' yoh nfoil's Idler, n° £9. PRO [467 Providence man is a moral agent, fent into tliis world to acquire habits of virtue and piety to fit him for a better hate, is a truth to which no confiftent theift will for a mo¬ ment refufe his aflent. But almoft all the moral good which is left among us, is the apparent effeft of phyfical evil. “ Goodnefs is divided by divines into fobernefs, righ- teoufnefs, and godlinefs. Let it be examined how each of thefe duties would be pradlifed if there were no phyfi¬ cal evil to enforce it. “ Sobriety or temperance is nothing but the forbear¬ ance of pleafure *, and if pleafure was not followed by pain, wrho would forbear it ? We fee every hour thofe in whom the defire of prefent indulgence overpowers all fenfe of pall, and all forefight of future mifery. In a remiflion of the gout, the drunkard returns to his wine, and the glutton to his feaft; and if neither difeafe nor poverty were felt or dreaded, every one would fink down in idle fenfuality, without any care of others, or of him- felf. To eat and drink, and lie down to fleep, would be the whole bufinefs of mankind. “ Righteoufnefs, or the fyftem of focial duty, may be fubdivided into juftice and charity. Of juftice, one of the heathen fages has ihown, with great acutenefs, that it was imprefled upon mankind only by the inconveni¬ ences which injuftice had produced. ‘ In the firft ages (fays he) men a£ted without any rule but the im- pulfe of defire they pradlifed injuftice upon others, and fuffered it from others in their turn j but in time it was difcovered, that the pain of fuffering wrong was greater than the pleafure of doing it j and mankind, by a general compadt, fubmitted to the reftraint of lawrs, and refigned the pleafure to efcape the pain.’ “ Of charity, it is fuperfluous to obferve, that it could have no place if there were no wantfor of a virtue which could not be pradtifed, the omiftion could not be culpable. Evil is not only the occafional but the efficient caufe of charity ; we are incited to the relief of mifery by the confcioufnefs that we have the fame nature with the fufferer 5 that we are in danger of the fame diftreifes, and may fome time implore the fame af- fiftance. “ Godlinefs or piety Is elevation of the mind towards the Supreme Being, and extenfion of the thoughts of another life. The other life is future, and the Supreme Being is invifible. None would have recourfe to an invifible power, but that all other fubjedls had eluded their hopes. None would fix their attention upon the future, but that they are difcontented with the prefent. If the fenfes were feafted with perpetual pleafure, they would always keep the mind in fubjedtion. Reafon has no authority over us but by its power to warn us againft evil. “ In childhood, wdrile our minds are yet unoccupied, religion is impreffed upon them j and the firft years of almoft all who have been well educated are palled in a regular difcharge of the duties of piety : But as we advance forward into the crowds of life, innumerable delights folicit our inclinations, and innumerable cares diftradl our attention. The time of youth is palfed in noify frolics ; manhood is led on from hope to hope, and from projedt to projedl; the diffolutenefs of plea¬ fure, the inebriation of fuccefs, the ardour of expedi¬ tion, and the vehemence of competition, chain down the mind alike to the prefent fcene : nor is it remem- 1 PRO bered how foon this mift of trifles muft be fcattered, Providence and the bubbles that float upon the rivulet of life be r * ' loft for ever in the gulf of eternity. To this confide- ration fcarce any man is awakened but by fome preffing and refiftlefs evil} the death of thofe from whom he de¬ rived his pleafures, or to whom he deftined his pof- feffions, fome difeafe which ffiows him the vanity of all external acquifitions, or the gloom of age which intercepts his profpedts of long enjoyment, forces him to fix his hopes upon another ftate ; and when he has contended with the tempefts of life till his ftrength fails him, he flies at laic to the fhelter of re¬ ligion. “ That mifery does not make all virtuous, experience too certainly informs us ; but it is no lefs certain, that of what virtue there is, mifery produces far the greater part. Phyfical evil may be therefore endured with patience, fince it is the caufe of moral good ; and patience itfelf is one virtue by wffiich we are prepared for that’ftate in which evil ihall be no more.” The calamities and the hardfhips of our prefent ftate, Objeclidnl then, are fo far from being real evils, of which provi-hom the deuce ought to be accufed, that in every point of view in which we can confider them, they afford the fureft0 J?t°ra proofs of the wdfdom of its adminiftration, and of itsb ’ goodnefs to man. The moft ferious difficulty lies in accounting for the permiffion of moral evil or guilt, in a fyftem governed by infinite benevolence and wifdom. Thofe wdio in a confiftent manner hold the dodlrine of the abfolute ne- ceffity of human aflions in its full extent, and acknow'- ledge all its confequences, find it eafy to elude this diffi¬ culty. They very fairly deny the exiftence of any fuch thing as moral evil in the abftradt ; and affert, that what wTe call a crime, is nothing more than an aftion which we always regard with a painful fenfation : that thefe apparent evils endure only for a time j and that all will at laft terminate in the perfedlion and happinefs of every intelligent being. Upon the fyftem of liberty, the fhorteft anfwer feems anfwerriL to be this: that fome things are abfolutely impoffible, not from any weaknefs in the Deity, but becaufe they infer abfurdity or contradiction. Thus it is impoffible for twice two to be any thing elfe than four ; and thus it is impoffible for Omnipotence itfelf to confer felf- approbation upon an intelligent being who has never deferved it 5 that is to fay, it is impoffible for a man of feufe to be pleafed with himfelf for having done a cer¬ tain aftion, w'hile he himfelf is confcious that he never did that aftion. But felf-approbation conllitutes the higheft, the moft unmingled, and permanent felicity, of which our nature is capable. It is not in the power of Omnipotence itfelf, then, to beftow the higheft and moft permanent felicity of our nature •, it muft be earned and deferved before it can be obtained. In the fame manner good defert, virtue or merit, cannot be confer¬ red; they muft be acquired. To enable us to acquire thefe, we muft be expofed to difficulties, and muft fuf* fer in a certain degree. If thefe difficulties had no in¬ fluence upon our conduf! and feelings, if they expofed us to no real danger, no fabric of merit and of feif- approbation could be reared upon them. All that the Supreme Being could do for us, was to confer fuch art original conftitution and charafler as would enable us to do well if we thou Id exert our utmoft powers. The 3 N 2 tmiverfe PRO [ 468 ] PRO Providence, univerfe is not ruled by favour, but by juldice. Com- 'r~ piete felicity mull; be purchaied. Guilt is an abufe of our freedom, a doing ill where we could have done well, and is entirely the work of man. Heaven could not avoid permitting its exilfence, and expofmg us to danger 5 for temptation is necelfary to virtue, and vir¬ tue is the perfection of our nature, our glory, and our happinefs. e us 1 ^ The permiffion of moral evil has been fo ably ac¬ counted for by Simplicius, a Pagan writer, and there¬ fore net bialfed by any partiality to the Jewiib or Chri- llian Scriptures, that we cannot deny ourfelves the plea- lure of laying his reafoning before our readers. He * SimpHc- alks *, “ Whether God may be called the author of lin, '■'/(F'2 p^iSd kecauk he permits the foul to ufc her liberty? and 187. ed. ’ anfwers the quellion thus : Salrruif. “ He who fays that God fhou-d not permit the exer- cife of its freedom to the loul, mull affirm one of thefe two things 5 either that the foul, though by nature ca¬ pable of indifferently chooling good or evil, ihould yet be conftantly prevented from chooiing evil j or elfe that it Ihould have been made of fuch a nature as to have no povjer of choofing evil. “ The former affertion (continues he) is irrational and abfurd 5 for what kind of liberty would that be in which there ffiould be no freedom of choice ? and wffiat choice could there be, if the mind were conftantlv re- llrained to one fide of every alternative ? With relpcCt to the fecond affertion, it is to. be obferved (lays he), that no evil is in itfelf defirable, or can be chofen as ✓sS Objection from the apparent cor fivfion of human atfaiis, evil. But if this power of determining itfelf either way in any given cafe muff be taken from the foul, it muff either be as fomething not good, or as fome great evil. But whoever faith fo, does not confider how many things there are which, though accounted good and defirable, are yet never put in competition with this free¬ dom of will: for without it we ftiould be on a level with the brutes •, and there is no perfon who would rather be a brute than a man. If God then Ihows his goodnefs in giving to inferior beings fuch perfeftions as are far below this, is it incongruous to the divine nature and goodnefs to give man a felf-determining power over his aftions, and to permit him the free exercife of that power ? Had God, to prevent man’s fin, taken away the liberty of his will, he would likewife have deftroyed the foundation of all virtue, and the very nature of man j for there could be no virtue were there not a poffibility of vice ; and man’s nature, had it continued rational, would have been divine, becaufe impeccable. There¬ fore (continues he), though we attribute to God, as its author, this felf-determining power, which is fo neceffary in the order of the univerfe 5 we have no reafon to at¬ tribute to hirp that evil which comes by the abufe of li¬ berty : For God doth not caufe that averfion from good which is in the foul when it fins 5 be only gave to the foul fuch a power as might turn itfelf t© evil, out of which he produces much good, which, without fuch a power, could not have been produced by Omnipotence itfelf.” So confonant to the doffrine of our feriptures is the reafoning of this opponent of the writings of Mofes ! Fas ejl et ab hojle doceri. The laft objection to the belief of a divine providence arifes from the apparent confufion of human affairs, that all things happen alike to all, that bad men are profpe- rous, and that a total, want of juftice appears to attend the divine adminiftrations. Even the beft men have at Providence. times been fhaken by this conlideration.—But there are w—' many reafons for rendering this world a mixed feene : it would become unfit for a ffate of trial and of education to virtue were it otherwife. It has been ffiown already, that phyfical evil is the anfwered, parent of moral good ; and therefore it would be abfurd to expeCt that the virtuous Ihould be entirely exempt¬ ed from that evil. For the occafional profperity of the wicked, many reafons have been affigped even by thole who, in their difquifitions, were not guided by that re¬ velation which has brought to light life and immorta¬ lity. “ God (fays Plutarch) Iparcs the wicked, that he by Phi- may fet to mankind an example of forebearance, and sarch. teach them not to revenge their injuries too hallily on each other. He fpares lome wicked men from early pumffiment, in order to make them inffruments of his juftice in punilhing others. And he fpares all for a time, that they may have leifure for repentance ; for men (fays the lame excellent moralift) look at nothing further, in the pumfhments which they iniliCt, than to fatisfy their revenge and malice, and therefore they pur- fue thofe who have offended them with the utmoit rage and eagernefs whereas God, aiming at the cure of thofe who are not utterly incurable, gives them ft{]et(2t»Xteirdctc “ lime to be converted.” But this objection receives the beft folution from the doctrine of the immortality of the human foul. —— And fee ! ’Tis come, the glorious morn 1 the fecond birth Of heav’n and earth ! awakening nature hears The new creating xvord, and ftarts to life, In every height’ned form, from pain and death For ever free. The great eternal'fcheme> Involving all, and in a perfeci whole Uniting, as the profpeCl wider fpreads, To realbn’s eye refin’d clears up apace. Ye % rainly wife ! Ye blind prefumptuous ! now,,. Confounded in the duff, adore that Pow’r And Wifdom oft arraign’d j fee now the caufe, Why unaffuming worth in fecret liv’d And died negleCIed : why the good man’s (hare In life was gall and bitternefs of foul: Why the lone widow and her orphans pin’d In ftarving folitude ; while luxury, In palaces, lay ftraining her low thought. To form unreal wants : why heav’n-born truth, And moderation fair, wore the red marks Of fuperftition’s fcourge ; why licenc’d pain, That cruel fpoiler, that ernbofom’d foe, Imbitter’d all .our blifs. Ye good diftreft ! Ye noble few ! who here unbending Hand Beneath life’s preffure, yet bearajp a while. And what your bounded view, which only law A little part, deem’d evil, is no more : The ftorms of wintry time will quickly pafs, And one unbounded fpring encircle all. Thomson’s Winter. 31 The :minor. taiit) oi the fill! the heft, anivver to thb objec¬ tion. PROVIDENCE-Plantation, a colony of New-England, which, with Rhode-ifland, formerly conftituted a charter government. Its chief town is Newport. Providence, one of the leal! of the Bahama iflands in the American ocean, but the beft of thofe planted and fortified by the Engliffi. It is feated on the eaft fide Pry‘.'I rit e £de of the gulf of Florida, il 25. o. iV0^' , PROVINCE, in Roman antiquity, a country of com fiderable extent, which, upon being entirely reduced un¬ der the Roman dominion, was new-modelled according to the pleafure of the conquerors, and fubjected to the Command of annual governors, fent from Rome ; being commonly obliged to pay fuch taxes and contributions as the fenate thought fit to demand. Of thefe countries, that, part of France next the Alps was one, and ftill retains the name Provence. Nicod derives the word a procul vivendo, “ living afar off but it is better deduced from pro and vittco “ I overcome.” Province, in Geography, a divifion of a kingdom or Rate, comprifing feveral cities, towns, &c. all under the fame government, and ulually diftinguilhed by the extent either of the civil or ecclefialtical jur.fdiction. The church diftinguidies its provinces by archbilhop- rics 5 in which fenfe, England is divided into two pro¬ vinces, Canterbury and York. The United Provinces are feven provinces of the Ne¬ therlands, who, revolting from the Spanilh dominios, made a perpetual alliance, offenfive and defenfive, at Utrecht, anno 1 qyq. See UNITED Provinces. PROVINCIAL, fomething relating to a province. It alfo denotes, in Romilh countries, a perfon who has the direflion of the feveral convents of a province. PROVISIONS, in a military fenfe, implies all man¬ ner of eatables, food or provender, ufed in an army, both for man and beaft. PROVOST of a city or town, is the chief municipal magillrate in feveral trading cities, particularly Edin¬ burgh, Paris, &c. being much the fame with mayor in other places. He prelldes in city-courts, and together with the bailies, who are his deputies, determines in all differences that arife among citizens. The provoft of Edinburgh is called lord, and the fame title is claimed by the provoff of Glafgow. The former calls yearly conventions of the royal boroughs to Edin¬ burgh by his miflives, and is, ex ojpcio, prelident to the convention when met. Provost, or Prevot-Royal, a fort of inferior judge formerly eftabibhed throughout Frace, to take cogni¬ zance of all civil, perfonal, real, and mixed caufes, among the people only. Grand P UOVOST of France, or of the Houfchold, had jurifdidlion in the king’s boufe, and over the officers therein ; looked to the policy thereof, the regulation of provifions, See. Grand PllOVOST of the Con/1 able, a judge who ma¬ nages proceffes againft the foldiers in the army who have committed any crime. He has four lieutenants diftributed throughout the army, called provofts of the army, and particularly provofts in the feveral regiments. Provost Mar/hal of an Army, is an officer appoint¬ ed to feize and fecure deferters, and all other crimi¬ nals. He is to hinder foldiers from pillaging, to in¬ dict offenders, and fee the fentence paffed on them ex¬ ecuted. He alfo regulates the weights and meafures, and the price of provifions, Sic. in the army. For the difeharge of his office, he has a lieutenant, a clerk, and a troop of marfhal-rucn on horfeback, as allb an ex¬ ecutioner. p R u There is alfo a provoft-marffnal in the navy, who has Frovofts charge over prifoneu, Sec. J ^ The French alfo had a provoft-general of the marines,, innj whole duty it was to profecute the marines when guilty of any crime, and to make report thereof to the council of war \ befides a marine provoff: in every veffel, who was a kind of gaoler, and took the prifoners into his care,- and kept the veffel clean. PROVOSTS of the Marjhals, were a kind of lieutenants of the marlhals of France ; of thefe there were 180 feats in France; their chief jurifdidlion regarded highwaymen, footpads, houfe-breakers, Sec. P ROVOST of the Mint, a particular judge inftituted for the apprehending and profecuting of falfe coiners. Provost, or Prevot, in the king’s Rabies; his office is to attend at court, and hold the king’s llirrup when he mounts his horie. There are four provofts of this kind, each of whom attends in his turn, monthly. PROW, denotes the head or fore-part of a ffiip, par¬ ticularly in a *dley j being that which is oppofite to the poop or ftern. PROXIMITY, denotes the relation of nearnefs, ei¬ ther in refpedf of place, blood, or alliance. PRUDENCE, in ethics, may be defined an ability- of judging what is belt, in the choice both of ends and means. According to the definition of the Roman mo- ralift, De Offiehs, lib. i. cap. 43. prudence is the know¬ ledge of what is to be defired or avoided. According¬ ly, he makesprudentia /De Legibus, lib. i.) to be a con- traclion of providentia, or forefight. Plato /De Legibus, lib.iii.) calls this the leading virtue } and Juvenal, Sat. x. obferves, Nullum numen abejlji ft prudentia. The idea of prudence includes evGxXue, or due conful- tation; that is, concerning fuch things as demand con- fultation in a right manner, and for a competent timer that the relolution taken up may be neither too preci¬ pitate nor too flow; and c-imna-tf, or a faculty of diicern- ing proper means when they occur 3 and to the perfec¬ tion of prudence, thefe three things are farther required, viz. hivorng, or a natural fagacity 5 acy^vo*, prefence of mind, or a ready turn of thought} and or expe¬ rience. 'I‘he extremities of prudence are craft or cun¬ ning on the one hand, which is the purfuit of an ill end by direft and proper though not honeft means *, and fol¬ ly on the other, which is either a miftake, both as to the end and means, or profecuting a good end by foreign and improper means. Grove’s MoralPhilofophy, vol. ii. chap. ii. PRUDENTIUS, or Aurelius Prudentius Cle¬ mens, a famous Chriftian poet, under the reign of Theo- dofius the Great, who was born in Spain in the year 348. He firft followed the profeffion of an advocate, was afterwards a judge, then a foldier, and at length had an honourable employment at court. We have a great number of his poems, which, from the choice of his fubjccls, may be termed Chriflian poems; but the ftyle is barbarous, and very different from the purity of the Auguftan age. The moft efteemed editions of Pru- dentius’s works are that of Amfterdam, in 1667, with Heinfius’s Notes, and that of Paris in 1687, in ufum Delphini. PRUNELLA, a genus of plants belonging to tire didynamja clafs j and in the natural method ranking under pro r 469 W. Long. 77. 3 j. N. Lat. 'Prunes, Pronin? the P Pi 12til order, u holoracece. See 'under Index PRUNES, are plums dried in the funlhine, or in an oven. PRUNING, in Gardening and Agriculture, is the lopping off the iuperfluous branches of trees, in order to make them bear better fruit, grow higher, or appear more regular. Pruning, though an operation of very general ufe, is neverthelefs rightly underflood by few ; nor is it to be learned by rote, but requires a ftrict obfervation of the different manners of growth of the feveral forts of fruit- trees ; the proper method of doing which cannot be known without carefully obferving how each kind is naturally difpofed to produce its fruit : for fome do this on the fame year’s wood, as vines \ others, for the moft part, upon the former year’s wood, as peaches, ne *n confequence of pruning j to prevent thefe ~ ' injurious effefts, a remedy has been propofed by Mr ^ _ , a _ ^ Bucknall, which on trial, it is faid, has been fuccefsful. By this method the branches to be removed are to be cut clofe to the place of leparation from the trunk, fmoothed well with a knife, and the wound is to be fmeared over with medicated tar, laid on with a painter’s brulh. The following is the compolition of this medicated tar. One quarter of an ounce of corro- five fublimate reduced to fine powder, by beating it with a wooden hammer, is introduced into a three pint earthen pipkin, with about a glafsful of gin or other fpirit. The mixture is to be wTell ftirred till the fubli* mate is diffolved. The pipkin is then gradually filled with vegetable or common tar, and conftantly liirred, till the mixture be blended together as intimately as poffible $ and this quantity will at any time be fufficient for 200 trees. To prevent danger, let the corrofive fublimate be mixed wuth the tar as quickly as poflible after it is purchafed } for being of a very poifonous na¬ ture to all animals, it Ihould not be fuffered to lie about a houfe, for fear of mifchief to fome part of the fa¬ mily. By applying this compofition, Mr Bucknall can, without the leaft danger, ufe the pruning hook on all forts of trees, much more freely than by the ufe of any article hitherto recommended. The following remarks by the author on pruning in general, feem worthy of notice, and w'e give them in his own words. “ I give no attention (fays he) to fruit branches, and wood bran¬ ches 5 but beg, once for all, that no branch fhall ever be fhortened, unlefs for the figure of the tree, and then conftantly taken off clofe to the feparation, by which means the wround foon heals. The more the range of the branches ftioots circularly, a little inclining upwards, the more equally will the fap be diftributed, and the better wrill the tree bear •, for, from that circumftance, the fap is more evenly impelled to every part. Do not let the ranges of branches be too near each other ; for, remember all the fruit and the leaves ftiould have their full fhare of the fun j and wdiere it fuits, let the middle of the tree be free from wood, fo that no branch ftiall ever crofs another, but all the extreme ends point up¬ wards. PRUNUS, a genus of plants belonging to the icof- andria clafs ; and in the natural method ranking under the 36th ordea, Pomacecc. See Botany Index. PRUSA, in Ancient Geography, a town fituated at Mount Olympus in Myfia, built by Prufias, who waged war wTith Croefus, (Strabo) ; with Cyrus, (Stephanus) 5 both cotemporary princes. Now called Burfa or Prafa, capital of Bithynia, in Afia Minor. E. Long. 29. 5. N. Lat. 39. 22. PRUSIAS, the name of feveral kings of Bithynia. Prusias, a town of Bithynia, anciently called Cios, from a cognominal river, and giving name to the Sinus Pv U A , rebuilt by Prufias the fon of Pruffia, Zela, after having been deftroyed by Philip the fon of Demetrius: it flood on the Sinus Cianus, at the foot of Mount Arganthonius. This is the Prufias who harbour¬ ed Hannibal after the defeat of Antiochus.—-Of this place was Afclepiades, furnamed Prujicus, the famous phyfician. PRUSSIA, a modern, but defervedly celebrated ^ate , kingdom of Europe, whofe monarch, along with PrufliaCCCCXLIV* Proper, poffeffes alio the eleftorate of Brandenburg, and fome other territories of confiderable extent. The di- ftriht properly called PruJJia is of great extent, and di¬ vided into the Ducal and Regal Pruflia, the latter be¬ longing to the republic of Poland till the late partition of the Poliftr territories. Both together are ef great extent j being bounded on the north by the Baltic, on the fouth by Poland and the duchy of Mazovia, on the weft by Pomerania, and on the eaft by Lithuania and r Samogitia. I he name is by lome thought to be deri-EtymoJo- ved from the Boruffi, a tribe of the Sarmatians, who, of the migrating from the foot of the Riphaean mounntains,name" were tempted by the beauty and fertility of the coun¬ try to fettle there. Others think that the name of this country is properly PoruJJia ; Po in the language of the natives fignifying near, and PoruJJia fignifying near Raf- Jia. To the latter etymology w’e find the king of Pruflia himfelf affenting in the treatiie intitled Memoirs of the Houfe of Brandenburg. However, it muft be owned, that thefe or any other etymologies of the word are very uncertain, and we find nothing like it mentioned by hi- ftorians before the tenth century. % The ancient ftatc of Pruflia is almoft entirely un-ExrreiIie known. However, the people are faid to have been^j^"^ very favage and barbarous j living upon raw flefli, andcientinhE- dlinking the blood of horfes at their feafts, according bitants. to Stella, even to intoxication (a). Nay, fo extreme¬ ly favage W'ere this people, that they were even unac¬ quainted with the method of conftrudling huts, and took up their dwelling in caves and cavities of rocks and trees, where they protected themfelves and children from the inclemencies of the weather. Among fuch a people it is vain to expeft that any tranfaftions would be record¬ ed, or indeed that any thing worthy of being recorded would be tranfacled. We lhall therefore begin our hi- ftory of Pruflia with the time when the Teutonic knights firft got footing in the country. (See TEUTONIC Knights'). On the expulfion of the Chriftians from the Holy Teutonic Land by Saladin, a fettlement was given to the Teu- knights tonic knights in Pruflia by Conrade duke of Mazovia, . £et the competitor of Bolellaus V. for the crown of Poland.^ counl1 -i heir firft refidence in this country wTas Culm ; to which try. territory they w'ere confined by the conditions of the do¬ nation, excepting what they could conquer from their pagan neighbours, all w’hich the emperor granted to them in perpetuity. Encouraged by this grant, the knights conquered the greateft (a) This author does not mention any particular method by which they communicated an inebriating quality to the blood of animals. Poflibly, however, the vital fluid may have a property of this kind, though unknown in our days where fuch barbarous cuftoms are difufed. Drunkennefs from drinking blood is frequently mentioned in Scrip-.- tare, but whether literally or metaphorically muft be decided by the learned. Pn’.flia. 4 Expelled. Hiftory of Bramlen- ■burg. * N® 27, -&.C. P Tl U [47 greateft part of the country which now goes by the name of Prujpa; and, not content with this, became very troublel’ome to Poland, infomuch that the monarchs of that kingdom were fometxmes obliged to carry on dan¬ gerous and bloody wars with them •, for an account of which we refer to the article Poland, n° 61. 67, &c. The Teutonic order continued in PrulTia till the year 1531. Their lail grand-mailer was Albeit marquis of .Brandenburg, and nephew to Sigifmund I. king of Po¬ land. He wras preferred to this dignity in hopes that his affinity to Sigifmund might procure a reilitution ot feme of the places which had been taken Irom the order during the former unluccefsful wars with Poland j but in this the fraternity were difappointed. Albert, hoiv- ever, was fo far from endeavouring to obtain any favour from his uncle by fair means, that he refuied to do ho¬ mage to him, and immediately began to make prepara¬ tions for throwing off his dependence altogether, and tecoveiing the -whole of Pruffia and Pomerania by force of arms. In this he was fo far from fucceeding, that, being foiled in every attempt, he wTas forced to re- fign the dignity of grand-mafter ^ in recompenfe for which, his uncle bellowed on him that part of Pruffia now called Ducal, in quality of a fecular duke. It was now the intereft of the houfe of Brandenburg to affilt in the expulfion of the fraternity} and accordingly, be¬ ing at lail driven out of Pruffia and Pomerania, they transferred their chapter to Mariendal in Franconia } but in that and other provinces of the empire where they fettled, little more than the name of the order, once io famous, now remains. The other moll confiderable part of his Pruffian ma- jefly’s dominions is the eleftorale of Brandenburg. Like other parts of Germany, it was anciently poi- feffed by barbarians, of whom no hilloiy can be given. Thefe were fubdued by Charlemagne, as is related un¬ der the article France * ; but being on every occafion ready to revolt, in 927 Henry the Fowler eltablifhed margraves, or governors of the frontiers, to keep the barbarians in awe. The firll margrave of Brandenburg was Sigefroy, brother-in-law to the above-mentioned emperor j under whofe adminiflraticn the biffioprics of Brandenburg and Havelberg were eflabliihed by Otho I. From this Sigefroy, to the fucceffion of the heufe of Hohenzollern, from whom the prefent ele£lor is defeen- ded, there are reckoned eight different families, who have been margraves of Brandenburg •, namely, the fa¬ mily of the Saxons, of Walbeck, Staden, Plenck, An¬ halt, Bavaria, Luxemburg, and Mifnia. The margraves of the four firft races had continual wars with the Van¬ dals and other barbarous people •, nor could their ravages be Hopped till the reign of Albert furnamed the Bear, the firft prince of the houfe of Anhalt. Fie wTas made margrave by the emperor Conrad III. and afterwards raffed to the dignity of eleilor by Frederic Barbaroffa, about the year 1100. Some years afterwards the king of the Vandals dying without iffue, left the Middle Marche by bis laft will to the eledlor, who was befides poffeffed of the Old Marche. Upper Saxony, the country of Anhalt, and part of Luface. In 1332 this line became extindl, and the electorate devolved to the empire. It was then given by the emperor Louis of Bavaria to bis fon Louis, who was the firft of the fixth xace. Louis the Fioman fucceeded his brother -? and 2 2 ] PR U as he alfo died without children, he was fucceeded by Pj.Fh. Otho, bis third brother, who fold the deflorate to the w”r>v emperor Charles IV. of the houfe of Luxemburg, for 200,000 florins of gold. Charles IV. gave the Marche to his fon Winceflaus, to whom Sigifmund fucceeded. I his eleftor, being embarraffed in his circumfiances, fold the New Marche to the knights of the I cutonic order. Joffe fucceeded Sigifnuu.dj but afpiring to the empire, fold the deflorate to William duke of Mif¬ nia ) who, after he had poffelTed it for one year, fold it again to the emperor Sigifmund. In 1417, Fre¬ deric VI. burgrave of Nuremberg, received the invefli- ture of the country of Brandenburg at the diet of Con- ftance from the hands of the emperor Sigifmund 3 who, two years before, had conferred upon him the dignity of eleftor, and arch-chamberlain of the Floly Roman empire. This prince, the fiift of the family of Hohenzol- lem, found himlelf poffeffed of the Old and Middle Marche, but the dukes of Pomerania had ufurped the Marche Ukraine. Again!! them, therefore, the eleflor immediately declared war, and icon recovered the province. As the New Marche ftill continued in the hands of the Teutonic kights, to whom it had been fold as we have already mentioned, the eltflor, to make up for this, took poffeffion of Saxony, which at that time happened to be vacant by the death of Al¬ bert the laft eleflor of the Anhalt line. But the em¬ peror, not approving of this Hep, gave the inveftiture of Saxony to the duke of Mifnia ; upon which Frede¬ ric voluntarily defifted from his acquifitions. This eleflor made a divifion of his poffeffions by will. Flis eldeft fon was deprived of his right on account of his having too clofely applied himlelf to fearch for the philofopher’s ftone; fo he left him only Voigtland. The deflorate was given to his lecond fon Frederic j Albert, furnamed Achilles, had the duchies of Franco- * nia; and Frederic, furnamed the Fat, had the Old Marche •, but by his death it returned to the deflorate of Brandenburg. Frederic I. was fucceeded by bis fon, called alfo Frederic, and furnamed Iron-tooth on account of his ftrength. He might with as great reafon have been furnamed the Magnanimous, fince he refufed two crowns, viz. that of Bohemia, which was offered him by the pope, and the kingdom of Poland to which he was invited by the people; but Frederic declared he would not accept of it unlefs Cafimir brother to La- diflaus the late king refafed it. Thefe inftances of magnanimity had fuch an effefl on the neighbouring people, that the ftates of Lower Lufatia made a vo¬ luntary furrender of their country to him. But as Lu¬ fatia was a fief of Bohemia, the king of that country immediately made war on the eleftor, in order to re¬ cover it. However, he was lo far from being fuccefs- ful, that, by a treaty of peace concluded in 1462, he was obliged to yield the perpetual fovereignity of Cor- bus, Peits, Sommerfeld, and lome other places, to the eleftor. Frederic then, having redeemed the New Marche from the'Teutonic order for the fum of 100,oco florins, and ftill further enlarged his dominions, refign- ed the fovereignty in 1469 to his brother Albert, fur- 6 named Achilles. Exploits of Albert was 37 years old when his brother refigned^^1^"" cbilks. Pruflia. U [ 473 ] P li U ^'S e:s:P^0^s> f°r which a part of the duchy of Cleves j and obtained of the Jlol- Pruffia and Branden- tmrg unit¬ ed. 8 Unfortu¬ nate reign of the elec tor George William. * See Jwe den. 9 Reign of Frederic William the Great. the ele&orate to him. ____ he had the furname of Achi/tes, had been performed while he was burgrave of Nuremberg. He declared war againft Lewis duke of Bavaria, and defeated and took him prifoner. He gained eight battles againft the Nurembergers, who had rebelled and contefted his rights to the burgraviate. In one of thefe he fought hngly againft 16 men, till his people came up to his afliftance. He made himfelf mafter of the town of Grieffenburg in the fame manner that Alexander the Great took the capital of the Oxydracae, by leaping from the top of the walls into the town, where he de¬ fended himfelf fingly againft the inhabitants till his men forced the gates and refcued him. The confidence which the emperor Frederic III. placed in him, gain¬ ed him the direction of almoft the whole empire. He commanded the Imperial armies againft Lewis the Rich duke of Bavaria ; and againft Charles the Bold duke of Burgundy, who had laid fiege to Nuis, but concluded a peace at the interpofition of Albert. He gained the prize at 17 tournaments, and was never dif- mounted. All thefe exploits, however, had been performed be¬ fore Albert obtained the deflorate. From that time we meet with no very important tranfaflions till the year 1594, when John Sigifmund of Brandenburg, having married Anne the only daughter of Albert duke of Pruftia, this united that duchy to the elec¬ torate, to which it has continued to be united ever fince ; and obtained pretentions to the countries of Ju¬ liets, Berg, Cleves, Marck, Ravenfburg, and Ravenftein, to the fucceffion of which Anne was heirefs. Sigifmund died in 16x9, and was fucceeded by his fon George William 5 during whofe government the deflorate fuffered the moft miferable calamities. At this time it was that the war commenced between the Proteftants and Catholics, which lafted 30 years. The former, although leagued together, were on the point of being utterly deftroyed by the Imperialifts under the command of Count Tilly and Wallenftein, when Guftavus Adolphus of Sweden turned the fcale in their favour, and threatened the Catholic party with utter deftruflion *. But by his death at the battle of Lut- zen, the fortune of war was once more changed. At laft, however, peace was concluded with the empe¬ ror j and, in 1640, the deflor died, leaving his do¬ minions to his fon Frederic William, furnamed the Great. This young prince, though only 20 years of age at the time of his acceflion, applied himfelf with the utmoft diligence to repair the Ioffes and devaftations occahoned by the dreadful wars which had preceded. He received the inveftiture of Pruflia perfonally from the king of Poland, on condition of paying 100,000 florins annually, and not making truce or peace with the enemies of that crown. His envoy likewife recei¬ ved the inveftiture of the deflorate from the emperor Ferdinand III. The deflor then thought of recover¬ ing his provinces from thofe who had ufurped them. He concluded a truce for 20 years with the Swedes, who evacuated the greateft part of his eftates. He likewife paid 140,000 crowns to the Swedifh garri- fons, which ftill poffeffed fome of his towns ; and he concluded a treaty with the Heffians. who delivered up Vol. XVII. Part IL Pruflia. landers the evacuation of iome other cities. In tne mean time, the powers of Furope began to be weary of a war which had continued for iuch a length of time with fuch unrelenting fury. The cities of Ofnaburg and Munfter being chofen as the moft proper places for negociation, the conferences were opened in the year 1645 5 but, by reafon of the mul¬ tiplicity of buhnefs, they were not concluded till two years after. France, which had efpoufed the interefts of Sweden, demanded that Pomerania Ihould be ceded to that kingdom as an indemnification for the expences which the war had coll Guftavus Adolphus and his fucceffors. Although the empire and the elector refu- fed to give up Pomerania, it was at laft agreed to give up to the Swedes Hither Pomerania, with the ifles of Rugen and Wollin, aifo fome cities 5 in return for which cefuon, the bilhoprics of Halberftadt, Minden, and Camin, were fecularized in favour of the eleftor, of which he was put in poffeffion, together with the lordftiips of Hochenftein and Richenitein, with the 10 reverfion of the archbifliopric of Magdeburg. This was Preaty the treaty of Weftphalia concluded 111 1648, and which We^pllaJ;a ferves as a bafis to all the poffeflions and rights of the COl’C UC ed’ German princes. The elector then concluded a new treaty with the Swedes, for the regulation of limits, and for the acquittal of fome debts, of which Sweden would only pay a fourth 5 and next year the deflorate, Pomerania, and the duchies of CJcves, were evacuatecL by the Swedes. ^ Notwithftanding all thefe treaties, however, theTheelec- Swedes foon after invaded Pomerania, but were en-tor fucceec^ tirely defeated by the eleflor near the town of Fehr-at a,jftcthe bellin. Three thoufand were left dead on the fpot,S'Ve eS’ among whom were a great number of officers; and a great many were taken prifoners. The eleflor then purfued his viftory, gained many advantages over the Swedes, and deprived them of the cities of Stralfund and Gripfwald. On this the Swedes, hoping to oblige the deflor to evacuate Pomerania, which he had. almoft totally fubdued, invaded Pruffia, from Li¬ vonia, with 16,000 men ; and advancing into the country, they burned the fuburbs of Memel, and took the cities of Tike and Infterburg. The deflor, to oppofe the invaders, left Berlin on the 10th of’Ja¬ nuary 1679, . at the head of 9000 men. The Swedes retired at his approach, and were greatly hafaffed by the troops on their march. So fuccefsful indeed was the deflor on this o.ccafion, that the Swedes loft aL moft one half of their army killed or taken prifoners. At laft, having, croffed the bay of Frifch-haff and* Courland on the ice, he arrived on the 19th of January wlifi his infantry, within three miles of Tilfe, where the Swedes had their head quarters. The fame day his general, Trefenfeldt, defeated two regiments of the enemy near Splitter 5 and the Swedes who were in Tilfe abandoned that place, and retired towards Courland. They were purfued by General Gortz and entirely defeated with fucli {laughter, that fcarce 13 3000 of them returned to Livonia. Yet, notwithftand-fs obli£ed ing all thefe viflories, the deflor, being preffed on 1°™ of tJl2 °ther fide ^ the. viflonous generals of France, peace ^ 1-1. lurenne and the prince of Conde, was obliged tothem* make peace with the Swedes. The conditions were 3 ° that ( P raffia *3 A ftrange eml>alfy from the ( ham of Tartary. T4 FretlericTir, obtains the title of kin? of Pruflia. P R U [ 47 that lire treaty of WeUphalia ftiould ferve for a bafis ' to the peace ; that the elector fliould have the proper¬ ty cf the cuiloms in all the ports of Further Pomera¬ nia, with the cities of Camin, Gartz, Grieffenburg, and Wildenbruck ; on his part, he confenled to give up to the Swedes all that he had conquered from them, and to give no affiftance to the king of Denmark, up¬ on condition that France delivered up to him his pro¬ vinces in Weftphalia, and paid him 300,000 ducats, as an indemnification for the damages done by the French to his ftates. This treaty was ftyled the peace of St Germain. With the treaty of St Germain terminated the mi¬ litary exploits of Frederic William, who palled the lath years of Iris adminiftration in peace. His great quali¬ ties had rendered him refpefted by all Europe, and had even been heard of in Tartary. Fie received an embafly from Murad Geray, cham ol the Tartars, courting his friendfhip. The barbarian ambafiador appeared in fuch tattered clothes as fcarce covered his nakednefs, fo that they were obliged to furnilh him with other clothes be¬ fore he could appear at court. His interpreter had a wooden nofe and no ears, in 1684, Frederic received into his dominions great numbers of Proteftants who fled out of France from the perfecutions of Louis XI V. afier he had revoked the edidt of Nantz. Twenty thoufand of them are faid to have fettled at this time in the elec¬ torate, where they introduced new arts and manufac¬ tures, that were of the utmoft benefit to the country. By this, however, he difobliged Louis XIV. for which reafon he concluded an alliance with the emperor \ and having furniflied him with 8000 troops again!! the Turks in Hungary, the emperor yielded to him the circle of Schvvibus in Silefia, as an equivalent for all his rights in that province. In 1688, the eledlor Frederic William died, and was fucceeded by his fon Frederic III. This prince was re¬ markably fond of fhow and ceremony, which, during the courfe of his government, involved him in much expence. The regal dignity feemedto be the greateft objeft of his. ambition. To obtain this, he joined with the emperor in the alliance againft France, in which he was engaged by William III. king of Britain. Fie alfo yielded up the circle of Schwibus, which had been given to his predeceffor ; and, in 1700, obtained from the emperor that dignity which he had fo earnellly defired. The terms on which it was obtained were, 1. That Frederic fhould never feparate from the empire thofe provinces of his dominions which depended on it. 2. That he fliould not, in the emperor’s prefence, demand any other marks of honour than thofe which he had hitherto enjoyed. 3. That his Imperial majefly, when he wrote to him, fhould only give him the title of Royal Dileciion. A. That neverthelefs the miniflers which he had at Vienna lliould be treated like thofe of other crowned heads. 3. That the eleftor fliould maintain 6000 men in Italy at his own expence, in cafe the emperor fliould be obliged to make w’ar on account of the fucceflion of the houfe of Bourbon to the crown of Spain. 6. That thofe troops ftiould continue there as long as the war lafted. Thus was the kingdom of Pruffia eftabliflied through the friendlhip of the emperor, with whom Frederic I. fo called as being the firft king of Pruflia, continued all his life in ftvidl alliance. Indeed he was a pacific 4 ] P R u prince ; and though contemptible in his p?rmn, and FrafTvv. incapable of atchieving great things, had this merit, —“4' that he always preferved his dominions in peace, and thus confulted the true intereft of his fubjecls much more than thofe monarchs who have dazzled the eyes ol the world by their military exploits, tie was indeed vain,, and fond of fliow, as we have already obferved; but had a good heart, and is laid never to have vio¬ lated his conjugal vow ; though it does not appear that he was greatly beloved by his royal conforts (of whom he had three) on that or any other account. T Frederic I. died in the beginning of 1713, and was prederic If- fucceeded by Frederic William. He was in almoftot Pruf'.la every thing the reverfe of his father. His difpoiiLions 3 mamii were altogether martial j fo that he applied himlelf en-Pnnce' tirely to the augmentation of his army, and perfebling them in their exercife, by which means they became the moft expert foldiers in Europe. His foible was an am¬ bition of having his army compofed Pru.ffians. behaved with the greated valour j but afterdated by having killed five times more of the enemy than they the Rut- themfelves lod, they were obliged to retire, though^ans* more formidable after their defeat than the Ruffians after their viflory. The king, in the mean time, ex¬ erted himfelf on every fide, and his enemies fled every- where before him ; but whild he purfued one body, another gained upon him in fome other part, and the winter came on fad, while his drength decayed, and that of his adverfaries feemed to increafe on every quarter. The Pruffian monarch, however, though diftrelTed, did not abandon himfelf to defpair, or lofe that won¬ derful prefence of mind which has fo eminently' didin^ gu.iffied him in all his military enterprifes. He indu- Itrioufly delayed a decifive action till the approach ofrhe’king winter j but at lad, after various movements, on No-gains a - vember 5.. 1757, he met at Rofhach with the unitedSreat vic~ army of his enemies commanded by the prince of Saxe!?’'!31, Plilburghaufen and the prince de Soubife. The allied L &f ' army amounted to 50,000 men complete; but mod of the troops of the Circles were new raifed, and many of them not well affedled to the caufe. The Pruf- fians did not exceed 25,000 men j but they were fu- perior to any troops in the world, and were infpired, by. the prefence of their king, with the mod enthufi- adic valour. The Audrians were defeated with the lofs of 3000 killed, eight generals, 250 officers of dif¬ ferent ranks, and 6oco private feldiers, taken prifon- ers, while night alone prevented the total dedrudlion o£ the army. By this battle the king was fet free on one fide j but this only gave him an opportunity of renewing his labours on another. The Auilrians had a great force, and now began to make a proportionable pro- grefs in Silefia. After a fiege of 16 days, they had re¬ duced the drong fortrefs of Schweidnitz, and obliged the Pruff m garrifon of 4000 men to furrender pri- ^ foners of war. Flearing then of the vi&ory at Rof-Schweid. bach, and that the king of Pruffia was in full marchn-tz takeI1 to relieve .Silefia, they refolved to attack the prince Jy.t!'e Al-" of Bevern in his drong camp under the walls of Bref- rianS* lau. They attacked the Prince’s army on November 22d; but their attack was fufiained with the greated resolution. The (laughter of the Audrians was pro-Battle with digious. A great part of the enemy had retired from the prince" the field of battle, and the red were preparing to retire,°f Bevern. when all at once the Pruffian generals took the fame re- folution. Their army had differed much in the engage¬ ment, and they became apprehenfive of a total defeat in cafe their intrenchments firould be forced in any part y for which reafon they quitted their drong pod, and retired behind the Oder. Two days after, the prince of Bevern, going to reconnoitre without effort, attended only by a groom, was taken prifoner by an advanced party of Croats, a fmall body of whom had croffed the Oder, Oa / P R U [ 477 J P R U lutz reco¬ ver their liberty. 35 Count Daun de¬ feated by the king of Prudia Pruflia. On tVis the town of Breflau immediately furrendered; ' where, as well as at Schweidnitz, the Auftrians found Breflau ta- Sreat quantities of provifions, ammunition, and money, ken by the All Silefia was on the point of falling into their hands, Auftrians. and the Pruflian affairs were going into the utmoft di- ftra&ion, when the king himfelf by a mod; rapid march paffed through Thuringia, Mifnia, and Lufatia, in fpite of the utmod efforts of the generals Haddick and Marfhal, who were placed there to oppofe him; and, entering Sileffa on the 2d of December, joined the prince of Bevern’s corps, who repaffed the Oder to meet him. The garrifon of Schweidnitz, who, as we have already obferved, had been made prifoners of war, alfo joined the king’s army unexpectedly ; and their prefence contributed not a little, notwithdanding the ^ fmallnefs of their number, to raife the fpirits of the Garrifon of whole army. They had fubmitted to the capitulation Schweid- xvith the greated reluctance j but as the Audrians were conducting them to prifon, they happened to re¬ ceive intelligence of the victory at Rofbach : on which they immediately rofe on the efcort that conducted them, and entirely difperfed it j and afterwards march¬ ing in fuch a direction as they thought might mod readily lead them to their king, they accidentally fell in with his army. His Prudian majedy now approached Breffau; on which the Audrians, confiding in their fuperiority, (for they exceeded 70,000, while the Pruflians fcarce amounted to 36,000), abandoned their drong camp, at Leuthen. the fame which the prince of Bevern had formerly oc¬ cupied, and advanced to give him battle. The king did not intend by any means to difappoint them, but advanced on his part with the greated celerity. The two armies met on December 5th, near the village of Leuthen. Count Daun made the bed difpofitions pof- fible. The ground occupied by his army was a plain, with fmali eminences in fome parts. Thefe eminences they furrounded with artillery •, and as the ground was alfo interfperfed with thickets, they fought to turn thefe likewife to their advantage. On their right and left were hills, on which they planted batteries of can¬ non. The ground in their front was interfe&ed by many caufeways ; and to make the whole more imprac¬ ticable, the Audrians had felled a great number of trees, and fcaitered them in the way. It was almod impoffible at the beginning of the engagement for the Prudian cavalry to aft, on account of thefe impedi¬ ments; but, by a judicious difpofition made by the king himfelf, all difficulties were overcome. His majedy had placed four battalions behind the cavalry of his right wing ; forefeeing that General Nadadi, who was pla¬ ced on the enemy’s left with a corps de referve, defign- .cd to attack him in flank. It happened as he had fore- feen : that general’s cavalry attacked the Pruflian right wing with great fury ; but he was received with fuch a fevere fire from the four battalions, that he was obli¬ ged to retire in diforder. The king’s flank then, well covered and fupported, was enabled to afl; with fuch order and vigour as repulfed the enemy. The Audrian artillery wras alfo filenced by that of the Pruflians ; however, the Audrians continued to make a gallant re- fiflance during the whole battle. After having been once thrown into diforder, they rallied all their forces about Leuthen, which was defended on every fide by entrenchments and redoubts. The Pruflians attacked them with the utmod impetuofity, and at lad became Pruifia. maders of the pod ; on which the enemy fled on allv-—-v"—"-' fides, and a total rout enfued. In this battle the Au¬ drians lofl 6000 killed on the fpot, 15,000 taken pri¬ foners, and upwards of 2QO pieces of cannon. ^ The confequences of this victory were very great. Breflau re~ Breflau wTas immediately inveded, and furrendered on taken. December 29th; the garrifon, amounting to 13,000 men, were made prifoners of war. The blockade of Schweidnitz was formed as clofely as the feafon of the year would permit; while detached Pruffian parties overran the whole country of Silefia, and reduced every place of lefs importance. The Ruffians, who had ra¬ vaged and dedroyed the country in fuch a manner that they could not fubfid in it, thought proper to retire out of the Pruflian dominions altogether. Thus Ge- gWfc^.s neral Lehwald was left at liberty to act againd the driven out Swedes ; and them he quickly drove out of Pruffian of Pomera- Pomerania, the wffiole of which country he not onlyn^a* recovered, but alfo fome part of Swedidi Pomerania. Phus the duchy of Mecklenburg being left quite ex- pofed, the king took ample vengeance on it by exa£L ing the mod fevere contributions of men and money. To complete this monarch’s good fortune alfo, the French, who had retired after the battle of Refbach, were noiv oppofed by the Hanoverians under Prince Ferdinand, who kept them fo well employed, that, du¬ ring the red of the war, the king of Pruffia had no more trouble from them. See Britain, N° 442. The beginning of the year 1758 was favourable togchweid- the arms of his Pruflian majedy. On the 3d of April nitz rttav he commenced his operations againd Schiveidnitz, and ken. puffied the fiege fo vigoroufly, that the place furren¬ dered in 13 clays. He then difpofed his forces in fuch a manner as might bed guard his dominions againd his numerous enemies. For this purpofe Count Dolma commanded a body of troops on the fide of Po¬ merania ; another confiderable body was poded be¬ tween Wohlau and Glogau, in order to cover Silefia from the Ruffians, in cafe they diould make their in¬ road that way. An army, in a little time after, was formed in Saxony, commanded by the king’s brother Prince Henry. This anny confided of 30 battalions and 45 fquadrons, and was defigned to make head againd the army of the empire; which, by great ef¬ forts made during the winter, and the jun&ion of a large body of Andrians, was again in a condition to a which alone was obliged to fuftain the) weight of the grand attack.. The AuftrianSj in the beginning of the engagement, had driven the Pruffians out of the vil¬ lage of Hochkirchen; and as the fate of the day de¬ pended on the poffeflion of that poll, the hotteft dif- pute was there. The Pruffians made three bloody and unfuccefsful attacks on the village ; on the fourth they carried it; but the Auftrians continually pouring in frefh troops, at laft drove them out with prodigious daughter on all tides. The king then ordered a retreat, which was conduced in good order, without being purfued; however, this bloody adlion coft him 7000 men, toge¬ ther with a great number of cannon. The Auftrians computed their own lofs at 5000. His Pruflian majefiy, having thus happily efcaped fuch imminent danger, took every poftible meafure to prevent the enemy from gaining any connderable ad¬ vantage from his defeat. Perceiving that the only ad¬ vantage they wiflied to derive from it was to cover the operations of their armies in Silefia, and that lie had now nothing to fear on the fide of Saxony, he largely reinforced his own army from that of Prince Henry, and haftened into Silefia, in order to raife the fiege of Neifs, which had been completely invefted on the 4th @£ Qclober. On the 24th of that month, therefore., he P R U Pr :ffia. his camp, and, making a great compafs, to avoid cbftrucficns from the enemy, arrived in the plains' of Gorlitz. A body of the Auftrians had in vain at¬ tempted to fecure this poft before him, and fome who arrived after him were defeated with the lofs of 800 men. From this place the king purfued his march with tne utmoff diligence; but was followed by General Laudohn, at the head of 24,000 men, who oonftantly hung on his rear, and haraffed his army. The king, however, knowing the importance of his expedition, continued his march without interruption, and luftered his antagoniff to obtain many little advantages without moieftation. Daun, however, not content with the op- pofition given by Laudohn, font a large body of horfe and foot by another route to reinforce the gener als Karfch and De Ville, who had formed the fiege of Neifs and the blockade of Cofel, while he himfelf paffed the Elbe, and advanced towards Drefden. All thefe precautions, however, were of little avail. The generals Karfch and De Ville, notwithfianding their reinforcement, no fooner heard of the king of Pruffia’s approach, than they railed the fiege of both places, and retired, leaving behind them a confiderable quantity cf military fiores. Xhe end of the Pruflian monarch’s march being thus accompli fired, he inftantly returned by the fame way he came, and haftened to the relief of Sax- ony, the capital of which (Drelden) was in great dan¬ ger from Marfhal Daun. The place was but indiffe¬ rently fortified, and garrifoned only by 12,000 men j fo that it could not promite to hold out long againft a numerous and well-appointed army. It was befides commanded by a large fuburb, of which, if once the enemy got poffeffion, all defence of the city muft then be vain. For this reafon M. Schmettau, the Pruflian <. j45. governor, determined to fet thefe fuburbs on fire, which Drefden ° was actually done November 10th, with an incredible burnt, lofs to the inhabitants, as in the fuburbs were carried on mofi of thofe valuable manufadfures which render the ci¬ ty of Drefden remarkable. This difappointed the de- figns of M. Daun ; but, though the action was agree¬ able to the laws of war, and had been executed with ail the caution and humanity of which fuch an aefion was capable,yet the Auftrians exclaimed againft: it as a piece of the moft unprovoked and wanton cruelty recorded in hiftory. After the king of Pruflia had approached Drefden, allS4winy 0p- the Auftnan armies retired into Bohemia, where they pielfid by took up their winter-quarters, as the king of Pmflia,hc kinS did in Saxony. This unhappy country he laid he would Fiufiii: now confider as his own by right of conqueffo But in- ftead of treating the conquered people as his lawful fubje&s, he oppreffed them in all poflible ways, by le¬ vying the molt fevere and exorbitant contributions furrounding the exchange with foldiers, and confining the merchants in narrow lodgings on ftraw-beds, till they drew upon their corrcfpondents for fuch foms as he- wanted. In 1759, as early as the 23d of February, the Pruf¬ fians commenced their military operations. General Woberfow marched with a body of troops into Poland, where he deftroyed feveral very large magazines be- longing to the Ruffians, and returned into Silefia without any lofs on the 18th of April. In the mean time, by fome movements of the king of Pruffia him¬ felf, the greateft part of the Auftrian troops had been- drawn P R U ’Trii-Tia. drawn towards the frontiers of Silefia. Prince Henry ■ ~ immediately took advantage of this opening, and on Bohemia April entered Eohemia with his army di- invaded by vided into two columns. One, commanded by him P R U Priiffia. Prince Henry. 48 A body of Auftrians felf, marched towards Peterfwade; the other, under General Hulfen, pafled by the towns of Pafberg and Commottau. That commanded by Prince Henry him- felf penetrated as far as Lobofchutz and Leitmeritz ; the enemy flying everywhere before them, and burn¬ ing or abandoning the vaft magazines which they had amaffed in thefe parts. The body under General Hul¬ fen had a more adtive employment. A flxong pafs at Pafberg was defended by a conflderable body of Auf- j ^ f trians. General Hulfen, having condudled his cavalry General ' another way in fuch a manner as to fall directly on Hulfen. their rear, attacked them in front with his infantry, drove them out of their intrenchments, and totally de¬ feated them wdth the lofs of a great number killed, and 2000 taken prifoners, wdrile that of the Pruflians did not exceed 70 in killed and wounded. After this ex¬ ploit they returned into Saxony, with hoftages for the contributions which they had largely exadled during the courfe of their expedition. Some other fucceffes obtained by Prince Plenry, clear¬ ed the country of Franconia of his enemies ; but now the approach of the Ruffians feemed once more to bring the affairs of the king of Pruffia to a crifis. Notwdth- ffanding the deftruftion of their magazines, they had continued to advance into Silefia, where they were op- pofed by Count Dohna j but as the troops he had with him rvete very far inferior to his enemies, he found it impoffible to do more, at leaft -with any appearance of fuccefs, than to obferve their motions and harafs them on their march. But this was fo difpleaflng to the king, that he difgraced his general, and appointed We- del to fucceed him, with orders to attack the Ruffians at all events. To enable him, however, in fome mea- fure to comply with this defperate order, he fent him fome reinforcements, which brought his army up to near 30,000. With thefe, on the 23d of July 1759, General Wedel attacked 70,000 Ruffians polled in the 49 . molt advantageous manner at Zulichau, and defended by a numerous artillery. Though the Pruffians march¬ ed on to certain dellruftion and dilgvace, they fuftained the attack for a long time with unparalleled refolution. At lalt, however, they gave wray, and were obliged to retire with the lofs of 4700 killed or taken prifoners, and 3000 wounded, The confequences of this viftory were, that the Ruf¬ fians penetrated into the king’s territories, and took poffeffion of the towns of Croffen and Frankfort on the Oder, which made it abfolutely neceffary for the king to come in perfon to oppofe them. Accordingly, on the 4th of Augult, he joined Wedel wdth a conflderable body of forces, having left the greatell part of his army in Saxony under Prince Henry. But as Marlhal Daun had fent a body of 12,000 horfe and 8000 foot under General Laudohn to the affiftance of the Ruffians, the king llill found himfelf unable to fight them j as, with this and fome other reinforcements, their army now amounted to upwards of 90,000. He therefore re¬ called General Finck, whom he had fent into Saxony with 9000 men ; but with all his reinforcements, it was found impoffible to augment his army to 50,000 complete. His lituation, however, was now fo critical 3 Pruffiansde- feated at Zulichau. 5° The Ruf¬ fians take Frankfort ■ on the Oder. 5r 480 ] that a battle was unavoidable^ and therefore, on the 12th of Augult, with this inferiority of number, the king attacked his enemies ftrongly intrenched, and de¬ fended by a prodigious number of cannon. In this ac¬ tion, his principal effort was againft the left wing of the Ruflian army. He began the attack, according to cu- ftom, with a heavy cannonade \ which having produced the defired effeft, he attacked that wing with feveral .. - battalions difpofed in columns. The Ruffian intrench- p/uj.^ ments were forced with great {laughter, and 72 piecesfeated by* of cannon w-ere taken. But Hill there was a defile totheRuf. be paffed, and feveral redoubts which covered the village,ians at of Cunnerfdorf to be maftered. Thefe were attacked j„rfner*" with the fame refolution, and taken one after another. The enemy made another {land at the village, and en¬ deavoured to preferve their ground there by pufhing forward feveral battalions of horfe and foot: but this alfo proved unfuccefsful; they were driven from pcfl to poll quite to the lafi: redoubts. For upwards of fix hours the Pruffians were fuccefsful, and everywhere broke the enemy with prodigious {laughter 5 drove them from almoft all the ground they had occupied be¬ fore the battle, took more than half their artillery, and fcarce any thing feemed Wanting to make the vidtPry complete. In theie circumifances, the king wrote the following billet to the queen : “ Madam, we have beat the Ruffians from their intrenchments. In two hours expedl to hear of a glorious viclory.” Of this vic¬ tory, however, he deprived himfelf, by an exceffive eagernefs for conqueft. The enemy, defeated almoft in every quarter, found their left wing, {battered as it was, to be more entire than any other part of their army. Count Soltikoff, the Ruffian general, therefore affembled the remains of his right wing, and, gathering as many as he could from his centre, reinforced the left, and made a Hand at a redoubt which had been erefted on an advantageous eminence in a place called the Jews burywg-ground. All the king’s generals are faid to have been of opinion, that he ought to allow the Ruf¬ fians the peaceable poffeffion of this poft. Their army had already fuffered fo much, that it would have been impoffible for them to have attempted any enterprife of confequence after the battle ; but their artillery was ftill numerous, the poft very ftrong, and the Pruffian troops greatly fatigued. Thefe reafons for a few mo¬ ments had fome weight with the king 5 but the natu¬ ral impetuofity of his temper getting the better of his reafon, he led on his wearied troops again and again ; till at laft, when their ftrength was in a man¬ ner totally exhaufted, they were attacked and utterly routed by the Auftrian and Ruflian cavalry, the former of which had hitherto remained quite inaflive, and were therefore quite freffi, and irrefiftible by the enfeebled Pruffians. The night, and the prudent ufe of fome eminences, prevented the total deftrudion of the ar¬ my j however, their lofs amounted to 20,000 men kil¬ led and wounded. The king, when he found the vic¬ tory totally loft, fent another billet to the queen, ex- preffed in the following manner : “ Remove from Berlin with the royal family 5 let the archives be carried to Potfdam ; the town may make conditions with the enemy.” Immediately after this defeat, the king fet himfelf about repairing his Ioffes with the utmoft diligence. In a few days every thing was again put in order in his camp. p R u [ 481 ] P R u 52 General to the rYu- ftrtans. Pruffia. camp. He replaced his artillery from Berlin 5 recalled -“"V—General Klieft with 5000 men from Pomerania 5 de¬ tached 6ooo from his own army to the defence of Saxo¬ ny ; and with the remainder put himfelf between the Ruffians and Great Glogau, covering that city which had been the, chief object of their defigns; and in ffiort, notwithftanding their victory, obliged them to return to Poland without accompliffiing any thing befides the car¬ nage at Cunnerfdorff. The mifortunes of the Pruffian monarch, however, were not at an end. Prince Henry, indeed, by a moft extraordinary and well-conduced march, entered Sax¬ ony, which was now totally overrun by the armies of the enemy. At the fame time, tlrong detachments ha¬ ving been fent into that country under generals Finck and Wunfch, the whole was in a ffiort time recovered except Drefden. Towards this place Marffial Daun retired, and in all probability would foon have been obliged to leave Saxony entirely. But the king’s im¬ patience could not be fatisfied without cutting off his retreat, and forcing him to a battle ; for which purpofe he fent General Finck with upwards of 12,000 men according to the Pruffian account, but 20,000 accord¬ ing to the Aurtrians, to feize fome paffes through which M. Daun could only take his route towards Bohemia. This commiffion was executed with great exa&nefs; Finck with but the Pruffian general, having probably advanced too Prurthns ^ar in!:0 denies, and neglefled to preferve a com- furrenders munication with the main army, gave his enemy an op¬ portunity of furrounding him, and at laft forcing him and his whole army to furrender prifoners of war. This difailer was foon after followed by another. General Durceke was poled at the right of the Elbe, oppofite to Meffen •, but on the approach of a large body of Au- llrians, they prepared to retreat over the river into a place where they hoped to be more fecure. But having been obliged by an hard froft to withdraw their bridge of boats, a thaw' fupervened, when they attempted to lay a bridge of pontoons, fo that they were again obli¬ ged to have recourfe to their boats. In this fituation, their rear-guard was attacked with great fury by the Auftrians, and all the foldiers who compofed it killed or taken. The lofs of the Pruffians on this occafion was computed at 3000 men. The year 1760 ffiovved the Pruffian monarch in a more dangerous fituation than he had ever yet experienced. Indeed his affairs now feemed to be altogether del'perate. His Ioffes w'ere not to be meafured by the number of the killed or prifoners, but by armies deftroyed or ta¬ ken. Forty generals had died or been killed in his fer- vice fince the beginning of Oftober 1796, exclufive of tbiofe who were wounded or taken prifoners. This of itfelf would have been an irreparable lofs, had not the very wars which deftrbyed thefe furniffied others equal¬ ly capable of filling their places. But another deficien¬ cy, which could not be remedied, ftill remained.—The king had, by his indefatigable induftry and exertions, fupplied all the deficiencies of men in his armies, but they were not the fame men as before. The hardy ve¬ terans, with whom he had originally taken the field, were now no more, and their places were fupplied by others who had neither the fame experience nor difci- pline ; fo that now he was obliged to fupply this defi¬ ciency by his own genius and heroifm. But whatever abilities the Pruffian monarch might VOL. XVII. Part II. S3 Defperate Pruffia. poffefs, and though he undoubtedly exerted them to the Pruffia. utmoft, it leemed only to be contending agaiult fate, v——• and his enemies gained ftill greater and greater advan- 54 tages. General Laudohn, with whom none but the^111^311* king himlelf feems to have been able to cope, by a fe-'^^ at ries of artful movements, drew into a diladvamageous fituation M. bouquet, one of the Pruffian generals, with a ftrong body of forces. Perceiving it impoffible for them to efcape, Laudohn then made a violent at¬ tack on their intrenchments in the dead of the night of June 23d. The Pruffians made a gallant defence, but at lait were all killed or taken prifoners except about 300. Of the Pruffians were killed 4000, and 7000 taken prifoners ; 58 pieces of cannon, and a great number of colours, were alfo loft. The vidory, how¬ ever, was dear bought j for the Auftrians loft above 12,000 men in killed and wounded j whom, however, they could better fpare than the Pruffians, on account of their numbers.—This adion was called the battle of Landjhut. f ^ Baron Laudohn failed not to improve this vidory Glatz ta- to the utmoft. Fie inftantly turned back from Land- ^en b>' tllC ffiut, and fell upon the city of Glatz 5 which he took Au^"ans. in a very ffiort time, with the garrifon wffio defended it, confifting of 2000 men. In this place were found 101 pieces of brafs cannon, with immenfe quantities of provifions and military ftores. From thence he marched againft Brefiau, and immediately inverted it. But, in the mean time, the king of Pruffia, whofe mo¬ tions had been all this time counteraded by M. Daun in Saxony, marched with his ufual rapidity towards Silefia. By this means he drew M. Daun out of Sax¬ ony ; and indeed the Auttrian general ufed fuch ex¬ pedition, that he gained two full days on the king. This was no fooner known to his Pruffian majefty, than he returned with the fame expedition that he ^ had advanced, and fat down before Drefden. OfRreffienbe- this M. Daun foon received intelligence, and returned but alfo. In the mean time, however, the buildings the city were terribly (battered by the king’s cannon theming of and bombs which continually played 011 it. His en- Pruffia. deavours, however, proved ineffedlual to reduce it before the arrival of M. Daun. The fiege had been begun on the 13 th of July, and on the 19th M. Daun appeared within a league of Drefden. The Pruffians then redoubled their efforts. They had that day received reinforcements of heavy cannon and mor¬ tars, with which they battered the place inceffantly. The cathedral church, New Square, feveral principal ftreets, and fome palaces, and the noble manufactory of porcelain, were entirely deftroyed. The fiege was continued till the 22d : but, on the night of the 21ft, M. Daun had thrown 16 battalions into the city; which rendered it impoffible for the king to continue longer before it with any profpeCt of fuccefs. He therefore raifed the fiege, and retired without moleita- tion, though there were three confiderable armies of the enemy in the neighbourhood. Breflau was fiercely bombarded by Laudohn, but the approach of Prince Henry obliged him to defift from his enterprife on the 5th of Auguft. But, in the mean time, the fortune of the king feem¬ ed likely to be terminated by one fatal ftroke. Find¬ ing it impoffible for him to carry on a defenfive war, he marched towards Silefia with fuch aftonilhing ra- 3 ? Pidity> him. P R U [48 ■pruflia. pidity, that before the middle of Auguft he had ad v“—'_v ' vanced 200 miles, leaving Marfhal Daun with his army Thr \u- ^ar behind him. This expedition he undertook in ft nan ge. order to engage General Laudohn before he could j.erals join have time to effedl a junction with Daun and Lacy, their forces another Auftrian general j which triple union feemed ^ to threaten him with unavoidable deftruftion at once. This, however, he found it impoflible to prevent: and the three armies, when joined, formed a moft tre¬ mendous line of encampments, extending no lefs than 30 Englifh miles; at the fame time that every one of their polls was llrong, and the communication be¬ tween them eafy. The king was llrongly encamped at Lignitz ; and for feveral days employed all his mi¬ litary Ikill in attempting to induce one of the bodies to detach itfelf from the reft, or to attack them at fome difadvantage ; but without effedl. At laft, the Auftrian generals, having maturely weighed all circum- ftances, refolved to attack the king’s camp itfelf, ftrong as it was ; and Marfhal Daun, remembering the advantage he had gained at Hochkirchen by an at¬ tack in the night-time, refolved to follow the fame plan now7. The plan therefore was laid in the follow¬ ing manner. The whole army, as foon as it ftiould begin to grow7 dark, was to march from their feveral polls to fuch fituations as w7ere marked out for each corps: they w7ere to ftrike their tents, but yet to keep up the fires in their camps, and to have the drums beat the tattoo as ufual, by which means they had a probability of furprifing the enemy; or if not, they judged it abfolutely impoflible for him to efcape them, though he fliould be ever fo much on his guard. In wdiat manner the king of Pruflia became acquainted with this plan, is not known. His friends attributed it to his own penetration and knowledge of the ftra- tagems of w7ar; the Auftrians, to intelligence given him by deferters. But, in whatever way he became ac¬ quainted with this defign, it is certain that he took the moft eftedtual methods of preventing it. As the Auftrian plan was to furround his camp, and this could not be done without the divifion of their army which he had fo long defired, he refolved to intercept one of the parties ; and if that ftiould be difabled from a&ing, he could then more eafily deal with the other two. Therefore, in the very evening calculated for the decifive attack on his camp, he quitted it with the utmoft privacy, and took an advantageous poll on the road through which General Laudohn was to pafs. The nature of this poll was fuch, that at the fame time that it Hopped the progrefs of Laudohn in front, Daun w7ould lie under great difficulties if he Ihould attempt his rear ; at the fame time that, for his further fecurity, the kirig ftrengthened the rear wnth feveral batteries. As foon as his army w7as drawm up, he divided it; leaving his right on the ground where it had been formed, to obferve Marffial Daun, and to maintain that poll ; whilft with his left he turned in or¬ der to fall on the corps under General Laudohn. In the mean time, that commander, ignorant of the fate which was awaiting him, advanced with the utmoft ex¬ pedition tow ards the place which had been affigned him, in order to fhare in the glory of deftroying the Pruf- fian monarch; when, at three in the morning, on the 15th of Auguft, a thick fog which covered the ground, fuddenly clearing up, difeovered, like the opening of 2 ] P R U a great feene, the dreadful front of the Pruffian army Pruffia. regularly embattled, and advantageoufly polled. Lau- v dohn, though furprifed, made the bell difpolitions that He ^fcats circumftances would admit of, and an obftinate engage- General merit enfued ; in which, however, he w7as at laft obliged Laudofan, to yield to the fuperior Ikill of his adverfary, wdth the an(l intimi- lofs of 10,000 killed, wmunded, and prifoners, 82 P^eces of cannon, and 23 pair of colours. The vi&ory, though complete, gave but a partial re¬ lief to the king of Pruffia. The moft elfential fervice it did wras the preventing of the Ruffians from joining thofe enemies which he already had. Count Czerni- chew had been advancing with 24,000 men, and had even paffed the Oder; but was fo intimidated by this news, that he inftantly repaffed that river on the fame bridges wffiich he had lately built, even though M. Daun fent him a ftrong body of troops in order to encourage him to advance. Soon after this battle, the king join¬ ed his brother Prince Henry at New Marche; and marched againft Daun, who had begun to form the blockade of Schweidnitz, fell upon a corps under Gene¬ ral Beck, made twro battalions of Croats prifoners, and difperfed the reft, wffiich obliged the enemy to abandon the enterprife they had juft undertaken. About the fame time, General Hulfen gained a confiderable advan¬ tage over the Imperial army in Saxony, with very trifling lofs on his part, by wffiich he effeftually prevented them from cutting off his communication with the city of Tor- ga». By thefe fucceffes the affairs of his Pruffian majefty feemed to revive : but there w7as no end of his enemies. The late manoeuvres had draw n him fo far into Silefia, that his communication w7ith Brandenburg was almoft wholly cut off. The Ruffian army, which after it had repaffed the Oder began to move out of Silefia, fent forward a powerful detachment under Count Czerni- chew towards the marche of Brandenburg. A body of 15,000 Auftrians, under the generals Lacy and Brentano, and the whole united body of Auftrians and Imperialifts wffiich a£led in Saxony, began their march in concert writh the Ruffians, and propofed to unite at the gates of Berlin. Thefe armies amounted to 40,000 men. To oppofe this formidable power, Ge¬ neral Hulfen called to his affiftance General Werner, who had been fent with a body of troops into Pome¬ rania ; but, after being joined by him, their united for¬ ces w7ere found not to exceed 15,000 or 16,000 men. To attempt a defence of the capital with this force would have been little fliort of madnefs : and therefore thefe commanders were obliged to leave Berlin to its fate ; Berliifta- which indeed, confidering the barbarity of the Ruffians ken by the and the animofity of the Auftrians, feemed to be a Auftrians dreadful one. However, by the powerful mediationan<*Ru*" of feveral foreign minifters, the town obtained terms ^anS" wffiich w7ere not altogether intolerable; but the maga¬ zines, arfenals, and founderies wrere deftroyed, and an immenfe quantity of military ftores feized, with a num¬ ber of cannon and other arms. The city w as firft obli¬ ged to pay 800,000 guilders, after wffiich a contribution of 1,900,000 crowns was laid on : yet, notwithftanding this, many violences w7ere committed, and the king’s palace w7as plundered and the furniture abufed in a fcan- dalous manner. The combined armies ftaid in Berlin only four days ; dreading the fevere vengeance of the king of Pruffia, who P R U [ 483 ] P R U . Fru{ria‘ . tHey heard was advancing towards that place with along the Andrian front. The Pruflians were thrice led Pruffia. &reat expedition. But fo great were the embarrafs- on to the attack ; but were every time repulfed and bro~ v ' Extreme ments which now attended that monarch, that it feem- ken with terrible daughter. The king at length com- embarrafT- ed almoft beyond^ human power to retrieve his af- manded a freih body of cavalry to advance which at tnent°f fairs. The Impenalifts, on their return from Berlin, firft compelled the Aultrians to retire; but*new rein- e ing- having no army to oppofe them, made themfelves ma- forcements continually coming in, this cavalry was in fters of Leipfic, Torgau, Meiffen, and Wirtemberg ; its turn obliged to fall back, and the Pruflians main- in which laft. city they found the grand magazine of tained themfelves with extreme difficulty, until General the Pruflians immenfely ftored with provifions, ammu- Ziethen, with the right wing, attacked5 the enemy in nition, &c. M. Stainville alfo, with a detachment from the rear, repulfed them, and poffefled himfelf of fome Broglio the French general’s army, laid the city and eminences which commanded the whole Auftrian ar- duchy of Halberftadt under contribution. In Eaftern my. Encouraged by this fuccefs, the Pruffian infantrv Pomerania, the Ruffians had befieged Colberg by fea once more advanced, maftered feveral of the enemy’s and land. In the Weftern Pomerania, the Swedes intrenchments, and made way for a new attack of their advanced with great celerity, hoping to fliare in the cavalry, which broke in with irreflftible fury on the plunder of Berlin. In Silefia, the king no fooner Auftrians, and threw feveral bodies of them into irrepa- began his march to the northward, than Laudohn ad- rable diforder. It was now about 9 o’clock, and of con- vanced, and laid fiege to the important fortrefs of Co- fequence both armies were involved in thick darknefs; fel; and, to complete this diurefs and embarraffment, yet the fire continued without intermiflion, and the bat- the king himfelf was attended at every ftep by Count talions with a blind rage difcharged at one another Daun with a fuperior army well prepared to take every without diftinguifliing friend from foe. M. Daun re¬ advantage. _ ^ ceived a dangerous wound in the thigh, and wTas car- . . In this defperate fituation the king, being joined by ried from the field, which probably haftened the defeat his generals Hulfen and Prince Eugene of Wirtemberg of his troops. The command then devolved on Count with the corps under their command, advanced up the p’Donnel; who, finding the greateft part of his troops Elbe, while M. Daun fell back to cover Leipfic and in diforder, the night advanced, and the enemy poffeffed 1 organ, but the latter, finding that the Pruflians direc- of fome eminences which commanded his camp, and ted their march towards the Elbe, encamped within from which it was in vain to think of driving them, or- reach of Torgau; one part of his army extending to dered a retreat, which was condu&ed with wonderful the Elbe, by which he was covered on that fide, whilft order and exa&nefs; none were loft in pafling the brid- on the other he was covered by hills and woods, fo that ges, and by far the greater part of their artillery was pre- it was impoflible to choofe a more advantageous fitua- ferved. The lofs of the Pruflians was eftimated at tion. The Prufllan army did not amount to 50,000 10,000 killed and wounded, and 3000 taken prifoners. men, whilft that of the Auftrians exceeded 86,000 : That of the Auftrians in killed and wounded is not yet fuch were the unfortunate circumftances of the king, known; but 8000 were taken prifoners, with 216 offi- that he was obliged to fight under all thefe difadvanta- cers, among whom were four generals, ges; and therefore he caufed his army to be informed, The confequence of the vi£tory of Torgau was, that A[j that he was now to lead them to a moft defperate at- the king recovered all Saxony except Drefden; and in0ny except tempt, that his affairs required it, and that he was de- the mean time General Werner having marched intoDrei'den termined to conquer or die. His foldiers unanimoufly Pomerania, the Ruffians ^raifed the fiege of Colberg,recovere^* 6l declared that they would die with him. and retired into Poland,' without having effe&ed any He defeats The 3d of November 1760 was the day on which thing further than wafting the open country. Werner Count this important affair Was decided. The king divided then flew to the affiftance of Weftern Pomerania, where .Oaun at }fts forces into three columns. General Hulfen was to he defeated a body of Swedes, and at laft drove them °r^ai1' take poll: with one in a wood that lay on the left of totally out of the country. General Laudohn too ab- the Auftrian army, and had orders not to move until he ruptly raifed the blockade of Cofel; and afterwards found the reft of the Pruffians engaged. General Zie- abandoning Landflmt, he retired into the Auftrian Si- then was to charge on the right; and the great attack lefia, leaving the Pruffian part entirely in quiet. M. in front was to be conduced by the king in perfon. Daun placed one part of his army in Drefden, and the His forces were difpofed in fuch a manner, that either other in fome ftrong polls which lie to the fouth and his right or left muff: take the enemy in rear and clofe weft of it, by which he commanded the Elbe, and pre- them in, fo as to difable them from undertaking any ferved his communication with Bohemia. The army of thing againft the part where he intended to effetft his the empire retired into Franconia, and placed its head- principal attack. On the other hand, M. Daun per- quarters at Bamberg. 'ceiving the king to be ferious in his defign of fighting, Though thefe fucceffes had, to appearance, retrieved to prevent confufion, fent all his baggage over the the king’s affairs in fome meafure, yet his ftrength Elbe, acrofs which he threw three bridges in cafe a re- feemed now to be wholly exhaufted ; and in the cam- treat fhould be neceffary. At the fame time he caufed p?-ign of 1761, he made no fuch vigorous efforts as he Torgau to be evacuated ; and then, extending his firft had formerly done. The Ruffians, dividing themfelves line to a village called 'Zinne on the left, he ftretched it into two bodies, invaded Silefia and Pomerania. In to another called CroJkvitZ on the right; fupporting the the former country they laid liege to Breflau, and in the right of his fecond line upon the Elbe. In this difpofi- latter to Colberg. Tottleben alfo, who had command- tion he was found, when, about two o’clock in the after- ed the Ruffian armies, was now removed on a fufpicion noon, the king began his attack. He was received by that he had correfponded with the king of Pruffia, and the fire of 200 pieces of cannon, which were difpofed General Romanzow put in his place; by which it was 3 E 2 exne- his time, he w^as all at once threatened with a fatal re- volution in verfe ot fortune by a new revolution in Ruffia. The^uhia' emperor was depofed, and his depofition was foon after followed by his death. The emprefs, who fucceeded him, fufpefted that her hufband had been milled by the counfels of his Pruffian majetty, againft whom, there¬ fore, (lie entertained a mortal enmity. She could not, however, in the very beginning of her reign, undertake again a war of fo much importance as that which had been juft concluded. She therefore declared her inten¬ tion of obferving the peace concluded by the late em¬ peror ; but, at the fame time, of recalling her armies from Silefia, Pruffia, and Pomerania ; which indeed the unfettled flate of the kingdom now made in fome degree neceffary. At the fame time a difeovery was made with regard to the king of Pruffia himfelf, which turn¬ ed the fcale greatly in his favour. The Ruffian fenate, flaming with relentment againft this monarch, and againft their late unfortunate fovereign ; and the em¬ prefs, full of fulpicion that the conduit of the latter might have been influenced by the councils of the for¬ mer, fearched eagerly amongft the papers of the late emperor for an elucidation or proofs of this point. They found indeed many letters from the Pruffian mo¬ narch, but in a ftrain abfolutely different from what they had expeited. The king had, as far as prudence would permit, kept a referve and diftance with regard to the too rath advances of this unhappy ally ; and, in particular, counfelled him to undertake nothing againft the emprefs his confort. The hearing of theie letters read is faid to have had fuch an effei! upon the emprefs, that fire burft into tears, and expreffed her gratitude towards the Pruffian monarch in the warmeft terms. Still, howrever, the Ruffian army was ordered to feparate from the Pruffians; but all the important places which the former had taken during the whole war were faith¬ fully reftored. The king, finding that the Ruffians rvere no more to take an aftive part in his favour, refolved to profit by their appearance in his camp ; and therefore, the very day after the order for their retura had arrived, he at¬ tacked the Auftrian army, and drove their right wing from fome eminences and villages where they were ad- vantageoufly polled ; by which means he entirely cut off their communication with Sclnveidnitz, fo that no¬ thing could be attempted for its relief. Prince Henry kept them in continual alarms for Bohemia; and a great P R U [ 485 ] r r u 6S Gpreral Laud hn utterly de¬ feated. Pruflia. great part of their attention, and no fmall part of their ■““v- forces, were engaged on that fide. Marfhal Daun, now- finding himfelf rendered almoft incapable of underta¬ king any thing, detached Geneaal Laudohn, with a force very much fuperior, to attack the prince of Be- vern, and drive him from the advantageous pott he oc¬ cupied. But the prince defended himlelf with lych re- folution, that all the efforts of Laudohn could not fuc- ceed before the king had time to come to his affdtance. The Auftrians, being then put between two fires, were routed and purfued with terrible daughter; after which, the king met with no more difturbance in his prepara¬ tions for the fiege, and the trenches were opened on the 18th of July. Marfhal Daun made no attempts to relieve the place; but the garrifon being very llrong, it held out for near two months from the opening of the trenches. It is faid that the attack was conducted, and the defence made, by two engineers who had writ¬ ten on the fubjeft of the attack and defence of forti¬ fied places ; and they were now praftically engaged to prove the fuperiority of their fydems. At lalt, how¬ ever, the garrifon, to the number of 8000 men, furren- dered prifoners of war ; and the whole body, except nine, were foon after drowned at the mouth of the O- der, on their paffage to their intended confinement in Konigfberg. The king of Pruftia, now become mafter of Schweid- nitz, turned bis attention towards Saxony, where he confiderably reinforced his brother’s army, and made preparations for laying fiege to Drefden. In this coun¬ try the Auftrians had lately met with fome fuccefs, and driven Prince Henry as far back as Freyberg ; but on the 29th of Oftober, they w7ere attacked by the Pruf- produees a fian army thus reinforced, and totally routed. Great peace. numbers were ftain, and near 6000 taken prifoners. This vidlory proved decifive : and the emprefs-queen, finding herfelf deferted by all her allies, was glad to conclude a treaty ; the fubftance of which was, that a mutual reftitution and oblivion fhould take place, and both parties fit down at the end of the war in the fame fituation in which they began it. This treaty is called the peace of Hubertjburg. The war was no fooner concluded than the king of Pruftia turned his attention to domeftic policy, and the recovery of his dominions from thofe innumerable ca¬ lamities which had befallen them during the war. He immediately diftributed lands to his difbanded foldiers, and gave them the horfes of his artillery to •..flift them in their cultivation. By his wife and prudent manage¬ ment, the horrors of war were foon forgotten ; and the country w7as quickly in as flouriftiing a ftate as ever. Notwithftanding this pacific difpofition, however, the king never ftackencd his endeavours for the defence of his country, by keeping a refpeflable army on foot; which might be able to aft on the leaft emergency. A new war In the year 1778, a new difference with the houfe of Auftria took place, concerning the duchy of Bavaria, ducts nothough the moft enormous warlike preparations memorable were made on both fides, and immenfe armies brought event. into the field, nothing of confequence w’as effefted. What little advantage there was, feems to have been on the Pruflian fide, fmee they made themfelves mafters of feveral towns, and kept the war in the enemy’s coun¬ try. However, the emperor acted with fo much caution, and fhowed fo much fkill in a defenfivc war, that all the 69 , The total defeat of the Auftri¬ ans at Freyberg commen¬ ces, but manoeuvres of his Pruftian majefty could gain no mate- Praflla. rial advantage ; as, on the other hand, his adverfary was too w ife to venture an engagement. A peace therefore was very foon concluded, and fince that time the hilxory of Pruffia, during the remainder of the great Frederic’s reign, affords no remarkable event which we have not mentioned in the life of that hero, and in the article 7r Poland. He left his crowm to his nephew7, wThofe The great charafter w7as not then much developed ; and it w7as ea- Frederic fily feen that a new kingdom, which had rifen hiddenly to fuch unexampled powrer and greatnefs as to excite the ^ew. jealoufy or apprehenfion of ail its neighbours, would require great abilities to preferve it from difmember- ment. The late king had indeed bequeathed the moft effec- State of the tual fecurities to his fuccelfor for the pi'efervation of nat‘on.> antl his dominions, that human wifdom could provide or de-^^1”11^ vile ; by leaving him a full treafury, the fineit army in the world, and a people enthuilallically attached to his memory and government. The new monarch, with thefe advantages, w7as not wanting to himfelf. The late king’s predilefticn for the French language and French literature were not grateful to his fubjefts. The prefent fovereign began his raign with declaring in council, “ Germans w7e are, and Germans I mean we lhall continue;” giving direftions, at the fame time, that their native language Ihould refume its natural rank and ftation, from which for near half a century it had been degraded by the French. This w7as a very popular meafure, and it w7as followed by another ftill more fo. Obferving that he had marked with great concern the progrefs of impiety and profanenefs on the one hand, and of enthufiafm on the other, he declared, that he would not have his fuhjefts corrupted either by fanatics or atheifts, and ftriftly prohibited all publications tend¬ ing to excite a contempt or indifference for religion. Such, on his immediate acceflion to the throne, was the pacific conduft of the monarch, which endeared him to his fubjefts, and commanded the approbation - ^ of all good men. An opportunity foon occurred, in He aftifts which he w7as thought to have difplayed fuch talents’he ^h- in negotiation and in military arrangements, as proclaim- ed him in every refpeft a w7orthy fucceflbr of his uncle. ft^s of e The States of Holland, who had long been jealous of Holland, the power of the ftadtholder, and inclined to a republi¬ can government without any permanent chief, had gain¬ ed fuch an afcendency in the ftates general, that in 1786 and 1787 they in effeft divefted the Prince of Orange of all his prerogatives, (fee UNITED Provinces. They proceeded even to the feizure and imprifonment of the prinesfs, filler to the king of Pruffia ; and depending upon fupport from France, treated with infolence every power connefted with them in Europe. The ccurt of Berlin did not witnefs thefe proceedings without indig¬ nation ; and the king formed his plan for reftoring the power of the ftadtholder with fuch fecrecy and prudence, that perhaps nothing could furpafs it but the bravery and military Ikill of the duke of Brunfwick, by whom it w7as carried into execution. In the fhort fpace of one month, that accomplilhed general led 18,000 Pruflians to Amfterdam, and reftored the juft prerogatives of the prince of Orange. The affairs of Pruffia during the early period of the French revolution, and the aftive but unfuceefsful part which that monarch took againft it, are interwoven with the P R tr r 4^ 1 P R u Prv.iua. tKe liiftorical details of that period under the articles -”-~y France and Britain, to which we refer our readers. For a number of years he adted the prudent part of Banding clear of hoftilities as much as poflible $ and when he did at laft interfere^ we find little in his con¬ duit: which is intitled to the praife either of eonfiftency or honour. Indeed it may perhaps be admitted, that on many occafions he ailed rather from nOceflity than choice 5 and finding that a conteft with France wras both abfurd and ruinous, he ehofe to facrifice a lefs evil to a greater good. Whether by confent or compulfion is not certainly known, the king of Pruffia ceded to France the duchies of Cleves and Berg, March i8o6j which were to be governed by Prince Murat, the bro¬ ther-in-law of Bonaparte, under the title of Joachim, duke of Cleves and Berg. The king of Pruflya likewife took pofleflion of the* Hanoverian Bates 30th Oilober 1806, at the time when Great Britain had no reafon to apprehend any fucll myflerious conduit from that quarter. He entered into a fecret treaty with France for the purpofe of Bmtting the northern ports; a meafure which gave fuch ofi'ence to this country, that the Britifii miniBer thought proper to take his leave of Berlin. At one period he came to a final determination to make no feparate treaty wnth the French government, and propofed a treaty of peace and alliance between his court and that of Britain. To give this as much effeit as poflible, the Pruflian princes of the blood began to raife volunteer regiments in Po¬ land and Silefia, the loyalty of the peafantry in thefe countries far exceeding the mofi fanguine expeilations. So low, however, were the king of Pruflia’s finances at the time of Lord Hutchinfon’s arrival at Memel, March 1807, that his lordfliip found it neceffary to ad¬ vance 8o,oqo1. for the fupport of his family and domef- tic houfehold. This being intimated to the Britifii mi- niflers, his majefiy recommended it to parliament to en¬ able him to implement the agreement. Yet not long after this period he adlually entered into a treaty of peace with the emperor of France, by virtue of which his territories were fo dreadfully mutilated, as to leave him little more of a fovereign than the name. He was required to renounce the whole of his dominions fituated between the Rhine and the Elbe •, the circle of Rothus, in Lower Lufatia •, all the provinces which formerly conflituted part of the kingdom of Poland 5 the city of .Dantzic ; and he was laid under the ..eceflity of (hut¬ ting all the ports and harbours in his whole dominions againfi the trade and navigation of Great Britain. Not above 18 months prior to this treaty, the king of Pruf¬ fia might have been faid to hold the fate of Europe in his hands ; but by means of it he was reduced to the very lowefi rank among the powers of Europe. Had he taken a decided part againfi France before the battle of Auflerlitz, he might have been able to fecure the inde¬ pendence of Europe ; but, having fuffered this aufpici- ous moment to pafs unimproved, the confequences were exactly fuch as might have been predi&ed, without any pretenfions to uncommon fagacity. The king of Pruflia being thus degraded by means of his own imprudence and want of found policy, endea¬ voured to eafe the burdens of his remaining fubjedls by reducing his civil and military efiablifhments. The army was reduced to 24,000 men, and General Kno- -bfcsdorf was fent to Paris to procure a diminution of the 1 contributions exa&ed from him, or to crave that pay- Prufila. ments might be accepted of by inflalments 5 and, in the ——y-™* mean time, the troops belonging to France were not to be withdrawn from the impoverilhed kingdom of Pruf- fia. Every decree iffued in Holland againfi the com¬ merce of Great Britain, this humbled monarch was obli¬ ged to adopt, and to order the publication of them in every part of his mutilated dominions. This Bate of in- fignificance may be expedted to continue as it is, till fuch a revolution takes place in the fentiments of the mofi powerful European monarchs as fliall induce them to throw off the tyrannical yoke of Bonaparte, and op- pofe to him a force which all his military ffrength fliall not be able to refifi j and annihilate his power and in¬ fluence in Europe. The united farces of Ruflia, Pruf» fia, and Aufiria, feconded by the operations of the tri¬ umphant navy of Great Britain, might find it poflible to accomplifh this 5 and furely it is not only the caufe of Europe, blit of humanity at large, and calls for the in¬ terference of every empire and kingdom capable of af¬ fording any effedtive aid. The total lofs fuflained by the king of Pruflia in con- fequence of the peace of Tilfit, has been efiimated at 10,coo fquare miles in extent, containing a population of more than 4,000,000 a lofs which muff be very feri- oufly felt, but which at one period, we believe, he had it in his pOwTer to have prevented j and it is very uncer¬ tain if ever the time Brail arrive vrhen it will be In Iris power to redeem it. The air of Pruflia is wholefome, artd the foil fruitful Air, ioi!, in grain 5 affording, befides, plenty of piteoal and other and popu« fuel. The rivers and lakes are well ftored with fiflr j and latIoni °f amber is found on its coaft towards the Baltic. The prin- ^>ru^a, cipal rivers are the Vifiula, Bregel, Memel, the Paffarge, and the Elbe; all of which frequently do damage by their inundations. The inhabitants of this country were, by Dr Bufching, computed at 635,998 perfons capable of bearing arms j and by another German author, at 450,000. Since the year 1719 it is computed that about 34,000 colonifls have removed hither from France, Switzerland, and Ger¬ many 5 of which number one half were Saltzburgers Thele emigrants have built 400 fmall villages, 11 towns, 50 new churches, and founded 1000 village-fchools. The man¬ ners of the people differ but little from thofe of the Ger¬ mans. The eflabliihed religions are thofe of Luther and Calvin, but chiefly the former 5 though almoft all other lefts are tslerated. The late king of Pruflia, by the afliftance of an ex-Commerce cellent police, brought the commerce and manufaftures antl manu- of this country to a very flourilhing Bate, which during faftures> his life were daily improving. The manufaftures of Pruflia confifl: in glafs, iron-work, paper, gunpowder, copper and brafs-mills, manufaftures of cloth, catnblet, linen, filk, gold and filver lace, flockings, and other ar¬ ticles. The inhabitants export variety of naval Bores, amber, lint-feed and hemp feed, oat-meal, fiflr, mead, tallow, and caviar ; and it is faid that 500 Blips are loaded with thofe commodities every year, chiefly from Koningflrerg. His Pruflian majefty is abfolute through all his do- Conftitu- minions •, but the late king was too v/ife to opprefs histIon- fubjefts, though he availed himfelf to the full of his power. The government of this kingdom is by a re¬ gency of four chancellors of Bate, viz. 1. The great-ma- fler 5 PRY [ , PrujHa fter 5 2. The great-burgrave j 3. The great-chancellor j Prynne an<^> 4’ The great-marlhal. There are alfo feme other councils, and 37 bailiwicks. The dates confift, 1. Of counfellors of date ; 2. Of deputies from the nobility ; and, 3. From the commons. Belides thefe inftitutions, the late king ereiled a board for commerce and naviga- yj tion. Revenues. ^ His Pruflian majefty, by means of the happy fitua- tion of his country, its inland navigation, and the ex¬ cellent regulations of his predeceflor, derives an amazing revenue from this country, which, about a century and a half ago, was the feat of boors and barbarifm. It is faid, tl> t amber alone brings him in 26,000 dollars an¬ nually. His other revenues arife from his demefnes, his duties of cudoms and tolls, and the fubfidies yearly granted by the feveral dates •, but the exaft fum is not known, though we may conclude that it is very confider- 78 able, from the immenfe charges of the late war. Military The military regulations introduced by the late king ftrength. Had a wonderfully quick operation in forming his troops and recruiting his armies. Every regiment has a par¬ ticular didrift adigned it, where the young men proper for bearing arms are regidered ; and when occafion of¬ fers, they join their regiment, and being incorporated with veterans they foon become w^ell difeiplined troops. The Prudian army, in the time of peace, confids of l75,0°o of the bed difeiplined troops in the world ; and during the lad war, that force was augmented to 300,000 men. As the Prudian army formerly depended chiedy upon the cantons of the different regiments for their recruit¬ ing, it mud differ in proportion with the lofs of territory a diminution of at lead 80,000 men, and be thus redu¬ ced to 170,000, which was nearly its drength as far back as the year 1772. We are informed that it is to be dill farther reduced to 150,000 regular troops, the whole of them to be natives of the country, one-third of whom are to do duty for one year, fo that every man will have a furlough of two.years in time of peace, and be in aftual Service every third year. Beddes this regular army, a militia is to be organized of 380,000 men, who are to do garrifon duty in time of war, which will enable the whole 150,000 regular troops to take the field againd yg any enemy, when necefiity requires it. Royal he royal arms of Prudia are argent, an eagle dif¬ arms, &c. played fable, crowned or, for Prudia : azure, the Im¬ perial feeptre, or, for Courland : argent, an eagle dif- played, gules, with femicircular wreaths, for the mar- quifate of Brandenburg : to thefe are added the refpec- tive arms of the feveral provinces fubjeft to the Prudian crown. There are two orders of knighthood ; the fird, that of the Black Eagle, indituted by Frederic I. on the day of his coronation at Koningfberg, with this motto, Suum cuique. The fovereign is always grand-mader $ and the number of knights, exclufive of the royal fami¬ ly, is limited to 30. Next to this is the order of Me¬ rit, indituted by his late majedy ; the motto is, Pour le merite. PRUSSIAN blue. See Prussiate of iron, Che¬ mistry Index. PRUSSIC acid. See Chemistry Index. PRYNNE., William, an Englidi lawyer, much didinguidied in the civil commotions under Charles I. was born at Swainfwick in Somerfetdiire in 1 6qq. His 87 1 PSA Hijlriomq/lix, written againd dage-plays in 1632, con- Prynne taming fome redeftiens that offended the court, he was II fentenced.by the dar-chamber to pay a fine of 5000I. praImana- to dand in the pillory, to lofe his ears, and to perpe- Z^r‘ tual impriionment. During his confinement, he wTote leveral more books ; particularly, in 1637, one entitled News from Ipfivich, which refiefting*- feverely on the bidiops, he was again fentenced by the dar-chamber to another fine of 5000I. to lofe the remainder of his ears in the pillory, to be branded on both cheeks with S. L. for feditious libeller, and to be perpetually imprifoned in Caernarvon cadle. Nothing but cutting off his hands could have, prevented Prynne from writing : he wrote dill 3 and in 1640, being fet at liberty by the houfe of commons, he entered London in a kind of triumph, was elefted into parliament for Newport in Cornwall’ and oppofed the bithops with great vigour, being the chief manager of Archbithop Laud’s trial. In the long parliament he was zealous in the Prefbyterian caufe 3 but when the Independents gained the afcendency, he oppofed them warmly, and promoted an agreement with the king. When the army garbled the houfe and refufed him entrance, he became a bitter enemy to them and their leader Cromwell, and attacked them with his pen fo feverely, that he was again imprifoned : but he pleaded the liberty of the fubjeft fo fuccefsfully, that he was enlarged, to write more controverfial books! Being redored to his feat after Cromwell’s death, with the other deluded members, he adided in promoting the redoration, and was appointed keeper of the Tower records 3 a place excellently well calculated for him, and where he was very ufeful by the colleftions he pub! lidied from them. He prefented 40 volumes of his ■ works, in. folio and 4^0» to Lincoln’s-inn library, of which fociety he was a member 5 and, dying in 1660 was buried under the chapel. PR\' TANES, in Grecian antiquity, were the pre- fidents of the fenate, whofe authority confided chiefly in affembling the fenate 5 which, for the mod part, was done once every day. The fenate confided of 500, 50 fenators being elefted out of each tribe : after which, lots were cad to de¬ termine in what order the fenators of each tribe diould prefide 5. which they did by turns, and during their pre- fidentdiip were called prytanes. However, all the 50 prytanes of the tribes did not govern at once, but one at a time, viz. for feven days 3 and after 35 days, ano¬ ther tribe came into play, and prefided for other five weeks ; and fo of the red. PSALM, a divine fong or hymn; but chiefly appro¬ priated to the 150 Pfalms of David, a canonical book of the Old Tedament. Mod of the pfalms have a particular title, fignifying either the name of the author, the perfon who was to fet it to mufic or fing it, the indrument that was to be ufed, or the fubjeft and occafion of it. Some have ima¬ gined that David was the foie author of the Book of Pfalms 3 but the titles of many of them prove the con¬ trary, as pfalm xix. which appears to have been written by Mofes. Many of the pfalms are inferibed with the names Koroh^ Ieduthun^ &c. from the perlons who were to fing them. PSALMANAZAR, George, the fiftitious name of a . pretended Formofan, a perfon of learning and in¬ genuity. He was born in France, and educated in a free- PSA , I Pfalmana- free fchool, and afterwards in a college of Jefuits, in zar- an archiepifcopal city, the name of which, as likewife thofe of his birth-place, and of his parents, are unknown. Upon leaving the college, he was recommended as a tutor to a young gentleman •, but foon fell into a mean rambling life, that involved him in difappointments and misfortunes. His firft pretence was that of being a fufferer for religion. He procured a certificate that he was of Iriih extraftion, that he left that country for the hike of the Catholic faith, and was going on a pilgri¬ mage to Rome. Being unable to purchafe a pilgrim’s garb, and obferving one in a chapel, dedicated to a mi¬ raculous faint, which had been fet up as a monument of gratitude by fome wanderipg pilgrim, he contrived to take both the Half and cloak away j and, being thus accoutred, begged his way in fluent Latin, accofting only clergymen or perfons of figure 5 whom he found fo generous and credulous, that, before he had gone 20 miles, he might eafily have faved money, and put him- felf in a much better drefs : but as foon as he had got what he thought was fufficient, he begged no more •, but viewed every thing worth feeing, and then retired to fome inn, where he fpent his money as freely as he had obtained it. Having heard the Jefuits fpeak much of China and Japan, he ftarted the wild fcheme, when he was in Germany, of paffing for a native of the ifland of Formofa ; and what he wanted in knowledge, he fupplied by a pregnant invention. He formed a new charadler and language on grammatical principles, which, like other oriental languages, he wrote from right to left with great readinefs j and planned a new religion, and a divifion of the year into 20 months, with other novelties, to credit his pretenfions. He was now a Japanefe convert to Chriftianity, travelling for inftruftion with an appearance more wretched than even that of common beggars. He then entered as a foldier in the Dutch fervice : but, ftill defirous of palling 'for a Japanefe, he altered his plan to that of being an unconverted heathen ■, and at Sluys, Brigadier Lauder, a Scots colonel, introduced him to the chaplain, who, with the view of recommending himfelf to the bilhop of London, refolved to carry him over to England. At Rotterdam, fome perfons having put flirewd queftions to him, that carried the air of doubt, he took one more whimfical ftep, which wras to live upon raw flefh, roots, and herbs •, which ftrange food he thought would remove all fcruples. The bifliop of London pa¬ tronized him Tvith credulous humanity ; and Pfalma- nazar found a large circle of friends, who extolled him as a prodigy. Yet were there fome wdro entertained a juft opinion of him, particularly the Drs Halley, Mead, and Woodward •, but their endeavours to expofe him-as a cheat only made others think the better of him, efpe- cially as thofe gentlemen verf efteemed no great admi¬ rers of revelation. But in this inftance at leaft, eafinefs of belief was no great evidence of penetration. He wTas employed to tranflate the church-catechifm into the Formofan language, which was examined, approved, and laid up as a valuable MS ; and the author, after writing his well-known Hi/lory of Formofa, wTas reward¬ ed and fent to Oxford to ftudy what he liked, wdiile his patron? and opponents were learnedly difputing at London on the merits of his w’ork. The learned members of the univerfity were no better agreed in their opinions than thofe at London j but at length Pfatyrians. 4S8 ] PSA the fceptics triumphed. Some abfurdities were difco- Pfalmar.a- vered in his hiftory, of fuch a natuie as to difcredit the whole narration, and faved him the trouble of an open declaration of his impofture •, which however he owmed at length to his private friends. For the remain¬ der of his life, his learning and ingenuity enabled him to procure a comfortable fupport by his pen ; he being con¬ cerned in feveral works of credit, particularly The Uni- verfal Hijlory. Fie lived irreproachably for many years, and died in 1763. PSALMIST, in the church of Rome, one of the leffer eccleiiaftical orders ; the fame with what among us is called clerk, precentor, or finger. PSALMODY, the art or act of linging pfakm. See Psalm. Pfalmody was always efteemed a confiderable part of devotion, and ufually performed in the Handing pofture: and as to the manner of pronunciation, the plain fdng was lometimes ufed, being a gentle infledion of the voice, not much different from reading, like the chant in ca¬ thedrals; at other times more artificial compofitions were ufed, like our anthems. As to the perfons concerned in finging, fometimes a fingle perfon fung along •, lometimes the wThole affembly joined together, wdiich was the moft ancient and general pradice. At other times, the pfalms were fung alter¬ nately, the congregation dividing themfelves into twro parts, and finging verfe about, in their turns. There was alfo a fourth way of linging pretty common in the fourth century, which w7as, w'hen a fingle perfon began the verfe, and the people joined with him in the clofe : this wras often ufed for variety, in the fame fervice with alternate pfalmody. The ufe of mufical inftruments in the finging of pfalms, feem to be as ancient as pfalmody itfelfj the firft pfalm we read of beifig fung to the timbrel, viz. that of Mofes and Mitiam, after the deliverance of the Ifraelies from Egypt •, and afterwards, mufical inftru¬ ments w7ere in conftant ufe in the temple of Jerufalem. See Organ. PSALTER, the fame with the book of pfalms. See the article Psalm. Among the religious in the Popifti countries, the term pfalter is alfo given to a large chaplet or rofary, confifting of 150 beads, according to the number of ■pfalms in the pfalter. PSALTERY, a mufical inftrument, much in ufe among the ancient Hebrews, who called it nebel. We know little or nothing of the precife form of the ancient pfaltery. That now in ufe is a flat inftniment, in form of a trapezium or triangle truncated at top : it is ft rung with 13 wire-chords, fet to unifon or odave, and mounted on two bridges, on the two fidcs: it is ftruck with a pledrum, or little iron rod, and fometimes with a crooked flick. Its cheft or body refembles that of a fpinnet. PSAMMETICUS, or Psammitichus, a renown¬ ed conqueror, who fubduirg 1 r other petty kings of Egypt, became the founder of the kingdom of Egypt, about 670 B. C. He is memorable likewife for taking the city of Azot, after a fiege of 29 years 5 and for difeovering the fources of the river Nile. See Egypt, N° 10. PSATYRIANS, a fed of Arians, who, in the council of Antioch, held in the year 360, maintained that P S E Pfellus, Pfeudo. that the Son was not like the Father as to will; that he was taken from nothing, or made of nothing ; and that in God, generation was not to be diftinguilhed from creation. Enfield's PSELLUS, Michael, a learned Chriftian of the pFvT °{ 11 th century> was> bX birth» a Conftantinopolitan of philojophy. confular rank, and flouri{hed under the emperor Con- ftantine Monomachus. His genius and induftry raifed him far above the level of his cotemporaries j aud the female hiftorian Anna Comnena fpeaks of him as one who had been more indebted for his attainments to his own excellent talent than to the inftrudlions of his pre¬ ceptors ; adding, that having, made himfelf mailer of all the wifdom of the Greeks and the Chaldeans, he was juftly efteemed the molt learned man of the age. Thus furnilhed, he became the chief inltruftor of the Con¬ ftantinopolitan youth. He was at the fame time the companion and the preceptor of the emperor, who was fo captivated by the Itudies and amufements in wdiich Pfellus engaged him, that, according to Zonaras, he ne¬ glected the concerns of the empire. The Byzantine hiltorians complain, that the emperor, deluded by the head of the philofophers (the title with which Pfellus Was honoured), loll the world. Meeting, towards the clofe of this life, with fomc difappointment, Pfellus re¬ tired into a monaltery, and foon afterwards died j the time of his death is uncertain. His works, which have been much celebrated, are, Commentaries upon Arilto- tle’s Logic and Phyfics; a Compendium of Queltions and Anfwers; and an Explanation of the Chaldean Ora¬ cles. The two latter works prove him to have been converfant, not only with Grecian, but with Oriental, philofophy. PSEUDO, from ij/iiidof, a Greek term ufed in the compolition of many words to denote falfe or Jpurious .* as the pfeudo-acacia, or baltard acacia j pfeuoo-fumaria, or baltard-fumitory 5 pfeudo-ruta, or baltard-rue, &c. We alfo fay, a pfeudo-apoltle or falfe apoltle; a pfeudo- prophet, or falfe prophet, &c. PsEUDO-China. See Smilax. PsEuno-Galena. or Black Jack. See Zinc, Ores of, Mineralogy Index. PSEUDO Tinea, in NaturalHi/lory, the name of a very remarkable fpecies of infeCt defcribed by M. Reaumur, approaching to the nature of the tinea, or clothes moth, while in the worm-ltate, but not making themfelves coats of the fubltance of leaves, cloth, &c. though they form a fort of cafes for their defence againlt a very ter¬ rible enemy. Thefe creatures are of the caterpillar kind, and have, in the manner of many of thefe infeCts, 16 legs. They feed on wax, and for food enter the bee-hives ; where they boldly engage the bees, and are not to be prevent¬ ed by them from feeding, though at the expence of their habitations and the cells of their refervoirs of honey: fo that it is no uncommon thing for a fwarm of bees to be forced to change their place of habitation, and make new combs elfewhere 5 leaving the old ones to this con¬ temptible victor, whom they know not how to drive out or difpoffefs. Virgil and Ariftotle, and all the authors who have written on bees, have complained of this deltruftive animal. It never eats the honey, but feeds only on the wax; attacking principally thofe waxy cells where the female bee depofites her eggs for the future progeny. Vol. XVII. Part II. [ 489 1 P S E The bees, who are a match for molt other creatures Pfeudo, by means of their dings, would eafily deltroy thefe pfeiulony- weak creatures, were it not for the impervious armour inus' , they were covered with. They form themfelves a coat V of armour of a double matter. The firft, which imme¬ diately covers the body, is of a kind of filk of their own fpmning; and the outer covering over this is of the bees-wax : this is laid confiderably thick $ and the crea¬ ture, juft thrufting out its head to feed, goes on devour¬ ing the cells undiiturbed, while a whole army of the inhabitants are in vain buzzing about him, and attempt¬ ing to pierce him with their ftings. He never forfakes his covering, but lengthens and enlarges it as he goes ; and gnawing down the Tides of the cells in his march, without flaying to eat them one by one, the havock and deftrudtion he occafions are fcarcely to be conceived. When the time of the change of this creature approaches, it contrafts its body within its double covering, and there changes into the nymph date j whence, after a proper time, it comes forth in form of a moth, with gra¬ nulated horns and a crooked probofcis. The bees have cunning enough to know their de- drudtive enemy in this new form ; and as this is a weak and defencelefs date, they attack and deftroy all the moths of this fpecies they meet with. They fel* dom are fo fortunate, however, as to kill the whole race as foon as produced j and if only one efcapes, it is able to lay a foundation of revenge for the death of its brethren. All the flies of the moth kind lay a vad number of eggs, and this is behind hand with none of them in that particular : the young ones produced from the eggs of one furviving female of this fpecies are fuf- ficient to dedroy many honey-combs; nay, many hives of them. The moth produced by this caterpillar flies but little j yet it is very nimble in avoiding danger, by running, which it does with great ftviftnefs. There is a fpecies of thefe pfeudo-tineoe, or wax-eating caterpillars, which infed the fubterraneous hives of wafps and other creatures which make wrax : the man¬ ner of living, feeding, and defending themfelves from their enemies, is the fame in all the fpecies. Thefe lad, if they are at any time didreffed for food, will eat their own dung;, the wax having pafled almod unaltered through their bodies, and being dill wax, and capable of affording them more nouriftiment on a fecond digef- tion. Thefe fpecies, though they naturally live on this foft food, yet if by any accident they meet with harder only, they know how to live upon it; and can eat a wray into the covers and leaves of books, and make themfelves cafes and coverings of the fragments of thefe fubdances. The accurate author f of thefe obfervations defcribes al-, p fo a kind oi fifeudo tmea which feeds on wool, and ano- ther that eats leather ; both making themfelves houfes ry of In. alfo of the materials they feed on. feels. There is alfo another kind very deftruftive to corn: thefe make themfelves a covering by fadening together a great number or the grains, and there living and eat¬ ing in fecret. All thefe creatures, whatever be their food or habitation, finally become phalence, or moths ; and may be diflinguifhed, even in this date, from the other fpecies, by having granulated horns of a remark¬ able drufture, and all of them a probofcis, or trunk, more or lefs incurvated. PSEUDONYMUS, among critics, an author who publiihes a book under a falfe or feigned name; as cryp~ 3 Q tonymu* VST [ 49° ] P S Y PfiJium tonymus is given to him who publithes one under a dif- p-'lC g^hed name, and anonymous to him who publifhes with- :iy' *' , out any name at all. PSIDIUM, the GUAVA ; a genus of plants belonging to the icofandria clafs, and in the natural method rank¬ ing under the 19th order, Ilefperidex. See Botany Index. A deception of the roots of guava is employed with fuccefs in dyfenteries: a bath of a decodtion of the leaves is laid to cure the itch and other cutaneous erup¬ tions. Guayava, or guava, is diftinguilhed from the colour of the pulp into two fpecies, the white and the red •, and, from the figure of the fruit, into the round, and the pear- fafhioned or perfumed guava. The latter has a thicker rind, and a more delicate talle than the other. The fruit is about the bignefs of a large tennis-ball j the rind or Ikin generally of a ruffet ftained with red. The pulp within the thick rind is of an agreeable flavour, and inter- Iperfed with a number of fmall white feeds. The rind, when flevred, is eaten with milk, and preferred to any other hewed fruit. From the fame part is made marma¬ lade ; and from the whole fruit is prepared the fineft jelly in the world. The fruit is very aUringent* and nearly of the fame quality with the pomegranate. The feeds are fo hard as to refill the eftefts of the ftopiachs of animals j fo that when voided with the excren «• nts, they take root, germinate, and produce thriving trees. Whole meadows in the Weft Indies are covered with guavas, which have been propagated in this manner. PSHTACUS, or Parrot, a genus of birds be¬ longing to the order of picte. See Ornithology Index. PSOAS, in Anatomy. See there, Table of the Muf- cles. PSOPHIA, a genus of birds belonging to the order of Ga/linee. See ORNITHOLOGY Index. PSORALEA, a genus of plants belonging to the diadelphia clafs, and in the natural method ranking un¬ der the 32d order, Papilionaccce. See Botany Index. PSYCHO! RIA, a genus of plants belonging to the pentandria clafs, and in the natural method ranking un¬ der the 47th order, Stc/latee. See Botany Index. PSYLLI, (Strabo, Ptolemy): a people in the fouth of Cyrenaica, fo called from King Pfyllus, (Agathar- gides, quoted by Pliny) : almoft all ovenvhelmed by firnd driven by n fouth wind (Herodotus.) They had fomething in their bodies fatal to ferpents, and their very fmell proved a charm againft them, according to Pliny, Lucan, &.c. Though wre may juftly look upon it as fabulous, that thefe people had any thing in their bodies diffe¬ rent from others •, it is, however, certain that there are in Egypt at this day fome perfons who have a me¬ thod of handling the moft poifonous ferpents without any hurt. Of thefe Mr Halfelquift gives the following account: “ They take the rnoft: poifonous vipers with their bare hands, play with them, put them in their bo- foms, and pfe a g;eat many mqre tricks with them, as I have often feen. I have frequently feen them handle thore that were three or four feet long, and of the moft horrid fort. I inquired and examined whe¬ ther they had cut out the vipers poifonous teeth ; but I have wish my own eyes feen they do not. We may therefore conclude, that there are to this day Pfylli in Egypt 5 but what art they ufe is not eafily known. Some people are very fuperftitious, and the generality believe this to be done by fome fupernatural art which they obtain from invifible beings. I do not know whe¬ ther their power is to be aferibed to good or evil; but I am perfuaded that tliofe who undertake it ufe many fupcrftitions. “ Tire art of fafeinating ferpents is a fecret amongft the Egyptians. It is worthy the endeavours ofallnatu- ralifts, and the attention of every traveller, to learn fome¬ thing deciiive as to this affair. How ancient this art is among the Africans, may be concluded from the an¬ cient Marii and Pfylli, who were from Africa, and daily fliowed proofs of it at Rome. It is very remarkable that this fliould be kept a fecret for more than 2000 years, being known only to a few, when we have feen how many other fecrels have within that time been re¬ vealed. The circumftances relating to the fafcinalion of ferpents in Egypt, related to me, were principally, 1. That the art is only known to certain families, who propagate it to their offspring. 2. 'The perfon who knows hpw7 to fafeinate ferpents, never meddles with other poifonous animals, fuch as feerpions, lizards, &c. There are different perfons who know7 how to fafeinate thefe animals j and they again never meddle with ferpents. 3. Thofe that fafeinate ferpents, eat them both raw and boiled, and even make broth of them, which they eat very commonly amongft them j but in particular, they eat fuch a diflr when they go out to catch them. I have been told, that ferpents fried or boiled are frequently eaten by the Arabians both in Egypt and Arabia, though they know not how to fafeinate them, but catch them either alive or dead. 4. After they have eaten their foup, they procure a blef- fing from their fcheik (prieft or lawyer), who ufes fome fuperftitious ceremonies, and amongft; others, fpits on them feveral times with certain geftures. This man¬ ner of getting a blefling from the prieft: is pure fuperfti- tion, and certainly cannot in the leaft help to fafeinate ferpents ; but they believe, or will at leaft perfuade others, that the power of fafeinating ferpents depends upon this circumftance.,, Noiwithftanding this teftlmony of Haflelquift, the flory of the incantation of ferpents, though frequently alluded to in Scripture, has been generally treated as a fable. It is, however, affirmed as a certain truth, both by Mr Bruce and M. Savary. “ There is no doubt (fays the former of thefe travellers) of its reali¬ ty. The Scriptures are full of it. All that have been in Egypt have feen as many different inftances as they chofe. Some have doubted that it was a trick ; and that the animals thus handled had been firft trained, and then deprived of their power of hurting j and fond of the difeovery, they have refted themielves upon it, without experiment, in the face of all antiquity. But I will not hefitate to aver, that I have feen at Cairo (and this may be feen daily without any trouble or ex¬ pence), a man who came from the catacombs, where the pits of the mummy birds are kept, who has taken a ceraftes with his naked hand from a number of others lying at the bottom of a tub, has put it upon his bare bead, covered it with the common red cap he wears, then taken it out, put it in his bread, and tied it about his neck like a necklace \ after which it has been ap¬ plied to a hen, and bit it, which died in a few minutes j P s Y [ 491 ] PTE Pfylli. and, to complete the experiment, the man has taken it by the neck, and beginning at his tail, has ate it as one would do a carrot or ftoek of celery, without any feem- ing repugnance. “ We know from hiflory, that where any country has been remarkably infelled with ferpents, there the people have been fcreened by this fecret. “ To leave ancient hiftory, I can myfelf vouch, that all the black people in the kingdom of Sennaar, whe¬ ther Funge or Nuba, are perteblly armed againif the bite of either fcorpion or viper. They take the cera- ftes in their hands at all times, put them in their bofoms, and throw them to one another as children do apples or balls, without having irritated them by this ufage io much as to bite. The Arabs have not this fecret na¬ turally, but from their infancy they acquire an exemp¬ tion from the mortal confequences attending the bite of thefe animals, by chewing a Certain root, and walh- ing themfelves ("it is not anointing) with an infulion of certain plants in w'ater.” From this account we fhould be apt to think, that thefe vipers really would not bite any who were thus armed againft their poifon 5 especially as he adds, that he “ conftantly obferved, that the viper, however live¬ ly before, upon being feized by any of thefe barbarians, feemed as if taken with licknefs and feeblenefs, frequent¬ ly (hut his eyes, and never turned his mouth towards the arm of the perfon who held him.” Yet in another place, fpeaking of the activity of the ceraftes, he fays, 44 I faw. one of them at Cairo, in the houfe of Julian and Rofa, crawl up the fide of a box in which there were many, and there lie ftill, as if hiding bimfelf, till one of the people who brought them to us came near him ; and though in a very difadvantageous poflure, flicking as it were perpendicularly to the fide of the box, he leaped near the diftance of three feet, and faftened between the man’s forefinger and thumb, fo as to bring the blood. The fellow (bowed no figns of either pain or fear, and even kept him with us full four hours, with¬ out his applying any fort of remedy, or feeming inclined to do fo.” It is difficult to fee how thefe two accounts can be reconciled. If thofe who catch vipers are in danger of being bit by them after they arc catched, certainly they muft be fo before, and then the whole relation becomes contradictory. Our author tells us, that thefe feats were performed for a feafon, by thofe who were artifi¬ cially armed againft the viper’s poifon, as well as thofe who had the exemption naturally ; but though put in poffeflion of the drugs, he never had the courage to make the experiment. That he (hould have made fuch a dreadful experiment on himfelf no perfon in his fenfes would expeft ; but it is indeed very furprifing, that he did not attempt by means of thefe medicines to arm fome of the brute creatures, of the lives of which he was fufficiently prodigal, againft the effefts of that deadly poifon by which fo many of them periffied. As fur¬ prifing it is, that he did not try what effefl the root or its decoflion would have upon the ferpents themfelves 5 or that, though he fays he had a fmall quantity of this extraordinary root by him, he gave neither drawing nor defeription of it. Though it is impoffible to reconcile the particulars of this account to one another, the general faft of the incantation is confirmed by the teftimony of M. Savary. This writer tells us, that he faw at the feaft of 3idi PTyllr Ibrahim, a troop of people, feemingly poflefled, with II naked arms and a fierce look, holding in their hands pte™scai*' enormous ferpents, which twined round their body, and 1 endeavoured to eicape. Thefe Pfylli, grafping them ftrongly by the neck, avoided the bite ; and notwith- ftanding their hiding, tore them with their teeth, and ate them alive, while the blood ftreamed from their mouth. PTARMIGAN. See Tetrad, Ornithology In¬ dex. PTELEA, SHRUB-TREFOIL j a genus of plants be¬ longing to the tetrandria clafs ; and in the natural me¬ thod i-anking with thofe of which the order is doubtful. See Botany Index. PTERIS, a genus of plants belonging to the order of filices, and to the cryptogamia clafs. See Botany Index. The fruCifications are in lines under the mar¬ gin. There aie 19 (pecies 5 the moft remarkable is the aquilina, or common female fern. The root of this is vifeid, naufeous, and bitterifh ; and like all the reft of the fern tribe, has a fait, mucilaginous tafte. It creeps under the ground in fome rich foils to the depth of five or fix feet, and is very difficult to be deftroyed. Frequent mowing in pafture-grounds, plentiful dung¬ ing in arable lands, but, above all, pouring urine up¬ on it, are the moft approved methods of killing it. It has, however, many good qualities to counterbalance the few bad ones. Fern cut while green, and left to rot upon the ground, is a good improver of land ; for its affies, if burnt, will yield the double quantity of fait that moft other vegetables will. Fern is alio an excellent manure for potatoes 5 for if buried beneath their roots, it never fails to produce a good crop.— Its aftringency is fo great, that it is ufed in many places abroad in dreffing and preparing kid and chamois lea¬ ther.—In feveral places in the north, the inhabitants mow it green, and, burning it to aihes, make thofe aihes up into balls, with a little water, which they dry in the fun, and make ufe of them to wa(h their linen with inftead of foap. In many of the Weftern Ifles the people gain a very confiderable profit from the lale of the allies to foap and glafs makers. In Glen Elg in Invernefslhire, and other places, the people thatch their houfes with the (talks of this fern, and fallen them down with ropes made either of birk-bark or heath. Some¬ times they ufe the whole plant for the fame purpofe, but that does not make fo durable a covering. Swine are fond of the roots, efpecially if boiled in their walh. In fome parts of Normandy we read that the poor have ■ been reduced to the miferable neceffity of mixing them with their bread. And in Siberia, and fome other north¬ ern countries, the inhabitants brew them in their ale, mixing one-third of the roots to two-thirds of malt. The ancients ufed the root of this fern, and the whole plant, in decoftions and diet-drinks, in chronic diforders of all kinds, arifing from obftruftions of the vifeera and the fpleen. Some of the moderns have given it a high charafler in the fame intentions, but it is rarely ufed in the prefent praflice. The country people, however, ftill continue to retain fome of its ancient ufes ; for they give the powder of it to deftroy worms, and look upon a bed of the green plant as a fovereign cure for the ric¬ kets in children. PTEROCARPUS, a genus of plants belonging to 3 Q. 2 the P T O [ 492 ] Pterocarpus the diadelphia clafs ; and in the natural method rank- Another, PtoleLa-s ^n§unc^er32 . dex. PTINUS, a genus of infefts belonging to the order of coleoptera. See Entomology Index. PI IS AN, is properly barley decorticated, or de¬ prived of its hulls, by beating in a mortar, as was the ancient practice ; though the cooling potion obtained by boiling fuch barley in water, and afterwards fweet- ening the liquor with liquorice-root, is what at prefent goes by the name of ptifan ; and to render it laxative, lome add a little fena or other ingredient of the fame in¬ tention. PTOLEMAIC SijJlem of Afronomy, is that in¬ vented by Claudius Ptolemseus. See Ptolemy, Clau¬ dius. PTOLEMAIS, in Ancient Geography ; the port of Arlinoe, fituated on the weft branch of the Nile, which concurs to form the ifland called Nomos Herac/eetes, to to the fouth of the vertex of the Delta. Ptolemais, (Strabo) ; the largeft and moft confi- derable town of the Thebais, or Higher Egypt, and in nothing fhort of Memphis •, governed in the manner of a Greek republic } fituated on the weft fide of the Nile, almoft oppofite to Coptos. This town, which was built by Ptolemy Phiiadelphus, is now known by the name of Ptolometa. The walls and gates are ftill entire, and there are a vaft number of Greek infcriptions, but only a few columns of the portico remain. There is like- wife an Ionic temple, done in the moft ancient manner of executing that order, of which Mr Bruce took a drawing, which is preferved in the king’s colicdion. PUB Publican. , of Cyrenaica, anciently called Barce. A Ptolemais third of the Troglodytica, furnamed Epitheras, from the chace of wild beafts, as elephants 5 lying in the fame parallel with Meroe (Strabo) j on the Arabian gulf (Pliny) ; 4820 ftadia to the fouth of Berenice. A fourth, of Galilee, anciently called Aca, or Aeon ; made a Roman colony under the emperor Claudius (Pliny). A fifth of Pamphyliaj fituated near the river Melas, on the borders of Cilicia Afpera. PTOLEMY Soter, or Lagus, king of Egypt, a renowned warrior, and an excellent prince : he eltablifti- ed an academy at Alexandria, and was himfelf a man of letters. Died 284 B. C. aged 92. Ptolemy Phiiadelphus^ his fecond fon, fucceeded him to the exclufion of Ptolemy Ceraunus. He was re¬ nowned as a conqueror, but more revered for his great virtues and political abilities. He eftabliflaed and aug¬ mented the famous Alexandrian library, which had been begun by his father. He greatly increafed the com¬ merce of Egypt, and granted confiderable privileges to the Jews, from whom he obtained a copy of the Old Teftament, which he caufed to be tranflated into Greek, and depofited in his library. This is fuppofed to have been the verfion called the Septuagint. He died 246 years B. C. aged 64. Ptolemy Ceraunus, the elder brother, fled to Se- leucus king of Macedon, who received him hofpitably j in return for which he aflaffinated him, and ufurped his crown. He then invited Arfinoe, who was his widow and his own After, to lhare the government with him j but as foon as he got her in his power, he murdered her and her children. He was at length defeated, killed, and torn limb from limb by the Gauls, 279 B. C. Ptolemy, Claudius, a celebrated mathematician and aftrologer, was born at Pelufium, and furnamed by the Greeks Mof Divine and Mof Wife. He flouriftied at Alexandria in the fecond century, under the reigns of Adrian and Marcus Aurelius, about the 138th year be¬ fore the Chriftian era. There are ftill extant his Geo¬ graphy, and feveral learned works on aftronomy. The principal of which are, 1. The Almageft ; 2. De Judi- ciis Afrologicis ; 3. Planifphcerium. His fyftem of the world was for many years adopted by the philofophers and aftronomers 5 but tire learned have rejefted it for the fyftem of Copernicus. See Astronomy, n° 16. PTYALISM, in Medicine, a falivation, or frequent and copious difeharge of faliva. The word is Greek, formed from tctou “ to fpit.” PUBERTY, denotes the age at which a perfon is capable of procreating or begetting children. See Man. Puberty, in Lave, is fixed at the age of 12 in females, and 14 in males ; after which they are reck¬ oned to be fit for marriage. But as to crimes and puniftiments, the age of puberty is fixed at 14 in both fexes. PUBES, in Anatomy, denotes the middle part of the hypogaftric region in men or women, lying between the two inguina or groins. Seciion af the Pubes. See Midwifery and Si~ GAVLTJAN Operation. Pubes, in Botany, the hair or down on the leaves of fome plants. See Hair. PUBLICAN, among the Romans, one who farmed the taxes and public revenues. PUBLICATION, P U F C 493 1 PUG PufFendorf. Publication PUBLICATION, the art of making a thing known to the world ; the fame with promulgation. PUBLIUS Syrus, a Syrian mimic poet, who flou- rifhed about 44 years before Chrilt. He was original¬ ly a Have fold to a Roman patrician, called DGmitius, who brought him up with great attention, and gave him his freedom when of age. He gained the elteem of the molt powerful men at Rome, and reckoned Julius Csefar among his patrons. He foon eclipfed the poet Laberius, whofe burlefque compofitions were in general efteem. There remains of Publius a colleftion of mo¬ ral fentences, written in iambics, and placed in alphabe¬ tical order. Oak PUCERON, a name given by naturalifts to a very remarkable fpecies of animal of the puceron kind. They bury themfelves in the clefts of the oak and fome other trees, and getting into the crevices, where the bark is a little Separated from the wood, they there live at eafe, and feed to their fill, wdthout being expofed to their common enemies. They are larger than the other pu- cerons, the winged ones being nearly as large as a com¬ mon houfe fly •, and thofe without wings are alfo larger than any other fpecies of the fame genus. The wing¬ ed ones are black, and the others of a coffee colour. Their trunk is twice the length of their bodies, and, when walking, it is carried ftraight along the belly, trail¬ ing behind it with the point up. When the creature has a mind to fuck a part of the tree that is juft before it, it draws up and fliortens the trunk, till it brings it to a proper length and d’re£Hon ; but when it fucks in the common way, it crawls upon the inner furface of the bark, and the turned up end of the trunk, which re- fembles a tail, fixes itfelf againft the wood that is be¬ hind it, or contiguous to its back, and fucks there. The extremity of this trunk holds fo faft by the wood, that when it is pulled away, it frequently brings a fmall piece of the wood away with it. The ants are as fond of thefe as of the other fpecies of pucerons, and that for the fame reafon, not feeding upon them, but on their dung, which is a liquid mat¬ ter of a fweet tafte, and is the natural juice of the tree, very little altered. Thefe creatures are the fureft guides where to find this fpecies of puceron ; for if we at any time fee a number of thefe crawling up an oak to a cer¬ tain part, and there creeping into the clefts of the bark, we may be aflured that in that place there are quanti¬ ties of thefe oak pucerons. The ants are fo extremely fond of the juices of the tree, when prepared for them by pafling through the body of this animal, that when the puceron has a drop not yet evacuated, but hanging only in part out at the paffage, an ant will often feize on it there. Pucerons, Vine fretters, or Plant lice. See Aphis. PUDENDA, the parts of generation in both fexes. See Anatomy, n° 107 and 108. PUERILITY, in difcourfe, is defined by Longinus to be a thought which, by being too far fetched, be¬ comes flat and infipid. Puerility, he adds, is the com¬ mon fault of thofe who affedt to fay nothing but what is brilliant and extraordinary. PUFFENDORF, Samuel de, was bom in 1631 at Fleh, a little village in Mifnia, a province in Upper Saxony ■, and was fon of Elias Puffendorf, minifter of that place. After having made great progrefs in the fciences at Leipfic, he turned his thoughts to the ftudy Puget. T— of the public law, which in Germany confifts of the Puffendorf knowledge of the rights of the empire over the princes and ftates of which it is compofed, and thofe of the ,, princes and ftates with refpsdt to each other. But though he ufed his utmoft efforts to diftinguifh himfelf, he defpifed thofe pompous titles which are fo much fought for at univerfities, and never would take the degree of dodtor. He accepted the place of governor to the fon of M. Coyet, a Swedifti nobleman, who was then am- baffador from Sweden to the court of Denmark. For this purpofe he went to Copenhagen, but continued not long at eafe there ; for the war being renewed fome time after between Denmark and Sweden, he was feiz- ed with the whole family of the ambaffador. During his confinement, which lafted eight months, as he had no books, and was allowed to fee no perfon, he amufed himfelf by meditating on what he read in Grotius’s trea- tife De Jure Belli et Pads, and the political writings of Mr Hobbes. Out of thefe he drew up a ftiort fyltem, to which he added fome thoughts of his own, and pub- lifhed it at the Hague in 1660, under the title of E/e- menta Jurifprudentice Univerfalis. This recommended him to the eledtor Palatine, who invited him to the uni- verfity of Heidelberg, where he founded in his favour a prefefforftiip of the law of nature and nations, which was the firft of that kind eftablifhed in Germany. Puffen¬ dorf remained at Heidelberg till 1673, when Charles XL of Sweden gave him an invitation to be profeffor of the law of nature and nations at Lunden ; which place the eledtor Palatine reludtantly allowed him to accept. He went thither the fame year; and after that time his reputation greatly increafed. Some years after, the king of Sweden fent for him to Stockholm, and made him his hiftoriographer, and one of his counfellors. In 1688, the eledtor of Brandenburg obtained the confent of his Swedifti majefty, that he (hould come to Berlin, in or¬ der to write the hiftory of the eledtor William the Great; and in 1694 mac^e a baron. But he died that fame year of an inflammation in his feet, occafion- ed by cutting his nails ; having attained his grand cli- madteric. Of his works, which are numerous, the fol¬ lowing are the principal: 1. A Treatife on the Law of Nature and Nations, written in German ; of which there is an Englifti tranflation with Barbeyrac’s Notes.. 2. An Introdudtion to the Hiftory of the Principal States which at prefent fubfift in Europe ; written in German ; which has been alfo tranflated into Englifti. 3. The Hiftory of Sweden, from Guftavus Adolphus’s* expedition into Germany to the abdication of Queen Chriftina. 4. The Hiftory of Charles Guftavus, two volumes folio, &c. PUFFIN. See Alca, Ornithology Index. PUGET, Peter Paul, one of the greateft painters and fculptors France ever produced, though but little noticed by their own writers, was born at Marfeilles* in 1623. In his youth he was the difciple of Roman, an able fculptor ; and then went to Italy, where he ftudied painting and architedlure. In painting he fo well imitated the manner of Peter de Cortona, that this painter defired to fee him, and entered into a friend- ftiip with him. In 1657, a dangerous diforder obliged him to renounce the peneil, and devote himfelf to fculp- ture ; and his reputation caufing him to be invited to Paris, he enjoyed a penfion of 1 200 crowns, as fculp¬ tor and dire6lor of the works relating to veffels and galleyai PUL galleys. He died at Marfeilles in 1695, and has left a number of admirable ftatues behind him both in France and Italy. PUGIL, in Phyjic, &c. fuch a quantity of flowers, feeds, or the like, as may be taken up between the thumb and two fore-fingers. It is reckoned the eighth part of the manipulus or handful. PULEGIUM, ox Pennt-Roijo/. See Mentha, Bo¬ tany Index. PULEX, the Flea, in Zoology, a genus of infedls belonging to the order of aptera. See Entomology Index. By keeping fleas in a glafs tube corked up at both ends, but lb as to admit frefh air, their actions and man¬ ners may be obferved. They are thus feen to lay their eggs, not all at once, but ten or twelve in a day, for fe- veral days fucceflively ; which eggs will be afterwards found to hatch fucceffively in the fame order. The flea may eafily be differed in a drop of water ; and by this fneans the ftornach and bowels, with their periftaltic mo¬ tion, may be difcovered very plainly, as alfo their teftes and penis, with the veins and arteries, though minute beyond all conception. Mr Leuwenhoek affirms alfo, that he has feen innumerable animalcules, fhaped like ferpents, in the femen mafculinum of a flea. This blood- thirfly infedl, which fattens at the expence of the human fpecics, prefers the more delicate Ikin of women ; but Barbut's Pre^s rie^t^er uPon epileptic perfons, nor upon the dead Ge’ji^ra *0/ or dyiHg- It loves to neftle in the fur of dogs, cats, and Infetts, rats. The nefts of river-fwallows are fometimes plenti- P' 330, 5c fully ftored with them. Fleas are apterous ; walk but little, but leap to a height equal to 200 times that of their own body. This amazing motion is performed by means of the ela- fticity of their feet, the articulations of which are fo many fprings. Thus it eludes, with furprifing agility, the purfuit of the perfon on whom it riots. Among the memorabilia of fleas, one, they fay, has been feen to draw a fmall filver piece of ordnance to which it -was fattened, the firing of the gun nowife daunting its intre¬ pidity. The owner carried it about in a little box lin¬ ed with velvet, every now and then placing it on her arm to let it feed ; but wdnter put an end to the being of this martial flea. Another flea that became Have to an Engliffiman, had, for its daily and eafy talk, to drag its golden chain and padlock, of the weight of one grain. A third flea ferved as a thrill-horfe to an Eng- llfli artift, who had made an ivory coach and fix, that carried a coachman and his dog between his legs, a po- ftilion, twro footmen, and four infide riders. At Surat fleas, bugs, and other voracious vermin, are in fo great veneration, that they have an hofpital endowed,, where every night a poor fellow, for hire, fuffers himfelf to be preyed upon. He is fattened naked on a bed, when the feaft begins at his expence. In Turkey there is a fimi- lar foundation for decayed dogs ; an inftitution lefs ri¬ diculous than the other. Mercurial ointment, brim- ftone, a fumigation with the leaves of pennyroyal, or frefh-gathered leaves of that plant fewed up in a bag, and laid in the bed, are remedies pointed out as deftruc- tive of fleas. PULEX Arboreus, in Natural Hiftory, the name given by Mr Reaumur to a very large genus of fmall animals. They are a kind of half-winged creatures : they have granulated antennae ; and fome of them, in their moil r 494 1 P U L perfect ttate, have complete wings. Thefe are dittin- guithed from the others by the name of tnufca-pulex or the wingedpulex. See Coccus, Entomology Index. . PULEX Aquations audiorum (monoculus pulex of Lin- naeus) is a fpecies of the genus Monocugus ; which fee, under Entomology Index. PULEX-Eaters, a name given by naturalifts to a fort of worms frequently found on the leaves of trees, where they devour the animals called pulices arborei. Of thefe there are feveral fpecies, which owe their origin to the eggs of different creatures ; for there are none of them in their ultimate ftate in this their time of feeding. According to the different animals whofe eggs they are hatched from, thefe are of different form and ftrubture. Some are hexapodes, or endued with fix feet; thefe belong to the beetle-tribe, and finally change into beetles like the parent animal from whofe eggs they fprung. Others have no legs, and are produced from the eggs of flies of various kinds. And, finally, others are genuine caterpillars, though fmall; but thefe are the moil rare of all. The two general kinds are the hexapodes, or beetle- worms ; and the apodes, or fly-worms. The fly which gives origin to the latt of thefe is a four-winged one ; and takes care always to depofit her eggs in a place where there are plenty of the pulices, ufually on the ttalk or young branches of a tree in the midft of large families of them. The worm, as foon as hatched, finds itfelf in the midft of abundance of food, preying at pleafure on thefe animals, which are wholly defence- lefs. The ftalks of the elder and woodbine are fre¬ quently found covered over with thefe pulices 5 and among them there may ufually be found one or more of thefe deftroyers feeding at will, fucking in the juices from their bodies, and then throwing away the dry fldns. Befides the worms of this four-winged fly, there is one of a two-winged wafp-fly, very deftruttive of thele animals. PULLEY, in Mechanics, one of the five mechanical powers. See Mechanics. PULMO, the Lungs, in Anatomy. See Anato¬ my Index. — PULMONARIA, Lungwort, a genus of plants belonging to the pentandria clafs, and in the natural method ranking under the 41ft order, Afperifolicc. See Botany Index. PULO, the name of feveral Afiatic iflands, in the Indian ocean, the principal of which only, it is faid, is inhabited. It is denominated PuLO-Condore, ah ifland about 13 miles long and three broad, which was vifited by Loid Macartney on his way to China. It has convenient anchoring places during ei¬ ther monfoon. Here his lordflup’s fquadron came to anchor on the 17th of May. The bay is formed by four fmall iflands approaching fo near to each other, as to ex¬ hibit the appearance of meeting together in different points. They all feem to be the rude fragments of pri¬ mitive mountains, vrhich have been detached from the great continent in the lapfe of ages. Condore lies in 8° 40' North Lat. and 105° 55' E. Long. The Englith at one period had a fettlement here, but being driven from it by fome Malay foldiers in their pay, probably for fome unjuftifiable treatment, no Euro¬ peans it is faid, have refided in it ever fince. When a party went on thore from Lord Macgrtney’s fquadron. they Pulex H Puio. —Y— PUL Pulo .11 Pulpitum they were welcomed by the natives with much urbanity of manners, and conduced to the houfe of their chief. ^ 1 heir drefs confided chiefly of blue cotton garments hanging loofely about them ; and their flat faces and no- ies feemed to denote that they were defcended from the Chinefe. miflionary being of the party, could not underiiand their language as they fpoke it { but as foon as committed to writing it was perfe&ly intelligible to him. This led to the conclufion, that^ the inhabitants of Pulo-Condore were originally Cochin Chinefe, who fled from their own country in confequence of their at¬ tachment to one of its fovereigns who had been dethro¬ ned by a number of his own fubje£ls. Here the fquadron was to purchafe provifions, and the people promifed to have the propofed quantity in readi- nefs, if poflible, at the appointed time. Next morning, a party of pleafure went from the Hindoftan to a fmall ifland near Pulo-Condore; but being apprehenfive of an approaching ftorm, they made towards the fiiip with all convenient fpeed. The weather again becoming fa¬ vourable, they let oft for the ifland again, and were aftonilhed, on their arrival, to find it wholly abandoned. In the principal cabin a letter was found, written in the Chinefe language, exprefling their terror at the arrival of fuch great (hips and powerful perfons 3 not being able to fatisfy their demands as to cattle and other provi¬ fions, the poor inhabitants of Pulo-Condore having fcarcely any to fupply, they therefore fled to preferve their lives ; declared themfelves to be few in number, and very poor, but honeft ; and concluded with re¬ queuing the great people to have pity on them, as they had left their ail behind, and earneftly implored them not to burn their cabins. ihe generous Englilh left them an intimation that they called merely for refrefliment on fair and equitable terms, without harbouring againft them any evil de- figns. They claimed a connection to a civilized nation, actuated by principles of humanity, by which they were prohibited from plundering or doing injury to others, who might have the misfortune to be fewer or weaker than themfelves. No doubt the poor terrified inhabi¬ tants would be agreeably furprifed to find, on their re¬ turn, not only that all their tents were in perfect fafety, but that nothing was either difturbed or removed, and a fmall prelent left to their chief in the principal dwelling. -PUL0-Lingeti, another ifland of the clutter mentioned above, is of fome extent, though inferior in fize to Pulo Condore. It is chiefly remarkable for a mountain in its centre, terminating in a fork like Parnaffus, but denominated by mariners the ajfcs cars. The people of Lord Macartney’s fquadron were conftantly difeovering new iflands, many of which were clothed with verdure; fome had lofty trees growing upon them ; others were nothing but naked rocks, the refort of innumerable birds, and whitened with their dung. PULO PENANG. See PRINCE, of Wales's IJland. PULP, in 'Pharmacy, the flefliy and fucculent parts of fruits extra&ed by infufion or boiling, and pafied through a fieve. PULPI 1 , an elevated place in a church, whence fermons are delivered. The French give the fame name to a reading delk. PULPI 1 UM, in the Grecian and Roman theatres, was a place where the players performed their parts. It was lower than the feena, and higher than the -orcheftra. [ 495 1 PUL It nearly anfwered to what we call the 11 age, as dillin- Pulpitum, guilhed from the pit and galleries. Pulpitum was alfo Plllfe- a moveable delk or pulpit, from which difputants pro- J’ v ' J nounced tneir differtations, and authors recited their works. PULSE, in the animal economy, denotes the beat¬ ing or throbbing of the heart and arteries. No doefrine has been involved in more difficulties than that or pulles ; fince, in giving a phyfiological ac¬ count of them, phyficians have efpouled quite oppofite fentiments; whilft fome doubt whether the pulfe is ow¬ ing to the fyftole or diaftole ; as alfo, whether the mo¬ tion of the heart and arteries is one and the fame, for a moment of time. With regard to motion, the pulfes are reckoned only four ; great and little, quick and flow. When quicknefs and greatnefs are joined together, it becomes violent; and when it is little and flow it is called a weak pulfe. They are alfo faid to be frequent and rare, equal and unequal; but thefe are not the eflential affe&ions of motion. Frequency and quicknefs are often con¬ founded with each other. A pulfe is faid to be hard or fffii with regard to the artery, according as it is tenie, renitent, and hard, or flaccid, foft, and lax : for the difpolition of the arteries contributes greatly to the change of the pulfe; wherefore it fometimes happens, that the pulfe in both arms is not alike, which is very common in a hemiplexy. Add to thefe a convulfive pulfe, which does not proceed from the blood, bu-t from the Hate of the artery ; and is known by a tre¬ mulous fubultory motion, and the artery feems to be drawn upwards : this, in acute fevers, is the fign of death ;. and is faid to be the pulfe in dying perfons, which is like wife generally unequal and intermitting. A great pulfe fhows a more copious afflux of the blood to the heart, and from thence into the arteries : a little pulfe the contrary. The pulfes of perfons differ according to the large- nefs of the heart and veffels, the quantity and tempe- ries of the blood, the elaftic force of the canals; as al¬ fo with regard to the fex, age, feafon, air, motion, food, fleep, watchings, and pafflons of the mind. The pulfe is larger and more quick in men than in women ; in the bilious and fanguineo-bilious, than in the phlegma¬ tic and melancholic. Thofe who are lean, with tenfe fibres, and large vefiels, have a greater and a fLonger pulfe, than thofe that are obefe, with lax fibres and fmall vefiels ; whence they are more healthy, robuft, ana apt for labour. In children, the pulfe is quick and foft; in adults greater and more violent. In the old, it is commonly great, hard, and flow. Labour, mo¬ tion, and exercife of the body, increafe the circulation* of the blood, the excretions, and particularly refpira- tion ; reft renders the circulation flow and weak ; in- tenfe fpeaking increafes the circulation, and confequent-, ly renders the pulfe large and quick. In watching, the pulfe is more evident; in fleep, more flow and languid. After drinking hot things, fuch as coffee and tea, or hot bath-waters, as well as after meals, the pulfe vi¬ brates more quick. But nothing produces a greater change in the pulfe than affeftions of the mind : in terror, it is unequal, fmall, and contradled : in joy, fre¬ quent and great ; in anger, quick and hard ; in fadnefs, flow, fmall, deep, and weak ; and in intenfe ftudy, lan¬ guid and weak. With regard to the air, when, after th<» predominancy PUL [ 496 ] P U M Pulfe, predommancy of a weft or fouth wind, it becomes north Pulteney. or ea^ ^he pulfe is ftronger and larger j as alfo when the quickfilver rifes in the barometer. But when the atmolphere is denfe, humid, rainy, with a long fouth wind} as alfo where the life is fedentary, the deep long, and the feafon autumnal, the pulfe is languid and fmall, and the perfpiration decreafed. In May it is great, and fometimes violent j in the middle of fummer, quick but weak ; in the autumn, flow, foft, and weak j in the winter, hard and great. A draftic purge and an emetic render the pulfe hard, quick, and weak, with lofs of ftrength *, chalybeates, and the bark, render it great and robult, and the complexion lively j volatiles amplify and increafe the pulfe $ acids and nitrous re¬ medies refrigerate the body, and appeafe the pulfe j opiates and the like render it fmall and weak, and decreafe the eiafticity of the folids •, and poifons render it fmall, contrafted, and hard. When the quantity of the blood is too great, bleeding raifes the pulfe. Pulse, is alfo ufed for the ftroke with which any medium is affefted by the motion of light, found, &c. through it. Sir Ifaac Newton demonftrates, that the velocities of the pulfes in an elaftic fluid medium (whofe eiafticity is proportionable to its denfity) are in a ratio compounded of half the ratio of the elaftic force direftly, and half the ratio of the denfity inverfely •, fo that in a medium whofe eiafticity is equal to its denfity, all pulfes will be -equally fwift. Pulse, in Botany, a term applied to all thofe grains or feeds w'hich are gathered wnth the hand j in contra- ■diftinftion to corn, &c. wThich are reaped, or mowed : or, It is the feed of the leguminous kind of plants, as beans, vetches, &c. j but is by fome ufed for artichokes, afparagus, &c. PULTENEY, William, the famous oppofer of Sir Robert Walpole in parliament, and afterward earl of Bath, wras defeended from one of the moft ancient fa¬ milies in the kingdom, and wTas born in 1682. Being well qualified in fortune, he early procured a feat in the houfe of commons, and diftinguiftied himfelf as a wTarm partifan againft Queen Anne’s miniftry •, whofe errors he had fagacity to deteft, and fpirited eloquence to ex- pofe. When King George I. came to the throne, Mr Pulteney was made fecretary at war, and foon after cofferer to the king’s houfehold ; but the good under- ftanding between this gentleman and Sir Robert Wal¬ pole, who then afred as prime minifter, was interrupted in 1725, on a fufpicion that Walpole was defirous of extending the limits of prerogative, and of promoting the interefts of Hanover, to the prejudice of thofe of Britain. His oppofition to Sir Robert was indeed car¬ ried to fuch ind’fcriminate lengths, that fome have been of opinion he often afted againft meafures beneficial to the public, merely from perional motives. It wrould be impraflicable here to trace his parliamentary conduft : fo it muft fuffice to obferve in general, that he became fo obnoxious to the crown, that in 173 1 the king called for the council-book, and with his own hand ftruck out his name from the lift of privy-counfellors 5 a proceed¬ ing that only ferved to inflame his refentment and in- Puhenet creafe his popularity. Thus he ftill continued to at- p I' tack the minifter with a feverity of eloquence and far- , cafm that wmrfted every-antagonift j fo that Sir Robert was heard to declare, he dreaded that man’s tongue more than another man’s fword. At length, when Walpole found the place of prime minifter no longer tenable, and refigned in 1741, among other promotions Mr Pulteney refumed his place in the privy-council, and was created earl of Bath j a title purchafed at the ex¬ pence of that popularity which afterward he naturally enough afFe&ed to contemn. In 1766, toward the clofe of the war, he publiftied A Letter to two Great Men, recommending proper articles to be infilled on in a treaty of peace j which, though the writer was then unknown, was greatly applauded, and went through feveral im- preflions. He died in 1764 j and as his only fon died before him, the title became extiu£l. PULVERIZATION, the art of pulverizing, or reducing a dry body into a fine powder 5 which is per¬ formed in friable bodies by pounding or beating them into a mortar, &c. j but to pulverize malleable ones, other methods muft be taken. To pulvelize lead, or tin, the method is this : Rub a round wooden box all over the infide with chalk •, pour a little of the melted metal nimbly into the box ; when Ihutting the lid, and lhaking the box brilkly, the metal will be reduced to powder. PUMEX, the Pumice-stone. See Mineralogy Index. Pumice-ftone is ufed in fome mechanical arts j as for rubbing and fmoothing the furface of metals, wood, pafteboard, and ftone; for which it is well fitted by reafon of its harfh and brittle texture •, thus fcouring and carrying off the little inequalities from the furfa- ces juft mentioned. PUMICE-stone. See Mineralogy Index. PUMP, an hydraulic machine for raifing water by means of the preffure of the atmofphere. It would be an entertaining and not an uninftruc-of ^ tive piece of information to learn the progreflive fteps vention of by which the ingenuity of man has invented the various pumps, methods of raifing water. A pump muft be confidered as the laft ftep of this progrefs. Common as it is, and overlooked even by the curious, it is a very abftrufe and refined invention. Nothing like it has been found in any of the rude nations whom the reftlefs fpirit of the Europeans has difeovered, either in the new continent of America, or the iflands of the Pacific ocean. Nay, it was unknown in the cultivated empire of China at the time of our arrival there by fea j and it is ftill a ra¬ rity every where in Afia, in places unfrequented by the Europeans. It does not appear to have been known to the Greeks and Romans in early times ; and perhaps it came from Alexandria, where phyfical and mathemati- cal|fcience was much cultivated by the Greek fchool un¬ der the proteftion of the Ptolemies. The performances of Ctefibius and Hero are fpoken of by Pliny and Vitru¬ vius as curious novelties (a). It is perhaps not difficult to trace the fteps by which thofe mechanicians were led to (a) In the early Greek writings, it does not appear that the words avrAeo, uvr^ist, &c. were ufed to ex- prefs any thing like what we call a pump. In all thefe palfages the wrords either exprefs generally the drawing of 4 water, P U M Plate CCCOXLIX. Fig. i. 2 Ctefibius’s pump. Pump, to tLe invention. The Egyptian wheel was a com- ^ men machine all over Afia, and is ilill in ufe in the re- moteft corners, and was brought by the Saracens into Spain, where it is Hill very common under its ancient name NOR I A. The Danifli miffionaries found in a re¬ mote village in the kingdom of Siam the immediate off- fpring of the noria (Lettres Edifiantes et Curieufes). It was a wheel turned by an afs, and carrying round, not a ft ring of earthen pots, but a ftring of wifps of hay, which it drew through a wooden trunk. This rude chain-pump was in frequent ufe for watering the rice fields. It is highly probable that it is of great antiqui¬ ty, although we do not recolleft its being mentioned by any of the Greek or Roman writers. The Arabs and Indians were nothing lefs than innovators ; and we may fuppofe with great fafety, that what arts we now find among them they pofteffed in very remote periods. Now the ftep from this to the pump is but ftiort, though it is nice and refined \ and the forcing pump of Ctefibi- us is the eafieft and moil natural. Let AB (fig. i.) be the furface of the water in the well, and D the height where it is to be delivered. Let DC be a long wooden trunk, reaching as deep under water as poffible. Let the rope EF be fitted with its knot of hay F. When it is drawn up through the trunk, it will bring up along with it all the water lying between C and A, which will begin to run out by the fpout D as foon as the knot gets to G, as far below D as C is below A. All this is very obvious ; and it re¬ quired but little refleefion to be allured, that if F was let down again, or puflied down, by a rod inftead of a rope, it w'ould again perform the fame office. Here is a very fimple pump. And if it was ever put in prac¬ tice, it behoved to Iho.w the fupporting pow’er of the at- mofphere, becaufe the w^aier would not only be lifted by the knot, but wrould even follow’ it. The imper- feflion of this pump behoved to appear at firft fight, and to fuggeft its remedy. By puffiing dowm the knot F, which w’e ffiall henceforth call the pifton, all the force expended in lifting up the water between A and G is thrown away, becaufe it is again let dowm. A valve G, at the bottom, would prevent this. But then there muft be a paflage made for the water by a lateral Fig a. tube KBD (fig. 2.). And if this be alfo fumilhed with a valve H, to prevent its lofing the water, wre have the pump of Ctefibius, as IketchAl in fig. 2. The valve is the great refinement : but perhaps even this had made its appearance before in the noria. For, in the more perfefl kinds of thefe machines, the pots have a flop or valve in their bottom, which hangs open wdiile the pot defeends with its mouth downwards, and then allows it to fill readily in the ciftern : wdiereas, without the valve, it would occafion a double load to the wheel. If we fiippofe that the valve had made its appearance fo Vol. XVII. Part II. [ 497 1 P U M early, it is not improbable that the common pump Pump. Iketched in fig. 3. was as old as that of Ctefibius. In this '~v 1 place jwe fliall firft give a Ihort deferiplion of the chief Fig. 5. varieties of thefe engines, confidering them in their fim- pleft form, and we ftiall explain in very general terms their mode of operation. We ffiall then give a concile . and popular theory of their operation, furnilhing princi¬ ples to direft us in their conftruftion; and we (hall con¬ clude with the defeription of a few peculiarities which may contribute to their improvement or perfedlion. _ There are but twm forts of pumps which eftentially difter; and all the varieties that we fee are only modifi¬ cations of thefe. One of thefe original pumps has a fo~ lid pifton ; the other has a pifton with a perforation and a valve. We ufually call the firft: a forcing pump, and the fecond a lifting ©r sucking pump. Fig. 2. is a Iketch of the forcing pump in its moft Forcing fimple form and fituation. It confifts of a hollow cylin- PumP dc- der AC ca, called the working Barrel, open at both ends, and having a valve G at the bottom, opening up- Z‘ w'ards. This cylinder is filled by a folid pifton EF, co¬ vered externally with leather or tow, by which means it fits the box of the cylinder exactly, and allows no water to efcape by its fides. There is a pipe KHD, which com¬ municates laterally with this cylinder, and has a valve at fome convenient place H, as near as poffible to its junc¬ tion with the cylinder. This valve alfo opens upwards. This pipe, ufually called the rising pipe, or main, ter¬ minates at the place D, where the water muft; be deli¬ vered. Now fuppofe this apparatus fet into the wrater, jts m^cj.. 0f that the upper end of the cylinder may be under or even operation, with the furface of the water AB ; the water will open the valve G, and after filling the barrel and > lateral pipe, will alio open the valve H, and at laft ftand at an equal height within and without. Now let the pifton be put in at the top of the working barrel, and thruft down to K. It will puffi the wrater before it. This will Unit the valve G, and the water will make its wray through the valve H, and fill a part B £ of the rifing pipe, equal to the internal capacity of the working bar¬ rel. When this downward motion of the pifton ceafcs, the valve H will fall down by its own weight and {hut this paflage. Now let the pifton be drawn up again : The valve H hinders the water in the rifing pipe from returning into the working barrel. But now the valve G is opened by the preflure of the external water, and the water enters and fills the cylinder as the pifton rifes. When the pifton has got to the top, let it be thruft down again : 1 he valve G will again be (hut, and the water will be forced through the paflage at H, and rife along the main, pufliing before it the water already there, and will now have its furface at L. Repeating this operation, the water muft at laft arrive at D, how- 3 R ever water, or, more particularly, the drawing it with a bucket or fomething fimilar. ’AvrXeg, which is the primitive, is a drain, fink, or receptacle for collefting fcattered water, either for ufe, or to get rid of it ; hence it came to fig- nify the fink or well of a ffiip ; and uvrteiv ivas fynonymous with our verb “ to bale the boat.” (OdyJ/l O. 476 M, 411. Eurip. Hecuba, 1023). ’Av-rToov is the veffelor bucket with which water is drawn. 'AvrXicc is the fervice (ge¬ nerally a punilhment) of drawing water. ’Aurterj “ to draw water with a buckethence the force of Ariftotle’s expreffion (Oecon. 1.) y«£g sjfysw cJvrAziv tout’ er<. See even the late authority of the New Teftament, John ii. 8. • iv. 7. 11. Here unMpet is evidently fomething which the woman brought along with her ; probably a bucket and rope. P U M Pump. S Lifting pump. Its mods cf derating. ever remote, and the next ftroke would raife it to e ; ' fo that during the next rife of the piilon the water in eD will be running off by the fpout. The effedf is the fame whatever be the pofition of the working barrel, provided only that it be under water. It may lie horizontally or Hoping, or it may be with its mouth and pifton rod undermoft. It is Hill the fame forcing pump, and operates in the fame manner and by the lame means, viz. the preffure of the fur¬ rounding water. The external force which muff be applied to produce this effect is oppofed by the preffure exerted by the wa¬ ter on the oppolite face of the pifton. It is evident, from the common laws of hydroftatics, that this oppo- ling preffure is equal to the weight of a pillar of water, having the face of the pifton for its bafe, and the per¬ pendicular height 5j^, and —AS, =: HS, and NS : MS=HA : HS, and NS — MS : NS = HA — HS : HA, or NM : NS=AS : AH, and NM X AHzrrNS X AS. Therefore, if AN, the diftance of the pifton in its higheft pofition from the water in the ciftern, and NM the length of its ftroke, be given, there is a cer¬ tain determined height AS to which the water can be raifed by the preffure of the air : For AH is a conftant quantity •, and therefore when MN is given, the rec¬ tangle AS X SN is given. If this height AS be lefs than that of the pifton in its loweft pofition, the pump will raife no water, although AN may be lefs than AH. Yet the fame pump will raife water very effe&ually, if it be firft of all filled with water ; and we have feen profeffional engineers much puzzled by this capricious failure of their pumps. A little knowledge of the prin¬ ciples would have prevented their difappointment. To infure the delivery of water by the pump, the 00 ] P u M ftroke muft be fuch that the re61 angle MN X AH may Pump; be greater than any reftangle that can be made of the —-v— parts of AN, that is, greater than the fquare of half n AN. Or, if the length of the ftroke be already fixed Mode of in* by other circumftances, which is a common cafe, we mutt ^■^r,hef. make AN fo ftiort that the fquare of its half, meaiured ^ater/ ° in feet, (hall be lefs than 33 times the ftroke of the pi- ft on. Suppofe that the fixed valve, inftead of being at the fur face of the water in the ciftern, is at S, or anywhere between S and A, the performance of the pump will be the fame as before : But if it be placed anywhere above S, it will be very different. Let it be at T. It is plain that when the pifton is puflied down from N to M, the valve at T prevents any air from getting down j and therefore, when the pifton is drawn up again, the air contained in the fpace MT t m will expand ixto the fpace NT t n, and its denfity will be This is lefs- MS than , which expreffes the denfity of the air which was left in the fpace TSr/ by the former operations.—. I he air, therefore, in FS r t will alio expand, will open the valve, and now the water will rife above S. The proportion of NS to NT may evidently be fuch that the water will even get above the valve T. This diminifties the Ipace N T t n ; and therefore, when the pitton has been puttied down to M, and again drawn up to N, the air will be ftill more rarefied, and the water will rife ft ill higher. The foregoing reafoning, however, is fuffici- ent to ftiow that there may ftill be a height which the water will not pafs, and that this height depends on the proportion between the ftroke of the pifton and its dif¬ tance from the water in the ciftern. We need not give the determination, becaufe it will come in afterwards in combination with other circumftances. It is enough that the reader fees the phyfical caufes of this limitation; And, laftly, we fee plainly that the utmoft fecurity will be given for the performance of the pump, when the fixed valve is fo placed that the pifton, when in its low- eft pofition, ftiall come into contadb with it. In this Valves not cafe, the rarefablion of the air will be the completeft eafily poflible ; and, if there were no fpace left between the m-tigh- pifton and valve, and all were perfe&ly air-tight, the rarefadtion would be complete, and the valve might be any thing lefs than 33 feet from the furface of the water in the ciftern. But this perfedl contact and tightnefs is unattainable ^ and though the pump may be full of water, its conti¬ nual downward preffure caufes it to filtrate flowly through every crevice, and the air enters through every pore, and even difengages itfelf from the water, with which a confiderable portion had been chemically com¬ bined. The pump by this means lofes water, and it requires feveral ftrokes of brilk working to fill it again : and if the leathers have become dry, fo much admiffion may be given to the air, that the pump will not fill it¬ felf with water by any working. It is then neceffary to pour water into it, which ftiuts up ibefe paffages, and foon fets all to rights again. For thefe reafons, it is al¬ ways prudent to place the fixed valve as low as other circumftances will permit, and to make the pifton rod of fuch a length, that when it is at the bottom of its ftroke it ftiall be almoft in contadl with the valve. When we P U M [ 5° ,3 Defcrip- tioa of the fucking- pump. F>S- 5- Pamp. we are not limited by oilier circusnftances, it is evident that the bell podible form is to have both the pifton and the fixed valve under the furface of the water of the cif- tern. In this fituatibn they are always wret and air¬ tight. The chief objection is, that by this difpolition tlity are not eafily come at wdien needing repair, fj'his is a rr. .'erial objection in deep mines, in fuch fituations, therefore, we mutt make the belt compenfation of differ¬ ent circumstances that we can. It is ufual to place the fixed valve at a moderate diltance from the furface of the water, and to have a hole in the fide of the pipe, by which it may be got out. This is carefully Ihut up by a plate firmly ferewed on, with leather or cement be¬ tween the parts. This is called the c/ac& door. It would, in every cafe, be very proper to have a fixed valve in the lower end of the pipe. This would com¬ bine all advantages. Being always tight, the pipe would retain the water, and it would leave to the valve above it its full effebl of increafing the rarefadlion. A fimilar hole is made in the working barrel, a little above the higheft pofition of the pilton. When this needs repair, it can be got at through this hole, without the immenfe trouble of drawing up the whole rods. Thus we have conducted the reader Hep by flep, from the fimplell form of the pump to that which long expe¬ rience has at laft felefted as the moil generally conve¬ nient. This we Ihall now deferibe in lome detail. The Sucking Pump confifts of two pipes DCCD, BAAB (fig. 5.) ; of which the former is called the Bar¬ rel, or the Working Barrel, and the other is called the SuSiwn-plpe, and is commonly of a fmaller diameter.— Thefe are joined by means of Handles E, F, pierced with holes to receive ferewed bolts. A ring of lea¬ ther, or of lead, covered with a proper cement, is put between them 5 which, being Ifrongly compreffed by the ferew-bolts, renders the joint perfedly air-tight.— The lower end A of the fudion-pipe is commonly fpread out a little to facilitate the entry of the w7ater, and fre¬ quently has a grating acrofs it at A A to keep out filth or gravel. This is immerged in the Handing water YZ. The working barrel is cylindrical, as evenly and fmooth- ly bored as poflible, that the piflon may fill it exactly through its whole length, and move along it with as little friction as may be confifient wfith air-tightnefs. The pifion is a fort of truncated cone OPKL, gene¬ rally made of wood not apt to fplit, fuch as elm or beech. The fmall end of it is cut off at the fides, fo as to form a fort of arch OQ(P, by w’hich it is fatt¬ ened to the iron rod or fpear. It is exhibited in differ- Fig, 6. and ent petitions in figures 6, 7. which will give a more di- 7- Hind notion of it than any defeription. The two ends of the conical part may be hooped with brafs. This cone has its larger end furrounded with a ring or band of ftrong leather fattened with nails, or by a copper hoop, w'hich is driven on it at the fmaller end. This band ffiould reach to feme diHance beyond the bafe of the cone ; the farther the better : and the whole mufl be of uniform thicknefs all round, fo as to fuffer equal 14 compreffion between the cone and the working barrel. Ncceinty ol Xhe feam or joint of the two ends of this band muH a^ughf- macje very dote^ but not fewed or Hitched together, prcpeily at- This would occafion bumps or inequalities, which would tended to. fpoH its tightnefs •, and no harm can refult from the want of it, becaufe the two edges will be fqueezed clofe to¬ gether by the compreffion in the barrel. It is by no Pump. 15 I ] P U M means neceffary that this comprefiion be great. This is a very detrimental error of the pump-makers. It occafions enormous friftion, and deHroys the very pur- pofe which they have in view, viz. rendering thfc piiion air-tight ; for it caufes the leather to wear through very loon at the edge of the cone, and it alfo wears the working barrel. This very toon becomes wide in that part which is continually paffed over by the pifion, while the mouth remains of its original diameter, and it be¬ comes impoffible to thruft in a piflon which thall com¬ pletely fill the worn part. Now, a very moderate pref- An eafy fare is fufficient for rendering the pump perfectly tight, m(X*e ot~ and a piece of glove leather would be fuflicient for this’tn^er^n2 purpofe, if loote or detached from the folid cone 5 for fuppofe fuch a loofe and flexible, but impervious, band of leather put round the piflon, and put into the barrel j and let it even be fuppoted that the cone does not com- prefs it in the fmallelt degree to its internal furface.— Pour a little water carefully into the infide of this fort of cup or diih ; it will caufe it to fvvell out« little, and apply itfelf clofe to the barrel all round, and even adjufi itfelf to all its inequalities. Let us fuppofe it to touch the barrel in a ring ol an inch broad all round. We can eafily compute the force with which it is prel- fed. It is half the weight of a ring of water an inch deep and an inch broad. This is a trifle, and the fric¬ tion occafioned by it not worth regarding j yet this trifling preffure is fuflicient to make the paffage per- ftclly impervious, even by the molt enormous preflure of a high column of incumbent water : for let this preffure be ever fo great, the preffure by which the lea¬ ther adheres to the barrel always exceeds it, becaufe the incumbent fluid has no preponderating power by which it can force its way between them, and it mufi inlinuate itfelf precifely fo far, that its preffure on the inflde of the leather fhall Hill exceed, and only exceed, the pref¬ fure by which it endeavours to infinuate itfelf; and thus the pilton becomes perfe — a Therefore when b, — a B—b B — b B B B b is lefs than the water_ But when will flop before it reaches the fixed valve. (i is lefs than tt b, the water will get above the B fixed valve, y becoming negative. Put-ip. But, P U M [ 503 ] P U M Pump. 20 The fame pump is ufed in an inverted pofition; Fig. 11. 21 and is cal¬ led a lift¬ ing pump. 22 Forcing- pump de- fcribed. Fig. 12. Eut it does not follow that the water will reach the pifton, that is, will rife fo high that the pifton will pafs through it in its defcent. Things now come into the condition of a pump of uniform dimenfions from top to bottom ) and this point will be determined by what was laid when treating of fuch a pump. There is another form of the fucking pump which is much ufed in great water works, and is of equal effi¬ cacy with the one now defcribed. It is indeed the famd pump in an inverted pofition. It is reprefented in fig. 11. where ABCD is the working barrel, im- merfed, with its mouth downwards, in the water of the ciltern. It is joined by means of tlanches to the riling pipe or main. This ufually confifls of two parts. The firft, BEFC, is bent to one fide, that it may give room for the iron frame TXYV, which carries the rod NO of the pifton M, attached to the traverfes RS, TOY of this frame. The other part, EGHF, is ufually of a lefs diameter, and is continued to the place of delivery. The pifton frame XTVY hangs by the rod Z, at the arm of a lever or working beam, not brought into the figure. The pifton is perforated like the former, and is furrounded like it with a band of leather in form of a taper-difti. It has a valve K on its broad or upper bafe, opening when preffed from below. The upper end of the work¬ ing barrel is pierced with a hole, covered with a valve 1, alfo opening upwards. Now fuppofe this apparatus immerfed into the ci- ftern till the water is above it, as marked by the line 2, 3, and the pifton drawn up till it touch the end of the barrel. When the pifton is allowed to defeend by its own weight, the water rifes up through its valve K, and fills the barrel. If the pifton be now drawn up by the moving power of the machinery with which it is conneffed, the valve K fhuts, and the pifton puthes the water before it through the valve I into the main-pipe EFGH. When the pifton is again let down, the valve I fhuts by its own weight and the preftiire of the water incumbent on it, and the barrel is again filled by the water of the ciftern. Drawing up the pifton pufhes this water into the main pipe, &c. and then the water is at length delivered at the place required. This pump is ufually called the lifting pump ; perhaps the fimpleft of all in its principle and operation.— It needs no farther explanation : and we proceed to de- feribe The Forcing Pump, reprefented in fig. 12. It confifts of a working barrel ABCD, a fuftion-pipe CDEF, and a main or rifing pipe. This laft is ufually in three joints. The firft GHKI may be confidered as making part of the working barrel, and is commonly caft in one piece with it. The fccond IKLM is join¬ ed to it by flanches, and forms the elbow which this pipe muft generally have. The third LNOM is pro¬ perly the beginning of the main, and is continued to the place• of delivery. At the joint IK there is a hanging valve or clack S ; and there is a valve R on the top of the fuftion-pipe. The pifton PQTV is folid, and is faftened to a flout iron rod which goes through it, and is fixed by a key drawn through its end. The body of the pifton is a fort of double cone, widening from the middle to each end, and is covered with two bands of very ftrong lea¬ ther, fitted to it in the manner already deferibed. The operation^ of this pump is abundantly fimple. Pump. When the pifton is thruft into the pump, it puflies the v—-1 air before it through the valve S, for the valve R re- 23 mains ftmt by its own weight. When it has reached ^ mode near the bottom, and is drawn up again, the air which filled the fmall fpace between the pifton and the valve S now expands into the barrel ; for as foon as the air begins to expand, it ceafes to balance the preffure of the atmofphere, which therefore ftiuts the valve S. By the expanfion of the air in the barrel the equilibrium at the valve R is deftroyed, and the air in the lu&ion-pipe lifts the valve, and expands into the barrel ; confequent- ly it ceafes to be a balance for the preffure of the atmo¬ fphere, and the water is forced into the fuftion-pipe. Puftiing the pifton down again forces the air in the bar¬ rel through the valve S, the valve R in the mean time {hutting. When the pifton is again drawn up, S {huts, R opens, the air in the fudlion pipe dilates anew, and the water riles higher in it. Repeating thefe operations, the water gets at laft into the xvorking barrel, and is forced into the main by puftiing down the pifton, and is puflied along to the place of delivery. The operation of this pump is therefore two-fold, is twafolt?, fucking and forcing. In the firft operation, the fame force muft be employed as in the fucking-pump, name¬ ly, a force equal to the weight of a column of water having the feftion of the pifton for its bafe, and the height of the pifton above the water in the ciftern for its height. It is for the fake of this part of the opera¬ tion that the upper cone is added to the pifton. The air and water would pafs by the fides of the lower cone while the pifton is drawn up; but the leather of the upper cone applies to the furface of the barrel, and pre¬ vents this. The fpace contained between the barrel and the valve S is a great obftruftion to this part of the operation, becaufe this air cannot be rarefied to a very great degree. For this reafon, the fueftion-pipe of a forcing-pump muft^ not be made long. It is not in¬ deed neceflary 5 for by placing the pump a few feet lower, the water wall rife into it without difficulty, and the labour of fuftion is as much diminiftied as that of im- pulfion is increafed. However, an intelligent artift; will always endeavour to make this fpace between the valve S and the loweft place of the pifton as fmall as poftible. The power employed in forcing muft evidently fur- mount the preflure of the whole water in the rifing pipe, and (independent of what is neceffary for giving the water the required velocity, fo that the proper quantity per hour may be delivered), the pifton has to withftand a force equal to the weight of a column of water having the feffion of the pifton for its bafe, and the perpendicular altitude of the place of delivery above the lower furface of the pifton for its height. It is quite indifferent in this refpeft what is the diameter of the rifing pipe; becaufe the preffure on the pifton de¬ pends on the altitude of the water only, independent of its quantity. We {hall even fee that a fmall rifing pipe will require a greater force to convey the water along it to any given height or diftance. When w’e would employ a pump to raife water in a crooked pipe, or in any pipe of moderate dimenfions, this form of pump, or fomething equivalent, muft be ufed. In bringing up great quantities of water from mines, the common fucking-pump is generally employ¬ ed,. Pnmn. ~S Meafure of the quanti¬ ty of water delivered by any pump. 16 The opera¬ tion of pumps not equable; •27 andithe mode of making them fo. &£■ 13- P U M [5 eel, as really the beft of them all; but it is the moft ex¬ pensive, becaufe it requires the pipe to be perpendicular, Straight, and of great dimenlions, that it may contain the pifton rods. Eut this is impracticable when the pipe is crooked. If the forcing pump, conftrufted in the manner now deferibed, be employed, we cannot ufe forcers with long rods. ’Iheie would bend wiien puthed down by their further extremity. In this cafe, it is ufual to employ only a fhort and ftiff rod, and to hang it by a chain, and load it with a weight fupenor to the weight of wa¬ ter to be raifed by it. The machinery therefore is em¬ ployed, not in forcing the water along the rifing-pipe, but in railing the weight which is to produce this effect by its fubfequent defeent. In this cale, it would be much better to employ the lifting-pump of fig. 11. For as the load on the forcers muff be greater than the refiftances which it muff fur- mount, the force exerted by the machine muff in like manner be greater than this load. This double excefs ■would be avoided by ufing the lifting-pump. It will readily occur to the reader that the quantity of water delivered by any pump will be in the joint pro¬ portion of the furface or bafe of the pifton and its veloci¬ ty : for this meafures the capacity of that part of the working barrel which the pifton paffes over. The velo¬ city of the water in the conduit pipe, and in its paffage through every valve, will be greater or lefs than the ve¬ locity of the pifton, in the fame proportion that the area oi the pifton or working barrel is greater or lefs than the area of the conduit or valve. For whatever quantity of water paffes through any feclion of the wrorking-barrel in a fecond, the fame quantity muft go through any one of thefe pallages. This enables us to modify the velocity of the water as we pleafe : rve can increafe it to any de¬ gree at the place of delivery by diminilhing the aperture through which it paffes, provided we apply fufficient force to the pifton. It is evident that the operation of a pump is by ftarts, and that the water in the main remains at reft, prefling on the valve during the time that the pifton is withdrawn from the bottom of the working barrel. It is in moft cafes definable to have tins motion equable, and in fome cafes it is abfolutely neceffary. Thus, in the engine for extinguifhing fires, the fpout of water going by jerks could never be dire&ed with a certain aim, and half of the water would be loft by the way; becaufe a body at reft cannot in an inftant be put in rapid motion, and the firft portion of every jerk of water would have but a fmall velocity. A very ingenious contrivance has been fallen upon for obviating this inconvenience, and pro¬ curing a ftream nearly equable. We have not been able to difeover the author. At any convenient part of the fifing pipe beyond the valve S there is annexed a capa¬ cious veffel VZ (fig. 13. N° 1 and 2.) clofe a-top, and of great ftrength. When the water is forced along this pipe, part of it gets into this veffel, keeping the air con¬ fined above it, and it fills it to fuch a height V, that the elafticity of the confined air balances a column reaching to T, we {hall fuppofe, in the rifing pipe. The next ffroke of the pifton fends forward more water, which would fill the rifing pipe to fome height above T. Eut the preffure of this additional column caufes fome mere of it to go into the air veffel, and comprefs its air fo much more that its elafticity now balances a longer co- 2 =4 ] P U M lumn. Every fuccceding ftroke of the pifton produces a Pump. like efteft. ihe water riles higher in the main pipe, but v~~ lome more of it goes into the air-veffel. At laft tire wa¬ ter appears at the place of delivery j and the air in the air-veffel is now fo much compreffed that its elafticity balances the preffure ol tne wliole column. 1 fie next ftroke of the pifton fends forward fome more water. If the diameter of the orifice of the main be fufficient to let the water flow out with a velocity equal to .that of the pifton, it will fo flow out, rifing no higher, and* pro¬ ducing no lenfible addition to the compreffion in the air-veflel. Eut it the orifice of the main be contract¬ ed to_ half its dimenflons, the water fent forward by the pifton cannot How out in the time of the ftroke without a greater velocity, and therefore a greater force. Part of it, therefore, goes into the air-veffel, and increafes the compreffion. When the pifton has ended its ftroke, and no more water comes forward, the compreffion of the air in the air-veffel being great¬ er than what was fufficient to balance the prellure of the water in the main pipe, now forces out fome of the water which is lying below it. This cannot return towards the pump, becaufe the valve S is now {hut. It therefore goes forward along the main, and produces an efflux during the time of the pifton’s rifing in or¬ der to make another ftroke. In order that this efflux may be very equable, the air-veflel muft be very large. If it be. fmall, the quantity of water that is difeharged by it during the return of the pifton makes fo great a por¬ tion of its capacity, that the elafticity of the confined air is too much diminifhed by this enlargement of its bulk, and the rate of efflux muft diminiih accordingly. The capacity of the air-veffel ftiould be fo great that the change of bulk of the comprefled air during the inac¬ tion of the pifton may be inconfiderable. It muft there¬ fore be very ftrong. It is pretty indifferent in what way this air-veflel is connefted with the rifing pipe. It may join it lateral¬ ly, as in fig. 13. N° 1. and the main pipe go on with¬ out interruption} or it may be made to furround an interruption of the main pipe, as in fig. 13. N° 2. It may alfo be in any part of the main-pipe. If the foie ef¬ fect intended by it is to produce an equable jet, as in ornamental water-works, it may be near the end of the main. This will require much lefs ftrength, becaufe there remains but a fliort column of water to comprefs the air in it. But it is, on the whole, more advanta¬ geous to place it as near the pump as poffible, that it may pioduce an equable motion m the whole main-pipe. 1 his is of confiderable advantage : when a column of water feveral hundred feet long is at reft in the main- pipe, and the pifton at one end of it put at once into motion, even with a moderate velocity, the ftrain on the pipe would be very great. Indeed if it were poffible to put the pifton inftantaneoufty into motion with a finite velocity, the ftrain on the pipe, tending to burft it, would be next to infinite. But this feems impoflible in nature ; all changes of motion which we obferve are gra- dual, .becaufe all impelling bodies have lome elafticity tion o}°~ or foftnefs by which they yield to compreffion. And,the piftons in the way in which piftons are commonly moved, vrz. by cranks, or fomething analogous to them, the motion is v -nj fLnfebhj' gradual. But ftiil the air-veffel tends to make the motion along the main-pipe lefs deffiltorv, and therefore diminifties thofe ftrains which would really take place 28 The deful- Pump. ■“~v— P U M [ 505 ] place in the mum pipe. It a£ls like the fprings of a foot high 29 Corrected 30 But on a wrong prin ciple. Thefe'equa- bie pumps deliver very tittle more water than the others. travelling-carriage, whofe jolts are incomparably lefs than thole of a cart j, and by this means really enables a given force to propel a greater quantity of water in the lame time. We may here by the way obferve, that the attempts of mecnamcians to correct this unequal motion of the pikon-rod are mifplaced, and it it could be done, would greatly hurt a pump. One of the bell methods of pro¬ ducing this effeft is to make the pifton-rod confift of tivo parallel bars, having teeth in the lides which front each otner. Let a toothed wheel be placed between them, having only the half of its circumference furnilhed with, teetn. It is evident, without any farther delcription, that if this wheel be turned uniformly round its axis, the pifton-rod will be moved uniformly up and down with¬ out intermiftion. 1 his has often been put in practice ; but the machine always went by jolts, and feldom lafted a few' days, tlnfldlled mechanicians attributed this to defect in the_ execution: but the fault is effential, and lies in the principle. 3 he machine could not perform one ftroke, if the in ft mover did not flacken a little, or the different parts Ci the machine did not yield by bending or by compref- fion ; and no ftrength of materials could withftand the violence of the ftrains at every reciprocation of the mo¬ tion. This is chiefly experienced in great works which aie put m motion by a water-wheel, or fome other equal power exerted on the mafs of matter of which the machine confifts. The water-wheel being of great weight, moves with confiderable fteadinefs or unifor¬ mity ; and when an additional refiftance is oppofed to it by the beginning of a new ftroke of the pifton, its great quantity of motion is but little affected by this addition, and it proceeds very little retarded ; and the machine rnuft either yield a little by bending and com- preiTun, or go to pieces, which is the common event. Cranks are free from this inconvenience, becaufe they accelerate the pifton gradually, and bring it gradually to reft, while the water-wheel moves round with almoft perfect uniformity. The only inconvenience (and it may be confiderable) attending this flow motion of the pftton at the beginning of its ftroke is, that the valves do not flint with rapidity, fo that fome water gets back through them. But wflien they are properly formed and loaded, this is but trifling. We muft not imagine, that becaufe the ftream pro¬ duced by the afliftance of an air barrel is almoft per¬ fectly equable, and becaufe as much water runs out du¬ ring the returning of the pifton as during its a&ive ftroke, it therefore doubles the quantity of water. No more water can run out than what is fent forward by the pifton during its effective ftroke. The continued ftream is produced only by preventing the whole of this water from being difeharged during this time, and by providing a propelling force to act during the pifton’s return. Nor does it enable the moving force of the pi¬ fton to produce a double effect: for the compreflion which is produced in the air-veffel, more than what is necefary for merely balancing the quiefeent column of water, reacts on the pifton, refifting its compreflion juft as much as the column of water would do which pro¬ duces a velocity equal to that of the efflux,' Thus if the water is made to fpout with the velocity of eight feet per fgcond, this would require an additional column of one Vox.. XVII. Part II. PuniB, P U M and this would juft balance the compreftion in me air-veffel, which maintains this velocity during tne noa-a£tion of the pifton. It is, however, a matter of iadt, that a pump furniftied with an air-veffel delivers a little more water than it would do without it. But the difference depends on the combination of many very diflimilar circumftances, which it is extremely difficult to bring into calculation. Some of thefe will be men¬ tioned afterwards. To deferibe, or even to enumerate, the immenfe va¬ riety of combinations of thefe three Ample pumps would fill a volume. We ftiall feledt a few, which are more deferving of notice. . f- common fucking-pump may, by a fmall ad-The fuck- dition, be converted into a lifting-pump, fitted for pro-’ngPump pelling the water to any diftance, and with any Velo-converted City, J into a lift¬ ing pump. Fig. 14. Fig. 14. is a fucking-pump, whofe working-barrel ACDB has a lateral pipe AEGHF connected with it clofe to the top. This terminates in a itiain or rifing pipe IK, furniftied or not with a valve L. The lop of the barrel is ftmt up by a ftrong plate MN, having a hollow neck terminating in a fmall flanch. The pifton rod QR paffes through this neck, and is nicely turned and polifhed. A number of rings of leather are put over the rod, and ftrongly compreffed round it by ano¬ ther flanch and feveral ferewed bolts, as is reprefented at OP. By this contrivance the rod is clofely grafped by the leathers, but may be eafily drawn up and down, while all pafiage of air or water is effectually pre¬ vented. The pifton S is perforated, and furniftied with a valve opening upwards. There is alfo a valve T on the top of the fu&ion-pipe YX j and it will be of ad¬ vantage, though not abfolutely neceffary, to put a valve L at the bottom of the rifing pipe. Now fuppofe the pxfton at the bottom of the working-barrel. When it Is drawn up, it tends to comprefs the air above it, be¬ caufe the valve in the pifton remains fimt by its own weight. The air therefore is driven through the valve L into the. rifing pipe, and efcapes. In the mean time, the air which occupied the fmall fpace between the pi¬ fton and the valve T expands into the upper part of the working barrel j and its elafticity is fo much dimi- nilhed thereby, that the atmofphere preffes the water of the ciftem into the fu&ion-pipe, where it will rife till an equilibrium is again produced. The next down¬ ward ftroke of the pifton allows the air, which had come fiom the fu&ion-pipe into the barrel during the afeent of the pifton, to get through its valve. Upon drawing up the pifton, this air is alfo drawn off through the rifing pipe. Repeating this procefs brings the wa¬ ter at laft into the working-barrel, and it is then driven along the rifing-pipe by the pifton. This is one of the bed forms of a pomp. The ra-AJv"ta rera&ion may be very perfe&, becaufe the pifton canof this con- be brought fo near to the bottom of the working-verfian. barrel: and, for forcing water in oppofition to great preffures, it appears preferable to the common forcing- pump ; becaufe in that the pifton rods are compreffed and expofed to bending, which greatly hurts the pump by wearing the pifton and barrel on one fide. This foon renders it lefs tight, and much water fquirts out by the fides of the pifton. But in this pump the piften rod is always drawn or pulled, which keeps it ftraight} 3 $ and 33 P U ,M [ 506 ] P U M nations. Pump, and rods exert a much greater force in oppolition to a J pull than in oppolition to compreffion. The collar of leather round the pifton-rods is found by experience to need very little repairs, and is very impervious to water. The whole is very acceffible for repairs j and in this re- fpefl much preferable to the common pump in deep mines, where every fault of the pifton obliges us to draw up fome hundred feet of pifton-rods. By this addition, too, any common pump for the fervice of a houfe is converted into an engine for extinguilhing fire, or may be made to convey the water to every part of the houfe ; and this without hurting or obftructing its common ufes. All that is neceffary is to have a large cock on the upper part of the working barrel oppo- fite to the lateral pipe in this figure. This cock ferves for a fpout when the pump is ufed for common pur- pofes : and the merely Ihutting this cock converts the whole into an engine for extinguilhing fire or for fup- plying diftant places with water. It is fcarcely necef¬ fary to add, that for thefe fervices it will be proper to conned! an air-velfel with fome convenient part of the * riling pipe, in order that the current of the water may 34 be continual. Equable We have frequently fpoken of the advantages of a ftreamspro- continued current in the main pipe. In all great works ^reat^worksa con^ c- fecj form which its own weight will give it by drawing up the pifton-rod, its capacity will be enlarged, the valve F will be (hut by its own wreight, the air in the bag will be rarefied, and the atmofphere will prefs the water into the bag. When the rod is thruft down again, this water will come out by the valve F, and fill part of the trunk. A repetition of the operation will have a fimilar effed ; the trunk will be filled, and the water will at laft be difcharged by the fpout. Here is a pump without fri&ion, and perfectly tight. For the leather between the folds of canvas renders the bag impervious both to air and water. And the can¬ vas has very confiderable ftrength. We know from experience that a bag of fix inches diameter, made of fail-cloth N° 3. with a fheep (kin between, will bear a column of 15 feet of water, and ftand fix hours work per day for a month without failure, and that the pump is confiderably fuperior in effeft to a common pump of the fame dimenfions. We mutt only obferve, that the length of the bag mutt be three times the intended length of the ftroke; fo that when the pifton-rod is in its higheft pofition, the angles or ridges of the bag may Pump. be pretty acute. If the bag be more ftretched than' r—4 this, the force which mult be exerted by the labourer becomes much greater than the weight of the column of water which he is railing. If the pump be laid aflope, which is very ufual in thefe occafional and hafty drawings, it is neceffary to make a guide for the pifton- rod within the trunk, that the bag may play up and down wulhout rubbing on the fides, wdiich would quick¬ ly wear it out. The experienced reader will fee that this pump is very like that of Goffet and De la Deuille, defcribed by Belidor, vol. ii. p. 120. and moll writers on hydraulics. It wmuld be ftill more like it, if the bag w^ere on the under fide of the partition E, and a valve placed farther down the trunk. But we think that our form is great¬ ly preferable in point of flrength. When in the other fituation, the column of water lifted by the pifton tends to burjl the bag, and this with a great force, as the intelligent reader well knows. But in the form re¬ commended here, the bag is comprejfed, and the ftrain on each part may be made much lefs than that which tends to burft a bag of fix inches diameter. The nearer the rings are placed to each other the fmaller will the ftrain be. The fame bag-pifton may be employed for a forcing pump, by placing it below the partition, and inverting the valve ; and it will then be equally ftrong, becaule the refiftance in this cafe too will aft by compreflion. We now come naturally to the confideration of the different forms which may be given to the pifton s and valves of a pump. A good deal of what we have been defcribing already is reducible to this head; but, having a more general appearance, changing as it were the whole form and ftrufture of the pump, it wras not im¬ proper to keep thefe things together. The great defideratum in a pifton is, that it be aspifto^ tight as. poflible, and have as little friftion as is confiftent fhoutd have* with this indifpenfable quality. We have already faid, little fric- that the common form, when carefully executed, hasti<,n- thefe properties in an'eminent degree. And according¬ ly this form has kept its ground amidft all the improve¬ ment which ingenious artifts have made. Mr Belidor, an author of the firfi: reputation, has given the defcrip¬ tion of a pifton which he highly extols, and is undoubt¬ edly a very good one, conftrufted from principle, and extremely well compofed. . It confifts of a hollow cylinder of metal g h (fig. 22.) An impro- pierced wdth a number of holes, and having at top av Pump. 6j Advanta¬ ges of tins piiton. 63 Another ingenious and ufeful pifton de- icribed. Fig- 31- 64 Another on a different principle. Fig. 32. 6S Its advan¬ tages. p u m r 5 and large water-way. The form of the valve (which has given it the name of the butterfly-valve) is extreme¬ ly favourable to the paffage of the water 5 and as it has but half the motion of a complete circular valve, lefs wa¬ ter goes back while it is (hutting. The following pifton is alio ingenious, and has a good deal of merit. OPPO (fig. 31.) is the box of the pifton, having a perforation covered above with a flat valve K, which refts in a metal plate that forms the top of the box. ABC BA is a ftirrup of iron to which the box is fixed by ferews c, a, a, a, whofe heads are funk in the wood. This ftirrup is perforated at C, to receive the end of the pifton-rod, and a nut H is fere wed on below to keep it fart. DEFED is another ftirrup, whofe lower part at DD forms a hoop like the foie of a ftirrup, which embraces a fmall part of the top of the wooden box. The lower end of the pifton-rod is ferewed 5 and before it is put into the holes of the two ftirrups (through which holes it Hides freely) a broad nut G is fcrew'ed on it. It is then put into the holes, and the nut H firmly fevewed up. The packing RR is then wound about the pifton as tight as pofiible till it completely fills the working barrel of the pump. When long ule has rendered it in any degree loofe, it may be tightened again by ferewing down the nut G. This caufes the ring DD to comprefs the packing be¬ tween it and the projediing (boulder of the box at PP; and thus caufes it to fwell out, and apply itfelf clofely to the barrel. We (hall add only another form of a perforated pifton; which being on a principle different trom all the prece¬ ding, will fuggeft many others; each of which will have its peculiar advantages. GO in fig. 3 2. reprefents the box of this pifton, fitted to the working barrel in any of the preceding ways as may be thought beft. AB is a crofs bar of four arms, which is fixed to the top of the box. CF is the pifton-rod going through a hole in the middle of AB, and reaching a little way beyond the bottom of the box. It has a (boulder D, which prevents its going too far through. On the lower end th ere is a thick metal plate, turned conical on its upper fide, fo as to fit a conical feat PP in the bottom of the pifton-box. When the pifton-rod is pufhed down, the friftion on the barrel prevents the box from immediately yielding. The rod therefore (lips through the hole of the crofs bar AB. The plate E, therefore, detaches itfelf from the box. When the (boulder D preffes on the bar AB, the box muft yield, and be puffed down the bar¬ rels, and the water gets up through the perforation. When the pifton rod is drawn up again, the box does not move till the plate E lodge in the feat PP, and thus (huts the water-way ; and then the pifton lifts the water which is above it, and afts as the pifton of a fucking pump. 1 his is a very fimple and effedlive conftruclion, and makes a very tight valve. It has been much recom¬ mended by engineers of the firft reputation, and is frequently uled ; and from its fimplicity, and the great folidity of which it is capable, it feems very fit for great works. But it is evident that the water-way is limited to lefs than one-half of the area of the workinrr- barrel. For if the perforation of the pifton be one-half of the area, the diameter of the plate or ball EF muft 12] P u M be greater; and therefore lefs than half the area will Pump, be left for the paflage of the water by its ndes. ' v— WTe come now to confider the ierms which may be {r given to the valves of a hydraulic engine. tioiisoa" The requilites of a valve are, that it (hall be tight, valves, of fufficient ftrength to refill the great 'preffures to which it is expoied, that it afford a (ufticient paflage for the water, and that it do not allow much to go back while it is (hutting. Wre have not much to add to what has been faid al- c!ar£7 ready on this fubjecl. The valves which accompany valves, the pump of fig. 5. are called clack valves, and are of all the moft obvious and common 5 and the conli rudtion deferibed on that occafion is as perfedl as any. We on¬ ly add, that as the leather is at laft deftroyed at the hinge by fuch inceffant motion, and it is troublefome, efpecially in deep mines, and under water,' to undo the joint of the pump in order to put in a new valve, it is frequently annexed to a box like that of a pifton, made a little conical on the outfide, (o as to (it a conical feat made for it in the pipe, as reprefented in fig. 33. and it pj has an iron handle like that of a balkct, by which it can ^ be laid hold of by means of a long grappling-hook let down from above. Thus it is drawn up ; and being very gently tapered on the (ides, it (licks very fail in its place. The only defect of this valve is, that by opening Defea itt very wide when puflied up by the ftream of water, it them, allows a good deal to go back during its (hutting again. In fome great machines which are worked by a (low turning crank, the return of the pifton is fo very (low, that a fenfible lofs is incurred by this; but it is nothing like what Dr Delaguliers fays, one-half of a cylinder whofe height is equal to the diameter of the valve For in fuch machines, the laft part of the upward ftroke is equally flow, and the velocity of the water through the valve exceedingly fmall, fo that the valve is at this time almoft (hut. ^ rJ he butterfly-valve reprefented in figures 29, &c. is Utility of free from mott of thofe inconveniences, and items the tlK bmter- moft perfect of the clack valves. Some engineers make %-vaIve‘ their great valves of a pyramidal form, confiding of four clacks, whofe hinges are in the circumference of the water-way, and which meet with their points in the middle, and are fupporied by four ribs which rife up from the (ides, and unite in the middle. This is an ex¬ cellent form, affording the moft fpacious water-way, and (hutting very readily. It feems to be the beft pof- fible for a pifton. The rod of the pifton is branched out on four fides, and the brandies go through the pi¬ fton-box, and are faftened below with ferews. Thefe branches- form the fupport for the four clacks. We have feen a valve of this form in a pump of fix feet di¬ ameter, which difeharged 20 hogffeads of water every ftroke, and made 12 ftrokes in a minute, railing the wa¬ ter above 22 feet. There is another form of valve, called the button or Button tail valve. It confifts of a plate of metal AB (fig. 34.) valves, turned conical, fo as exaftly to fit the conical cavity a b Fig. 34. of its box. A tail CD projecls from the under Vide, which paffes through a crofs bar EF in the bottom of the box, and has a little knob at the end, to hinder the valve from rifing too high. This valve, when nicely made, is unexceptionable. It 2 Pump. Though fomewhat imperfedl iii the wa ter-way. 73 A very fim pie valve defcribed. FiS- 35- 74 A valve by Belidor uniting e- very requi- iite. 75 Another valve on the fame principle. % 3 k P U M [ 5 It has great ftrength, and is therefore proper for all fe- ' vere (trains, and it may be made perfectly tight by grinding. ^ Accordingly it is ufed in all cafes where this is of indifpenfable conference. It is moft durable, and the only kind that will do for paflages where (team or hot water is to go through. Its only imperfection is a fmall water-way; which, from what has been faid, cannot exceed, or indeed equal, one^half of the area of the pipe. If we endeavour to enlarge the water-way, by giving the cone very little taper, the valve frequently (ticks fo fait in the feat that *no force can detach them.— And this fometimes happens during the working of the machine ; and the jolts and blows given to the machine in taking it to pieces, in order to difcover what has been the reafon that it has dilcharged no water, fre¬ quently detach the valve, and we find it quite loofe, and cannot tell what has deranged the pump. When this is guarded againft, and the diminution of the water- way is not of very great eonfequence, this is the bed form of a valve. Analogous to this is the fimplefl: of all valves, repre- fented in fig. 35. It is nothing more than a fphere of metal A, to which is fitted a feat with a fmall portion EC of a fpherical cavity. Nothing can be more effec¬ tual than this valve ; it always falls into its proper place, and in every pofition fits it exaftly. Its only imperfeffion is the great diminution of the water-way. If the diameter of the fphere does not confiderably ex¬ ceed that of the hole, the touching parts have very little taper, and it is very apt to (lick faft. It oppofes much lefs refiftance to the paffage of the water than the flat under-furface of the button-valve. N. B. It would be an improvement of that valve to give it a taper-fhape below like a boy’s top. The fpherical valve mult not be made too light, otherwife it will be hurried up by the water, and much may go back while it is returning to its place. Belidor defcribes with great minutenefs (vol. ii. p. 22i, &c.) a valve which unites every requifite. But it is of fuch nice and delicate coriftruftion, and its de¬ fers are fo great when this exa&nefs is not attained, or is impaired by ufe, that we think it hazardous to in¬ troduce it into a machine in a fituation where an intel¬ ligent and accurate artifl is not at hand. For this reafon we have omitted the defcription, which cannot be given in few words, nor without many figures; and defire our curious readers to confult that author, or per- ufe Dr Defagulier’s tranflation of this paffage. Its principle is precifely the fame with the following rude contrivance, with which we fliall conclude the defcrip- tive part of this article. Suppoie ABCD (fig. 36.) to be a fquare wooden trunk. EF is a piece of oak-board, exactly fitted to the trunk in an oblique pofition, and fupported by an iron pm which goes through it at I, one-third of its length from its lower extremity E. The two ends of this board are bevelled, fo as to apply exactly to the fides of the trunk. It is evident, that if a ftream of water come in the direaion BA, its preffure on the part IF of this board will be greater than that upon El. It will therefore force it up and rufli through, making it Hand almoil parallel to the fides of the trunk. To prevent its rifing fo far, a pin mufl be put in its way. When this current of water changes its direc- Vol. XVII. Part IE 13 ] P U M tion, the preffure on the upper fide of th'e board being Pump, again greateft on the portion IF, it is forced back again —“* to its former fituation , and its two extremities retting on the onpofite Tides of the trunk, the paffage is com¬ pletely (lopped. 1 his board therefore performs the office of a valve ; and this valve is the moft perfeft that can be, becaufe it offers the freed paffage to the water, and it allows very little to get back while it is fhuttingj for the part IE brings up half as much water as IF al¬ lows to go down. It may be made extremely tight, by fixing two thin fillets H and G to the fides of the trunk, and covering thofe parts of the board with lea¬ ther which applies to them 3 and in this (late it perfect¬ ly refembles Belidor’s fine valve. And this conftrudtion of the valve fuggefts, by the Defcription way, a form of an occafional pump, which may beof^noc- quickly fet up by any common carpenter, and will be c‘u,Jna' very effectual in fmall heights. Let ab c de (fig. 36.) 1,7^0^ be a fquare box made to Hide along this wooden trunk ftnnfteu. without (hake, having two of its fides projecting up- Gg- in¬ wards, terminating like the gable-ends of a houie. A piece of wood e is mortifed into thefe two (ides, and to this the pifton-rod is fixed. This box being furniffied with a valve fimilar to the one below', will perform the office of a pifton. If this pump be immerfed fo deep in the water that the pifton fliall alio be under water, we fcruple not to fay that its performance will be equal to any. The pifton may be made abundantly tight by co¬ vering its outfide neatly with foft leather. And as no pipe can be bored with greater accuracy than a very or¬ dinary workman can make a fquare trunk, we prefume that thfs pump will not be very deficient even for a con- (iderable futftion. ^ We now7 proceed to the laft part of the fubjetft, to The mo- conflder the motion of water in pumps, in reference to t^on.°^ wa" the force which muft be employed. What we have1:61 m hitherto faid with refpect to the force which muft be 1 " ^ applied to a pifton, related only to the fuftaining the water at a certain height : but in aftual fervice we muft not only do this, but we muft difeharge it at the place of delivery in a certain quantity \ and this muft require a force fuperadded to what is neceflary for its mere fupport at this height. _g This is an extremely intricate and difficult fubjeft, an intri- and very imperfectly underftood even by profelfed en-cate Gb- gineers. The principles on which this knowledge muft-i:C^ be founded are of a much more abftrufe nature than the ordinary law's of hydroftatics ; and all the genius of New'ton was employed in laying the foundation of this part of phyfical fcience. It has been much cultivated in the courfe of this century by the firft: mathematicians of Europe. Daniel and John Bernoulli have written very elaborate treatifes on the fubject, under the very appafite name of Hydrodynamics ; in which, although The theory they have added little or nothing to the fundamental dtnomina- propofitions eftabliffied in fome iort by Newton, and te(1 Hydr0‘ acquiefced in by them, yet they have greatly contribu- dynamics* ted to' our progrefs in it by the methods which they have purfued in making application of thofe fundamen¬ tal propofitions to the moft important cafes. It muft be acknowledged, however, that both thefe propofi¬ tions, and the extenfions given them by thefe authors are fupported by a train of argunYnt that is by no means unexceptionable \ and that they proceed on af- fumptions or poftulaies which are but nearly true in ft F an y Pump. So though imperfect is very ufe- ful. Si Fundamen. tal propoli- tion. 8z ?ts utility. P U M [ 51 any cafe, and in many are inadmiflibfe : and it remains to this hour a wonder or puzzle how thefe propofitions and their refults correfpond with the phenomena which we obferve. But fortunately this correfpondence does obtain to a certain extent. And it feems to be this correfpond¬ ence chiefly which has given thefe authors, with New¬ ton at their head, the confidence which they place in their refpeftive principles and methods: for there are confiderable differences among them in thofe refpedfs 5 and each feems convinced that the others are in a miitake. Meflieurs d’Alembert and De la Grange have greatly corredled the theories of their predeceflbrs, and have proceeded on poftulates w'hich come much nearer to the real hate of the cafe. But their inveftigations involve us in fuch an inextricable maze of analytical invefuga- tion, that even when we arc again conduced to the light of day by the clue w'hich they have given us, we can make no ufe of what we there difeovered. But this theory, imperfedl as it is, is of great fervice. It generalizes our obfervations and experiments, and en¬ ables us to compofe a praBicaldoBrine from a heap of fa&s which otherwife muft have remained folitary and unconnected, and as cumberfome in their application as the charadters of the Chinefe writing. The fundamental propofition of this practical hydro¬ dynamics is, that wTater or any fluid contained in an open veffel of indefinite magnitude, and impelled by its weight only, will flow through a fmall orifice with the velocity which a heavy body would acquire by falling from the horizontal furface of the fluid. 'Thus, if the orifice is 16 feet under the furface of the w'ater, it will iffue w ith the velocity of 32 feet in a fecond. Its velocity correfponding to any other depth h of the orifice under the furface, will be had by this eafy proportion : “ As the fquare root of 16 is to the fquare root of h; fo is 32 feet to the velocity required: or, alternately, 16 : 32= V ^ : and v— ^ ^ -v///, = h: that is, multiply the fquare root of ^ •>. the height in feet by eight, and the produdl is the re¬ quired velocity. On the other hand, it frequently occurs, that wre want to difeover the depth under the furface which will V produce a known velocity v. Therefore, h =1 Pump. and h 64 that is, divide the fquare of the velo¬ city by 64, and the quotient is the depth wanted in feet. This propofition is fufficient for all our purpofes. For fince water is nearly a perfeft fluid, and propagates all impreffions undiminifhed, we can, in place of any preffure of a pifton or other caufe, fubflitute a perpen¬ dicular column of w7ater wBofe wreight is equal to this preffure, and will therefore produce the fame efflux.— Thus, if the furface of a pifton is half a fquare foot, and it be preffed down with the weight of 500 pounds, and we would wifh to know with wfflat velocity it would caufe the water to flow through a fmall hole, we know that a column of water of this weight, and of half a foot bafe, would be 16 feet high. And this propofition §3 4 ] P U M teaches us, that a veffel of this depth will have a velo¬ city of efflux equal to 32 feet in a iecond. If theretore our preffing powTer be oi Inch a kind that it can continue to prefs forward the pilion with the force of 500 pounds, the w'ater will flow with this velocity, whatever be the fize of the hole. All that remains is, to determine what change «f aBualprejjure on the pifton refults from the motion of the pifton itlelf, and to change the velocity of efflux in the fubduplicate ratio of the change of aftual preffure. But before we can apply this knowledge to the cir- Remark cumftances wfflich take place in the motion of water in previous pumps, wTe muft take notice of an important modifica-toyts aP” tion of the fundamental propofttion, w’hich is but very l)*!caUun‘ obfeurely pointed out by any good theory, but is efta- bliftied on the moft regular and unexceptionable obfer- vation. If the efflux is made through a hole in a thin plate, and the velocity is computed as above, we ftiall difeover the quantity of wTater which iffues in a fecond by obfer- ving, that it is a prifm or cylinder of the length indica¬ ted by the velocity, and having its tranfverfe feftion equal to that of the orifice. Thus, in the example al¬ ready given, fuppofing the hole to be a fquare inch, the folid contents of this prifm, or the quantity of wTater if- fuing in a fecond, is iXfl^X 12 cubic inches, or 384 cubic inches. This wTe can eafily meafure by receiving it in a veffel of known dimenfions. Taking this me¬ thod, wTe uniformly find a deficiency of nearly 38 parts in 100 ; that is, if w'e ftiould obtain 100 gallons in any number of feconds, we (hall in fact get only 62. This is a moft regular facl, whether the velocities are great or fmall, and w-hatever be the fize and form of the ori¬ fice. The deficiency increafes indeed in a very minute degree wdth the velocities. If, for inftance, the depth of the orifice be one foot, the difeharge is T0V0V i ^ it be 15 feet, the difeharge is -/oVoV This deficiency is not owing to a diminution of velo¬ city ; for the velocity may be eafily and accurately mea- fured by the diftance to which the jet will go, if direft- ed horizontally. This is found to correfpond very near¬ ly wdth the propofition, making a very fmall allowance for fri&ion at the border of the hole, and for the refin¬ ance of the air. Sir Ifaac Newton aferibed the defici¬ ency with great juftice to this, that the lateral columns of W'ater, furrounding the column which is incumbent on the orifice, prefs towards the orifice, and contribute to the expence equally with that column. Thefe lateral filaments, therefore, iflue obliquely, crofting the motion of the central ftream, and produce a contra&ion of the jet; and the whole ftream does not acquire a parallel motion and its ultimate velocity till it has got to fome diftance from the orifice. Careful obfervation {bowed him that this was really the cafe. But even his genius could not enable him to afeertain the motion of the la¬ teral filaments by theory, and he W'as obliged to mea¬ fure every thing as he faw it. He found the diameter of the jet at the place of the greateft contraftion to be precifely fuch as accounted for the deficiency. His ex¬ plication has been unanimouily acquiefced in •, and expe¬ riments have been multiplied to afeertain all thofe cir- cumftances w'hich our theory cannot determine a priori. The moft complete fet of experiments are thofe of Mi- chelotti, made at Turin at the expence of the prince of Piedmont. P U M [515] P U M Pa;np. Piedmont. Here jets were made of I, 2, 3, and 4 —■v ' inches diameter j and the water received into ciiterns mod accurately formed of brick, and lined with ftucco. It is the refult of thefe experiments which we have ta¬ ken for a meafure of the deficiency. We may therefore confider the water as flowing through a hole of this contracted dimenfion, or fubftitute this for the real orifice in all calculations. For it is evi¬ dent that if a mouth-piece (fo to call it) were made, whofe internal fhape precifely tallied with the form which the jet airtimes, and if this mouth-piece be applied to the orifice, the water will flow out without any obftruc- tion. The veffel may therefore be confidered as really having this mouth-piece. Nay, from this we derive a very important obferva- tion, “ that if, inftead of allowing the water to flow through a hole of an inch area made in a thin plate, we make it flow through a hole in a thick plank, fo formed that the external orifice fhall have an inch area, but be widened internally agreeably to the fhape which nature forms, both the velocity and quantity will be that which the fundamental propofition determines. Michelotti meafured with great care the form of the great jets of three and four inches diameter, and found that the bounding curve rvas an elongated trochoid. He then made a mouth-piece of this form for his jet of one inch, and another for his jet of two inches *, and he found the difcharges to be -r9c-7c9o aHd -rofe 5 a"d he, with juftice, afcribed the trifling deficiency which flill remained, partly to friftion and partly to his not having exaflly fuited his mouth-piece to the natural form. We imagine that this laft circumifance was the foie caufe : For, in the fidt place, the water in his experiments, before get¬ ting at his jet-holes, had to pafs along a tube of eight inches diameter. Now a jet of four inches bears too great a proportion to this pipe j and its narrownefs un¬ doubtedly hindered the lateral columns from contribut¬ ing to the efflux in their due proportion, and therefore rendered the jet lefs convergent. And, in the next place, there can be no doubt (and the obfervations of Daniel Bernoulli confirm it) but that this convergency begins within the veffel, and perhaps at a very confider- able diflance from the orifice. And we imagine, that if accurate obfervations could be made on the motion of the remote lateral particles within the veffel, and an in¬ ternal mouth-piece were fhaped according to the curve which is defcribed by the remoteft particle that we can obferve, the efflux of water would almoft perfedfly tally with the theory. But indeed the coincidence is already fufficiently near for giving us very valuable informa¬ tion. We learn that the quantity of rvater which flows through a hole, in confequence of its own weight, or by the adlion of any force, may be increafed one half by properly fhaping the paffage to this hole ; for we fee that it may be increafed from 62 to near 99. But there is another modification of the efflux, which we confefs our total incapacity to explain. If the w?ater iffues through a hole made in a plate whofe thicknefs is about twice the diameter of the hole, or, to exprefs it tetter, if it iffues through a pipe whofe length is about twice its diameter, the quantity difcharged is nearly °f what refults from the propofition. If the pipe be longer than this, the quantity is diminifhed by fric¬ tion, which increafes as the length of the pipe increafes. If the pipe be fhorter, the water will not fill it, but de¬ taches itfelf at the very entry of the pipe, and flaw-s jPurng. with a contra£!ed jet. When the pipe is of this length, and the extremity is flopped with the finger, fo that it begins to flow with a full mouth, no fubfequent contrac¬ tion is obferved ; but merely ftriking on the pipe with a key or the knuckle is generally fufficient to detach the water in an inftant from the tides of the pip£, and re¬ duce the efflux to This effcft is mod unaccountable. It certainly arifes from the mutual adhefion or attraflion between the wa¬ ter and the tides of the pipe ; but how this, afting at right angles to the motion, fflould produce an increafe from 62 to 82, nearly -j, we cannot explain. It fhows, however, the prodigious force of this attraftion, wdiieh in the fpace of two or three inches is able to communi¬ cate a great velocity to a very great body of water. In¬ deed the experiments on capillary tubes fhowr that the mutual attraffion of the parts of water is fome thoufands of times greater than their wxight. We have only further to add, that every increafe of pipe beyond two diameters is accompanied with a dimi¬ nution of the difeharge ■, but in what ratio this is dimi- nithed it is very difflcult to determine. We fhall only obferve at prefent that the diminution is very great. A pipe of 2 inches diameter and 30 feet long has its difeharge only -fA of what it wmuld be if only 4 inches long. If its length be 60 feet, its difeharge will he no more than T?A-. A pipe of 1 inch diameter would have a difeharge of A^, and T-A, in t'ne fame lituation. Hence we may conclude that the difeharge of a 4-inch pipe of 30 feet long will not exceed -j of what it would he if only 8 inches long. This will fuihce for our pre¬ fent purpofes 5 and the determination of the velocities and difeharges in long conduits from pump-machines muff be referred to the article IVjTER-lVorks. At pre¬ fent we {ball confine our attention to the pump itfelf, and to what will contribute to its improvement. Before we can proceed to apply this fundamental propofition to our purpofe, we muff anticipate in a loofe way a propofition of continual ufe in the conffrudlion of water works. Let water be fuppofed ftagnant in a veffel EFGFI*’^^’ (fig. 37.), and let it be allowed to flow out by a cylin¬ drical pipe HIKL, divided by any number of partitions B, C, I), &c. Whatever be the areas B, C, D, of thefe orifices, the velocity in the intermediate parts of the pipe will be the fame *, for as much paffes through any one orifice in a fecond as paffes through any other in the fame time, or through any feefion of the inter¬ vening pipe. Let this velocity in the pipe be V, and let the area of the pipe be A. The velocity in the ori¬ fices B, C, D, mull be VA VA VA “B-’ C ’ D > &C Let g be the velocity acquired in a fecond by a heavy body. Then, by the general propofition, the height of water * . . VA. in the veffel which will produce the velocity in B V»A* the firft orifice alone, is . After this pufage the velocity is again reduced to V in the middle of th^. fpace between the firft and fecond orifices. In the fe- VA cond orifice this velocity is changed to . This 3 T 2 alone Pump. S4 To deter- srdne the motion of water, 5tc. P U M alone would have required a height of water £ 51 V* A* ^Cx" But the water is already moving with the velocity V, which would have refulted from a height of water in the veffel (which we lhall, in the language of the art, call V* the HEAD OF water) equal to —. Therefore there V1 A* V1 is only required a head of water — , or 2^’ V* Az ~X Qi — 1 • Therefore the whole height neceffary for producing the efflux through both orifices, fo as flill to preferve the velocity V in the intervening pipe, V* A* A1 is — X-n + T^ — 1 • 1° like manner the third orifice 2g is* 1 C* V* A* D would alone require a head of water — X w 1 ; 2g JD* V* A* A* and all the three would require a head —X-vr, -b -rm-f- 2g B* ' C ' — 2. By this indudlion may eafily be feen what A* D* head is neceffary for producing the efflux through any number of orifices. Let the expence or quantity of water difcharged in an unit of time (fuppofe a fecond) be expreffed by the fymbol Q. This is meafured by the product of the ve¬ locity by the area of the orifice, and is therefore irVA, VA VA O* — XB, or~xC, &c. and V* = ^ There¬ fore we may compute the head of water (which we fhall exprefs by H) in reference to the quantity of wa¬ ter difcharged, becaufe this is generally the interefting circumftance. In this view we have H A* A* A* wi-rri + 2gA X SS fn the fuck¬ ing-pump, -2: which {hows that the head of water neceffary for producing the difcharge increafes in the proportion of the Iquare of the quantity of water winch is difcharged. Thefe things being premifed, it is an eafy matter to determine the motion of water in a pump, and the quan¬ tity difcharged, refulting from the aftion of any force on the pifton, or the force which muff be applied to the pifton in order to produce any required motion or quantity difcharged. We have only to fuppofe that the force employed is the preffure of a column of water of the diameter of the working barrel 5 and this is over and above the force which is neceffary for merely fup- porting the water at the height of the place of delivery. The motion of the water will be the fame in both cafes. Let us, firft of all, ccnfider a fucking-pump. The motion here depends on the preffure of the air, and will be the fame as if the pump were lying horizontally, and communicated with a refervoir, in which is a head of water fufficient to overcome all the obftru&ions to the motion, and produce a velocity of efflux fuch as we de¬ fire. And here it muft be noted that there is a limit. No velocity of the pifton can make the water rife in the luftion-pipe with a greater velocity than w7hat would 6 ] P U M be produced by the preffure of a column of water 33 feet high j that is, about 46 feet per fecond. Let the velocity of the pifton be V, and the area of the working barrel be A. Then, if the water fills the barrel as fait as the pifton is drawn up, the difcharge during the rife of the pifton, or the number of cubic feet of water per fecond, muft be rz: VxA. This is always fuppofed, and wn have already afcertained the circumftances which enfure this to happen. If, there¬ fore, the water arrived with perfect freedom to the pi¬ fton, the force neceffary for giving it this velocity, or for difcharging the quantity VxA in a fecond, would be equal to the wnight of the pillar of wTater whofe height . V* is —, and bafe A. 2g It does not appear at firft: fight that the force ne¬ ceffary for producing this difcharge has any thing to do with the obftrudlions to the afcent of the wrater into the pump, becaufe this is produced by the preffure of the atmofphere, and it is the aftion of this preffure which is meafured by the head of wrater neceffary for produ¬ cing the internal motion in the pump. But w7e muft al¬ ways recollecl that the pifton, before bringing up any water, and fupporting it at a certain height, was preffed on both fides by the atmofphere. While the air fup- ports the column below the pifton, all the preffure ex¬ pended in this fupport is abftrafted from its preffure on the under part of the pifton, while its upper part ftil! fupports the whole preffure. The atmofphere continues to prefs on the under furface of the pifton, through the intermedium of the water in the fudlion-pipe, with the difference of thefe two forces. Now, while the piftou is drawn up with the velocity V, more of the atmofphe- ric preffure muft be expended in caufing the water to follow the pifton ; and it is only with the remainder of its whole preflure that it continues to prefs on the under furface of the pifton. Therefore, in order that the pifton may be raifed with the velocity V, a force muft be ap¬ plied to it, over and above the force neceffary for mere¬ ly fupporting the column of water, equal to that part of the atmofpheric preffure thus employed ; that is, equal to the weight of the head of water neceffary for forcing the water up through the fu&ion-pipe, and producing the velocity V in the working barrel. Therefore let B be the area of the mouth of the fu&ion-pipe, and C the area of the fixed valve, and let the fu£lion-pipe be of equal diameter with the working barrel. The head neceflary for producing the velocity V* /A2 A* \ V on the working barrel is —1 )• If d exprefs the denfity of water j that is, if d be the. V2 number of pounds in a cubic foot of water, then d A — 2g will exprefs the weight of a column whofe bafe is A V* and height—, all being reckoned in feet. Therefore 2g the force which muft be applied, when eftimated m d A V* / A* A* \ pounds, will be A -f --x ). The firft general obfervation to be made on what has been faid is, that the power which muft be employed to produce the neceffary motion, in oppofition to all the obftacles, is in the proportion of the fquare of the. velo¬ city Pump, P U M [5 mp. city wliich we would produce, or the fquare of the quan- r'—"' ty of water ■we would dilcharge. We have hitherto proceeded on the fuppofition, that there is no contraction of the jet in palling through thefe twyo orifices. This ive know would be very far from the truth. We muft therefore accommodate things to thefe circumftances, by diminilhing B and C in the ratio of the contraction, and calling the diminilhed areas b and , , KdY* (A? A3 \ c; then we have p — { -7 ( 1 ). Kb' 1 c* J What this diminution may be, depends on the form of the parts. If the fixed valve, and the entry into the pump, are Amply holes in thin plates, then b— •y(W- B and c—The entry is commonly widened or trumpet-fhaped, which diminilhes greatly the contrac¬ tion : but there are other obitacles in the way, ariling from the Itrainer ufually put round it to keep out filth. The valve may have its contraCHon greatly diminifbed alfo by its box being made bell-thaped internally j nay, even giving it a cylindrical box, in the manner of fig. 33. is better than no box at all, as in fig. 5. j for fuch a cylindrical box will have the unaccountable effeCl of the the Ihort tube, and make b— B, inftead of B. Thus we fee that circumftances feemingly very trifling may produce great effeCts in the performance of a pump. We Ihould have obferved that the valve itfelf prefents an obftacle which diminifhes the motion, and requires an increafe of power j and it would feem that in this re- fpeCl the clack or butterfly valve is preferable to the button valve. Example. Suppofe the velocity of the pifton to be 2 feet or 24 inches per fecond, and that the two con¬ tracted areas are each £ of the area of the pump, which 2s not much lefs than what obtains in ordinary pumps. Vs / A1 A3 \ We have “(jr + 71 —i) = 4i4(25 + 25—1) — 36,75 inches, and the force which we muft add to what will merely fupport the column is the rveight of a pillar of water incumbent on the pifton, and fomething more than three feet high. This would be a fenfible portion of the whole force in railing water to fmall heights. We have fuppofed the fuCHon-pipe to be of the fame diameter with the working barrel; but it is ufual to make it of fmaller diameter, generally equal to the wa¬ ter way of the fixed valve. This makes a conuderable change in the force neceffary to be applied to the pi¬ fton. Let a be the area of the fuCtion-pipe, the area of the entry being liill B ; and the equivalent entry with¬ out contraction being Itill b, we have the velocity at AV the entrance ~ —r-, and the producing head of water— b AV After this the velocity is changed to in A2W 2g bl the fu&ion-pipe, with which the water arrives at the A V valve, where it is again changed to , and requires for A2 VJ this change a head of water eoual to -. But 1 aye the velocity retained in the fuClion-pipe is equivalent to A2 V2 the efteCI of a head of water ——. Therefore the 2^ a2 heaxl neceftiry tor producing fuch a current through the 17 ] p u M fixed valve, that the water may follow the pifton with Pump. the velocity V, is A2 V 2g b- A2> + A2 V2 A2 V2 - 1 —— 2g c* 2g ax This is evidently lefs than A* a is lefs than A, and therefore YlfAL 2g\bz c2 before, becaufe is greater than unity, which was the laft term of the former formula. I here is fome advantage, therefore, derived from making the diameter of the fuClion-pipe lefs than that of the working barrel: but this is only be¬ caufe the paffage of the fixed valve is fmaller, and the infpeCtion of the formula plainly points out that the area of the fuCHon-pipe thould be equal to that of the fixed valve. When it is larger, the water muft be accelerated in its paffage through the valve; which is an ufelefs ex¬ pence of force, becaufe this velocity is to be immediate¬ ly reduced to V in the working-barrel. If the forego¬ ing example be computed with a equal to -2- of A, we lhall find the head H equal to 29 inches inftead of 37. But this advantage of a fmaller fuClion -pipe is in all cafes very moderate 5 and the pump is always inferior to one of uniform dimenfions throughout, having the ori¬ fice at the fixed valve of the fame area. And if thefe orifices are confiderably diminilhed in any proportion, the head neceflary for overcoming the obftacles, fo that the required velocity V may ftill be produced in the working barrel, is greatly increafed. If we fuppofe the area a ^ of A, which is frequently done in houfe pumps, where the diameter of the iuction-pipe does feldom ex¬ ceed \ of that of the working-barrel ; and fuppofe every thing made in proportion to this, which is alio ufual, becaufe the unikilled pump-makers ftudy a fymmefcry which fatisfies the eye ; we fhall find that the pump taken as an example will require a head of water — 13 feet and upwards. Befides, it muft be obferved that the friftion of the fuction-pipe itfelf has not been taken into the account. This alone is greater, in moil cafes, than all the obftruftions we have been fpeaking of; for if this pipe is three inches diameter, and that of the working-barrel is fix, which is reckoned a liberal al¬ lowance for a fuflion-pipe, and if the fixed valve is 25 feet above the furface of the pit-water ; the frieftion of this pipe will amount to one-third of the whole propel¬ ling force. Thus we have enabled the reader to afeertain the force neceflary for producing any required difeharge of water from a pump of known dimenfions : and the con- verfe of this determination gives us the difeharge which will be produced by any given force. Tor making: A2 A2 A2 ^ .. , . \ _ _j_ ~ (which is a known quantity, refulting. b~ ‘ c‘ a from the dimenfions of the pump) V2 2 pH — M, and V2 — -fr-, and V 2g ’ M ’ :M, *.e have H 2^H M ' Now H is that part of the natural power which we have at com¬ mand which exceeds what is neceflary for merely fup- porting the column of water. Thus, if we have a pump whofe pifton has an area of i of a fquare foot, its diameter being 61- inches and we have to raife the water 32 feet, and can apply a power of 525 pounds to the pifton • we wifti to know at what rale the pifton will be moved, and the quantity of water difeharged ?• P U M [ si Pump. Merely to fupport tire column of water of this height aRct diameter, requires 500 pounds. Therefore the re¬ maining power, which is to produce the motion, is 25 pounds. This is the weight of a column 1 foot 4 inches high, and H = 1,333 ^eet* ^et us fuPP°fe ^ diame¬ ter of the fuction-pipe \ of that of the working-barrel, A fo that -- = 4. We may luppofe it executed in the beft manner, having its lower extremity trumpet-fhaped, formed by the revolution of the proper trochoid. The contraftion at the entry may therefore be confidered 8 ] P U M A A1 as nothing, and ~ 4, and — 16. We may fuppofe the orifice of the fixed valve equal to A1 area of the fu£Hon-pipe, fo that — is alfo =: and there is no contraftion here j and therefore is alfo 16. A2 A2 b1 c1 And laftly, — A2 is alfo 16. Therefore or M, = 16-f- 16 — 16, 16. We have alfo 2g ~ 64. Now = J?± =^,309 feet, and the pifton wrill Vs/A —* Pump. quires for its produiftion a head of water l } ' This is the height of a column of water whofe bafe is not A but A—a. Calling the denfity of water — confiderably greater than before. We cannot afcertain this value with great pre- cifion, becaufe it is extremely difficult, if poffible, to determine the refiftance in fo complicated a cafe. But the formula is exaft, if b can be given exactly $ and we know within very moderate limits what it may amount to. In a pump of the very beft conftruflion, with a button valve, b cannot exceed one-half of A ; A3 and therefore —— cannot be lefs than 8. In this b1 V2 A3 . V* cafe, T— will be--^-. In a good fteam-engme pump 2 go* 8 0 V* V is about three feet per fecond, and -r- is about i-| o feet, which is but a fmall matter. We have hitherto been confidering the fucking-pump an^ 1( ^ alone : but the forcing pump is of more importance, forring- and apparently more difficult of inveftigation.—Here pump, we have to overcome the obftruftions in long pipes, with many bends, contraftions, and other obftruftions. But the confideration of what relates merely to the pump is abundantly limple. In moft cafes we have only to force the water into an air-veffel, in oppofition to the elafticity of the air compreffed in it, and to fend it thither with a certain velocity, regulated by the quan¬ tity of water difcharged in a given time. The elafticity of the air in the air-veflel propels it along the Main. We are not now fpeaking of the force neceffary for counterbalancing this preffure of the air in the air-veffel, which is equivalent to all the fubfequent ob/iru&ions, but only of the force neceflary for propelling the water out of the pump with the proper velocity. We have in a manner determined this already. The pifton is folid, and the water which it forces has to pafs through a valve in the lateral pipe, and then to move in the direction of the main. The change of di- reffion requires an addition of force to what is necef¬ fary for merely impelling the water through the valve. Its quantity is not eafily determined by any theory, and it varies according to the abi'uptnefs of the turn. It appears from experiment, that when a pipe is bent to a right angle, without any curvature or rounding, the velocity is diminiftied about At- This would aug¬ ment the head of water about This may be added to the contra6Hon of the valve hole. Let c be its na¬ tural aiea, and whatever is the contraftion competent to its form increafe it X'T, and call the contra&ed area V1 A* c. Then this will require a head of water = — . 2g c This move with the velocity of 2 feet 4 inches nearly. Its velocity will be lefs than this, on account both of the fri£lion of the pifton and the friftion of the water in the fu£tion-pipe. Thefe two circumftances will pro¬ bably reduce it to one foot eight inches j and it can hardly be lefs than this. We have taken no notice of the friction of the rvater in the working-barrel, or in the fpace above the pifton \ becaufe it is in all cafes quite infignificant. The longeft pipes employed in our deep mines do not require more than a few inches of head to overcome it. But there is another circumftance which muft not be omitted. This is the refiftance given to the pifton in its defcent. The piftons of an engine for drawing wra- ter from deep mines muft defcend again by their own weight in order to repeat their ftroke. This muft re¬ quire a preponderance on that end of the working-beam to which they are attached, and this muft be overcome by the moving power during the efteclive ftroke. It makes, therefore, part of the wffiole wmrk to be done, and muft: be added to the weight of the column of wa¬ ter wffiich muft be raifed. This is very eafily afcertained. Let the velocity of the pifton in its defcent be V, the area of the pump- barrel A, and the area of the pifton-valve a. It is evident, that while the pifton defcends with the velo¬ city V, the w’ater wffiich is difplaced by the pifton in a fecond is (A—#) V. This muft pafs though the hole of the pifton, in order to occupy the fpace above, which is left by the pifton. If there were no contrafliarr, the water would go through with the velocity V j but as there will always be fome contradlion, let the dimi¬ niftied area of the hole (to be difcovered by experiment) be bt the velocity therefore will be V • This re- P U M [ 519 ] P U M Pump. * 87 Ufe of ex¬ periments. d AVVAa 2g . This muft be added to the head —, neceffary for mere- 2 g J ly giving the velocity V to the water. Therefore the V2 / A2 \ whole is — ^ ^ 1 j \ and the power p neceflary for for this purpofe is It cannot efcape the obiervation of the reader, that in all theie formulae, expreffing the height of the co¬ lumn 01 water which would produce the velocity V in the working barrel of the pump the quantity which multiplies the conflant fadlor — depends on the 2 g 2 con trailed paflages which are in different parts of the pump, and increafes in the duplicate proportion of the fum of thofe contrailions. It is therefore of the utmoft confequence to avoid all fuch, and to make the main which leads from the forcing-pump equal to the working barrel. It it be only of half the diameter, it has but one-fourth of the area, the velocity in the main is four times greater than that of the pifton, and the force ne- ceffary for difcharging tne fame quantity of water is 16 times greater. It is not, however, poffible to avoid thefe contrac¬ tions altogether, without making the main pipe wider tnan the barrel. For if only fo wide, with an entry of the fame fize, the valve makes a confiderable obtlruc- tion.. Unfkilful engineers endeavour to obviate this by making an enlargement in that part of the main which contains the valve. This is feen in fig. 14. at the valve L. If this be not done with great judgement, it will increafe the obftruclions. lor if this enlargement is full of water, the water mull move in the direction of its axis with a dimmifhed velocity ; and when it comes iu- to the main, it muff again be accelerated. In fhort, any abrupt enlargement which is to be afterwards con- tracfed, does as much harm as a contradtion, unlefs it be fo fiiort that the water in the axis keeps its velocity till it reaches the contradtion. Nothing would do more fervice to an artift, who is not well founded in the theory ot hydrodynamics, than to make a few' fimple and cheap experiments with a veffel like that of fig. 37. Let the horizontal pipe be about three inches diameter, and made in joints which can be added to each other. Let the joints be about fix inches long, and the holes from one-fourth to a whole inch in diameter. Fill the veffel with water, and obferve the time of its finking three or four inches. Each joint fliould have a final! hole in its upper fide to let out the air ; and when the water runs out by it, let it be flopped by a peg. He will fee that the larger the pipe is in proportion to the orifices made in the partitions, the efflux is more dirni- nifhed. We believe that no perfon would fufpedt this who has not confidered the fubjedf minutely. _ -A’l angular enlargements, all boxes, into which the pipes from different working barrels, unite their water before it goes into a main, muff therefore be avoided by an artiil who would execute a good machine ; and the different contractions which are unavoidable at the feats of valves and the perforations of pifions, &c. fhould be diminifhed by giving the parts a trumpet- fhape. In the air-veffels reprefented in fig. 13. this is of very great confequence. Xhe throat O, through which the water is forced by the expanfion of the confined air, Famp. fflould always be formed in this manner. For it is this y-“—^ which produces the motion during the returning part of the ilroke in the pump conftruCled like fig. 13. N° 1. and during the whole llroke in N° 2. NegleCting this leemingly trilling circumftance will diminiih the per¬ formance at leafl one-fifth. The conftruaion of N° 1. is the bed, for it is hardly poffible to make the paffage of the other fo free from the effcCls of contraction. The motion of the water during the returning ilroke is very much contorted. ^ There is one circumilance that we have not taken any Accekra- notice of, viz. the gradual acceleration of the motion oftion of ihe water in pumps. When a force is applied to the pifton,motionot' it does not in an inftant communicate all the velocitywater in which it acquires. It aCls as gravity afts on heavy bo-pUmF* dies ; and it the refinances remained the fame, it would produce, like gravity, an uniformly accelerated motion. But we have feen that the refinances (which are always meafured by tile force which juft overcomes them) in¬ creafe as the fquare of the velocity increafes. They therefore quickly balance the adlion of the moving- power, and the motion becomes uniform, in a time lb Ihort that we commit no error of any confequence by fuppofing it uniform from the beginning. It would have prodigioufly embarrafftd our inveftigations to have introduced this circumftance } and it is a matter of mere fpeculative curiofity : for moll of our moving pow-ers are unequal in their exertions, and thefe exertions are regulated by other laws. The preffure on a pillon mo¬ ved by a crank is as variable as its velocity, and in mcft cafes is nearly in the inverfe proportion of its velocity, as any mechanician will readily difcover. The only cafe in which we could confider this matter with any de¬ gree of comprehenfibility is that of a lleam-engine, or of a pifton which forces by means of a wTeight lying on it. In both, the velocity becomes uniform in a very fmall fraction of a fecond. We have been very minute on this fubjefl. For al- Deficiency though it is the only view of a pump which is of any of elemen- importance, it is hardly ever underflcod even by profef-tary k00^5 fed engineers. And this is not peculiar to hydraulics, ?n'his fu,?" but is feen m all the brancncs q£ practical mechanics.^ The elementary knowledge to be met with in fuch books as are generally perufed by them, goes no farther than to ftate the forces which are in equilibrio by the in¬ tervention of a machine, or the proportion of the parts of a machine which will fet two known forces in equili¬ brio. But when this equilibrium is deftroyed by the fu- periority of one of the forces, the machine muft move j and the only interefting queftion is, what will be ihe tnotion I- 1 ill this is an fivered with fome precifion, we have learned nothing of any importance. Few enffl- neers are able to anfiver this queftion even in the fimpleft cafes 5 and they cannot, from any confident fcience, fay what w-ill be the performance of an untried machine. They guefs at it with a fuccefs proportioned to the mul¬ tiplicity of their experience and their own fagacity. Yet this part of mechanics is as fufceptible of accurate computation as the cafes of equilibrium.—We therefore thought it our duty to point out the manner of proceed¬ ing fo circumftantially, that every Hep fhould be plain and eafy, and that convidlion fliould always accompany our progrefs. This we think it has been in our power to do, by the very Ample method of fubftituting a co- ligsm PUN [ 520 ] PUN Pim lumn of water afting by its weight in lieu of any natu- ich“on ra^ Power which we may chance to employ. - To fuch as wifli to profecute the ftudy of this impor¬ tant part of hydraulics in its moft abifrufe parts, we re¬ commend the perufal of the diflertations of Mr Pitot and Mr Boffut, in the Memoirs of the Academy of Pa¬ ris •, alfo the differtations of the Chevalier de la Borda, 1766 and 17675 alfo the Hydrauliqne of the Chevalier De Buat. We lhall have occafion to confider the mo¬ tion of the water in the mains of forcing or lifting pumps which fend the water to a diftance, in the article WATER-Works ; where the reader will fee how fmall is the performance of all hydraulic machines, in compari- fon of what the ufual theories, founded on equilibrium only, would make him expeft. PUN, or PuxN, an expreflion where a word has at once different meanings. The praftice of punning is the miferable refuge of thofe who with to pafs for wits, without having a grain of wit in their compofition. James the I. of England delighted in punning 5 and the tafte of the fovereign was ftudied by the courtiers, and even by the clergy. Hence the fermons of that age abound with this fpecies of falfe wit. It continued 'to be more or lefs fafhionable till the reign of Queen Anne, when Addifon, Swift, Pope, and Arbuthnot, ■with the other real wits of that claffical age, united their efforts to banifh punning from polite compofition. It is (till admitted fparingly in converfation 5 and no one ' rvill deny that a happy pun, when it comes unfought, contributes to excite mirth in a company. A profeffed J>unj}er, however, who is always pouring forth his fenfe- lefs quibbles, as Sancho Pan^a poured forth his pro¬ verbs, is fuch an 'intolerable nuifance in fociety, that we do not wonder at Pope or Srvift having written a pamphlet with the title of God^s Revenge again/} Pun¬ ning. PUNCH, an inftrument of iron or fteel, ufed in fe- veral arts, for the piercing or ftamping holes in plates of metals, &c. being fo contrived as not only to perforate, But to cut out and take away the piece. The punch is a principal inftrument of the metal-button makers, fhoe- jnakers, &c. Punch is alfo a name for a fort of compound drink, much ufed here, and in many parts abroad, particu¬ larly in Jamaica, and feveral other parts of the Weft Indies. Its bafts is fpring-water 5 which being rendered cool¬ er, brifker, and more acid, with lemon or lime juice, and fweetened again to the palate with fine fugar, makes what they call JJjerbet; to which a proper quantity of fpirituous liquor, as brandy, rum, or arrack, being add¬ ed, the liquor commences punch. PUNCHEON, PuNCHlN, or Punc/iion, a little block or piece of fteel, on one end whereof is feme figure, letter, or mark, engraven either in creux or relievo, impreflions whereof are taken on metal, or fome other matter, by ftriking it with a hammer on the end not engraved. There are various kinds of thefe puncheons ufed in the mechanical arts 5 fuch, for inftance, are thofe of the goldfmiths, cutlers, pewte- rers, &c. The puncheon, in coining, is a piece of iron fteeled, whereon the engraver has cut in relievo the feveral figures, arms, effigy, infeription, &c. that there are to be in the matiices, wherewith the fpecies are to Pvrch^n be marked. Minters diftinguiffi three kinds of pun- cheons, according to the three kinds of matrices f>un.d*ua' to be made ; that of the effigy, that of the crofs or '0J~ , arms, and that of the legend or infeription. The firft includes the whole portrait in relievo 5 the fecond are fmall, fuch only containing a piece of the crofs or arms 5 for inftance, a fleur-de-lis, an harp, a coronet, &c. by the affemblage of all which the entire matrice is formed. The puncheons of the legend only contain each one letter, and ferve equally for the legend on the effigy fide and the crofs fide. See the article Coin¬ age. For the puncheons ufed in ftamping the matrices wherein the types of printing charafters are call, fee LETTER-Foundery. Puncheon is alfo ufed for feveral iron tools, of va¬ rious fizes and figures, ufed by the engravers en creux on metals. Seal-engravers particularly ufe a great num¬ ber for the feveral pieces of arms, &c. to be engra¬ ven, and many ftamp the whole feal from a Angle pun¬ cheon. Puncheon is alio a common name for all thofe iron inftruments ufed by ftone-cutters, fculptors, blackfmiths, &c. for the cutting, bidding, or piercing their feveral matters. Thofe of fculptors and ftatuaries ferve for the re¬ pairing of ftatues when taken out of the moulds. The lockfmiths ufe the greateft variety of puncheons 5 fome for piercing hot, others for piercing cold ; fome flat, fome fquare, fome round, others oval, each to pierce holes of its refpeftive figure in the feveral parts of locks. Puncheon, in Carpentry, is a piece of timber pla¬ ced upright between two polls, wffiofe bearing is too great 5 ferving, together with them, to fuftain fome large weights. This term is alfo ufed for a piece of timber raifed up ¬ right, under the ridge of a building, wherein the legs or a couple, &c. are jointed. PuNCHEON, is alfo the name of a meafure for li¬ quids. Rum is brought from the colonies in pun¬ cheons, which are large calks containing about 130 gallons. PUNCTUATION, in Grammar, the art of point¬ ing, or of dividing a difeourfe into periods, by points exprefling the paufes to be made therein. The points ufed are four, viz. the period, colon, femi- Colon, and comma. See the particular ule of each under its proper article, Comma, Colon, Period, and Semi¬ colon. In general, we (hall only here obferve, that the comma is to diftinguith nouns from nouns, verbs from verbs, and fuch other parts of a period as are not necef- farily joined together. The femi-colon ferves to fufpend and fuftain the period when too long.: the colon, to add fome new fupernumerary realbn, or confequence, to what is already laid : and the period, to clofe up the fenfe and conftrufticn, and releafe the voice. It has been afferted, that punttuation is a modern art, and that the ancients were entirely unacquainted with the ufe of our commas, colons, &c. and wrote not ot*ly without any diftinciion of numbers and periods, but al¬ fo without diftinftion of words : which cuftom, Lip- ftus obferves, continued till the hundred and fourth O- lympiad 5 4 P U N T 52 Y’lmchn- lympiad j during which time the i’enfe alone divided the non. difcouvfe. What within our own knowledge at this day puts this beyond difpute, is the Alexandrian manufcript, which is at prefent in the king’s library, at the Britith Mufreum. Whoever examines this, wall find that the whole is writ¬ ten continuo duEtu, without diilindlion of words or fen- tences. How the ancients read their works written in this manner, it is not eafy to conceive. After the praftice of joining words together ceafed, notes of diilinction were placed at the end of every word. In all the editions of the Fajli Capitohm thefe points occur. The fame are to be feen on the Cohimna Rqflrata. For want of thefe, we find much confufion in the Chronicon Mannoreutn, and the covenant between the Smyrnseans and Magnefians, which are both nowT at Oxford. In Salmafius’s edition of Dcdicatio Jiatuce n- gillce Herodis, the like confufion occurs, where we find AETPITE and uri. Of thefe marks of diftindlion, the Walcote inferip- tion found near Bath may ferve as a fpecimen : IVLIUSv VITAL I Sv FABRI CESISv LEGv XXVv Vv V STIPENDlORUMv &c. After every word here, except at the end of a line, we fee this mark v. There is an infeription in Montfau- con, which has a capital letter laid in an horizontal po- fition, by way of interftitial mark, which makes one apt to think that this way of pointing was fometimes accor¬ ding to the fancy of the graver. P. FERRARIVS HERMES CAECINIAE H DIGNAE CONIVGI H KARISSIMAE NVMERIAE H &c. Here we obferve after the words a T laid horizontally, but not after each word, which proves this to be of a much later age than the former. As the improvement of flops appears not to have ta¬ ken place while manuferipts and monumental inferip- tions were the only known methods to convey know¬ ledge, it is conjectured that it was introduced with the art of printing. The 14th century, to which we are fuppofed to be indebted for this invention, did not, how¬ ever, beftow thofe appendages we c&WJlopx: whoever will be at the pains of examining the firft printed books, will difeover no flops of any kind ; but arbitrary marks here and there, according to the humour of the printer. In the 16 h century, We obferve their firft appearance. We find, from the’books of this age, that they were not all produced at the fame time } thofe we meet with there in ufe, being only the comma, the parenthefis, the interrogation, and the full point. i o prove this, we need but look into Bale’s A&s of Englifti Votaries, black letter, printed 1550. Indeed, in the dedication of this book, which is to Edward VI. we difeover a co¬ lon : but, as this is the only one of the kind throughout the work, it is plain this flop was not eftablilhed at this time, and fo warily put in bv the printer $ or if it was, that it was not in common ufe. Thirty years after this time, in that fenfible and judicious performance of Sir Thomas Elyot, entitled The Covernour, imprinted ■1 ij8o, we fee the colon as frequently introduced as any other flop ; but the femicolon and the admiration were Vol. XVII. Part 11. 1 ] PUN" ftill Wanting, neither of thefe being vifible in this book. Purdlua- In Hackluyt’s Voyages, printed 1599, we fee the femi- tl0n’ , colon : and, as if the editors did not fully apprehend the v propriety of its general admiflion, it is but fparingly introduced. It has been faid, indeed, that the femicolon w'as brought into ufe at a much earlier period ; but it appears that it was only for the purpofe of an abbrevi¬ ation, as in (namq;) {ncq;') for namque, neque, and not in the fenfe in which it is now employed, Month. Mag. v. 411; The femicolon, indeed, as well as all the ordinary points, is ufed in a work entitled “ Imagines Deorum,” printed at Leyden, in the year 1581, in Roman charac¬ ters. We likewife meet with them in the tranflation of a juftly celebrated book, written in French by that wife and good man, Philip Mornay, lord of Pleflis ; in the “ Schoolmafter” of Roger Afcham, printed in 1570, with the exception of the femicolon j and in ihe “ Trewneffe of the Chriftian Religion,” by Sir Philip Sidney, publithed in 15S7, in which we find the afte- rilk, brackets, the interrogation, the comma and the fe¬ micolon, all as we now ufe them; and the colon and period are fquare dots. In an alchemical manufcript of the date of 1572, the femicolon is faid to be met with, as well as the other three points which are in common ufe. The colon and period are abundant in a work entitled “ Dionifius de Situ Orbis,” printed at Venice in 1498, but none of the other flops or points. The Angle point (.) appears to be the moft ancient. Since the year 1485 the colon tvas introduced j the comma is firft feen about the year J 521 ; and the more refined femicolon was brought into ufe about the year 1570. The invention of the femicolon is moft probably due to the Englith j for from the Leyden edition of Pliny, I5i;3, it is evident that the Dutch printers were not then in the practice of ufing it ; and if in 1570, they were, Roger Afcham would probably have employed it; for the Dutch were the principal claflical printers in his time ; but we find that fome Englifti books were mark¬ ed with it at that period. The admiration was the laft flop that was invented, and feems to have been added to the reft in a period not fo far diftant from our own time. Thus we fee that thefe notes of diftinciion came into ufe as learning was gradually advanced and improved ; one invention indeed, but enlarged by feveral additions. But notwithftanding what has been faid relative to the ufe of flops as being a modern invention, we fhall find reafon to be fatisfied that the ancients were not un¬ acquainted with the method of making paufes in fpeak- ing and writing, if we attend to the following elaborate inveftigation of Mr Warburton, which we {hall lay be¬ fore our readers in the words of the author. “ Some fpecies of paufes and divifions of fentences in fpeaking and writing muft have been coeval with the knowledge of communicating ideas by found or by fym- bols. “ Suidas * fays, that the period and the colon were * Tie Three- difeovered and explained by Thrafymachus, about years before the Chriftian tera. Cicero f fays, thatf Cicero Thrafymachus was the firft who fludied oratorical num- 0rat- § 33- bers, which entirely confifted in the artificial ftrufture of periods and colons. It appears from a paffage in Ari- ftotle i, that punctuation was known in his time. The „ 3 U learned U1,C-S? Paii (filia¬ tion. * Bern. Or- bis erud. Literat. tab 30. edit. 1689. f Cie.de Orat. lib. iii § 26. Ibid. 7. Orat. pro Muraena, § 2 5- | Sen. E- pifi. 40. PUN t 52 learned Dr Edward Bernard * refers tlie knotvledge of pointing to the time ot that phiiofopher, and lays, that it con filled in the different polition of one fmgle point. At the bottom of a letter $ thus, (A.) it was equivalent to a comma } in the middle (A*J it was equal to a colon; at the top (A’) it denoted a period, or the concluiion oi a lenience. “ This mode was eauly praciifed in Greek manu- i'eripts, while they were written in capitals. But when the fmall letters were adopted, that is, about the ninth century, this diftinction could not be oblerved j a change was therefore made in the fcheme of puncluation. Xhi- dales lileras hodierno ufu didmus eas in vetujhs codici- btis, qua; prjcatn formam fervant, ac folutce funt, nec niHtub coliigantur. Hujus midi liter re unc tales objervan- tur in libris omnibus ad nonutn ufquefeeculum. Monti. .Palseog. Recens. p. xii. According to Cicero, the ancient Romans as well as the Greeks made ule of points. He mentions them under the appellation of librariorum notce; and in leveral parts of his works he fpeaks of ‘ inierpuncice claufuLe in orationibus\ of ‘ claufuLe atque interpunBce verboruni', oi mterpunBiones verborum, is’c f. “ Seneca, who died A. D. 65, exprefsly fays, that Latin writers in his time, had been ufed to punctuation. ‘ Nos 4, cum fcnbinms interpungere confucvimusl Mu- retus and Lipfius imagined that thefe words alluded to tlie infertion of a point after each word ; but they cer¬ tainly were mlftaken, for they mud neceffarily refer to marks of pun&uation in the divifion of fentences, becaufe in the paflage in which thefe ivords occur, Seneca is fpeak- ing of one Haterius, who made no paufes in his ora¬ tions. “ According to Suetonius in his Mud. Gram. Valerius Probus procured copies of many old books, and employ¬ ed him lei f in correcting, pointing and illudrating them 5 devoting his time to this and no other part of grammar. Multa exemplaria contraBa emend arc, ac diftinguere et ad- no tare cur avit ; folihuic, nec ulh preeterea, grammatices parti deditus. “ It appears from hence that in the time of Probus, or about the year 68, that Latin manuferipts had not been ufually pointed 5 and that grammarians made it their bu- finefs to fupply this deficiency. “ Quintilian, who wrote his celebrated treatife on Oratory, about the year 88, fpeaks of commas, colons, and periods 5 but it mud be obferved, that by thefe terms he means claufes, members, and complete fentences, and not the marks of pundualion “ CElius Donatus |j publiihed a treatife on Grammar A.D.340. jn tpie four!-’n C£ntuiy, in which he explains the diflinBio, the media dfinBio, and the fubdiJlinBio : that is, the ufe of a Angle point in the various pofitions already men¬ tioned. “ Jerom *, who had been the pupil of Donatus, in his Latin Verfion of the feriptures, made ule of certain didindions or dividons, which he calls cola and com- mata. It has however been thought probable, that thefe divilions were not made by the addition of any points or Hops ; but were formed by writing, in one line, as many words as conftituted a claufe, equivalent to what w>e di- dingnilli by a comma or a colon. Ihefe divifions were called trrrfctn or foustr* •, and had the appearance of diort irregular verfes in poetry. There are feme Greek ma- lib. nu('(?r;pts ftpi extant, which are written in this manner f. § QuinSl kb. ix. c. 4 ^ Hieron. Pisef. m PJaiam. Vide ttiam Preef. in yofuarn, See. tom.iii. p. 26. I Vide Montf. Palceog. 2 J PUN “ The bed treatife upon punduatton I have feen, and Pundum from which thefe authorities are partly taken, was pub- II lilhed fame years fmee and dedicated to Sir Clifton uu"J!neA; Wintringbam, Bart, the name of the author I know ^ Moi!{h iiot _ > Mag. vi, PUNCTUM sapiens, in Anatomy, the fird rudi-jsb'. meats of the heart in the formation of the foetus, rvhere a throbbing motion is perceived. This is faid to be ea- fily obferved with a microfcope in a brood-egg, wherein after conception, we fee a little fpeck or cloud, in the middle whereof is a fpot that appears to beat or leap a confiderable time before the foetus is formed for hatching. See the articles Foetus and Anatomy. PliNCTUMjlans, a phrafe by which the fchoolmen vainly attempt to bring within the reach of human comprehenfion the pofitive eternity of God. Thofe fubtile reafoners feem to have difeovered that nothing, which is made up of parts, whether continuous or dif- crete, can be ablblutely infinite, and that therefore eter¬ nity cannot confilt of a boundlefs feries of fucceffive moments. Yet, as if fuch a feries bad always exided, and were commenfurate in duiation with the fupreme Being, they compared his eternity to one of the mo¬ ments which compofe the flux of time arrefted in its courfe : and to this eternal moment they gave the name of punBnm fans, becaufe it was fuppofed to Hand dill, whild the red followed each other in fuccefiion, all va- nifhing as foon as they appeared. We need not wade time or room m expofing the abfurdity of this conceit, as we have elfewhere endeavouied, in the bed manner we can, to afeertain the meaning of the words eternity and infinity, and to fhow that they cannot be predicated of time or fpace, of points or moments, whether flowing or Handing dill. See METAPHYSICS, Part II. chap. 7. 8. and Part III. chap. 6. PUNCTURE, in Surgery, any wound made by a fRarp-pointed indrument. PUNDITS, or Pendits, learned Bramins devoted to the fludy of the Sanfcrit language, and to the ancient fcience, laws, and religion cf Hindodan. See Philoso¬ phy, no° 4—12. PUNICA, the pomegranate tree, a genus of plants belonging to the icofandria clafs, and in the natural method ranking under the 36th order, Pomacece. See Botany Index. PUNISHMENT, in Law, the penalty which a per- fon incurs on the commiflion of a crime. See the article Crime and Punifhment. The ingenuity" of men has been much exerted to tor¬ ment each other ^ but the following are the punifhments that have been ufually adopted in the different countries of the world. The capital punifhments have been be¬ heading,' crucifixion, burning, reading, drowning, fcal- ping, hanging by the neck, the arm, or the leg, ftar- ving, fawing, expofing to wild beads, rending afunder by horfes drawing oppofite ways, burying alive, fhoot- ing, blowing from the mouth of a cannon, compulfory deprivation of deep, rolling in a barrel duck with nails pointed inwards, poifoning, preffing flowly to death by a weight laid on the bread, cading headlong from a rock, tearing out the bowels, pulling to pieces with red- hot pincers, the rack, the wheel, impaling, flaying alive, &c. &c. The punidiments fuort of death have been fine, pillo¬ ry, imprifonment, compulfory labour at the mines, gal- kys, PUR [ 523 ] PUR Punning leys, highways, or corredion houfe } whipping, baftina- II ding) mutilation by cutting away the ears, the nofe, Purflew. ^le t-ongUej breafts of women, the foot, the hand; fqueezing the marrow from the bones with fcrews or wedges, caftration, putting out the eyes, banifhment, running the gauntlet, drumming, {having oft' the hair, burning on the hand or forehead, &c. PUNNING. See Pun. PUPIL, in the Civil Law, a boy or girl not yet arri¬ ved at the age of puberty ; i. e. the boy under 14 years, the girl under 12. Pupil, is alfo ufed in univerfities, &c. for a youth un¬ der the education or difcipline of any perfon. Pupil, in Anatomij, a little aperture in the middle of the uvea and iris of the eye, through which the rays of light pafs to the cryftalline humour, in order to be painted on the retina, and caufe vifion. See Anatomy Index. PURCELL, Henry, a juftly celebrated mailer of mufic, began early to diftinguiih himfelf. As his ge¬ nius was original, it wanted but little forming, and he rofe to the height of his profeffion with more eafe than others pafs through their rudiments. He was made or- ganift to Weftminfter abbey in the latter end of the reign of Charles II. In that of William, he fet feveral longs for Dryden’s Amphijtrion and his King Arthur, which were received with juft applaufe. His notes in his operas were admirably adapted to his words, and fo echoed to the fenfe, that the founds alone feemed ca¬ pable of exciting thofe paflions which they never failed to do in conjundlion. His mufic was very different from the Italian. It was entirely Englilh, and perfecl- ]y mafeuline. His principal works have been publhhed under the title of Orpheus Britannicus. He died in 1695, in the 37 th year of his age, and was interred in Weft¬ minfter abbey, where a monument is eredled to his me¬ mory, PURCHAS, Samuel, an Englifh divine, famous for compiling a valuable coiledlion of voyages, was born in I ijyy, at Thackfted in Effex. After ft tidying at Cam¬ bridge, he obtained the vicarage of Eaftwood in his na¬ tive county ; but leaving that cure to his brother, he fet¬ tled in London, in order to carry on the great work in which he was engaged. He publiftied the firft volume in folio 1613, and the four laft, 12 years after, under the title of Purchas his Pilgrimage, or Relations oj the world, and the Religions ohferved in all ages and places. Meanwhile he was collated to the redory of St Mar¬ tin’s, Ludgate, in London, and made chaplain to Dr Abbot, archbithop of Canterbury. His Pilgrimage, and the learned Hackluyt’s Voyages, led the way to all the other colledions of that kind, and have been juftly valued and eftcemed. But unhappily, by his publifhing, he in¬ volved himfelf in debt: he did not, however, die in p«- fon, as forae have afferted ; but at his own houfe, about the year 1628. PURCHASE, in Law, the buying or acquiring of lands, &c. with money, by deed or agreement, and not by defeent or right of inheritance. Purchase, in the fea-language, is the fame as draw in : thus, when they fay, the capftan purchafes a-pace, they only mean it draws in the cable a-pace. PURE, fomething free from any admixture of fo¬ reign or heterogeneous matters. PURFLEW, a term In heraldry, expreffing errains, Purgatoryv peans, or any of the furs, when they compofe a bordure Purgatiom round a coat of arms : thus they fay, He beareth gules, a bordure, parflew, vairy 3 meaning, that the bordure is vairy. PURGATION, the art of purging, fcouring, or purifying a thing, by feparating, or carrying off any impurities found therein. Thus, In pharmacy, purgation is the cleanfing of a medicine by retrenching its fuperftuities. In chemiftry, it is ufed for the feveral preparations of metals and minerals in¬ tended to clear them of their impurities, more ufually called purification and refining. In medicine, purgation is an excretory motion arifing from a quick and orderly contrablion of the flelhy fibres of the ilomach and inteftines, whereby the chyle, cor¬ rupted humours, and excrements lodged therein, are pro¬ truded further and further, and at length quite excluded the body by ftool. See Materia Medica. Purgation, in Law, figuifies the clearing a perfon’s felt of a crime of which he is fufpedtod and aceufed be¬ fore a judge. This purgation is either canonical or vul¬ gar. Canonical purgation is preferibed by the canon- law, and the form thereof in the fpiritual court is ufual¬ ly thus : The perfon lufpeifted takes his oath that he is innocent of the crime charged againft him 3 and at the fame time brings Ibrae of his neighbours to make oath that they believe he {'wears truly. Vulgar purgation was anciently by fire or water, or elfe by combat, and was practifed here till abolilhed by our canons. See Battel, in law ; Ordeal, Sec. PURGATIVE, or PURGING Medicines, medica¬ ments, which evacuate the impurities of the body by ftool, called alfo cathartics, PURGATORY, a place in which the juft, who de¬ part out of this life, are fuppofed to expiate certain of¬ fences which do not merit eternal damnation. Brough¬ ton has endeavoured,to prove, that this notion has been held by Pagans, Jews, and Mahometans, as well as by Chriftians 3 and that in the days ol the Maccabees the .hews believed that fin might be expiated by facrifice after the death of the ftnner, cannot be queftioned. Much abufe has been poured upon the church oiPapiJl mif- Rome for her dodlrine of purgatory, and many falfe re- reprefented prefentations have been made ol the dodlrine itfelf. The V1',1 el‘,e~ following view of it is taken from a work which is ccn- lidered as a ftandard by the Eritifh Catholics. 1. Every fin, how flight foever, though no more than an idle word, as it is an offence to God, deferves puniihment from him, and will be punilhed by him hereafter, if not cancelled by repentance here. 2. Such fmall fins do not deferve eternal puniihment. 3. Few depart this life fo pure as to be totally exempt from fpots of this na¬ ture, and from every kind of debt due to God’s juftice. 4. Therefore few will efcape without fuffering fome¬ thing from his juftice for fuch debts as they have carried with them out of this world 3 according to that rule of divine juftice, by which he treats every foul hereafter according to its works, and according to the ftate in which he finds it in death. From thefe propofitions, which the Papift confiders as fo many felf-evident truths, he infers that there mull be fome third place of punifh- ment 3 for, fince the infinite goodneis of God can ad¬ mit nothing into heaven which is not clean and pure from all fin both great and fmall 3 and his infinite ju¬ ftice can petmit none to receive the reward of blifs, 3 U 2 whq PUR [ 524 ] PUR Purgatory who as yet are not out of debt, but have fomething in ^ juftice to fuffer ; there muft of neceffity be fome place , “ ' " 'or ilate, where fouls, departing this lile, pardoned as to the eternal guilt or pain, yet obnoxious to fome tempo¬ ral penalty, or with the guilt of fome venial faults, are purged and purilied before their admittance into hea¬ ven. And this is what he is taught concerning purga¬ tory. Which, though he knows not where it is, of what nature the pains are, or how long each foul is de¬ tained there ; yet he believes, that thofe that are in this place, being the living members of Jefus Chritl, are relieved by the prayers of their fellow members here on earth, as alfo by alms and maffes offered up to God for their fouls. And as for fuch as have no relations or friends to pray for them, or give alms, or procure maf- ies for their relief', they are not neglected by the church, which makes a general commemoration of ail tire faith¬ ful departed in every mafs, and in every one of the cano¬ nical hours of the divine office. Such is the Popifh dodtrine of purgatory, which is built chiefly upon 2 Macc. xii. 43, 44, 45 ; St Matth. xii. 31, 32; and 1 Cor. hi. 13. By Proteftants the books of Maccabees are not acknowledged to be in- fpired fcripture j but if they were, the texts referred to would rather prove that theie is no fuch place as pur¬ gatory, fince Judas did not expect the fouls departed to reap any benefit from his fin-offering till the refurrec- tion. Our Saviour, in St Luke, fpeaks of remilfion in this world, and in the world to come ; but furely neither of thefe is purgatory. The world to come is the Hate after the refuneftion, and the remiffion fpoken of is the fentence of abfolution to be pronounced on the penitent from the feat of general judgement. In the abfcure verfe referred to in the epiftle to the Corin¬ thians, the apolfle is, by the belt interpreters, thought to fpeak of the difficulty with which Chriftians ffiould be faved from the dellrudlion of Jerufalem. Of the Hate of fouls departed he cannot well be fuppofed to fpeak, as upon difembodied fpirits fire could make no impreffion. We cannot help, therefore, thinking with the church of England, that “ the Romifh do£trine of purgatory is a fond thing, vainly invented, and ground¬ ed on no warranty of fcripture but we muft confefs at the fame time, that it appears to us to be a very harmlefs error, neither hoftile to virtue nor dangerous to fociety. See Resurrection. PURIFICATION, in matters of religion, a cei'e- mony which confifts in cleanfing any thing from a fup¬ pofed pollution or defilement. The Pagans, before they facrificed, ufually bathed or waffied themfelves in water; and they were particularly careful to waffi their hands, becaufe with thefe they were to touch the vidtims confecrated to the gods. It was alfo cuftomary to wralh the veflel with which they made their libations. The Mahometans alfo ufe purifications pre¬ vious to the duty of prayer ; which are alfo of two kinds, either bathing, or only waffiing the fare, hands, and feet. The firft is required only in extraordinary cafes, as after having lain with a wmtnan, touched a dead body, &c. But left fo neceffary a preparation for their devotions ffiould be omitted, either where water cannot be had, or when it may be of prejudice to a perfon’s health, they are allowed in fuch cafes to make ufe of fine fand, or duft, in- ftead of it} and then they perform this duty by clapping their open hands on the fand, and paffing them over the parts, in the fame manner as if they were dipped in water. There were alfo many legal purifications among the Hebrews. When a woman was brought to bed of a male child, lire was efteemed impure for 40 days } and when of a female, for 60 : at tup end of which time {he carried a lamb to the door of the temple to be offered for a burnt-offering, and a young pigeon or turtle for a fin-offering j and by this ceremony the was cleanfed or purified. PURIM, or The YEAST of Lots, a folemn feflival of the JewTs, inftituted in memory of the deliverance they received, by means of Mordecai and Either, from Pla- man’s wicked attempt to deftroy them. PURITAN, a name formerly given in derifion to: the diffenters from the church of England, on account of the profeflion to follow the pure word of God, in oppofition to all traditions and human conflitutions. It was likewife given in the primitive church to the No- vatian fchifmalics, becaufe they would never admit to- communion any one who from dread of death had apo- ftatized from the faith. PURITY, the freedom of any thing from foreign ad¬ mixture. PuRITT of St/j/e. See Oratory, p. 4ii,&c. PURLIEU, lignifies all that ground near any foreft, which being made foreft by King Henry II. Richard I. and King .lohn, was afterwards by perambulations ami grants of Henry III. fevered again from the fame, and made purlieu ; that is to fay, pure and free from the laws of the foreft.—The word is derived from the French, pur “ pure,” and lieu “ place.” PURLINS, in building, thofe pieces of timber that lie acrofs the rafters on the infide, to keep them from, finking in the middle of their length. By the a£l of parliament for rebuilding London, it is provided, that all purlins from 15 feet 6 inches to 18 feet 6 inches long, be in their fquare 9 inches, and 8 inches ; and all in length from 18 feet 6 inches to 21 feet 6 inches, be in their fquare 12 inches and 9 inches. PURPLE, a colour compofed of a mixture of red and blue. See COLO UR-Making, N° 29, and Dyeing, Index. PURPURA, in Natural Ilifery. See Murex, Con* CHOLOGY Index. The Tyrian method of dyeing purple was with a liquid extra&ed from this fifh. It has been affirmed, however, that no fuch method was ever prac- tifed. “ At Tyre (fays Mr Bruce) I engaged two fiffi- ermen, at the expence of their nets, to drag in thofe places where they faid ffiell-fifir might be caught, in hopes to have brought out one of the famous purple-fifli. I did not fuceed •, but in this I was, I believe as lucky as the old fifiiers had ever been. The purple-fiffi at Tyre feems to have been only a concealment of their know¬ ledge of cochinealas, had they depended upon the filh for their dye, if the whole city of Tyre applied to no¬ thing elfe but fifhing, they would not have coloured 20 yards of cloth in a year.” PURPURE, in Heraldry. The colour fo called, which fignifies purple, is in engraving reprefented by diagonal lines, from the left to the right. See Heral¬ dry. It PUS r 525 ] PUT It may ferve to denote an adminiftrator of juflice, a lawgiver, or a governor equal to a fovereign : and ac¬ cording to G. Leigh, if it is compounded with Pas Or, Arg. Gul. Ax. Ver. Sab. PUERE, or Perkin. PURSER, an officer Riches. Quietnefc. Politics. Ji3 'j Fidelity, j Cruelty. ^ Sadnefs. See Agriculture Index. aboard a man of war, who re¬ ceives her victuals from the victualler, fees that it be well flowed, and keeps an account of what he every day de¬ livers to the Reward. He alfo keeps a lilt of the ihip’s company, and fets down exactly the day ot each man’s admiffion, in order to regulate the quantity of provihons to be delivered out, and that the paymafter or treafurer of the navy may iffue out the deburfements, and pay off the men, according to his book. PURSLAIN. See Portulaca, Botany Index. PURVIEW, a term ufed by fame lawyers for the body of an act of parliament, or that part which begins with “ Be it ena£ted &c.” as contradiftinguiffied from the preamble. PURULENT, in Medicine, fomething mixed with, or partaking of, pus or matter. PUS, in Medicine, a white or yellowiffi matter defign- ed by nature for the healing and cementing of wounds and fores. The origin and formation of pus is as much un¬ known as that of any other animal fluid. In an in¬ augural differtation publiffied at Edinburgh by Dr Hendy, the author fuppofes pus to be a fecreted fluid. It has been thought by many, that pus is ei¬ ther a fediment from ferum when beginning to putre¬ fy, or that it is the fame fluid infpiffated by the heat of the body. But both thefe opinions are refuted by fome experiments of our author, which fhow, that pus is much lefs inclined to putrefaiffion than ferum, and the putrefaction of both is haftened by an addition of fome of the red part of the blood. Some other expe¬ riments were made in order to try whether pus could be artificially produced. A thin piece of lamb’s fleffi, applied to an ulcer difcharging laudable pus, and cover¬ ed over with lead, did not affume the appearance of pus, but became fetid, and was much leffened. Serum, in its inflammatory and in its ordinary Rate, and lymph in different Rates, were applied to the fame ulcer, which Rill difcharged good pus ; but none of thefe were converted into pus j on the contrary, they became very putrid. In oppofition to thefe arguments of our author, however, it may be alleged, that if pus was a fecreted fluid, the veffels by which it was fecreted would cer¬ tainly be vifible •, but no fuch thing has ever been ob- ferved : on the contrary, it is certain that pus cannot be formed unlefs the air is excluded from the wound. Thefe difputes, however, are of no great confequence : but in fome cafes it becomes a matter of real import¬ ance to diRinguiih pus from mucus ; as thus we may be enabled to know whether a cough is confumptive, or merely catarrhous. See Mucus. Mr Home, in a difl'ertation on the properties of pus, in which he avails himfelf of the experiments of Mr Hunter, as delivered in his Phyfiological Lettuces, fays, “ that the characleri- flic of pus is its being compoled of globules; and he p thinks that the prefence of globules feems to depend upon j the pus being in a perfedt Rale. It differs from the blood in the colour of the globules •, in their not being foluble in water, which thole of the blood are ; and from the fluid in which they fwim being coagulable by a folution of fal ammoniac, which ferum is not.” Re- fpefting the formation of pus, our author adopts the idea fuggefled by Mr Hunter, that the veffels of the part af¬ fume the nature of a gland, and fecrete a fluid which becomes pus. Mr Home afcertains, by experiment, that pus, at its formation, is not globular, but a tranf- parent fluid, of a confiilence, in ibme fort, reiemblmg jelly ; and that the globules are formed while lying up¬ on the furface of the fore j requiring, in fome inRances, while the influence of the external air is excluded, fifteen minutes for that purpoie. PUSTULE, a pimple, or fmall eruption on the Ikin full of pus •, fuch as the eruptions of the fmallpox. PUTAMINE/E, (from putamen “ a (hell,”) the name of the 25111 order of Linnaeus’s fragments of a natural method j confiRing of a few genera of plants allied in habit, whole fleihy feed-veffel or fruit is fre¬ quently covered with a hard woody ihell. See Bota¬ ny. PUTEOLI, (Livy, Strabo) : a town of Campania ySwin- fo caked either from its wells, there being many hot andbume'sTra- cold fprings thereabouts j or from its flench, putor, cauted by fulphureous exhalations, (Varro, Strabo).^ It is now called Pu%%uoli, and is pleafantly and advan- tageoufly fituated for trade. In a very remote age, the Cumeans made it their arfenal and dockyard 5 and to this naval eflablifliment gave the fublime appellation of Dicearchia or Juft Power. The Romans were well aware of the utility of this port, and took great pains to improve its natural ad¬ vantages. Nothing remains of their works but a line of piers, built to break the force of a rolling fea : they are- vulgarly called the bridge of Caligula, becaufe that mad¬ man is laid to have marched in triumph from Puzzuoli to Baia on a bridge 5 but his was a bridge of boats. The ruins of its ancient edifices are widely fpread along the adjacent hills and Ihores. An amphitheatre Rill exifls entire in mofl of its parts, and the temple of Serapis offers many curious fubje&s of obfervation \ half of its buildings are Rill buried under the earth thrown upon It by volcanical commotions, or accumu¬ lated by the Grumblings of the hill ; the inclolure is- fquare, environed with buildings for priefls and baths for votaries j in the centre remains a circular platform, with four flights of Reps up to it, vafes for fire, a cen¬ trical altar, rings for viblims, and other appendages of facrifice, entire and not difplaeed 5 but the columns that held its roof have been removed to the new palace of Carerta (Tee Caserta). Behind this round place of worffiip Rand three pillars without capitals, part of the pronaos of a large temple •, they are of cinoline marble, and at the middle of their height are full of holes eaten in them by the file fiffi *. * P^o^at The prefent city contains near 10,000 inhabitants, P>a£lylut, and occupies a fmall peninlula ; the cathedral was a pa ^ln!“ gan temple, dedicated to the divinities that prefided over commerce and navigation. E. Long, j4. 40. N. Let. 41, 15.. PUT [ 526 ] PUT Yiiti In the neighbourhood of Puteoli are many relicks of ^ >’h _ ancient grandeur, of which none defervc.s more attention tion ' i-han tlie Campanian way paved with lava, and lined on ——Y—»w each fide with venerable towers, the repofitories of the dead, which are richly adorned with tlucco in the infide. This road was made in a moft folid expenfive manner by order of Domitkn, and is frequently the fubjedl of em comium in the poems of Statius. PUT! caraja, in Botany, is a genus of Indian plants, of which the chara&ers, as given by Sir William Jones in the Afiatic Refearches, vol. ii. p. 351. are thefe. The calyx is five-cleft, the corolla has five equal petals, the pericarpium a thorny legumen and two feeds, the leaves oval and pinnated, and the Hem armed. “ The feeds (fays the learned Prefident) are very bitter, and perhaps tonic ; fince one of them, bruifed and given in two dozes, will, as the Hindoos affert, cure an intermit¬ tent fever.” PUTORIUS, See Mustela, Mammalia Index. PUTREFACTION, is the natural procefs by which Organized bodies are diffolved, and reduced to what may be called their original elements. Putrefaction differs from chemical folution 5 becaufe in the latter, the diffolved bodies are kept in their ftate of folution by being combined with a certain agent from which they cannot eafily be feparated ; but in pu- trefaftion, the agent which diffolves the body appears not to combine with it in any manner of way, but mere¬ ly to feparate the parts from each other. It differs alfo from the refolution of bodies by dittillation with violent fire 5 becaufe, in diffillation new and permanent com¬ pounds are formed, but by putrefa&ion every thing feems to be refolved into fubftances much more fimple and in- deftruftible than thofe which are the refult of any che¬ mical procefs. The bodies moft liable to putrefaction are thofe of animals and vegetables, efpecially when full of juices. Stones, though by the action of the weather they will moulder into duft, yet feem not to be fubjecl to any thing like a real putrefaction, as they are not refolved into any other fubftance than fand, or fmall duft, which Hill preferves its lapideous nature.' In like manner, ve¬ getables of any kind, when deprived of their juices by drying, may be preferved for many ages without being fubjefted to any thing like a putrefactive procefs. The fame holds good with refpeCl to animals ; the parts of which, by fimple drying, may be preferved in a found ftate for a much longer time than they could be without the previous exhalation of their juices. PutrefaCfion is generally allowed to be a kind of fer¬ mentation, or rather to be the laft ftage of that procefs ; which, beginning with the vinous fermentation, goes on through the acetous, to the ftage of putridity, where it flops. It is argued, however, and feemingly not without a great deal of reafon, that if putrefa&ion be a fermentation, it muft neceffarily be a kind diftincf from either the vinous or acetous •, fince we frequently obferve that it takes place where neither the vinous nor the ace¬ tous ftages have gone before •, of confequence, it muft be, in fome cafes at leaft, entirely independent of and un- connecled with them. In feveral other refpe&s it dif¬ fers fo much from thefe proceffes, that it feems in fome degree doubtful whether it can with propriety be called a fermentation or not. Both the vinous and acetous fer¬ mentations are attended with a confiderable degree of 3 heat : but in the putrefaction of animal matters efpeci- Pctrcfae- ally, the heat is for the moft part fo fmall, that we can- , tIon' not be certain whether there is any degree of it or not produced by tire procefs. In cafes, indeed, where the quantity of corrupting animal matter is very great, fome heat may be perceived ; and accordingly JDr Monro tells us, that he was fenfible of heat on thrufting his hand into the fielli of a dead and corrupting whale. But the moft remarkable difference between the putre¬ factive fermentation and that of the vinous and acetous kinds is, that the end of both thefe proceffes is to pro¬ duce a new and permanent compound j but that of the putrefaClive procefs is not to produce any new form, but to deftroy, and refolve one which already exifts into the original principles from wduch all things feem to proceed. Thus, lire vinous fermentation produces ardent fpirits ; the acetous, vinegar : but putrefaction produces nothing but earth, and fome effluvia, which, though moft difagreeable, and even poifonous to the human bo¬ dy, yet, being imbibed by the earth and vegetable crea¬ tion, give life to a new race of beings. It is commonly fuppofed, indeed, that volatile alkali is a production of the putrefaClive procefs : but this feems liable to dif- pute. The vapour of pure volatile alkali is not hurtful to the human frame, but that of putrefying fubftances is exceedingly fo j and, excepting in the cale of urine, the generation of volatile alkali in putrid fubftances is very equivocal. This fubftance, which produces more alkali than any other, is much lefs offenfive by its putrid fetor than others •, and all animal fubftances produce a volatile alkali on being expofed to the aCtion of fire, of quick¬ lime, or of alkaline falls. In thefe cafes the volatile al¬ kali is not fuppofed to be produced by the quicklime or fixed fait, but only to be extricated from a kind of ammoniacal fait pre-exiiling in the animal matters 5 the probability is the fame in the other cafe, viz. that vola¬ tile alkali is not produced, but only extricated, from thefe fubftances by putrefaClion. The only thing in which the putrefaClive fermenta¬ tion agrees with the other kinds is, that in all the three there is an extrication of fixed air. In the putrefaClive procefs, it has been thought that this efcape of the fix¬ ed air deprives the body of its cohefion : and Dr Mac- bride has written a treatife, in which he endeavours to prove, that fixed air is the very pow-er of cohefion itfelf, and that all bodies w'hen deprived of their fixed air en¬ tirely lofe their cohefion. According to this hypothefis, the caufe of putrefaClion is the efcape of fixed air j but it is impoflible to give a reafon why fixed air, after having fo long remained in a body, and preferved its cohefion, Ihould of a fudden begin to fly off without being aCled upon by fomething elle. To a fimilar objeClion the hypothefis of thofe is liable, who fuppofe putrefaClion to be occafioned by the efcape of phlogifton ; for phlc- gifton is now known to be a chimera : and though it wrere a reality, it wTouid not fly off without fomething to carry it oft', any more than fixed air. Animalcules have been thought to be the caufe of putrefaClion : but if animal fubftances are covered fo as to exclude the ac • cels of flies or other infeCls, no fuch animalcules are to be dilcovered though putrefaClion has taken place \ and indeed it requires little prool to convince us, that ani¬ mals are produced in corrupted bodies only becaufe fuch fubftances prove a proper nidus for the eggs of the pa¬ rent iufeCls. To PUT [ ; Patrefac- To underftand the true caufe of putrefaction, we ttoru muft take notice of the circumftances in which the pro- 1 cefs goes on molt rapidly. Thefe are, heat, a little moifture, and confined air. Extreme cold prevents pu- trefaftion, as well as perfeCt drynefs j and a free circu¬ lation of air carries off the putrid effluvia ; a ftagnation of which feems to be neceffary for carrying on the pro- cefs. It feems alfo to hold pretty generally, that pu¬ trefying bodies fwell and become fpecifically lighter; for which reafon the carcafes of dead animals, after having funk in water, rife to the top and float. This laft phenomenon, as has been obferved under the article Blood, n° 29. fhows that thefe bodies have received a certain quantity of an elaftic principle from the air, which thus fwells them up to fuch a fize. It may be laid indeed, that this increafe of fize in putrefying bo¬ dies is owing only to the extrication of air within them- felves: but this amounts to the fame thing •, for the air which exifts internally in the body of any animal, is entirely divefted of elallicity while it remains there, and only fhows its elallic properties upon being extri¬ cated. The elaftic principle which combines with the air fixed in the animal fubtlance, therefore, muft come from the external atmofphere 5 and confequently the agent in putrefaftion muft be the elaftic principle of the atmofphere itfelf, probably the fame with elementary fire. But, granting this to he true, it is difficult to fhow why putrefaction fhould not take place in a living body as well as in a dead one •, feeing the one is as much ex- pofed to the action of the air as the other. This dif¬ ficulty, however, is not peculiar to the prefent hypothe- fis ; but will equally occur whatever we may fuppofe the caufe of putrefaction to be. The difficulty feems to be a little cleared up by Dr Prieltley, who (hows, that, by means of refpiration, the body is freed from many nox¬ ious effluvia which would undoubtedly deftroy it •, and by the retention of which, he thinks, a living body would putrefy as foon as a dead one. The way in v.-hich refpiration prevents the putrefaftion of the body, is evidently the fame with that in which the wind pre¬ vents fifti or fieffi hung up in it from becoming putrid. The conftant infpiration of the air is like a ftream of that element continually blown upon, the body, and that not only upon its furface, but into it 5 by which means putrefaction is prevented in thofe parts that are moft liable to become putrid. On tire other hand, the *SeeBluove have a remarkable inftance in the fever which took place in Germany in the war of 1755 : one rea¬ fon of which is faid to have been an infebtion of the air by the vaft numbers of people killed in battle, to which was added a calm in the atmofphere for a long time ; the putrid effluvia being by this prevented from flying off*. When Mr Howell with 145 others were * See Me- imprifoned in the black-hole at Calcutta, after paffing ‘Heine, n° PUT [52 Putrefac- a niglit in that difmal habitation, he found himfelf in tlon- a high putrid fever. When failors in long voyages are ’ obliged to feed upon putrid aliments *, when, through ilonny weather, they are much expofed to wet 3 in the -one cafe the putrefcent effluvia being kept from flying off, and in the other a greater quantity being thrown in¬ to the body than what it naturally contain', the fcurvy, malignant fevers, &c. make their appearance (a). Nei¬ ther can thefe difeafes be removed without removing every one of the caufes juft now mentioned : for as pu¬ trid difeafes will be the confequence of confined air, naftinefs, &c. though the provifions be ever fo good 3 fo, on the other hand, if the provifions be bad, the belt air, and moft exa£l cleanlinefs, nay, the belt medicines in the world, -will be of no fervice 3 as hath been often obferved in the fcurvy. From this account of the nature, caufe, and method of preventing putrefaction by means of a current of air, we may eafily fee the reafon why it does not take place in fome other cafes alfo. Bodies will not pu¬ trefy in vacuo, becaufe there the atmofphere has not accefs to impart its elaftic principle 3 and though in the vacuum itfelf the principle we fpeak of does un¬ doubtedly exift, yet its a&ion there is by far too weak to decompofe the ftnuffure of an animal body. In ex¬ treme cold, the reafon why putrefaftion does not take place has been already fflown. If the heat is extreme¬ ly great, the procefs of ignition or burning lakes place inftead of putrefa&ion. If the body is very dry, pu¬ trefaction cannot take place, becaufe the texture is too firm to be decompofed by the weak aCtion of the ela- fiic principle. Putrefaftion may alfo be prevented by the addition of certain fubftances 3 but they are all of them fuch as either harden the texture of the body, and thus render it proof againft the action of the ela- ffic fluid, or, by diffolving its texture entirely, bring it into a ftate fimilar to what it would be brought by the utmoft power of putrefaCtion, fo that the procefs cannot then take place. Thus various kinds of falls 8 ] PUT and acids harden the texture of animal fubffances, and Punrfac- thus are fuccefsfully ufied as antifeptics. The fame don. thing may be laid of ardent fpirits ; while oils and gums y—» of various kinds prove antifeptic by a total exclufion of air, which is neceffary in lome degree for carrying on the procefs of putrefaction. Many vegetables, by the aftringent qualities they poffefs, harden the texture of animal fubftances, and thus prove powerfully antifepti'c 3 while, on the other hand, fixed alkaline falls, quicklime, and cauftic volatile alkali, though they prevent putre¬ faction, yet they do it by diffolving the fubftances in fuch a manner that putrefaction could do no more though it had exerted its utmoft force. There is only one other antifeptic fubftance whofe effeCts deferve to be confidered, and that is fugar. This, though neither acid nor alkaline, is yet one of the moft effectual means of preventing putrefaCtion : and this feems to be owing to its great tendency to run into the vinous fermentation, which is totally inconfiftent with that of putrefaCtion 3 and this tendency is fo great, that it can fcarce be coun¬ teracted, by the tendency of animal fubftances to putrefy in any circumftances whatever. Some kinds of air are remarkably antifeptic, though this fubjeCt has not been fo fully inquired into as could be wilhed. The moft powerful of them In this refpeCt is the nitrous air 3 next to it, is fixed air 3 but the powers of the other airs are not fo well known. It is probable that the antifeptic properties of fixed and nitrous air, are owing to their quality of extinguifhing fire, or at leaft that the principle is the fame 3 but, till the nature of thefe two kinds of air are better known, little can be find with certainty on the fubjeft. Sir John Pringle has made experiments to determine the powers of certain fubftances to promote or to pre¬ vent putrefaftion. From tbefe experiments he has form¬ ed the following Table, fhowing the relative antifeptic powrers of the faline fubftances mentioned. Having found that two drams of beef put in a phial with two ounces of water, and placed in a heat equal to 900 of Fahrenheit’s (a) This aeriform fluid, which is exhaled from animal bodies in a ftate of putrefaCtion, aCts at certain times more powerfully than at others, and is indeed in one ftage of the procefs infinitely more noxious than any other elaftic fluid yet difeovered. In the Gentleman’s Magazine for Auguft 1788, Dr St John, informs us, that he knew a gentleman -who, by fligbtly touching the inteftines of a human body beginning to liberate this corrofive gas, was affeCted with a violent inflammation, which in a very ftiort fpace of time extended up almoft the entire length of his arm, producing an extenfive ulcer of the moft foul and frightful appearance, which continued for fe- veral months, and reduced him to a miferable ftate of emaciation. The fame writer mentions a celebrated profef- for who w’as attacked with a violent inflammation of the nerves and fauces, from which he with difficulty recover¬ ed, merely by ftooping for an inftant over a body which was beginning to give forth this deleterious fluid. Hence he infers, that the fame gas modified or mixed, or united with others, may be the occafion of the plague, which has fo often threatened to annihilate the human fpecies. It is happy, however, for mankind that this particular ftage of putrefaClion continues but for a few hours 3 and, what may appear very remarkable, this deftruOive gas is not very difagreeable in fmell, and has nothing of that abominable and loathfome fetor produced by dead bodies in a lefs dangerous fta*e of corruption 3 but has a certain fmell totally peculiar to itfelf, by which it may he inftantly difeovered by any one that ever fmelled it before. This is an objeft very worthy the attention of phyficians : it is both extremely interefting, and very little known 3 but at the fame time it is a ftudv in the higheft degree unplea- fant, from the deteftable fmell and naftinefs which attend the putrefadlion of animal bodies 3 and a man muft be armed with uncommon philanthropy and refolution to attempt it. Dr St John thinks it probable that there is a rapid fixation of the balls of vital air in dead bodies at a certain -Hate of putrefadl'on, on account of the luminous appearance which they fomet me? make, and which exlfts but fer a few hours : hut whether this luminous appearance takes place in every body, or whether it precedes or fo”ows the exhalations of the corrofive gas above-mentioned, he had not, when he wrote his paper, been able to dik-over. 2 PUT [ 529 ] P U T Putrefac- F«hrenhelt’s thermometer, became putrid in 14 hours, tl0n‘ and that 60 grains of fea-falt preferved a fimilar mixture '' of beef and water more than 30 hours, he made the an- tifeptic power of the fea-falt a itandard, to which he compared the powers of the other falls. The algebraic charafter -j- hgnifies, that the fubftance to which it is annexed had a greater antifeptic power than is expreiied by the numbers: Sea-fait, or the ftandard - - 1 Sal-gem - - - - 1 -j- Vitriolated tartar - - . 2 Spiritus Mindereri - - - 2 Soluble tartar - - - - 2 Sal diureticus - - - 2-j- Crude fal ammoniac - - -3 Saline mixture - - - 3 Nitre - - - - - 44- Salt of hart fhorn - •• - 44- Salt of wormwood - - 44- Borax - - - - 12 Salt of amber - - - 20 Alum - -30 N. B. The quantities of fpiritus Mindereri and of the faline mixture were fuch, that each of them contain¬ ed as much alkaline fait as the other neutral falts. Myrrh, aloes, afafcetida, and terra Japonica, were found to have an antifeptic power 30 times greater than the ffandard. Gum ammoniacum and fagapenum fhowcd little antifeptic power. Of all refinous fubftances, camphor was found to re¬ fill putrefaftion moft powerfully. Sir John Pringle be¬ lieves that its antifeptic power is 300 times greater than that of fea-falt. Chamomile flowers, Virginian fnake-voot, pepper, ginger, faffron, contrayerva root, and galls, were found to be 12 times more antifeptig than fea-lalt. Infufions of large quantities of mint, angelica, ground- svy, green tea, red-rofes, common wormwood, muftard, and horfe-radifh, and alfo decoftions of poppy-heads, were more antifeptic than fea-ialt. Decoftions of wheat, barley, and other farinaceous grains, checked the putrefaction by becoming fopr. Chalk, and other abforbent pow’ders, accelerated the putrefaftion, and refolved meat into a perfeCt mucus. The fame pow'ders prevented an infufion of farinaceous grains from becoming mucilaginous and four. One dram of fea-falt w-as found to preferve two drams of frefh beef in twm ounces of water, above 30 hours, uncorrupted, in a heat equal to that of the human body, or above 20 hours longer than meat is preferved in wra- ter without fait: but half a dram of fait did not pre¬ ferve it more than two hours longer than pure water. Twenty-five grains of fait had little or no antifeptic quality. Twenty grains, 15 grains, but efpecially 10 grains only of fea-falt, were found to accelerate and heighten the putrefaftion of two drams of fiefli. Thefe fmall quantities of fea fait did alfo foften the flelh more than pure wTater. The fame learned and ingenious phyfician made ex¬ periments to difeover the effefts of mixing vegetable with animal matters. Two drams of raw beef, as much bread, and an ■ounce of water, being beat to the confiftence of pap, VOL. XVII. Part II. and expofed to oo0 of heat according to Fahrenheit’s Putratkc- thermometer, began to ferment in a few hours, and , tl0ri' continued in fermentation during Lwro days. When ^ it began to lerment and fvvell, the putrefaClion had be¬ gun ; and in a few hours afterwards, the fmell was of- fenfive. Next day the putrid fmell ceafed, and an acid tafte and fmell fucceeded. Frefh alimentary vegetables, as fpinach, afparagus, feurvy-grafs, produced fimilar ef- fefts as bread on tlelh, but in a weaker degree. From feveral other experiments he found, that animal fub- ftances excite the fermentation of vegetable fubftanceS, and that the latter fubihances correcl the putrefcency of the former. By adding faliva to a fimilar mixture of tlefii, bread, and water, the fermentation was retarded, moderated, but rendered of twice the ufual duration, and the acid produced at laid was weaker than when no faliva was ufed. By adding an oily fubftance to the common mixture of ftefti, bread, and water, a ftronger fermentation was produced, which could not be moderated by the quan¬ tity of laliva ufed in the former experiment, till fome fixed alkaline fait was added j which fait was found, without faliva, to flop fuddenly very high fermentations. Fie did not find that fmall quantities of the following falts, fal ammoniac, nitre, vitriolated taitar, fal diureti¬ cus, fait of hartfhorn, fait of wormwood, were feptic, as fmall quantities of fea-falt were. Sugar was found to refift putrefatflion at firfl, as other falts do, and alfo to check the putrefaftion after it had begun by its own fermentative quality, like bread and other fermentative vegetables. Lime-water made fome fmall refiftance to putrefac¬ tion. Port-wine, fmall-beer, infufions of bitter vegetables, of bark, and the juice of antifcorbutic plants, retarded the fermentation of mixtures of fleih and bread. But an unftrained decoftion of bark confiderably increafcd that fermentation. Crab-eves accelerated and increafed the fermentation of a mixture of fieih and bread. Lime-water neither retarded nor haftened the fer¬ mentation of fuch a mixture : but when the fermenta¬ tion ceafed, the liquor was neither putrid nor acid, but fmelt agreeably. Fiefh pounded in a mortar was found to ferment fooner than that which had not been bruited. The tough inflammatory cruft of blood was found to be moft putrefeent: next to which the craflamentum, or red coagulated mafs •, and laftly the ferum. Dr Macbride’s experiments confirm many of tbofe above related, efpecially tbofe which {how that the fer¬ mentation of vegetable fubftances is increafed by a mix¬ ture of animal or putrefeent mattery that the putref¬ cency of the latter is correfted by the fermentative quality of the former 5 and that the putrefaftion and fermentation of mixtures of animal and vegetable fub¬ ftances were accelerated by additions of abforbent earths and of Peruvian bark. He alfo found, that although unburnt calcareous earths were feptic, quicklime and lime-water prevented putrefaftion, but that they de- ftroyed or diflblved the texture of flefti. The experiments of the author of the EJfaipourfer- vir a IHiftoire de la PutrefaElion, {how that metallic 3 X ' falls, P Y A t 53° 1 P Y L Putrefac- falts, refinous powders, extracts of bark, and opium, are uon very powerfully antifeptic, and that falts with earthy Pyanepfia. ^a^es are le{'s antifeptic than any other falts. 1 v L PUTTOCK-Shrouds. See Puttock-SHROUDS. PUTTY, in its popular fenfe, is a kind of pafle compounded of whiting and lintfeed oil, beaten together to the confidence of a thick dough. It is ufed by glaziers for the faftening in the fquares of glafs in fafh-windows, and by painters for Hopping up the crevices and clefts in timber and wainfcots, &c. Putty fometimes alfo denotes the powder of calci¬ ned tin, ufed in polilhing and giving the laft glofs to works of iron and Heel. Terra PUZZULANA, or Pozzolana, is a grayilh kind of earth ufed in Italy for building under water. The bed is found about Puteoli, Baiae, and Cumae, in the kingdom of Naples, from the fird of ■which places it derives its name. It is a volcanic pro- duft, compofed of heterogeneous fubdances, thrown out from the burning mouths of volcanoes in the form of adies; fometimes in fuch large quantities, and with fo great violence, that whole provinces have been co¬ vered with it at a confiderable didance. In the year 79 of the common era, the cities of Herculaneum, Pompeia, and Stabia, although at the didance of many miles from Vefuvius, were, neverthelefs, buried under the matters of thefe dreadful eruptions ; as Bergman relates in his Treatife of the Volcanic Products. This volcanic earth is of a gray, brown, or blackidi colour j of a loofe, granular, or dudy and rough, porous or fpongy texture, refembling a clay hardened by fire, and then reduced to a grofs powder. It contains va¬ rious heterogeneous fubdances mixed with it. Its fpe- cific gravity is from 2500 to 2800 •, and it is, in fome degree, magnetic: it fcarcely effervefces with acids, though partially foluble in them. It eafily melts per fe; but its mod didinguilhing property is, that it hardens very fuddenly when mixed with y of its weight of lime and water 5 and forms a cement, which is more durable in water than any other. According to Bergman’s Analyfis, 100 parts of it contain from 55 to 60 of filiceous earth, 20 of argil¬ laceous, five or fix of calcareous, and from 15 to 20 of iron. Its effedls, however, in cement may perhaps depend only on the iron which has been reduced into a particular fubdance by means of fubterraneous fires j evident figns of which are obfervable in the places where it is obtained. If the date in Henneberg, or Kennekulle in the province of Wedergottland, diould happen to get fire, the uppermod dratum, which now confids of a mixture of iron and different kinds of rocks, called graberg in the account given of them, they might perhaps be changed partly into dag and partly into terra pu’z'zolana. It is evidently a martial argillaceous marl, that has differed a moderate heat. Its hardening power arifes from the dry date of the half-baked argillaceous par¬ ticles, which makes them imbibe water very rapidly, and thus accelerates the deficcation of the calcareous part; and alfo from the quantity and femiphlogidicated date of the iron contained in it. It is found not only in Italy hut in France, in the provinces of Auvergne and Limoges ; and alfo in England and clfewhere. PUZZUOLI. See Puteoli. PYANEPSIA, in antiquity, an Athenian fedival celebrated on the feventh day of the month Pyanepjlon ; Pyanepfia which, according to the generality of critics, was the II fame with our September. , Plutarch refers the inditution of this fead to The- ’’ feus, who, after the funeral of his father, on this day paid his vows to Apollo, becaufe the youths who re¬ turned with him fafe from Crete then made their entry into the city. On this occafion, thefe young men put¬ ting all that was left of their provifions into one kettle, feaited together on it, and made great rejoicing. Hence was derived the cudom of boiling pulfe on this fedival. The Athenians likewife carried about an olive branch, bound about with wood, and crowned with all forts of fird-fruits, to fignify that fcarcity and barrennefs were ceafed, finging in proceffion a fong. And when the folemnity was over, it wras ufual to ereft the olive- branch before their doors, as a prefervative againd fcarcity and want. PYCNOSTYLE, in the ancient architefture, is a building wfhere the columns dand very clofe to each other ; only one diameter and a half of the column be¬ ing allowed for the intercolumniations. According to Mr Evelyn, the pycnodyle chiedy be¬ longed to the compofite order, and wras ufed in the mod magnificent buildings j as at prefent in the peridyle at St Peter’s at Rome, which confids of near 300 co¬ lumns j and in fuch as yet remain of the ancients, among the ruins of Palmyra. PYGARGUS, a fpecies of falco. See Ornitholo¬ gy Index. PYGMALION, in fabulous hidory, a king of Cy¬ prus, who, being difguded at the difiblute lives of the women of his ifiand, refolved to live in perpetual celi¬ bacy ; but making a datue of ivory, he fell fo paf- fionately in love with it, that the high fedival of Ve¬ nus being come, he fell down before the altar of that goddefs, and befought her to give him a wife like the datue he loved. At his return home, he embraced, as ufual, his ivory form, when he perceived that it became fenfible by degrees, and was at lad a living maid, who found herfelf in her lover’s arms the moment Ihe faw the light. Venus bleffed their union ; and, at the end of nine months, die was delivered of a boy, w7ho was named Paphos. 4 PYGMY, a perfon not exceeding a cubit in height. This appellation was given by the ancients to a fabu¬ lous nation inhabiting Thrace 5 who brought forth young at five years of age, and wrere old at eight : thefe were famous for the bloody war they waged with the cranes. As to this dory, and for the natural hidory of the true pygmy, fee Simia, Mammalia Index. PYKAR, a broker in India, infericr to thofe called da/la/s, w7ho tranfafts the bufinefs at fird hand with the manufacturer, and fometimes carries goods about for fale. PYKE, a watchman in India, employed as a guard at night. Likewufe a footman or runner on bufinefs. They are generally armed with a fpear. PYLADES, a fon of Strophius, king of Phocis, by one of the fiders of Agamemnon. He was educa¬ ted together with his coufin Oredes, with whom he formed the mod inviolable friendfhip, and whom he afiided to revenge the murder of Agamemnon, by af- fafiinating Clytemnedra and iEgydhus. He alfo ac¬ companied him into Taurica Cheifonefusj and for his fer- vices P Y R [ 531 ] P Y R Pylorus vices Oreiles rewarded him, by giving him his lifter p II .. Eledtra in marriage. Pylades had by her two fons, » yl^r‘l Medon and Strophius. The friendlhip of Oreftes and Pylades became proverbial. PYLORUS, in Anatomy, the under orifice of the ftomach. See Anatomy, N° pi. PYLUS, in Ancient Geography, a towTn of Elis ; its ruins to be feen on the road from Olympia to Elis, (Pau- fanias) •, lituated between the mouths of the Peneus and Selles, near Mount Scollis, (Strabo). Built by Pylas of Megara, and deftroyed by Hercules, (Paufanias). Another Pylus in Triphylia, (Strabo) ; by which the Alpheus runs, (Paufanias) j on the confines of Arcadia, and not in Arcadia itfelf, (id.)—A third in Meffenia, (Strabo, Ptolemy) ; fituated at the foot of Mount ./Ega- leus on the fea-coaft, over-againft the iftand Sphagea or Sphadleria: built by Pylas, and fettled by a colony of Leleges from Megara ; but thence expelled by Ne- leus and the Pelafgi, and therefore called Nelea, (Ho¬ mer). A fandy territory. The royal refidence of Ne- leus, and of Neftor his fon : the more ancient and more excellent Pylus *, whence the proverb Py/us ante Pylutn, (Ariftophanes, Plutarch), ufed when we want to re- prefs the arrogance and pride of any one : faid to be afterwards called ConjphaJium. It made a figure in the Peloponnefian war •, for being rebuilt by the Athenians, it proved of great benefit to them for the fpace of 15 years, and of much annoyance to the Lacedemonians, (Thucydides). All the three Py/f were fubjeft to Ne¬ ftor, (Strabo). PYRAMID, in Geometry, a folid Handing on a tri¬ angular, fquare, or polygonal bafts, and terminating in a point at the top } or, according to Euclid, it is a fo¬ lid figure, confifting of feveral triangles, whofe bafes are all in the fame plane, and have one common vertex. Pyramids are fometimes ufed to preferve the memory , of lingular events, and fometimes to tranfmit to pofte- rity the glory and magnificence of princes. But as they are efteemed a fymbol of immortality, they are molt commonly ufed as funeral monuments and temples to the gods. Such is that of Ceftius at Rome; the pyramids of Dafhur drawn by Pocock : and thofe other celebrated ones of Egypt, as famous for the enormity of their fize as their antiquty. Of thefe the largeft are the pyramids of Gee%a, fo called from a village of that name on the banks of the Nile, diftant from them about 11 miles. The three which moft attract the attention of travellers Hand near one another on the weft fide of the river, almoft oppofite to Grand Cairo, and not far from the place where the ancient Memphis flood. They were vifited by M. Savary, of whofe defcription of them rve lhall here give an abftracft. He took his journey’' in the night-time, in order to get up to the top of the great one by funrife. Having got within fight of the two great ones, while the full moon {hone upon them, he informs us, that they ap¬ peared, at the diftance of three leagues, like two points of rock crowned by the clouds. It is in the rich territory which furrounds them that fable has placed the Elyfian fields. The canals which iaterfecft them are the Styx and Lethe. “ The afpecls of the pyramids, varied according to the circuits he made in the plain, and the pofition of the clouds, displayed thcmfclves more and more to view. At half paft three in the morning rve arrived (fays he) at the foot of the greateft. We left our clothes at the gate of the palfage which leads to the infide, and de- icended, carrying each of us a flambeau in his hand. Towards the bottom you muft creep like ferpents to get into the interior paffage, which correfponds with the former. We mounted it on our knees, fupporting ourfelves with our hands againft the fides. Without this precaution one runs the rilk of flipping on the in¬ clined plane, where the flight notches are infufficient to flop the foot, and one might fall to the bottom. To¬ wards the middle wre fired a piftol, the frightful noile of which, repeated in the cavities of this immenfe edi¬ fice, continued a long time, and awakened thoufands of bats, which flying round us, {truck againft our hands and faces, and extinguifhed feveral of our wax candles. They are much larger than the European bats. Ar¬ rived above, we entered a great hall, the gate of which is very low. It is an oblong fquare, wholly compofed of granite. Seven enormous Hones extend from one wall to the other, and form the roof. A farcophagus made of a Angle block of marble lies at one end of it. It is empty $ and the lid of it has been wrenched off. Some pieces of earthen vafes lie around it. Under this beautiful hall is a chamber not fo large, where you find the entrance to a conduit filled with rubbilh. After examining thefe caves, where daylight never penetrated, we defeended the fame way, taking care not to fall in¬ to a well, which is on the left, and goes to the very foundations of the pyramid. Pliny makes mention of this well, and fays it is 26 cubits deep. The internal air of this edifice never being renewed, is fo hot and mephitic that one is almoft fuffocated. When we came out of it, we were dropping with fweat, and pale as death. After refreftiing ourfelves with the external air, we loft no time in afeending the pyramid. It is com¬ pofed of more than 200 layers of ftone. They overlap each other in proportion to their elevation, which is from two to four feet. It is neceflary to climb up all thefe enormous fteps to reach the top. We undertook it at the north-eaft angle, which is the leaft damaged. It took us, however, half an hour with great pains and many efforts to effeft it. “ The fun was rifing, and we enjoyed a pure air, with a moft delicious coolnefs. After admiring the profpeft around us, and engraving our names on the fummit of the pyramid, we defeended cautioufly, for we had the abyfs before us. A piece of ftone detaching itfelf under our feet or hands might .have fent us to the bottom. “ Arrived at the foot of the pyramid, we made the tour of it, contemplating it with a fort of horror. When viewed clofe, it feems to be made of maffes of rocks j but at a hundred paces diftance, the largenefs of the Hones is loft in the immenfity of the whole, and they appear very fmall. “ To determine its dimenfions isftilla problem. From the time of Herodotus to our days it has been meafured by a great number of travellers and learned men, and their different calculations, far from clearing up doubts, have only increafed the uncertainty. The following table will ferve at leaft to prove how difficult it is to come at the truth. Pyramid- X 3 Heigh: Pyramid. P Y U £ ' 1> Height of the great Pyramid. Ancients. Herodotus Strabo Diodorus Siculus Pliny Moderns. Le Bruyn Profpcr Alpinus Thevenot Niebuhr Greaves Width of one of its fides. French Feet. 8co - 8co 6 25 - 600 6oo and a fradlion. 700 708 616 - 7°4 625 - - 750 520 - 682 443 - - 710 444 ' 648 'a are Number of layers of Stone which form it. Greaves - - 207 Maillet - - 208 Albert L hr, vend tin - 260 Pncocke - - 212 Eelon - - 2jO Thevenot - - 208 p appears that MeiTrs Greaves and Niebuhr have prodigioudy deceived themfelves in meafuring the per¬ pendicular height of the great pyramid. All the tra¬ vellers allow that it has at kail 200 layers of done. Thefe layers are from two to four feet high. Accord¬ ing to Pococke, they are from four feet and a half to four feet high, being not fo high at the top as at the bafe. Profper Alpinus informs us, that the elevation of the fid layer is five feet, but it diminilhes infen- fibly in proportion as one mounts. Thevenot men¬ tions 208 Heps of large Hones, the thicknefs of which makes the height of them about two feet and a half one with another : He meafured fome of them more than three feet high. 1 have meafured feveral of them which were more than three feet high, and I found none lefs than two ; the lead height of them we can take as a medium therefore is two feet and a hall, which, even according to Mr Greaves’s calculation, who reckons 207 layers, would make 517 feet 6 inches perpendicular height. Meffrs Greaves, Maillet, Theve¬ not, and Pococke, who only differ in the number of the layers from 207 to 212, ail mounted by the north-eaft angle, as the had injured. I followed the fame route, and counted only 208 Heps. But if we reriecl that the pyramid has been open on the fide next the defert, that the ftones on that fide have been thrown down, that the fand which covers them has formed a confider- able hill, we (hall not be adonifhed that Albert Liew- endein, Belon, and Profper Alpinus, who mult have mounted by the fouth-ead or fouth-vveft angle, which are lefs expofed to the funds of Libya, diould have found a greater number of Heps : fo that the calculation of thefe travellers, agreeing with that of Diodorus Si¬ culus and Strabo, appears to be neared the true height of the pyramid taken at its natural bafe ; whence we may conclude with reafon that it is at lead 600 feet high. Indeed this is authenticated by a paffage of Strabo. Thefe are his words: : Towards the mi ddle of the height of one of the fides is a done that may he raifed up. It fhuls an oblique paffage which leads to a coffin placed in the centre of the pyramid.1 This pad ] P Y H fage, open in cur days, and which in the time of Strabo Pyramid, was towards the middle of one face of the pyramid, is “-"v—— at prelent only 100 feet from the bafe. So that the ruins of the covering ox the pyramid, and of the Hones brought from within, buried by the fand, have formed a hill in this place 200 feet high. Pliny confirms this opinion. The great fphynx was in his time upwards of 62 feet above the furtace of the ground. Its whole body is at prefent buried under the land. Nothing more appears of it than the neck and head, which 27 feet high. If even the Iphynx, though defended by the pyramids againit the northerly winds, which bring torrents of fand from Libya, be covered as high as 38 feet, what an immenfe quantity muff have been heaped up to the northward of an edifice whole bafe is upwards of 700 feet long ? It is to this we mud attribute the prodigious difference between the accounts of the hi- ftorians who have meafured the great pyramid at didant periods, and at oppofite angles. Herodotus, who faw it in the age neared to iis foundation, when its true bafe was dill uncovered, makes it 800 feet fquare. This opinion appears very probable. Pliny aifo fays that it covered the fpace of eight acres. “ Meffrs Shaw, Thevenot, and the other travellers who pretend that this pyramid was never finithed, be- caufe it is open and without coating, are in an error. It is only neceffary to oblerve the remains of the mortar, with the fplinters of white marble which are to be found in many parts of the deps, to lee that it has been coated. After reading attentively the defeription given of it by the ancients, every doubt vanilhes, and the tiuth is as clear as day-light. Herodotus tells us, ‘ The great py¬ ramid was covered with polidied Hones, perfectly well jointed, the fmalled of which was 30 feet long. It was built in the form of deps, on each of which were placed wooden machines to raife the Hones from one to another.’ According to Diodorus, ‘ The great pyra¬ mid is built of Hones, very difficult of workmanfhip, but of an eternal duration. It is prefevved to our days (towards the middle of the Augullan age) without be¬ ing in the lead injured. The marble was brought from the quarries of Arabia.’ This hidorian thought that the whole building was compofed of Hones, dmilar to thofe of the coating, which were of very hard marble. Had there been fome pieces torn off, he would have perceived under that covering a calcareous done rather foft. Pliny fays that it ‘ is formed of Hones brought from the quarr’es of Arabia. It is not far from the vil¬ lage of Bufiris (which dill exids under tire name of Bouft'), where thole perfons refide who are fo fkilful as to climb up to the top.’ “ This paflage fhows that Pliny, deceived by the appearance, was in the fame error with Diodorus Siculus. It demondrates alfo that it was covered : for what difficulty would there have been for the inhabi¬ tants of Bufiris to fcale a building raifed by deps ? but it was really a prodigy for them to get up it when it formed a mountain, the four inclined planes of which prefented a furface covered with polilhed marble. It is indeed an incontedable taT, that the gieat pyramid was coated. It is as certain too that it has been ffiut, as Strabo gives us to underdand; and that by removing a done placed in the middle ot one of the fides, one found a paffage which led to the tomb of the king. But I fixall leave Mr Maillet, who vifited it 40 times with all imaginable Pyramid. P Y R [ SJ3 1 P Y R imaginable attention, the honour of relating the means employed to open it. I have examined the in fide ot it in two different journeys,: twice I have mounted it: and I cannot help admiring the fagacity with which that author has developed the mechaniim oi that aftouilhing edifice. Our author next proceeds to give a particular de- fcription of the methods by which it is molt probable that the pyramids were doled, and the immenle labour requifite to open them. We muff remark, that the final outlet to the workmen he fuppofes to have been the well at the entrance formerly mentioned. This well de- fcends towards the bottom of the pyramid by a line not quite perpendicular to the horizon, but {lanting a little, in fuch a manner as to referable the figure ot the He¬ brew letter Lamed. About 60 feet from the aperture there is a fquare window in this paffage, from whence we enter a fmall grotto hewn out of the mountain ; which in this place is not a fclid itone, but a kind of gravel concreted together. The grotto extends about i 9 feet from call to weft, where there is another groove hollowed likewife, but almoft perpendicular. It is two feet four inches wide by two and a half in height. It defcends through a (pace of I 23 feet, after which we meet with nothing but land and ftoncs. M. Savary is convinced that the only ivfe of this paffage was to lerve as a retreat for the labourers who conftmcted the py¬ ramid ; and of this he looks upon the Hope of the con¬ duit, its winding road, its fmallnefs, and its depth, to be certain proofs. The way out of it he fuppofes to have been formed by a paffage over which hung a row of Hones, which they had difcovered the fecret ot iufpend- ing, and which falling down into the paffige by the means of tome fpring they let in motion, ihut up the en¬ trance tor ever, as foon as the workmen were withdrawn from the pyramid. It feems to be an unqueftionable fa7 38,6 12,25 10,125 FI s 6.2 4>9 3^9 3>5 2.2 3 >5 2,9 2,1 F7 I>333 1,125 0,9 °,7 o,5 0,3 G5 F4 1,0 0,85 0,6 °,5 o,45 o,33 0,25 0,225 0,2 N. B. The diameter of the nipple muft always be equal to that of the former. We ftiall now ftiow the method of finding the dia¬ meters or calibres of rockets, according to their weight ; but we muft firft obferve, that a pound rocket, is that 3 Y juft 53« P Y R O T Apparatus, jui^ capable of admitting a leaden bullet of a pound £eci*of'Firt- an^ f° of the reft. The calibre for the different works, hzes may be found in the two lollowing tables, one of u~—v—— 'which is calculated for rockets of a pound weight and 8 under ; and the other for thofe from a pound to co Method of nds> Koair.g the diameters of rockets ac- I ABLE I. Of the Calibre of Moulds of a pound weight cording to and below. their weight. Ounces 16 12 8 7 6 5 4 3 2 I Lines. 194 1? lS Ml i4t J3 124 ii| 9h 64 Drams M 12 10 8 6 4 2 Lines. 74 7 64 64 5t 44 3i The ufe of this table will be underftood merely by infpeftion •, for it is evident that the mould for a rocket of 12 ounces ought to be 17 lines in diameter j one of eight ounces, 15 lines j one of io drams, 6y lines 5 and fo of the reft. On the other hand, if the diameter of the rocket be given, it will be eafy to find the weight of the ball cor- refponding to that calibre. For example, if the diame¬ ter be 13 lines, it will be immediately feen, by looking for that number in the column of lines, that it cerre- fponds to a ball of five ounces. II. Table of the Calibre of Moulds frovi one to 30 pounds ball. Pounds. 1 2 3 4 5 6 7 8 9 10 11 12 rM 14 15 16 *7 Calibre. IOO 126 I44 I58 I7I 181 I9I 200 208 215 222 228 235 241 247 2 f 2 257 Pounds. 18 J9 20 21 22 23 24 25 26 27 28 29 3° 31 32 33 34 Calibre. 262 267 271 275 280 284 288' 292 296 200 3°4 3°7 310 3I4 Ml 320 323 Pounds. 35 36 37 S8 39 40 41 42 43 44 45 46 47 48 49 5° Calibre. 326 33° 333 336 339 341 344 347 350 353 355 358 061 363 366 368 The ufe of this fecond table is as follows: If the weight of the ball be given, which we fhall fuppofe to be 24 pounds, feek for that number in the column of pounds, and oppofite to it, in the column of calibres, will be found the number 388, Then fay, as icq is to E C H N Y. Chap. I. I9i, fo is 288 to a fourth term, which will be the num- Apparatus, ber of lines of the calibre required j or multiply the Materials, number found, that is 288, by 19^, and from the pro-&^|.^u'e' duce 5616, cut off the two laft figures j the required ■ ( calibre, therefore, will be 56,16 lines, or four inches eight lines. On the other hand, the calibre being given in lines, the weight of the ball may be found with equal eafe. If the calibre, for example, be 28 lines, fay as 19*- is to 28, fo is 100 to a fourth term, which will be 143.5, or nearly 144. But in the above table, oppofite to 144 in the fecond column, will be found the number 3 in the firft; which ftiews that a rocket, the diameter or calibre of which is 28 lines, is a rocket of a three pounds ball. Fig. 7. reprefents a mould, in which the cafes arc driven folid ; L the nipple, with a brafs point at top, (flat at top, and of the fame length as the neck of the Fio- 7* cafe), which, when the cafe is filling, ferves to ^0P jyjouys fcr the neck, and prevent the compofiticn from falling fe,pents or out, as without this point it would 5 and, in conic-wheel-’ quence, the air ■would get into the vacancy in the cafes- charge, and at the time of firing caufe the cafe to be burft. Thefe moulds are made of any length or diame¬ ter, according as the cafes are required 3 but the diame¬ ter of the rollers muff be equal to half the bore, and the rammers made quite folid. The nipple and cylin¬ ders muft bear the fame proportion as thofe for rockets. The rolling and formation of cafes is fo intimately connected with the conftru&ion of moulds m&fortners, that we ihall introduce what we have to fay on that fubjecl into the fame feflion. Sky-rocket cafes are to be made 6f of their exterior diameter long 5 and all other cafes that are to be filled in moulds muft be as long as the moulds, within half its interior diameter. Rocket cafes, from the fmalleft to four or fix pounds, Mcihod c? are generally made of the ftrongeft fort of cartridge roll ng paper, and rolled dry 3 but the large fort are made ofcafes. pafted pafteboard. As it is very difficult to roll the ends of the cafes quite even, the beft way will be to keep a pattern of the paper for the different forts of cafes; which pattern ffiould be fomewhat longer than the cafe it is defigned for, and on it marked the number of fheets required, which will prevent any paper being cut to wafte. Having cut the papers of a proper fize, and the laft ffieet for each cafe with a flope at one end, fo that when the cafes are rolled it may form a fpiral line round the outfide, and that this flope may always be the fame, let the pattern be fo cut for a guide. Before you begin to roll, fold down one end of the firft: fheet, fo far that the fold will go two or three times round the former : then, on the double edge, lay the former with its handle eft the table 3 and when you have rolled on the paper within two or three turns, lay the next ffieet on that part which is loofe, and roll it all on. Having thus done, you muft have a fmoolh board, about 20 inches long, and equal in breadth to the length of the cafe. In th» middle of this board muft be a handle placed lengthwife. Under this board lay the cafe, and let one end of the board lie on the table 3 then prefs hard on it, and puffi it forwards, which will roll the paper very tight 3 do this three or four times be¬ fore you roll on any more paper. This muft be repeat¬ ed with every other fheet of paper, till th^ cafe is thick enough 5 Chap. I. Apparatus, enough j but if the rolling board be drawn backwards, &1SofFire ^ loofen the paper : you are to obferve, when you works. *ro^ 011 t^ie ^eet» that the point of the dope be pla- u—y—— ced at the fmall end of the roller. Having rolled your cafe to fit the mould, pufh in the fmall end of the form¬ er F, about one diameter from the end of the cafe, and put in the end-piece within a little diftance of the form¬ er ; then give the pinching cord one turn round the cafe, between the former and the end-piece } at firft pull gently, and keep moving the cafe, which will make the neck fmooth, and without large wrinkles. When the cafes are hard to choak, let each (heet of paper (except the firft and laft, in that part where the neck is formed) be a little moiftened with w7ater: immediately after you have Itruck the concave Itroke, bind the neck of the cafe round with fmall twine, which mult not be tied in a knot, but faltened with two or three hitches. Having thus pinched and tied the cafe fo as not to give way, put it into the mould without its foot, and •with a mallet drive the former hard on the end-piece, which will force the neck clofe and fmooth. This done, cut the cafe to its proper length, allowing from the neck to the edge of the mouth half a diameter, wdiich is equal to the height of the nipple; then take out the former, and drive the cafe over the piercer with the long rammer, and the vent will be of a proper fize. Wheel-qafes mult be driven on a nipple with a point to clofe the neck, and make the vent of the fize required j which, in molt cafes, is generally one-fourth of their in¬ terior diameter. As it is very often difficult, when the cafes are rolled, to draw the roller out, you may make a hole through the handle, and put in it a fmall iron pin, by wffiich you may eafily turn the former round and Fig, 3, Pu^ ^ out' Fig* 8. fhow7S the method of pinching cafes ; P a treddle, which, when prefled hard with the foot, will draw7 the cord tight, and force the neck as clofe as you pleafe j a fmall wheel or pulley, with a groove round it for the cord to run in. Cafes for wheels and fixed pieces are commonly rol¬ led wet} and when they are required to contain a great length of charge, the method of making thofe cafes is this: The paper mufl: be cut as ufual, only the laft fheet mult not be cut with a fiope : Having the paper ready, pafte each fheet on one fide; then fold down the firft fheet as before directed : but be careful that the pafte does not touch the upper part of the fold j for if the roller be wetted, it will tear the paper in drawing it out. In pafting the laft flieet, obferve not to wretthe laft turn or twro in that part where it is to be pinched 5 for if that part be damp, the pinching cord will flick to it, and tear the paper •, therefore, when you choke thofe cafes, roll a bit of dry paper once round the cafe, be¬ fore you put on the pinching cord ; but this bit of paper muft be taken oft after the cafe is choked. The rolling board, and all other methods, according to the former directions for the rolling and pinching of cafes, muft be It ufed to tbefe as well as all other cafes. Tourbillon Tourhi/Ion cafes are generally made about eight diame- cafes. terslong*, but if very large, feven will be fufficient: tour- billons will anfwer very well from four ounces to two pounds *, but when larger there is no certainty. The Cafes are belt rolled wet with pafte, and the laft Iheet muft have a flraight edge, fo that the cafe may be all of a thicknefs : when the cafes have been rolled in the manner of wheel cafes, pinch them at one end quite 539 clofe ; then with the rammer drive the ends down flat, Apparatus, and afterwards ram in about one-third of a diameter of Matena!s» dried clay. The diameter of the former for thefe cafes muft be the fame as of that for fky-rockets. - v-~ - N. B. Tourbillons are to be rammed in moulds with¬ out a nipple, or in a mould without its fooc. For balloons, firft prepare an oval former turned Balloon ca- of fmooth wood ; over which, parting a quantity offes. or paper brown or cartridge paper, let it lie till the pafte has flielIs‘ quite foaked through $ this done, rub the former with foap or greafe, to prevent the paper from flicking to it j then lay the paper on in fmall flips, till you have made it one-third of the thicknefs of the intended fhell. This being done, fet it to dry j and when dry, cut it round the middle, and the two halves will eafily come off: but obferve, when you cut, to leave about, one inch un¬ cut, which will make the halves join much better than if they had been quite feparated. When there are fome ready to join, place the halves evenly together, pafte a flip of paper round the opening to hold them together, and let that dry ; then lay on paper all over as before, everywhere equal, excepting that end which goes down¬ wards in the mortar, which may be a little thicker than the reft ; for that part which receives the impulfe from the powder in the chamber of the mortar requires the greateft ftrength. When the fliell is thoroughly drv, burn a round hole at top, with fquare iron, large enough for the fuze: this method will do for balloons from four inches two-fifths, to eight inches diameter ; but if they are larger, or required to be thrown a great height, let the firft fliell be turned of elm, inftead of being made of paper. For a balloon of four inches two fifths, let the former be three inches one-eighth diameterj and five inches and a half long. For a balloon of five inches and a half, the diameter of the former muft be four inches, and eight inches long. For a balloon of eight inches, let the diameter of the former be five inches and 1 <;-i6ths, and 11 inches feven-eights long. For a 10-inch bal¬ loon, let the former be feven inches three-fixteenths dia¬ meter, and 14 inches and a half long. The thicknefs of a fhell for a balloon of four inches two-fifths, muft be one-half inch. For a balloon of five inches and a half, let the thicknefs of the paper be five-eighths of an inch. For an eight-inch balloon, feven-eighths of an inch. And for a 10-inch balloon, let the fhell be one inch ' one-eighth thick. Shells that are defigned for ftars only, may be made quite round, and the thinner they are at the opening, the better ; for if they are too ftrong, the ftars are apt to break at the burfting of the ftiell: when making the fhell, ufe a pair of calibre compaffes, or a round gage, fo that the paper may not be laid thicker in one place than another ; and alfo to know when the fhell is of a proper thicknfefs. Balloons muft always be made to go eafy into the mortars. Port-fire cafes muft be made very thin, and rolled on Cafes1 tor formers, from two inches to 4 of an inch diameter, and port-fires-, from two to fix inches long : they are pinched clofe at one end, and left open at the other. When they are to be filled, put in but little compofition at a time, and ram it lightly, fo as not to break the cafe : three or four rounds of paper, with the laft round parted, will be ftrong enough for thefe cafes. Common portfires are intended for the purpofe of fir- 3 Y 2 PYROTECHNY. 54^ PYROTECHNY. Chap. I. ■Apparatus, ing tlie works, tkeir fire being very flow Materials, - - - - - - - ■ - - - Sec. ol Fire- mon port¬ fires 15 Meth d of gri! d.ng the ingre¬ dients. Fig. 9 v , and the heat Material.', 0f q1£ f]ame f0 intenfe, that, if applied to rockets, lead¬ ers, &c. it will fire them immediately. Portfires may be made of any length, but are feldom made more than 21 inches long : the interior diameter of portfire moulds fiiould be io-i6ths of an inch, and the diameter of the former halt an inch. The cales muft be rolled wet with pafte, and one end pinched, or folded down. The moulds ihould be made oi brafs, and fuch as will take in two pieces lengthwife ; when the cafe is in the two lides, they are held together by brals rings, or hoops, which are made to fit over the outfide. \ he bore of the mould muft not be made quite through, lb that there wfill be no occafion for a foot. Thefe portfires, when uled, are held in copper lockets, fixed on the end of a long flick : thefe lockets are made like port-crayons, on¬ ly with a fcrew inftead of a ring. There have been many methods contrived for grind¬ ing the ingredients for fire-works to a powder, fuch as large mortals and peftles made of ebony and other hard ■wood, and horizontal mills with brafs barrels 5 but none have proved fo effectual and fpeedy, as that of the meal- ing-table, reprefented in fig. 9. made of elm, with a rim round its edge four or five inches high •, and at the nar¬ row' end A, furnifhed with a ftider that runs in a gtoove, and forms part of the rim : lb that when you have taken cut of the table as much powder as you can with the Fig. io. copper (hovel (fig. 10.), fvveep all clean out at the Aider A. When about to meal a quantity of pou ch r, obferve not to put too much in the table at once ; but when you II< have put in a good proportion, take the muller (fig. 11.) and rub it till all the grains are broken 5 then lift it in a lawn fieve that has a receiver and top to it, fuch as is ufed by apothecaries, and that which does not pal's through the fieve, muft be returned again to the table, and ground till it is fine enough to go through the fieve. Sulphur and charcoal are ground in the fame manner, only the muller muff be made of ebony •, for thefe ingre¬ dients being harder than powder, would flick in the grain of elm, and be difficult to grind. As fulpbur is apt to flick and clod to the table, it will be bell to keep one for that purpofe, by which means you will always have your brimftone clean and well ground. Fig. is. Fig. 1 2. reprefents the plan of an apparatus, or lathe, 16 for boring rockets. A the large wheel, -which turns f^orirn-5 *'*ie one that w'orks the rammer C : thefe ram- rockets thatmers are different fizes according to the rockets j are rammed they muft be of the fame diameter as the top of the in- foiid. tended bore, and continue that thicknefs a little longer than the depth of the bore required, and their points muft be like that of an augre : the thick end of each rammer muft be made fquare, and all of the fame fize, fo as to fit into one focket, into which they are faftened by a fcrew I). E the guide for the rammer, which is made to move backwards and forwards that, after the rammer has been marked three diameters and a half of the rocket from the point, fet the guide, allowing for the thicknefs of the fronts of the rocket boxes, and the neck and mouth of the rocket •, fo that when the front of the large box is clofe to the guide, the rammer rnay not go too far up the charge. F, boxes for bold¬ ing the rockets, which are made fo as to fit one within ; their fides muft be equal in thicknefs to the difference of the diameters of the rockets, and their interior diameters works. Fig- 13- Fiz. 14. Fig. 15. equal to the exterior diameters of the rockets. To pre- Apparatus, vent the rocket from turning round while boring, a piece ,;VIatE(rhi''’ of wood muft be placed againft the end of the box in l' the infide, and preffed againit the tail of the rocket. Tins will alfo hinder the rammer from forcing the roc¬ ket backwards. G, a rocket in the box. H, a box that Aides under the rocket-boxes to receive the borings for the rockets, which fall through holes made on pur¬ pofe in the boxes ; thefe holes muft be juft under the mouth of the rocket, one in each box, and all to corre- fpond with each other. Fig. 13. is a front view of tire large rocket-box. I, an iron-plate, in which are holes of different fizes, through which the rammer p-affes ; this plate is faftened with a fcrew in the centre, fo that when the rammer is changed, the plate is turned round, but the hole you are going to ufe muft always be at the bottom : the fronts of the other boxes muft have holes in them to correfpond with thole in the plate. K, the lower part of the large box ; w hich is made to fit the infide of the lathe, that all the boxes may move quite fteadily. Fig. 14. is a peripeclive view of the lathe. L, the guide for the rammer, which is fet by the icrew at bot¬ tom. Fig. 15. A view of the front of the guide facing the rammer. M, an iron plate, of the fame dimtnfions as that on the front of the box, and placed in the lame di- reefion, and alfo to turn on a Icrew in the centre. N, tlie rocket-box which Aides batkwards and forwards : when a rocket is fixed in the box, it is to be puftred for¬ wards againft the rammer j and when the fcoop of the rammer appears to be full, draw the box back, and knock out the compofnion : this muft be done till the rocket is bored, or it will be in danger of taking fire •, and if the boring be done in a hurry, wet the end of the rammer now and then with oil to keep it cool. Having bored a number of rockets, you muft have taps of different ferts according to the rockets. Thefe taps are a little longer than the bore : but when ufed they mufti be marked 3 f diameters from the point, al¬ lowing for the thickhefs of the rocket’s neck ; then, holding the rocket in one hand, tap it with the other. One of thefe taps is reprefented by fig. 16. They are made in the fame proportion as the fixed piercers, and are hollowed their whole length. There are hand machines for boring, which anfwer Hand ma- very well, though not fo expeditious as the lathes. But chine for they are not fo expenfive, and they may be worked by 'x-r^k- one man 5 whereas the lathe evil! require three. Fig. 17. Fig. 17. reprefents the machine. O, the rocket boxes, which are to be fixed, and not to Aide as thofe in the lathe. PQ^ are guides for the rammers, that are made to Aide together, as the rammer moves forward: the rammers for thefe machines muft be made of a proper length, al¬ lowing for the thicknefs of the front of the boxes, and the length of the mouth and neck of the cafe ; on the fquare end of thefe rammers muft be a round fhculder of iron, to turn againft the outfide of the guide O. by which means the guides are forced forwards, it, the flock which turns the rammer, and which, while turn¬ ing, muft be prefled towards the rocket by the body of the man who works it 5 all the rammers are to be made to fit one ftock. Fig. 16. 17 Sect. Chap. I. ges of fire works Apparatus Materials Gect. II. Of the Ingredients fo*" compojing the Charges of See. of Fire- Fire-works. v, oiks. l8 The charges or compofitions with which the cafes Ingredients that we have deferibed are to be filled, confiif chierly of for the char-gunp0,V(ier^ or 0f a powder compofed of the fame mate ¬ rials in various proportions, and tome other combutlible fubttances, intended either to give tne compofition a ftronger impelling force, or to increafe the beauty and fplendour of the exhibition. As the nature and compo¬ fition of gunpowder have been tuily explained under the article Gunpowder, it is unneceffary to confider them in this place j but as the makers of fire-works common¬ ly employ confiderable quantities of the tubftances of which gunpowder is compofed, it may be proper to give forae direflions for obtaining thefe in the greated purity. We may alfo notice, that gunpowder, in its ordinary date, is called corn powder; while, when ground down, as direaed in N° 15. u is denominated meal powder. The ingredient on which the force of the compofitions chiefly depends, is nitre, or faltpetre 5 but as this fub- flance, in its ufual date, is very impure, being much contaminated with earthy matter, and as pine ifltre is now become very expenfive, it is of contequence to know how the nitre of commerce may be purified. Nitre, like mod other faline bodies, is much more fo- luble in boiling water, than in water of the ordinary temperature. If, therefore, the nitre of commerce be diffolved in a fmall quantify of boiling water, and the f'olution be properly drained, the liquor, when cold, will afford crydals that are very pure. The following is the mod convenient method of proceeding. Diilolve the nitre in boiling water, in the proportion of about an Englifh quart, or Scotch chopin, to each pound of nitre ; and that the folution may be more eafily effect¬ ed, let the nitre be reduced to powder, and let the vef- fel containing the nitre and water be kept at the boil¬ ing heat till all the fait is diffolved. . Then drain the liquor while hot through thick blotting paper, placed in a clean funnel, and fet by the filtered liquor in a fhallow veffel, in feme cold place, till crydals are form¬ ed, Thefe mud be removed from the liquor, and dried with a gentle heat •, and if the remaining liquor be (lowly evaporated over the fire, in an earthen unglazed veffel, till a film appears on the top, and then fet by to cryftallize as before, an additional quantity of pure nitre will be procured; and thus, by repeated evaporations and crydallizations, the whole of the fait will be ob¬ tained. Nitre may be obtained in great purity from damaged gunpowder, which may often be bought at a cheap rate. The damaged powder mud; be ground with a fmall quantity of hot water, in a large wooden or done mor¬ tar, or it may be boiled over a gentle fire, with as much water as will cover it. When the water feems to have P Y R O T E C H N Y. 54* Nitre may be fpeeckly reduced to a fine powder, by Apparatus, diffolving i in a little more than its own weight of boil- pjre. iny; water, m a kettle with a round bottom, keeping 19 Nine. 20 Method of panning nitre. Mettied of procuring nitre from damaged gun-pow¬ der. diffolved as much of the nitre as it will retain, it is to be poured off from the fediment, and filtered or ftrained through a flannel bag, then heated again, and, while hot, filtered through blotting paper, and fet by to cry- dallize, as in the former cafe. Fredi quantities of hot water are to be fucceflively added to the fediment, and ftrained as before, till the whole of the nitre is ob¬ tained. . w _ works. the folution over a gentle fire, and continually ftirnng ' it with a wooden fpatula till all the water is evaporated, 22 and the remaining powder is pretty well dried. CareSp«jdy me* muft be taken, however, not to fuffer it to remain too |.o^rdel.jng long, or expofe it to too great a heat, otherwife it will n;ue. & be melted into a firm cake. The drying may be Com¬ pleted by fullering it to lie for a fufficient time on paper before the fire. 23 Sulphur or brimftone, may be employed in three Sulphur, ftates/ 1. As it is brought from the neighbourhood of volcanoes, or what is called fulphur woum. 2. Koll brim¬ ftone, which is fold by moll grocers, and is employed for making matches ; and, 3. Flowers of fulphur, or fublimed fulphur. The firft of thefe is the cheapeft, and anfwers very well for coarfe fire-works •, the fecond is confidered as the ftrongeft, and is mold ufed ; but the third is the pureft fulphur, and will anfwer bell for the nicer and more delicate fire-works. It alio has the ad¬ vantage of being in a ftate of fine powder, whereas the the two former require to be ground or mealed, as di¬ rected in N° 15. 24' ( Charcoal may, in general, be procured at the Poops Charcoal, of founders and hardware dealers ; but when this is not the cafe, it may eafily be prepared by putting a quan¬ tity of fmall pieces of wood into a large earthen cru¬ cible or iron pot, and covering them to the head with fand, and placing the crucible or the pot in the middle of a ttrong fire, where it muft be kept red hot for an hour or two, in proportion to the quantity oi wood. Charcoal Ihould he chofen foft and light, and fuch as may eafily be reduced to powder. It Ihould be kept in a dry place, but is always bell when frefii burned. Several other ingredients are employed in the compo¬ fition of fire-works, fuch as camphor, antimony (fful- phuret of antimony'), rafpings of ivory, yellow amber, fal ammoniac, verdigris, common pitch, and Greek pitch, all of which are ufed on different occafions, to produce a change of colour in the fire ; filings of iron and copper, for giving a fparkling appearance to the flame, and fait of benjamin {benzoic acid) to produce an agreeable odour. Iron filings anfwer very well for ordinary fire-works ; Method of but they do not produce fuch a brilliant appearance as powdering powdered caff-iron. The introduction of this latter iscaftiron- an improvement of the Chinefe, and its ufe is now very general. Caft-iron being of fo hard a nature as not to be cut by a file, we are obliged to reduce it into grains, though this is rather difficult to perform; but if.we confider- what beautiful fparks this iron yields, no pains ihould be fpared to granulate fuch an effential material: to do this, procure at an iron-foundery fome thin pieces of iron, fuch as generally run over the mould at the time of call¬ ing : then have a fquare block made of calf-iron, and an iron fquare hammer about four lb. weight; then, ha¬ ving covered the floor with cloth or fomething to catch the" beatings, lay the thin pieces of iron on the block,, and beat them with the hammer till reduced into fmall grains ; which afterwards lift with a very fine fieve, to feparate the fine duff, which is fometimes ufed in fmall cafes of brilliant fire, infiead of (feel duft ; and when 25 76 ypu have got out all the duft, lift what remains with -a fieve 1. Apparatus, fieve a little larger, and fo on with fieves of different Sc^omre-?268’ ^ the iron pafes through about the bignefs of works. fmall bird-fliot : the iron, thus beaten and lifted, is to be »—V-— put feparately, according to its finenefs, into wooden boxes or oiled paper, to keep it from rufting. When ufed, obferve the difference of its fize, in proportion to the cafes for which the charge is intended ; for the coarfe fort is proper only for very large gerbes of fix or eight pounds. s When thefe pieces of iron cannot be procured, an old caft-iron pot may be employed} but care muff be taken that its furface be perfectly freed from ruff. This pulverized caff iron is fometimes called iron /and, and is denominated, according to its finenefs, fand of the fiift, fecond, third, &c. order, that of the firft order being the fineft. It fometimes happens, that fire-works may be re¬ quired to be kept a long time, or fent abroad; neither of which could be done with brilliant fires, if made with filings unprepared, for this reafon ; that the falt- petre being of a damp nature, it caufes the iron to ruff j the confequence of which is, that when the works are fired, there will appear but very few brilliant fparks, but inftead of them a number of red and droffy fparks •, aim befides, the charge will be fo much weakened, that if this were to take place in wheels, the fire would fcarcely be ftrong enough to force them round. But to prevent fuch accidents, the filings may be thus prepared : Melt in a glazed earthen pan fome brimftone over a flow fire, and when melted throw in fome filings; which keep ftirring till they are covered with brimftone : this muft be done while it is on the fire ; then take it off, and ftir it very quickly till cold, when it muft be rolled on a board with a wooden roller, till broken as fine as corn powder \ after which lift from it as much of the brimftone as poffible. There is another method of pre¬ paring filings, fo as to keep two or three months in wunter; this may be done by rubbing them between ftrong. brown paper, wdrich before has been moiftened with linfeed oil. N. B. If the brimftone fhould take fire, it may be extinguifhed, by covering the pan clofe at top : it does not fignify what quantity of brimftone is ufed, provided there is enough to give each graia of iron a coat; but as much as will cover the bottom of a pan of about one foot diameter, will do for five or fix pounds of filings or 2 5 caft-iron for gerbes. Chinefe fire. Before we enumerate the various compofitions gene¬ rally employed in filling cafes for rockets, wheels, &c. we fhall defcribe two compofitions that are much valued for the brilliancy of their appearance. One of thefe is called Chinefe fire, and is either red or white. The fol¬ lowing tables thew the proportions of the different ingre¬ dients for each of thefe compofitions \ as they are adapt¬ ed to rockets (in the conftrudlion of which the Chinefe fire is much employed) of from l 2 to 36 lbs. For If kite Chinefe Fire. Calibres. Pounds. X 2 to 15 18 to 21 24 to 36 Saltpetre. Bruited Gunpowder. Pounds. I I I Apparatus, Materials, Sec. of Fire¬ works. Charcoal. Sand of the third order Oz. 7 8 8 Dr. 8 O 8 Oz. 11 11 12 Df. O 8 o Compofition of Red Chinefe Fire. Calibre'. Pounds. I 2 to 15 18 to 21 24 to 36 Saltpetre. Pounds. I I I Sulphur. uunce:. 3 3 4 Charcoal. Ounces 4 5 6 Sand of the firft O' der. Oz. 7 7 Dr. O 8 o The other compofition is called fpur fire, becaufe the fparks yielded by it have a ftarry appearance like the rowel of a fpur. Spur-fire.—This fire is the mofi: beautiful and curious of any yet known 5 and wTas invented by the Chinefe, but now is in greater perfeclion in England than in Chma. As it requires great trouble to make it to per- lechon, it will be neceffary that beginners fliould have full jnftrudions; therefore care fhould be taken that all the ingredients are of the beft, that the lamp-black is not damp and clodded, that the faltpetre and brimftone are thoroughly refined. This compofition is generally rammed in one or two ounce cafes about five or fix inches long, but not drove very hard ; and the cafes muft have their concave ftroke ftruck very fmootb, and the choak or vent not quite fb large as the ufual propor¬ tion : this charge, when driven and kept a few months, will be much better than when rammed ; and wall not fpoil, if kept dry, in many vears. As the beauty of this compofition cannot be feen at fo great a diftance as brilliant fire, it has a better effedl in a room than in the open air, and may be fired in a chamber without any danger : it is of fo innocent a na¬ ture, that, though with an improper phrafe, it may be called a cold fire ; and fo extraordinary is the fire pro¬ duced from this compofition, that, if well made, the fparks wall not burn a handkerchief when held in the midft of them •, you may hold them in your hand while burning, with as much fafety as a candle; and if you put your hand within a foot of the mouth of the cafe, you will feel the fparks like drops of rain. When any of thefe fpur-fires are fired fingly, they are called artifi¬ cial fiowerpots; but fome of them placed round a tranf- parent pyramid of paper, and fired in a large room, make a very pretty appearance. I he compofition confifts of faltpetre, four pounds eight ounces ; fulphur two pounds, and lamp-black one pound eight ounces;'or, faltpetre one pound, fulphi r half a pound, and lamp-black four quarts.—This com¬ pofition is very difficult to mix. The falipetre and*" brimftone muft be firft fifted together, and then put in¬ to a marble mortar, and the lamp-black with them which you work dowm by degrees with a wmoden peftle* till all the ingredients appear of one colour, which will be Something grayifh, but very near black : then drive a little into a cafe for trial, and fire it in a dark place • and if the fparks, which are called fiars, or pinks, come out in clufterSj and afterwards fpread well without any other fparks, it is a fign of its being good, otherwife not ; for if any droffy fparks appear, and the ftars not full, it is then not mixed enough ; but if the pinks are very fmall, and foon break, it is a fign that it has been rubbed too much. This o ^ Spur tire. Chap. I. P Y R O T E C H N Y. 31 For rocket (tars. Apparatus, This mixture, when rubbed too much, will be too &?5rFire/ierCe’ and h.ardly fh°W any ^ars ’ and’ on l'ne contrary, works. Vvdien not mixed enough, will be too weak, and throw I,. ■ 1. ■ 1 out an obfcure fmoke, and lumps of drofs, without any ftars. I he following compofitions are thole commonly em- ployed in ordinary fire-works. Charges for Rockets of four ounces.—Mealed powder 1 lb. 4 oz. Qry-rockets. faltpetre 4 oz. and charcoal 2 oz. Rockets of eight ounces.—I. Mealed powder 1 lb. laltpetre 4 oz. brimltone 3 oz. and charcoal 14 oz. 11. Meal-powder if lb. and charcoal 4^ oz. Rockets of one -Meal-powder 2 lb. faltpetre 8 oz. brimltone 4 oz. charcoal 2oz. and fteel-filings if oz. Sky-rockets in general.—I. Saltpetre 4 lb. brimltone 1 lb. and charcoal if lb. II. Saltpetre 4 lb. brim¬ ltone If lb. charcoal 1 lb. 12 oz. and meal-powder 2 oz. LargeJky-rockets.—Saltpetre 4 lb. meal-powder 1 lb. and brimltone 1 lb. Rockets of a middling fze 1. Saltpetre 8 lb. ful- phur 3 lb. meal-powder 3 lb. II. Saltpetre 3 lb. ful- phur 2 lb. meal powder 1 lb. charcoal 1 lb. White fars. Meal-powrder 4 oz. faltpetre 12 oz. fulphur vivum 6 oz. oil of fpike 2 oz. and camphor 5 oz. Blue fars.—Meal-powder 8 oz. faltpetre 4, fulphur 2, fpirit of wane 2, and oil of fpike 2. Coloured or variegated fars. Meal-powder 8 drams, rochpetre 4 oz. fulphur vivum 2, and camphor 2. Brilliant fars.—Saltpetre 3f oz. fulphur if, and meal-powder J-, worked up with fpirits of wine only. Common ^rr.—Saltpetre 1 lb. brimitone 4 oz. an¬ timony 4-}, ifinglafs f, camphor f, and fpirit of wane Tailed fars.—Meal-powder 3 oz. brimftone 2, falt¬ petre 1, and charcoal (coarfely ground) Drove fars.—I. Saltpetre 3 lb. fulphur 1 lb. brafs dull 12 oz. antimony 3. II. Saltpetre 1 lb. antimony 4 oz. and fulphur 8. Fixed pointed fars.—Saltpetre 8f oz. fulphur 2, anti¬ mony 1 oz. 10 dr. Stars of afne colour.—Sulphur 1 oz. meal-powder 1, faltpetre 1, camphor 4 dr. oil of turpentine 4 dr. Gold rain for Jky-rockets.—I. Saltpetre 1 lb. meal- powder 4 oz. fulphur 4, brafs-duft 1, faw-duft 2f, and glafs-duft 6 dr. II. Meal-powder 12 oz. faltpetre 2, charcoal 4. III. Saltpetre 8 oz. brimftone 2, glafs-duft I. antimony brafs-duft f, and faw-duft 12 dr. Silver rain. I. Saltpetre 4 oz. fulphur, meal-pow¬ der, and antimony, of each 2 oz. fal prunella f oz. II. Saltpetre f lb. brimftone 2 oz. and charcoal 4. III. Saltpetre 1 lb. brimftone lb. antimony 6 oz. IV. Saltpetre 4 oz. brimftone 1, powder 2, and fteel- duft \ oz. I. Meal-powder 6 lb. faltpetre 4, brimftone 3, char¬ coal 5. II. Saltpetre 1 lb. brimftone ff oz. charcoal 6. III. Saltpetre 1 lb. brimftone 4 oz. charcoal 12. IV. Saltpetre 4 lb. brimftone if lb. charcoal 1 lb. 12 oz. V. Brimftone 2 lb. faltpetre 4 lb. and meal-powr- der 4. VI. Saltpetre 1 lb. meal-powder 4 oz. brim- ftbne 8f, charcoal 2. VII. Meal-powder 1 lb. faltpetre 3, brimftone 1 ; fea-coal 1 oz. charcoal 8f, faw-duft |, fteel-duft f, and coarfe charcoal oz. VIII. Meal- powder i^ lb. faltpetre 3, fulphur if, charcoal 12 oz. faw-duft: 2. • Sinking charge for water-rockets.—Meal-powder 8 oz. charcoal -f oz. 543 . Rains. 33 For water rockets. Wheel-cafes from two ounces to four pounds.—I. Meal- Apparatus, powder 2 lb. faltpetre 4 oz. iron-filings 7. II. Meal- Materia!s? powder 2 lb. faltpetre 12 oz. fulphur 4, fteel-duft 3.^^’ III. Meal-powder 4 lb. faltpetre 1 lb. brimftone 8 oz. ■ v - - j charcoal 4f. IV. Meal-powder 8 oz. faltpetre 4, faw- 34 duft if, fea-coal V. Meal-powder 1 lb. 4 oz.For wheels, brimftone 4 oz. 10 dr. faltpetre 8 oz. glafs-duft 2f. VI. Meal-powder 12 oz. charcoal 1, faw-duft f. VII. Saltpetre 1 lb. 9 oz. brimftone 4 oz. charcoal 4f. VIII. Meal-powder 2 lb. faltpetre 1, brimftone f, and fea-coal 2 oz. IX. Saltpetre 2 lb. brimftone 1, meal- powder 4, and glafs-duft 4 oz. X. Meal-powder 1 lbf ialtpetre 2 oz. and fteel-duft 3f. XI. Meal-powder 2 lb. and fteel-duft 2 and a half oz. with 2 and a half of the fine duft of beat iron. XII. Saltpetre 2 lb. 13 oz. orimflone 8 oz. and charcoal. Slow fire for wheels.—:. Saltpetre 4 oz. brimftone 2, and meal-powder 1 and a half. II. Saltpetre 4 oz. brim¬ ftone 1, and antimony 1 oz. 6 dr. III. Saltpetre 40Z. and a half, brimftone 1 oz. and mealed powder 1 and a half. Dead fire for wheels. I. Saltpetre 1 \ oz. brimftone f, lapis-calaminaris f, and antimony 2 dr. I. Meal-powder 4 lb. faltpetre 2, brimftone and char-For ||ed coal 1. II. Meal-powder 2 lb. faltpetre 1, and fteel-flanding duft 8 oz. III. Meal-powder 1 lb. 4 oz. and char-cafes- coal 4 oz. IV. Meal-powder 1 lb. and fteel duft 4 oz. V. Meal-powder 2^ lb. brimftone 4 oz. and fea coal 6. VI. Meal-powder 3 lb. charcoal 5 oz. and faw-duft 1 and a half. I. Meal-powder 8f lb. faltpetre 1 lb. 2 oz. fteel-duft For fun 2 lb. 10 oz. brimftone 4. II. Meal-powder 3 lb. fait-cafes, petre 6 oz. and fteel-duft yf. Meal-powder 11 lb. faltpetre I, brimftone 4 oz. fteel-For a bril- duft 1 lb. and a half. liant fire. Meal-powder 6 lb. and beat-iron 2 lb. 1 oz. and a half. „ 38 Charge for four ounce Tourbillons Meal powder 2 or ^erbeSl lb. 4 oz. and charcoal 4 oz. and a half. For tour- Right ounce Tourhilions.—Meal-powder 2 lb. and billons, charcoal 4^- oz. Large Tourbillons.—Meal-powder 2 lb. faltpetre 1, brimftone 8 oz. and beat iron 8. _ N. B. Tourbillons may be made very large, and of different-coloured fires: only you are to obferve, that the larger they are, the weaker muft be the charge j and, on the contrary, the fmaller, the ftronger their charge. . ^ I. Saltpetre 4 lb. brimftone 2, meal-powder 2, anti-For water mony 4 oz. faw-duft 4, and glafs-duft 1 and a fourth. II. balloons. Saltpetre 9 lb. brimftone 3 lb. meal-powder 6 lb. rofin 1 2 oz. and antimony 8 oz. L Meal-powder 1 lb. and charcoal 1 lb. II. Meal-For water powder 1 lb. and charcoal 9 oz. fquibs. I. Meal-powder 1 lb. and charcoal 1 oz. II. Meal- 4Z power 9 oz. charcoal 1 oz. Mine ports For firing rockets, &c. I. Saltpetre 12 oz. brim-°r ' none 4 oz. and meal-powder 2 oz. II. Saltpetre 8 oz. Port fires, brimftone 4 oz. and meal-powder 2 oz. III. Saltpetre 1 lb. 2oz. meal-powder 1 lb. and a half, and brimftone 1 o oz. This compofition muft be moiftened with one gill of lin¬ ked oil. IV. Meal-powder 6 oz. falt-petre 2 lb. 2 oz. and brimftone 10 oz. V. Saltpetre 1 lb. 4 oz. meal- powder 4 oz. brimftone 5 oz. faw'-duft 8 oz. VI. Salt¬ petre 8 oz. brimftone 2 oz. and meal-powder 2 oz. For illuminations.—Saltpetre 1 lb. brimftone 8 oz, and meal-powder 6 oz. 4 Saltpetre' 44 Cone s or fniral wheels. 45 Crowns or globes. Air balloon fuzes. 47 Serpents for J, pots des brin. 43 Fire pumps 49 A flow white flame. 5° Amber lights. 51 Other lights. 52 A red fire. 53 A common fire. 54 For liars different colours. J44 Apparatus, Saltpetre I lb. and a half, briraftone 6 oz. meal-powder Materials, oz> and glafs-tluft 14 oz. Saltpetre 6 oz. brimltone 2 lb. antimony 4 oz. and camphor 2 oz. I. Saltpetre 1 lb. 10 oz. brimftone 8 oz. and meal- powder x lb. 6 oz. II. Saltpetre 1 lb. and a half, brimlfone 8 oz. and meal-powder 1 lb. 8. oz. Meal-powder x lb. 8 oz. faltpetre 12 oz. and char¬ coal 2 oz. I. Saltpetre 5 Ib.brimftone I lb. meal powder 1 lb. and a half, and glafs dull 1 lb. II. Saltpetre 5 lb. 8 oz. brim- llone 2 lb. meal-powder 1 lb. 8 oz. and glafs-duft 1 lb. 8 oz. Saltpetre 2 lb, brimftone 3 lb. antimony 1 lb. II. Saltpetre 34 lb. fulphur 2-f lb. meal-powder I lb. anti¬ mony half a lb. glafs-duft 4 oz. brafs-duil I oz. N. B. Thefe compofitions, driven x^ inch in a 1 oz. cafe, will burn one minute, which is much longer time than an equal quantity of any compofition yet known ' will laft. Meal-powder 9 oz. amber 3 oz. This charge may be drove in fmall cafes, for illuminations. Saltpetre 3 lb. brimftone 1 lb. meal-powder 1 lb. an¬ timony iolr oz. All thefe muft be mixed with the oil of fpilie. Meal-powder 3 lb. charcoal 1 2 oz. and faw-duft 8 oz. Saltpetre 3 lb. charcoal 10 oz. and brimftone 2 oz. I. Meal powder 4 oz. faltpetre 2 oz. brimftone 2 oz. fteel-duft 1 oz. and a half, and camphor, white amber, an- 0f timony, and ipercury-fublimate,of each oz. II. Roche- petre 10 oz. brimftone, charcoal, antimony, meal-pow¬ der, and camphor, of each | oz. moiftened with oil of turpentine. Thefe compofitions are made into ftars, by being worked to a pafte with aqua vitae, in which has been diffolved fome gum-tragacanth •, and after you have rolled them in powder, make a hole through the middle of each, and firing them on quick-match, leav¬ ing about 2 inches between each. III. Saltpetre 8 oz. brimftone 2 oz. yellow amber 1 oz. antimony 1 oz. and powder 3 oz. IV. Brimftone 2\- oz. faltpetre 6 oz. olibanum or frankincenfe in drops 4 °''i* ? maftick, and mercury-fublimate, of each 4 oz. meal-powder 5 oz. white amber, yellow amber, and camphor, of each 1 oz. antimony and orpiment half a oz. each. V. Saltpetre 1 lb. brimftone half a lb. and meal-powder 8 oz. moif¬ tened with petrolio-oil. VI. Powder half a lb. brim- ilone and faltpetre, of each 4 oz. VII. Saltpetre 4 oz. brimftone 2 oz. and meal-powder 1 oz. Stars that carry tails of /parks.—I. Brimftone 6 oz. crude antimony 2 oz. faltpetre 4 oz. and rofin 4 oz. II. Saltpetre, rofin, and charcoal, of each 2 oz. brim- ilone 1 oz. and pitch 1 cz. Thefe compofitions are fometimes melted in an ear¬ then pan, and mixed with chopped cotton-match, before they are rolled into ftars •, but wall do as well if wet¬ ted, and worked up in the ufual manner. Stars that yield fome /parks.—I. Camphor 2 oz. falt¬ petre 1 oz. meal-powder 1 oz. II. Saltpetre 1 oz. ditto melted half a oz. and camphor 2 oz. When you wrould make ftars of either of thefe coinpofitions, you muft wet them with gum water, or weak fpirits, in which has been diffolved fome gum-arabic, or gum-tragacanth, that the whole may have the confiftence of a pretty thick li¬ quid j having thus done, take 1 oz. of lint, and ftir it 2 PYROTECHNY. Chsp. I. about in the compofition till it becomes dry enougl roll into ftars. Stars of a yellowifh colour.—Take tragacanth or gum-arabic, pounded and filled through „ /-orrvn1-!i->r in hranriv O 07. {Hltnetre to Apparatus, Materials, r 6-cc. of Fire- oz. of gum- workSi a fine lieve, camphor diffolved in brandy 2 oz. faltpetre I lb. fulphur half a lb. coarfe powder of glafs 4 oz. wftfite amber I oz. and a half, orpiment 2 oz. Being well incorporated, make them into itars after the common me¬ thod. Stars of another kind.—Take 4 oz. of camphor, and melt it in half a pint of fpirit of w ine over a flow fire j then add to it ^ lb. of gum-arabic that has been diffolved ; with this liquor mix 1 lb. of faltpetre, 6 oz. of fulphur, and 5 oz. of meal-pow'der ; and after you have iiirred them well together, roll them into liars proportionable to the rockets for which you intend them. 55 As variety of fires adds greatly to a colledlion ofColours pru» works, it is neceffary that every artilt Ihould know' theduce,d„by different effedl of each ingredient. For which reafon, the differ¬ ent compa- we lhall here explain the colours they produce ol them-£t;onSt felves ; and likewife howr to make them retain the fame when mixed with other bodies: as for example, lulphur gives a blue, camphor a white or pale colour, faltpetre a clear white-yellow, amber a colour inclining to yellow, fal-ammoniac a green, antimony a reddilb, rofin a cop¬ per colour, and Greek-pitch a kind of bronze, or be¬ tween red and yellow'. All thefe ingredients are luch as fhow themfelves in a flame, viz. White fame.—Saltpetre, fulphur, meal-powder, and camphor ; the faltpetre mull be the chief part. Blue fame.—Meal-powder, faltpetre, and fulphur vi- vum •, fulphur mull be the chief: or meal-powder, falt¬ petre, brimftone, fpirit of wine, and oil of Ipike ; but let the powder be the principal part. Flame inclining to red.—Saltpetre, fulphur, antimony, and Greek-pitch j faltpetre the chief. By the above method may be made various colours of fire, as the praftitioner pleafes j for, by making a few trials, he may caufe any ingredient to be predominant in colour. 56 The fet colours of fire produced by fparks are di-Sparkling vided into four forts, viz. the black, white, grey, and^P^’ red. The black charges are compofed of two ingredi-cho.dked ents, which are meal-powder and charcoal *, the white ofcafe!l. three, viz. faltpetre, fulphur, and charcoal j the grey of four, viz. meal-pow'der, falt-petre, brimllone, and char¬ coal •, and the red of three, viz. meal-powder, charcoal, and fawr-duft. There are, befides thefe four regular or fet charges, tw'o others, which are dillinguilhed by the names, of compound and brilliant charges; the compound being made of many ingredients, fuch as meal-powder, falt¬ petre, brimftone, charcoal, faw-duft, fea-coal, antimony, glafs-duft, brafs-duft, fteel-filings, call-iron, tanner’s dull, &c. or any thing that will yield fparks •, all which muft: be managed with diferetion. The brilliant fires are compofed of meal-powder, faltpetre, brimftone, and fteel- duft } or with meal-powder and ileel-filings only. ^ The beauty of fire-works depends much on the com-of mixing pofitions being w'ell mixed j therefore great care muft the compa- be taken in this part of the work, particularly for the htlons• compofition for fky-rockets. When there are 4 or five pounds of ingredients to be mixed, which is a fufficient quantity at a time (for a larger proportion will not do !• 58 Cotton quick match. Chap. I. P Y R O T Apparatus, fo well), firft put the different ingredients together j ^c^oTrire t^len wor^ them with your hands, till you think they Works. ~are P^y well incorporated : after which put them into y—— a law-n fieve with a receiver and top to it ; and if, after it is lifted, any remains that will not pais through the Heve, grind it again till fine enough j and if it be twice lifted, it will not be amifs •, but the compofitions for wheels and common works are not fo material, and need not be fo fine. But in all fixed w'orks, from which the fire is to play regularly, the ingredients muit be very fine, and great care taken in mixing them well toge¬ ther and in all compofitions in which are iron filings, the hands muft not touch ; nor will any works which have iron or Heel in their charge keep long in damp weather, unlefs properly prepared, according to the for¬ mer diredlions. Cotton quick match is generally made of fuch cotton as is put in caudles, of ieveral fixes, from one to fix threads thick, according to the pipe for which it is defigned ; which pipe muft be large enough for the match, when made, to be puftied in eafily without breaking. Having doubled the cotton into as many threads as is proper, coil it very lightly into a flat-bottomed copper or earthen pan •, then put in the faltpetre and the liquor, and boil them about 20 minutes ; after which coil it again into another pan, as in fig. , and pour on it what liquor remains ; then put in feme meal pow-der, and prefs it down with the hand till it is quite wet ; afterwards place the pan be¬ fore the wooden frame (fig. 18.) which muft be fufpend- ed by a point in the centre of each end; and place yourfelf before the pan, tying the upper end of the cot¬ ton to the end of one of the fides of the frame. When every thing is ready, an afiiftant muft turn the frame round, while die cotton paffes through the Land, holding it very lightly, and at the fame time keeping the hand full of the w’et pow’der ; but if the powder fliould be too wet to ftick to the cotton, more muit be added, fo as to keep a continual fupply till the match is all wound up ; it may be w'ound as clofe on the frame as you pleafe, fo that it may not ftick together ; when the frame is full, take it off the points, and lift dry meal- powder on both fides the match, till it feem qui e dry : in winter the match will be a fortnight before it is fit for ufe ; when it is thoroughly dry, cut it along the out- fide of one of the fides of the frame, and tie it up in fkains for ufe. N. B. The match muft be wmund tight on the frames. The ingredients for the match, are, cotton i lb. I 2 oz. faltpetre t lb. fpirit of wine 2 quarts, water q quarts, ifin- glafs 3 gills, and meal-pow’der jo lb. To diffolve 4 oz. of ifinglafs, take 3 pints of water. Touch pa- Diffolve, in fpirit of wane or vinegar, a little faltpetre ; per fkcap- then take ibrne purple or blue paper, and wet it with this liquor, and wken dry it will be fit for ufe; wken this paper is to he parted on any fire-works, take care that the pafte does not touch that part which is to burn. The method of ufing this paper is by cutting it into flips, long enough to go once round the mouth of a fer- pent, ciacker, &c. When thefe flips are parted on, leave a little above the mouth of the cafe not parted ; then prime the cafe with meal-powder, and twift the pa¬ per to a point. We are indebted to the Chinefe for the contrivance in', objedts a which may be employed for reprefenting ani- in firefi VoL. XVII. Part II. ping fire¬ works. 60 Pafte for reprefent E C H N Y. 54.5 mals and other objects in fire. To prepare tins pafte, Apparatus, take fulphur reduced to a very fine powder, or flowers lVjaterials, of fulphur, and having formed it into a pafte with rtarch,.^^^116" cover with it the figure you are defirous of reprefenting —v —r,./ on fire : it is here to be obferved, that the figure muft firft be coated over with clay, to prevent it from being burnt. W hen the figure has been covered with this pafte, befprinkle it while ftill moift with pulverized gunpowder; and when the whole is perfe&ly dry, arrange fome fmall matches on the principal parts of it, that the fire may be fpeedily communicated to it on all fides. I he fame pafte may be employed on figures of clay, to form devices and various defigns. Thus, tor example, feftoons, garlands, and o.her ornaments, the flowers of which might be imitated by fire of different colours, could be tormed on the frieze of a piece of architecture covered with plafter. The Chinefe imitate grapes ex¬ ceedingly well, by mixing pounded fulphur with the pulp of the jujube, inftead of flour palle. 6l It is ufual to paint the frames or Itands of large fire-Method of works of fome dark colour, but this renders them very preferving combuftible. It would be better to wafh them with thefi|e-work* following compofition, which will both give them a proper colour, and render them lefs combuftible. Take by acci- equal parts of brick-duft, coal-afhes, and iron-filings,dent, and mix them with a double fize while hot. With this v/afli over the frames, &c. and when dry repeat the wafli- ing. Chap. II. Of the principal varieties of Fire-WorkS) and the tnfi approved JVLithods of conjlruBing them. Artificial fire-wrorks differ from each other very Dkifion of much in point of hmplicity of conftrudlion. Some re- fire-w'orks. quire very little dexterity in the preparation ; and are either employed as appendages to works of greater im¬ portance, or, if ufed by themfelves, are confined to the fports of fchoolbovs. Of this nature are fquibs,ferpents, crackers, fars, [parks, macrons, faucijfons, pin-voheels, leaders, and gerbes or Roman candles. Others are very complex in their ftrudture, require confiderable addrefs and ingenuity, and form the amufement of fafhionable circles on occafion of public rejoicings or private fefti- vity : Such are rockets ot various kinds, vuheels, funs, globes, balloons, pyramids, &c. W'e fliall firft deferibe the more fimple kinds, and then give an account of the method of conftrudling thofe of a more complex na¬ ture. Sect. I. Of Simple Fire-works. As in the fubfequent dire&ions for fire-works, we Leadm. fhall have frequent occafion to mention pipes of com¬ munication commonly called leaders, by which the fe- veral parts of a compound fire-wrork are connedled with each other, it will be proper to fhou' how thefe are con- ftrudted. Leaders confift of finall tubes of paper of dif¬ ferent lengths, accord’ng to the diftance to which they muft extend; and thefe tubes are filled with a combufti¬ ble compofition that will not burn to" faft. The belt paper for leaders is that called elephant; which is cut into long flips 2 or 3 inches broad, fo that they may go 3 or 4 times round the former, but not more: v/hen they are very thick, they are too ftrong 3 & for 546 P Y R O T Varieties for the paper which fallens them to the works, and will of Conftruc- fometimes fly off without leading the fire. The for- y , mers for thefe leaders are made from 2 to 6-i6ths of an V inch diameter j but 4-i6ths is the fize generally ufed. The formers are made of fmooth bral's wire : when ufed, rub them over with greafe, or keep them wet with pafte, to prevent their flicking to the paper, which muft be pafted all over. In rolling pipes, make ufe of a rolling-board, but ufe it lightly : having rolled a pipe, draw out the former with one hand, holding the pipe as light as poflible with the other j for if it prefs againff the former, it will flick and tear the paper. N. B. Make the leaders of different lengths, or in clothing works many will be wafted. Leaders, for marron batteries muft be made of ftrong cartridge paper. H Serpents- Joining and placing leaders is a very effential part of fire-works, as it is on the leaders that the perform¬ ance of all complex wmrks depend j for wdrich reafon the method of conducting pipes of communication lhall be here explained in as plain a manner as poflible. Your works being ready to be clothed, proceed thus : Cut your pipes of a fufficient length to reach from one cafe to the other; then put in the quick-match, which muft always be made to go in very eafy : when the match is in, cut it off within about an inch of the end of the pipe, and let it projeft as much at the other endj then faften the pipe to the mouth of each cafe with a pin, and put the loofe ends of the match into the mouths of the cafes, with a little meal-powder : this done to all the cafes, pafte over the mouth of each twm or three bits of paper. 'The preceding method is ufed for large cafes, and the following for fmail, and for illuminations : Firft thread a long pipe •, then lay it on the tops of the cafes, and cut a bit off the under fide, over the mouth of each cafe, fo that the match may appear: then pin the pipe to every other cafe ; but before you put on the pipes,^ put a little meal powder in the mouth of each cafe. If the cafes thus clothed are port fires on illuminated works, cover the mouth of each cafe with a fingle paper ; but if thev are choked cafes, fituated fo that a number of fparks from other works may fall on them before they are fired, fecure them with three or four papers, which muft be pafted on very fmooth, that there may be no creafes for the fparks to lodge in, wdiich often fet fire to the works before their time. Avoid as much as pof- fible placing the leaders too near, or one acrofs the other fo as to touch, as it may happen that the flaflr of one will fire the other ; therefore if your works fhould be fo formed that the leaders muft crofs or touch, be fare to make them very ftrong, and fecure at the joints, and at every opening. When a great length of pipe is required, it muft be made by joining feveral pipes in this manner : Having put on one length of match as many pipes as it will hold, pafte paper over every joint ; but, if a ftill greater length is required, more pipes muft be joined, by cut¬ ting about an inch off one fide of each pipe near the end, and laying the quick-match together, and tying them faft with fmail twine; after which, cover the joining with pafted paper. One of the fimpleft fire-works is what is called a fer- pent, which confifts of a cylindrical paper cafe, about ,1 or 5 inches long, and not made very thick. AC, E C H N Y. Chap. II. fig. 19. reprefents the ufual form of the ferpent, except Varieties that in general they have not the contraction in theuc"' middle, reprefented in this figure. The name ferpent. ^ . has been given to this fire-work, either from the hit- fing noife which it makes when fired, or from the zig zag or undulating diredtion in which it moves, when properly conftrudted. The cafe or cartridge is rolled round a cylindrical ftick, rather larger than a goofe quill, and provided at one end with a narrow appendage, fuch as that ufed for rockets, fig. 3. by means of which it is choaked at one end. This cafe is filled about half way with fome of the compofitions deferibed for making fmail rockets, fee N° 30, rammed moderately hard in the proper mould, and then it is either choaked in the middle, or fome obftrudling body, fuch as a fmall piece of paper, is introduced, and the remainder of the cafe is filled with grained or corn powder. Lafily, this other extremity is well fecured with twine, and com¬ monly dipt into melted pitch ; a little moiftened meal powder is introduced into the extremity next the choak, and a piece of touch paper being properly faftened on this end, the ferpent is complete. 65 Crackers are compofed of a pretty long paper cafe, Crackers, filled with the proper compofition, as will be deferibed immediately, and folded up in fuch a manner as, when fired, to make fucceffive reports at ftiort intervals. To conftruft thefe crackers, cut fome cartridge paper into pieces 3-* inches broad, and one foot long ; one edge of each fold down length-wife about ^ of an inch broad then fold the double edge down ^ of an inch, and turn the fingle edge back half over the double fold ; then open it, and lay all along the channel, which is formed by the folding of the paper, fome meal-poivder ; then fold it over and over till all the paper is doubled upr rubbing it down every turn ; this done, bend it back¬ wards and forwards, 2 inches and a half, or thereabouts, at a time, as oft as the paper will allow ; then hold all thefe folds flat and dole, and with a fmall pinching cord give one turn round the middle of the cracker, and pinch it clofe ; then bind it with a packthread as tight as poflible ; then, in the place where it was pinched, prime one end of it, and cap it with touch-paper. When thefe crackers are fired, they will give a report at every turn of the paper: if you would have a great number of reports, the paper muft be cut longer, or join them after they are made ; but if they are made very long before they are pinched, you muft have a piece of wood with a groove in it, deep enough to let in half the cracker ; this will hold it ftraight while pratff it is pinching. Fig. 20. reprefents a cracker com-CCCCLnn plete. _ # 66 Stars are fmall balls, prepared of a ccmpofition which Stars.j emits a brilliant, radiating light, and are much employ¬ ed in the conftrudlion of rockets, Roman candles, and fimilar fire-works. They are made of various fizes, but generally about as large as a mufket bullet. Compofitions for ftars have been deferibed in N° 31. and 54. The in¬ gredients muft be thoroughly incorporated, and in form¬ ing the ball, unlefs the pafte is fufficiently glutinous, it muft be wrapped up in a piece of paper, or linen rag, tied clofelv round with pack thread, and a hole muft be pierced through its middle for the infertion of a piece of match. Thefe ftars, when lighted, will exhibit a moft beautiful appearance ; for the fire, as it iffues from the two ends of the hole in the middle, will extend to a Chap. II. P Y R O T Varieties a great diilance, atid thus make the fiery ball appear of Conftruc- much larger. . tl<)n~ StrungJiars, Firft take fome thin paper, and cut it into pieces of one inch and a half fquare, or thereabouts; then on each piece lay as much dry ftar-coinpofition as the paper will eafiiy contain j then twill: up the paper as tight as polhble 5 when done, rub fome pafte on your hands, and roll the liars between them 5 then fet them to dry : the liars being thus made, get fome llax or fine tow, and roll a little of it over each liar ; then palte the hand and roll the liars as before, and fet them again to dry \ when they are quite dry, with a piercer make a hole through the middle of each, into which run a cotton quick-match, long enough to hold 10 or 12 liars at 3 or 4 inches diltance : but any number of liars may be Itrung together by joining the match. Tailed Jiars. Thefe are called tailed Jiars, becaufe there are a great number of fparks ifl'uing from them, which reprefent a tail like that of a comet. Of thefe there are two forts; which are rolled, and driven : when rolled, they mull be moillened with a liquor made of half a pint of fpirit of wine and half a gill of thin fize, of this as much as will wet the compofition enough to make it roll eafy ; when they are rolled, lift meal-pow¬ der over them, and fet them to dry. When tailed liars are driven, the compofition mull be moillened with fpirit of wane only, and not made lb wet as for rolling : 1 and 2 oz. cafes, rolled dry, are bell for this purpofe; and when they are filled, unroll the cafe within 3 or 4 rounds of the charge, and all that are unrolled cut off; then palte down the loofe edge : 2 or 3 days after the cafes are filled, cut them in pieces 5 or 6 8ths of an inch in length : then melt fome wrax, and dip one end of each piece into it, fo as to cover the compofition : the other end mull be rubbed with meal- powder wetted with fpirit of wine. Driven Jiars. Cafes for driven liars are rolled with pafte, but are made of paper very thin. Before they are filled, damp the compofition with fpirit of wine that has had fome camphor diffolved in it : ram them indif¬ ferently hard, fo that the cafe be not broken or facked ; to prevent winch, they Ihould fit tight in the mould. They are driven in cafes of feveral fizes, from 8 drams to four oz. When they are filled in half ounce cafes, cut them in pieces of three fourths of an inch long ; if 1 oz. cafes, cut them in pieces of 1 inch ; if 2 oz. cafes, cut them in pieces of 1 and one fourth inch long ; and if 4 oz. cafes, cut them in pieces of 1 inch and a half long: having cut the liars of a proper fize, prime both ends with wTet meal-powder. Thefe liars are feldom put in rockets, they being chiefly intended for air balloons, and driven in cafes, to prevent the compofition from being broken by the force of the blowing powder in the fhell. Rolling Jiars are commonly made about the fize of a mulket ball ; though they are rolled of feveral fizes, from the bignefs of a piftol ball to 1 inch dia¬ meter ; and fometimes very fmall, but are then called fparks. Great care mull be taken in making ftars, firft, that the feveral ingredients are reduced to a fine pow der; fecondly, that the compofition may be wrell worked and mixed. Before beginning to roll, take about a pound of compofition, and wet it with the fol¬ lowing liquid, enough to make it Hick together and roll eafy : Spirit of wine 1 quart, in which diffolveone fourth E c H N Y. 547 of an ounce of ifinglafs. If a great quantity of compo- Varieties fition be w'etted at once, the fpirit will evaporate, anq of Conftnu*- leave it dry, before it is rolled into ftars : having rolled , tl°’1' . up one proportion, {hake the ftars in meal-powxier, and fet them to dry, which they will do in 3 or 4 days; but if they fhould be wanted for immediate ufe, dry them in an earthen pan over a {low heat, or in an oven. It is very difficult to make the ftars all of an equal fize when the compofition is taken up pro- mifeuoufiy with the fingers; but by the following method they may be made very exadly. When the mixture is moiftened properly, roll it on a flat fmooth ftone and cut it into fquare pieces, making each fquare large enough for the ftars intended. There is another method ufed by fome to make ftars, which is by rol¬ ling the ccmpofition in long pieces, and then cutting off the ftar, fo that each ftar will be of a cylindrical form : but this method is not fo good as the for¬ mer ; for, to make the compofition roll this wray, it muft be made very wret, which makes the ftars heavy, as well as weakens them. All ftars muft be kept as much from air as pollible, otherwife they will grow W’eak and bad. Sparks differ from ftars, only in their fize and dura- Sparks, tion, as they are made fmaller than ftars, and are fooner extinguilhed. The lollow'ing is the moft approved me¬ thod of making them. Having put into an earthen vef- fel an ounce of mealed gunpow der, 3 oz. of pi wdered faltpetre, and 4 oz. of camphor, reduced to powder by rubbing it in a mortar with a little fpirit of wine ; pour over this mixture fome weak gum water, or fome weak brandy, in wffiich fome gum dragant has been difiblved, till the compofition acquires the confiftence of thick foup. Then take fome lint or caddice, which has been boiled in brandy, vinegar, or wdth faltpetre, and after¬ wards dried and unravelled, and throw into the compo- fition as much of it as is neceffary to abforb the w hole, taking care to ftir it well. This matter is to be formed into fmall balls of about the fize of a pea, wffffch being dried in the air, are to be fprinkled with meal gunpow¬ der, that they may more readily take fire. Another method of making fparks is, to take fome faw dull of any wood that burns readily, fuch as fir, and boil it in water that has been faturated with faltpetre. When it has been boiled for fome time, the veffel is to be removed from the fire, and the folution of nitre pour¬ ed off, fo as to leave the faw duft at the bottom. The faw duft thus impregnated with nitre, is then to be poured on a table, and, while moift, to be fprinkled wfith powdered fulphur, to which a little bruifed gunpowrder has been added ; and when the whole is well mixed, and of a proper confiftence, fparks are to be made of it as before. Marroons are fmall boxes made either of paper or 6S pafteboard, and of a roundifh or cubical form, fo pre- Marro0&s‘ pared as when fired to make a loud and hidden report. They are ufually employed, either as appendages to other fire-wwks, or a great many of them are fo ar¬ ranged, as to explode fucceffively at certain intervals. Formers for marroons are from three fourths of an inch to one and a half diameter; but the paper for the cafes tw ice the diameter of the former broad, and long enough to go three times round. When you have rolled a cafe, pafte down the edge and ti? one end dole ; then with the former drive it down to take away the wrin- 3 Z 2 klcs, * 543 P Y R O T E C H N Y. Fiar. 21. 69 Marroon batteries. Varieties kies, and make St fiat at bottom ; tlien fill the cafe with oi Gunltcuc- eoni-powder one diameter and one fourth high, and fold . down the reft of the cafe tight on the powder. The marroon being thus made, wax fome Strong pack-thread with fhoemakers wax : this thread wind up in a ball, . then unwind two or three yards of it, and that' part which is near the ball make fait to a hook ; then take a marroon, and Hand as far from the hook as the pack¬ thread will reach, and wand it lengthwife round the marroon as dole as poffible, till it will hold no more that way j then turn it, a.,d wind the packthread on the fhovt way, then lengthwife again, and fo on till the pa¬ per is all covered ; then make fait the end of the pack¬ thread, and beat down both ends' of the marroon to bring it in ihape. The method of firing marroons is by making a hole at one end with an awl, and putting in a piece of quick-match 5 then taking a piece of ftrong paper, in which wrap up the marroon with trvo leaders, which mult Ire put down to the vent, and the paper tied tight round them with fmall twine : thefe leaders are bent on each fide, and their loofe ends tied to the other marroons, and are nailed in the middle to the rail of the Hand, as in fig. 21. The ufe of winding the packthread in a ball is, that it may be let out as wanted, according to the quantity the marroon may require j and that it may not be tied in knots, which would fpoil the marroon. Thefe oblong irurroons are, by the French, called Sattcijjbns, as they are fuppofed to re¬ ferable a fauffage. Batteries of Marroons.—Thefe, if well managed, will keep time to a march, or a How piece of mufic. Mar¬ roon batteries are made of feveral Hands, with a num¬ ber of crofs rails for the marroons ; which are regulated by leaders, by cutting them of different lengths, and nailing them tight, or loofe, according to the time of the mufic. In marroon batteries you muH ufe the large and fmall marroons, and the nails for the pipes mufi have flat heads. The proper marroon boxes are made of Hrong paffe- board, cut as reprefented in fig. 22., fo as to fold up in the form of a cube, one fide of which is to be left unce- mented till the box be filled. The cavity being filled with gun-powder, flrong paper is to be paffed over the box in various direftions, and the whole is to be wrap¬ ped round with flrong pack thread dipt in glue. Lafl- ly, a hole is to be made in the corner of the box, and a piece of match introduced, by which it may be fired. Sometimes it is required to render marroons luminous, or to prepare them in fuch a way, that they fliall emit a brilliant light before they burfl. To effeft this, they are to be covered on the outfide with one of the compo- fitions direfted for flars, and then rolled in bruifed gun¬ powder. Pin wheels ^'or Pin Wheels.—Firfl roll fome paper pipes, about 14 inches long each j thefe pipes mufl not be made thick of paper, two or three rounds of elephant paper being fufficient. When the pipes are thoroughly dried, you mufl have a tin tube 12 inches long, to fit eafy in¬ to the pipes ; at one end of this tube fix a fmall conical cup, called a funnel; then bend one end of one of the pipes, and put the funnel in at the other as far as it will reach, and fill the cup with compofition: then draw out the funnel by a little at a time, (baking it up and down, and it will fill the pipe as it comes out. Chap. II. Having filled fome pipes, have fome fmall circular ' -.netics blocks made about one inch diameter and half an inch ot Guniti nc- thick : round one oi theie blocks wind and pafle a pipe, f and to the end of this pipe join another 5 which mufl be done by twilling the end ot one pipe to a point, and putting it into the end of the other with a little pafle : in this manner join four or five pipes, winding them one upon the other fo as to form a fpiral line. Having wound on your pipes, pafte two flips of paper acrois them to hold them together : befides thefe Hips of pa¬ per, the pipes muft be palled together. There is another method of making thefe wheels, viz. by winding on the pipes without pafte, and flicking them together with fealing-wax at every half turn ; fo that when they are fired, the end will fall loofe every time the fire paffes the wrax, by which means the circle of fire will be confiderably increafed. The formers for thefe pipes are made from one and a half to q-ibths of an inch diameter \ and the compofition for them is as follows : Meal-powder 8 oz. faltpetre 2 oz. and fulphur 1 : among thefe ingredients may be mixed a little fteei- filings or the duft of caft iron : this compofition ftiould be very dry, and not made too fine, or it will flick in the funnel. Thefe wfiieels may be fired on a large pin, and held in the hand with fafety. ^ There is a pleafing decoration frequently added to shower of rockets, called a f:ower of fire, rain, or rain fall, and it fire or rain, is called gold or filver rain, according as its colour is more or lefs intenfe. It confifts of leveral fmall cafes filled with a brilliant compofition, fuch as the following variety of Chinefe fire, viz. meal povrder 1 pound, flower of fulphur 2 oz. and iron land of the firft order, 5 °z- Gold and filver rain compofitions are rammed in cares that are pinched quite clofe at one end : if rolled dry, 4 or 5 rounds of paper wall be ftrong enough •, but if they are pafted, 3 rounds will do ; and the thin fort of car¬ tridge-paper is beft for thofe fmall cafes, in rolling which you muft not turn down the infide edge as in other cafes, for a double edge would be too thick for fo fmall a bore. The moulds for rain-falls fliould be made of brafs, and turned very fmooth in the infide 5 or the cafes, which are fo very thin, would tear in coming out; for the charge muft be rammed in tight; and the better the cafe fits the mould, the more driving it will bear. Thefe moulds have no nipple, but inftead of it they are made flat. As it would be very tedious and troublefome to (hake the compofition out of fuch fmall ladles as are ufed for thefe cafes, it wfill be neceffary to have a funnel made of thin tin, to fit on the top of the cafe, by the help of which they may be filled very faft. For fingle rain-falls for 4 oz. rockets, let the diameter of the former be 2-i6ths of an inch, and the length of the cafe 2 inches; for 8 oz. rockets, 4-i6ths and 2 dia¬ meters of the rocket long 5 for 1 lb. rockets, j-i6ths, and 2 diameters of the rocket long ; for 2 lb. rockets, 5- i6ths, and 3 inches and a half long ; for 41b. rock¬ ets, 6-i6ths, and 4 inches and a half long j and for 6- pounders, 7-i6ths diameter, and 5 inches long. Of double rain-falls there are two forts. For ex¬ ample, fome appear firft like a ftar, and then the rain j and fome appear firft like rain, and then like a ftar. When you wrould have ftars firft, you muft fill the cafes, within half an inch of the top, with rain-compofition, and the remainder with ftar-compofition) but when you in¬ tend Chap. II. P Y R O T E C H N Y. 549 Varieties tend the rain fhould be dr ft, drive the cafe half an inch of Conftmc-with ftar-compofition, and the reft with rain. By this tl01!- method may be made many changes of firej for in large rockets you may make them firft burn as ftars, then rain, and again as ftars ; or they may firft ftiow rain, then ftars, and finifh with a report \ but when thus ma¬ naged, cut open the firft rammed end, after they are fil¬ led and bounced, at which place prime them. The ftar-compofition for this purpofe muft be a little ftronger than for rolled ftars. Gerbts. Gerbes confift of a ftrong cafe of thick paper or pafte- board, filled with a brilliant compofition, and generally with ftars or balls placed at fmall diftances, fo that the compofition and the balls are introduced alternately. Immediately below' each ball is placed a little grained powder. Thefe laft gerbes are fometimes called Roman candles. When fired, they firft throw' up a beautiful jet of flame, which in fome meafure refembles a water- fpout, whence the name. Gerbes are either employed fingly, or batteries are formed of them, and frequently thofe filled with brilliant fire without balls, are placed in row's along the front of the frames of large compound fire-w'orks. They are fometimes made perfedtly cylin¬ drical ; at others they have a contracted part at the top called the nech. Fig. 23. ar.d Fig. 23. reprefents a wooden former; fig. 24. a gerbe 24- complete, w'ith its foot or ftand. The cafes for gerbes are made very ftrong, on account of the ftrength of the compofition •, which, when fired, comes out with great velocity ; therefore, to prevent their burfting, the paper fhould be pafted, and the cafes made as thick at the top as at the bottom. They fhould alfo have very long necks, for this reafon 5 firft, that the particles of iron ■will have more time to be heated, by meeting with greater refiftance in getting out, than with a thort neck, w'hich w'ould be burnt too wide before the charge be confumed, and fpoil the effetlft : fecondly, that with long necks the ftars will be throwm to a great height, and will not fall before they are fpent, or fipread too much ; but, when made to perfedftion, will rife and fpread in fuch a manner as to form exactly a ■wheat flieaf. In ramming of gerbes, there will be no need of a mould, the cafes being fufficiently ftrong to fupport themfelves. But you mutt be careful, before you begin to ram, to have a piece of wood made to fit in the neck ; for if this be not done, the compofition will fall into the neck, and leave a vacancy in the cafe, which will caufe the cafe to burft as foon as the fire arrives at the vacancy. You muft likewife obferve, that the firft ladleful of charge, or fecond, if proper, be of fome weak compofi¬ tion. When the cafe is filled, take out the piece of wood, and fill the neck with fome flow charge. Gerbes are generally made about fix diameters long, from the bottom to the top of the neck 5 their bore muft be one- fifth narrower at top than at bottom. The neck S is one-fixth diameter and three-fourths long. T, a wooden foot or ftand, on which the gerbe is fixed. This may be made with a choak or cylinder four or five inches long to fit the infide of the cafe, or with a hole in it to put in the gerbe •, both thefe methods wall anfwer the fame purpofe. Gerbes produce a moft brilliant fire, and are very beautiful when a number of them are fixed in the front of a building or a colleftion of fire¬ works. V N. Ik Gerbes are made by their diameters, and their Vaneties cafes at bottom one-fourth thick. The method of ^on^ruc* ing the interior diameter of a gerbe is this : Suppofing tl°n’ j the exterior diameter of the cafe, when made, to be five inches, then, by taking two-fourths for the fides of the cafe, there will remain inches for the bore, which will be a very good fize. Tbefe gerbes ftiould be ram¬ med very hard. Small Gerbes, or volute Fountains, May be made of tour ounces, eight ounces, or one pound cafes, pafted and made very ftrong, of any length: but before they are filled, drive in clay one diameter of their orifice high j and when the cafe is filled, bore a vent through the centre of the clay to the compofition : the common proportion -will do for the vent, which muft be primed with a flow' charge. Thefe cafes, with¬ out the clay, may be filled with Chinefe fire. Sect. II. Of Compound Fire-works. 73 Among the moft pleafing compound fire-works are Rockets, rockets, which are of various kinds. Some are made to afeend to a great height in the air, where they burft, and throw out the contents of the head with which they are provided. Thefe are called Jhj-rockets. Others are fo conftrufted as to run with great velocity along a line, and are called line-rockets. Some are arranged at the extremities of the fpokes of a wheel, and are deno¬ minated wheel-rockets; while a fourth variety have their cafes made w'ater tight, and are filled with a very ftrong compofiiion, fo as to admit of their burning below wa¬ ter. Tbefe laft are called water-rockets. Sky-rockets are tied to a ftick, which renders their afeent into the air more equable and fteady. ^ Fig. 25. reprefents a rocket complete without itssky-rock- ftick. Its length from the neck is five diameters one-ets. fixth : the cafes Ihould always be cut to this length after Gg- 25' they are filled. M is the head, which is two diameters high, and one diameter one-fixth and a half in breadth $ N the cone or cap, whofe perpendicular height muft be one diameter one-third. Fig. 26. the collar to which Fig. 2d. the head is fixed : this is turned out cf fir or any light wood, and its exterior diameter muft be equal to the in¬ terior diameter of the head ; oneriixth will be lufficient for its thicknefs, and round the outfide edge muft be a groove ; the interior diameter of the collar muft not be quite fo wide as the exterior diameter of the rocket; when this is to be glued on the rocket, twTo or three rounds of paper muft be cut off the cafe, which will make a (boulder for it to reft upon. Fig. 27. a former Fig. 2 j.,, for the head : two or three rounds of paper well pafted will be enough for the head, which, when rolled, put the collar on that part of the former marked O, which muft fit the infide of it •, then, w'ith the pinching cord pinch the bottom of the head into the groove, and tie it with fmall twine. Fig. 28. a former for the cone. Fig. 2S. To make the caps, cut the paper in round pieces, equal in diameter to twice the length of the cone to be made j which pieces being cut into halves, will make two caps each, without wafting any paper; having formed the caps, psfte over each of them a thin white paper, which muft be a little longer than the cone, fo as to projedt about half an inch below the bottom : this projediion of paper, being notched and pafted, ferves to fallen the cap to the head. When PYROTECHNY. 550 Varieties W hen you JoaJ the heads of the rockets with ftars, tionIUC"ra”1S’ ferPents» crachers, or any thing elfe, according to ■—-y- • fancy, remember always to put one ladleful of meal- powder into each head, which will be enough to burft the head, and dilperfe the ftars, or whatever it contains: when the heads are loaded with any cafes, let their mouths be placed downwards ; and after the heads are filled, pafte on the top of them a piece of paper before putting on the caps. As the fize of the liars often dif¬ fers, it would be needlefs to give an exact number for each rocket; but this rule may be obferved, that the heads may be nearly filled with whatever they are to contain. Chap. II, 75 Dimenfions and poife of rocket- iticks. Dimenjions and Poife of Rocket fUchs. Weight of the Rocket. lb Length of the ftick. Thicknefs at top. Breadth Square at at top. bottom Ft in. 14 O 12 10 4 1 i of Inches. Inches. Imhes. Poife from the point of the cone. F:. in. M 1,25 1,125 °,725 °>5 0,375° °,3 0,25 0,125 0.1 1,85 1,40 i, 0,80 0,70 o,55 o,45 o,35 0,20 0,15 o,75 0,62c 0,525 o,375 0,25 o,35 0,15 0,10 0,16 o,5 4 3 2 2 1 1 1 11 8 5 1.5 9, 9, 1, 10,5 8.5 3, o, o, o,5 Fig. 2 fpi-Cadueeus ral lines, by reafon of their being placed obliquely, one1’00'^6^’ oppofite to the other ; and their counterpoife in their cen¬ tre, which caufes them to rife in a vertical direclion. Rockets for this purpofe muft have their ends choaked clofe, without either head or bounce, for a weight at top would be a great obftruflion to their mounting. No caduceus rockets afeend fo high as fingle, becaufe of their'’ \ So Honoiary Jockets. 552 P Y R O T Varieties their ferpentine motion, and likewifc the refiftance of of Conftruc-ajr^ {s rauc}1 greater than two rockets of the fame ■ fize would meet with if fired fingly. Fig. 30. thews the method of fixing thefe rockets : the tticks for this purpofe muft have all their tides equal, and the Tides tliould be equal to the breadth of a flick .proper for a tky-rocket of the fame weight as thofe you intend to ufe, and made to taper downwards as ufual, long enough to balance them, one length of a rocket from the crofs ilick j which muft be placed from the large ftick fix diameters of one of the rockets, and its length feven diameters •, fo that each rocket, when tied on, may form with the large ftick an angle of 60 de¬ grees. In tying on the rockets, place their heads on the oppofite Tides of the crofs ftick, and their ends on the op- pofite tides of the long ftick ; then carry a leader from the mouth of one into that of the other. When thefe rockets are to be fired, fufpend them between two hooks or nails, then burn the leader through the middle, and both will take fire at the fame time. Rockets of one lb. are a good fize for this ufe. Honorary rockets are the fame as tky-rockets, except that they carry no head nor repoit, but are ciofed at top, on which is fixed a cone : then on the cafe, clofe to the top of the ftick is tied on a two ounce cate, about five or fix inches long, filled with a ftrong charge, and pinched clofe at both ends ; then in the reverfe Tides, at each end, bore a hole in the fame manner as in tourbil- lons, to be prefently defcribed ; from each hole carry a leader into the top of the rocket. When the rocket is fired, and arrived to its proper height, it will give file to the cafe at top •, which will caule both rocket and ftick to fpin very faft in their return, and repiefent a worm of fire defcending to the ground. There is another method of placing the finall cafe, which is by letting the ftick r fe a little above the top of the rocket, and tying the cafe to it, fo as to reft on the rocket : thefe rockets have no cones. A third method by which they are managed is this : In the top of a rocket fix a piece of ivood, in which drive __ a fmall iron fpindle j then make a hole in the middle of the fmall cafe, through which put the fpindle : then fix on the top of it a nut, to keep the cafe from falling off •, when this is done, the cafe will turn very faft, without the rocket: but this method does not aniwer fo w-ell as either of the former. Fig. 31. is the honorary rocket complete. The heft fized rockets for this purpofe are thofe of one lb. Having fome rockets made, and headed according to fancy, and tied on their flicks ; get fome fheet tin, and cut it into round pieces about three or four inches dia¬ meter •, then on the ftick of each rocket, under the mouth of the cafe, fix one of thefe pieces of tin 16 inches from the rocket’s neck, and fupport it by a wooden bracket, as ftrong as poflible: the ufe of this is, that when the rocket is afcending the fire may play with great force on the tin, which will divide the tail in fuch a manner that it will form an arch as it mounts, and will have a very good effe£l when well managed : if there is a fhort piece of port-fire, of a ftrong charge, tied to the end of the ftick, it will make a great addition ; but this muft be lighted before the rocket is fired. Take fix, or any number of fky-rockets, of any fize j fame direc- cu(. pome ^rong packthread into pieces of three or E C H N Y. si To make a rocket form an arch in r rifing. Si To make fcveral rockets rife in the tion. and at the fame diltftnce. four yards long, and tie each end of thefe pieces to a 3 Chap. II. rocket in this manner : Having tied one end of the Varieties packthread round the body of one rocket, and the other ot t on^ruc- end to another, take a fecond piece of packthread and , make one end of it faft to one of the rockets already tied, and the other end to a third rocket, fo that all the rockets, except the two on the outfide, will be faftened to two pieces of packthread : the length of thread from one rocket to the other may be what the maker pleafes } but the rockets muft be all of a fize, and their heads filled with the fame weight of ftars, rains, &c. Having thus done, fix in the mouth of each rocket a leader of the fame length 5 and when about to fire them, hang them almoft clofe ; then tie the ends of the leaders together, and prime them : this prime being fired, all the x'ockets will mount at the fame time, and divide as far as the firings will allow, and this divifion they will keep, provided they are all rammed alike, and well made. They are fometimes called chained rochets. Signal rockets are made of feveral kinds, accordingSignalrock- to the different fignals intended to be given ; but in ar-ets. tificial fire works, two forts are only ufed, which are one with reports and the other without j but thofe for the ufe of the navy and army are headed with ftars, feipents, &c. Rockets which are to be bounced muft have their cafes made one and a half or two diameters longer than the common proportion ; and after they are filled, drive in a double quantity of clay, then bounce and pinch them after the ufual manner, and fix on each a cap. Signal fky-rockets without bounces, are only iky- rockets ciofed and capped : thefe are very light, there¬ fore do not require fuch heavy flicks as thofe with load¬ ed heads ; for which reafon the rocket may be cut from the ftick, or elfe be made thinner. Signal rockets " ith reports are fired in fmall flights j and often both thefe, and thofe without reports, are ufed for a fignal to begin firing a colleflion of works. Two, three, or fix fky-rockets, fixed on one ftick,To fix fe- an.l fired together, m ake a grand and beautiful appear-veral mck- ance } for the tails of all will feem but as one of an im-|.ts menfe fize, and the breaking of fo many heads at once will refemble the burfiing of an air-balloon. The ma¬ nagement of this device requires a fkilful hand j but if the following inftvudlions be well obferved, even by thofe who have not made a great progrefs in this art, there will be no doubt of the rockets having the defired effedft. Rockets for this purpofe muft be made with the great- eft exadlnefs, all rammed by the fame hand, in the fame mould, and filled with the fame proportion of compofi- tion ; and after they are filled and headed, muft all be of the fame weight. The ftick muft alfo be well made (and proportioned) to the following direflions : firft, fuppofing the rockets to be half pounders, whofe flicks are fix feet fix inches long, then if two, three, or fix of thefe are to be fixed on one ftick, let the length of it be nine feet nine inches : then cut the top of it into as ma¬ ny fides as there are rockets, and let the length of each fide he equal to the length of one of the rockets without its head •, and in each fide cut a groove (as ufual) ^ then from the grooves plane it round, down to the bottom, where its thicknefs muft be equal to half the top of the round part. As their thicknefs cannot he exadtly ascertained, we (hall give a rule which generally anfwers for Chap. II. P Y R O T E C H N Y. Varieties for any number of rockets above two : the rule Is this 5 of Conftruc- j]ie at; top mult be thick enough, when the , ti0li‘ grooves are cut, for all the rockets to lie, without pref¬ ling each other, though as near as pofllble. When only two rockets are to be fixed on one flick, let the length of the flick be the lall given proportion, but fhaped after the common method, and the breadth and thicknefs double the ufual dimenfions. The point of poife mutt be in the ufual place (let the number of rockets be what they will) : if flicks made by the above direftions fhould be too heavy, plane them thinner 5 and if too light, make them thicker 5 but always make them of the fame length. When more than two rockets are tied on one Hick, there will be fome danger of their flying up without the flick, unlefs the following precaution is taken : For cafes being placed on all tides, there can be no notches for the cord which ties on the rockets to lie in j therefore, in- flead of notches, drive a fmall nail in each fide of the flick, between the necks of the cafes : and let the cord, which goes round their necks, be brought clofe under the nails; by this means the rockets will be as fecure as when tied on fingly. The rockets being thus fixed, car¬ ry a quick-match, without a pipe, from the mouth of one rocket to the other ; this match being lighted will give fire to all at once. Though the directions already given may be fuffi- cient for thefe rockets, we fhall here add an improve¬ ment on a very effential part of this device, which is, that of hanging the rockets to be fired ; for before the following method was contrived, many attempts proved unfuccefsful. Inflead, therefore, of the old and common manner of hanging them on nails or hooks, make ufe of the following contrivance : Have a ring made of llrong iron wire large enough for the flick to go in as far as the mouths of the rockets; then have another ring fup- ported by a fmall iron, at fome diflance from the poll or Hand to which it is fixed : then have another ring fit to receive and guide the fmall end of the flick. Rockets thus fufpended will have nothing to obflruft their fire ; but when they are hung on nails or hooks , in fuch a manner that fome of their mouths are againll or upon a rail, there can be no certainty of their rifing in a vertical g. dire&ion. To fire To fire rochets without fiicks, you muft have a Hand, rockets of a block of wood, a foot diameter, and make the bot- without tom f0 that ^ may ftand Heady : in the centre of the top of this block draw a circle two inches and a half diameter, and divide the circumference of it into three equal parts 5 then take three pieces of thick iron wire, each about three feet long, and diive them into the block, one at each point made on the circle ; when thefe wares are driven in deep enough to hold them fall and upright, fo that the diflance from one to the other is the fame at top as at bottom, the Hand is com¬ plete. The Hand being thus made, prepare the rockets thus : l ake fome common fky-rockets of any fize, and head them as you pleafe ; then get fome balls of lead, and tie to each a fmall wire twro or two feet and a half long, and the other end ol each ware tie to the neck of a rocket. Thefe balls anfwer the purpofe of Hicks when made of a proper weight, which is about two- thirds the weight of the rocket; but when they are of a proper fize, they wall balance the "rocket in the fame Vol« XVIL Part II. tricks. 553 manner as a Hick, at the ufual point of poife. To fire Varieties thefe, hang them, one at a time, between the tops of the°^c?nftrua' wires, letting their heads reft on the point of the wares,. tl°n~ . and the balls hang down between them : if the wires flrould be too wide for the rockets, prefs them together till they fit 5 and if too clofe, force them open j the wires for this purpofe mult be foftened, fo as not to have any Ipring, or they will not keep their pofition when preffed clofe or opened. sg Cafes for fcrolls fliould be made four or five inches in'Scrolls for length, and their interior diameters three-eighths of an rockets, inch : one end of thefe cafes mult be pinched quite clofe before beginning to fill; and when filled clofe, the other- end : then in the oppofite fides make a fmall hole at each end, to the compofition, as in tourbillons ; and prime them with wet mealqxmder. You may put in the head of a rocket as many of thefe cafes as it will contain : being fired they turn very quick in the air, and form a fcroll or fpiral line. They are generally filled with a llrong charge, as that of ferpents or brilliant fire. „ Rockets that pafs under the denomination offiwarm-Swa.nners. ers, are thofe from two ounces downwards. Thefe roc¬ kets are fired fometimes in flights, and in large water- works, &c. Swarmers of one and two ounces are bor¬ ed, and made in the fame manner as large rockets, ex¬ cept that, when headed, their heads mull be put on without a collar : the number of Hrokes for driving one ounce mull be eight, and for two ounces twelve. All rockets under one ounce are not bored, but mult be filled to the ufual height with compofition, w'hich generally confifls of fine meal-powder four ounces, and charcoal or fleel-dufl two drams : the number of flrokes for ramming thefe fmall fwarmers is not material, provi¬ ded they are rammed truly, and moderately hard. The necks of unbored rockets mult be in the fame proportion as in common cafes. gg Care mufl be taken, in placing the rockets, when they Stands for are to be fired, to give them a vertical direflion at theirrocketE* firlt fetting out ^ which may be managed thus : Have twm rails of w-ood, of any length, fupported at each end by a perpendicular leg, fo that the rails may be ho¬ rizontal, and let the diflance from one to the other be almoft equal to the length of the flicks of the rockets intended to be fired ; then in the front of the top rail drive fquare hooks at eight inches diltance, with their points turning fidewife, fo that wdien the rockets are hung on them, the points will be before the flicks and keep them from falling or being blown off by the wdnd , in the front of the rail at bottom mufl be llaples, dri¬ ven perpendicular under the hooks at top ; through thefe flaples put the fmall ends of the rocket flicks. Rockets are fired by applying a lighted port-fire to then- mouths. N. B. When Iky-rockets are made to perfection, and fired, they will Hand two or three feconds on the hook before they rife, and then mount up brilkly, with a Heady motion, carrying a large tail from the ground all the way up, and juft as they turn, break, and difperfe the liars. Girandole chefts are generally compofed of four fides'Gira^ole of equal dimenfions 5 but may be made of any diame-chefts for ter, according to the number of rockets defigned to be^'S^tsot fired; their height mull be in proportion to the rockets,roc^et:i‘ but mult always be a little higher than the rockets with their flicks. When the fides are joined, fix in the top 4 A • as I 554 Varieties as far down the cheft as the length of one of the roc- of Con (true- kets wjt}1 its cap on> In this top, make as many fquare ■ Uo"' or round holes to receive the rocket ilicks as there are to be rockets j but let the diftance between them be fuf- ficient for the rockets to ftand without touching one another j then from one hole to another cut a groove large enough for a quick match to lie in : the top being thus fixed,put in the bottom, at about one foot and a half diftance from the bottom of the cheft } in this bottom muft be as many holes as in the top, and all to cone- fpond : but thefe holes need not be lb large as thole in the top. To prepare the cheft, a quick match muft be laid in all the grooves, from hole to hole : then take fome fky- rockets, and rub them in the mouth with -wet meal- powder, and put a bit of match up the cavity of each j which match muft be long enough to hang a little be¬ low the mouth of the rocket. The rockets and cheft being prepared according to the above directions, put the flicks of the rockets through the holes in the top and bottom of the cheft, fo that their mouths may reft on the quick-match in the grooves: by which all the rockets will be fired at once ; for by giving fire to any part of the match, it will communicate to all the roc¬ kets in an inftant. As it would be rather troublefome to direcl the flicks from the top to the proper holes in the bottom, it will be neceffary to have a fmall door in one of the fides, through which, when opened, you may fee how to place the flicks. 1 lights of rockets being feldom fet off at the beginning of any fire-works, they are in danger of being fired by the fparks from wheels, &c. j therefore, to preferve them, a cover fhould be made to fit on the cheft, and the door in the fide 90 kept {hut. Line-rockets are made and rammed as the fky-rockets, rockets. gut have no heads, and the cafes muft be cut clofe to the clay 5 they are fometimes made with fix or feven chan¬ ges, but in general not more than four or five. The method of managing thefe rockets is the following: Firft, have a piece of light wood, the length of one of the rockets turned round about two inches and a half dia¬ meter, with a hole through the middle lengthwife, large enough for the line to go eafily through } if four chan¬ ges are intended, have four grooves cut in the fwivel, one oppofite the other, in which to lay the rockets. The mouths of the rockets being rubbed with wet meal-powder, lay them in the grooves head to tail, and tie them faft ; from the tail of the firft rocket carry a leader to the mouth of the fecond, and from the fe- cond to the third, and fo on to as many as there are on the fwivel, making every leader very fecure •, but in fixing thefe pipes, take care that the quick-match does not enter the bores of the rockets: the rockets being fixed on the fwivel and ready to be fired, have a line 100 yards long, ftretched and fixed up tight, at any height from the ground ; but be fure to place it hori¬ zontally : this length of line will do for half-pound rockets 5 but if larger, the line muft be longer. Be¬ fore you put up the line, put one end of it through the fwivel 5 and when you fire the line rocket, let the mouth of that rocket which is firft fired face that end of the line where you ftand; then the firft rocket will carry the reft to the other end of the line, and the fecond will bring them back •, and fo they will run out and in ac¬ cording to the number of rockets: at each end of the Chap. II. line there muft be a piece of flat wrood for the rocket Varieties to ftrike againft, or its force will cut the line. Let the ™ Conftme. line be well foaped, and the hole in the fwivel very ^ fmooth. 91 To line rockets may be fixed a great variety of fi-Different gures, fuch as flying dragons, Mercuries, ftiips, &c. 5 or fl corations they may be made to run on the line hke a wheel ; which is done in this manner. Have a flat fw ivel made ve¬ ry exactly, and on it tie two rockets obliquely one on each fide, w hich will make it turn round as it goes, and form a circle of fire ; the charge for thefe rockets fhould be a little weaker than common. If you would fhow two dragons fighting, get two fwivels made fquareT and on each tie three rockets together on the under fide then have tw7o flying dragons made of tin, and fix one of them on the top of each fwivel, fo as to ftand upright j in the mouth of each dragon put a fmall cafe of com¬ mon fire, and another at the end of the tail; put two or three port-fires, of a ftrong charge, on one fide of their bodies, to Ihow them. This done, put them on the line, one at each end ; but let there be a fwivel in the middle of the line to keep the dragons from ftriking together : before firing the rockets, light the cades on the dragons ; and if care be taken in firing both at the fame time, they will meet in the middle of the line, and feem to fight. Then they will run back and return with great violence, which will, have a very pleafing ef¬ fect, The line for thefe rockets muft be very long, or they will ftrike too hard together. 9Z Cafes for Chinefe flyers may be made of different Cafes for fizes, from one to eight ounces : they muft be made thick Chn cfe of paper, and eight interior diameters long j they are‘i}ers- rolled in the fame manner as tourbillons, wiih a ftraight parted edge, and pinched clofe at one end. The method of filling them is, the cafe being put in a mould, w hofe cylinder, or foot, muft be fiat at top without a nipple, fill it within half a diameter of the middle ; then ram in half a diameter of clay, on that as much com- pofition as before, on which drive half a diameter of clay ; then pinch the cafe clofe, and drive it down fiat : after this is done, bore a hole exaftly through the cen¬ tre of the clay in the middle; then in the oppolite fides, at both ends, make a vent ; and in that fide intended to be fired firft make a fmall hole to the compolition near the clay in the middle, from w’hich carry a quick-match, covered with a Angle paper, to the vent at the other end 5 then, wThen the charge is burnt on one fide, it wall, by means of the quick-match, communicate to the charge on the other (w-hich may be of a different fort). I he flyers being thus made, put an iron pin, that muft be fixed in the wmrk on which they are to be fired, and on which they are to run, through the hole in the middle^ on the end of this pin muft be a nut to keep the flyer from running oft'. If they are to turn back again after they are burnt, make both the vents at the ends on the fame fide, which will alter its courfe the contrary way. Table rockets are defigned merely to fhow the truth of driving, and the judgment of a fire-worker; they rockets, having no other effeff, when fired, than fpinning round in the fame place where they begin, till they are burnt out, and fhowing nothing more than an horizontal circle of fire. The method of making thefe rockets is,—Have a cone turned out of hard wrood two inches and a half in dia¬ meter, and as much high : round the bafe of it drive a line j PYROTECHNY. Chap. 11. P Y R O T Varieties 1'mc •, on tins line fix four fpokes, each two inches long, of Conftruc-f0 as {l;an(l one oppofite the other j then fill tour nine- , tlun' , inch one pound cafes with any ftrong compofition, within two inches of the top : thefe cafes are made like tourbillons, and muft be rammed with the greateft ex- aclnefs. The rockets being filled, fix their open ends on the fhort fpokes j then in the fide of each cafe bore a hole near the clay ; all thefe holes, or vents, muft be fo made that the fire of each cafe may a£l the fame way j from thefe vents carry leaders to the top of the cone, and tie them together. When the rockets are to be fired, fet them on a fmooth table, and light the leaders in the middle, and all the cafes will fire together (fee fig. 32.) and fpin on the point of the cone. Thefe rockets may be made to rife like tourbillons, by making the cafes {hotter, and boring four holes in the Under fide of each at equal diftances : this being done they are called double tourbillons. Note, All the vents in the under fide of the cafes muft be lighted at once *, and the {harp point of the cone cut oft, at which place make it fpherical. Aeriai Fireworks called aerial globes or bombs confift of globes or a fpherical cafe made of ftrong paper, or of wTood, pre- bombs. pared as will be immediately deicribed, and thrown from a mortar commonly made of pafteboard, w'ith a copper Fig. 33. chamber to contain the charge, fuch as AB, fig. 33. This fmall mortar muft be made of light wood, or of paper parted together, and rolled up in the form of a cylinder, or truncated cone, the bottom excepted } which, as already faid, muft be of wrood. I he cham¬ ber for the powder AC muft be pierced obliquely, with a fmall gimlet, as leen at BC ; fo that the aperture B correfponding to the aperture of the metal mortar, in which this paper mortar muft be placed svhen the globe is fired, the fire applied to the latter may be communi- ted to the powder w’hich is at the bottom of the cham¬ ber AC, immediately below the globe. By thefe means the globe will catch fire and make an sgreeable noife as it riles into the air ; but it wmuld not fucceed fo w'ell if any vacuity were left between the powder and the globe. A profile or perpendicular fe£lion of fuch a globe is reprefented by the right-angled parallelogram ABCD, fig. 34.5 the breadth of which AB is nearly equal to the height AD. The thicknefs of the wood to¬ wards the two fides L, M, is equal to about the twelfth part of the diameter of the globe ; and the thicknefs E, F, of the cover, is double the preceding, or equal to a fixth part of the diameter. The height GK, or HI of the chamber GHIK, where the match is applied, and which is terminated by the femicircle LGKM, is equal to the fourth part of the breadth AB, and its breadth GH is equal to the fixth part of AB. We muft here obferve, that it is dangerous to put wooden covers, fuch as EF, on aerial balloons or globes, for thefe covers may be fo heavy as to wound thofe on whom they happen to fall. It will be fufficient to place turf or hay above the globe, in order that the powder may exoerence fome refiftance. The globe muft be filled with feveral pieces of cane or common reed, equal in length to the interior height of the globe, and charged with a flow compofition, made of three ounces of pounded gunpowder, an ounce of ful- E C H N Y. 555 phur moiftened with a fmall quantity of petroleum oil, Varieties and two ounces, of charcoal j and in order that thefeot Gonftruc- reeds or caaes may catch fire fooner, and with more fa-, t'°i“ ■ cility, they muft be charged at the lower ends, which reft on the bottom of the globe, with pulverized gun¬ powder moiftened in the fame manner with petroleum oil, or well befprinkled with brandy, and then dried. The bottom of the globe ought to be covered with a little gunpowder half pulverized and half grained j which, when fet on fire by means of a match applied to the end of the chamber GH, will fet fire to the lower part of the reed. But care muft have been taken to fill the chamber with a compofition fimilar to that in the reeds, or with another flowT compofition made of‘eight ounces of gunpowder, four ounces of faltpetre, two ounces of fulphur, and one ounce of charcoal : the whole muft be well pounded and mixed. Inftead of reeds, the globe may be charged with run¬ ning rockets, or paper petards, and a quantity of fiery ftars or fparks mixed with the pulverifed gunpowder, placed without any order above thefe petards, which muft be choaked at unequal heights, that they may perform their effedt at different times. Thefe globes may be conftrudled in various other ways, which it would be tedious here to enumerate. We {hall only obferve, that wdien loaded they muft be well covered at the top ; they muft be wrapped up in a piece of cloth dipped in glue, and a piece of woollen cloth muft be tied round them, fo as to cover the hole which contains the match. 95 Fuzes for air balloons are fometimes turned out of Fnz'^')r dry beech, with a cup at top to hold the quick match, or other firing material •, but if made with parted paper, they will do as well : the diameter of the former for fuzes for coehorn balloons muft be half an inch ; for a royal fuze, five-eighths of am inch ; for an eight inch iuze, three-fourths of an inch *, and for a ten inch fuze, feven-eighths of an inch. Having rolled the cafes, pinch and tie them almoft clofe at one end : then drive them down, and let them dry. Before beginning to fill them, mark on the outfide of the cafe the length of the charge required, allowdng for the thicknefs of the bottom ; and when the compofition is rammed in, take two pieces of quick-match about fix inches long, and lay one end of each on the charge, and then a little meal-powder, which ram down hard ; the loofe ends of the match double up into the top of the fuze, and cover it with a paper cap to keep it dry. When the {hells are put into the mortars, uncap the fuzes, and pull out the loofe ends of the match, and let them hang on the fides of ^he bal¬ loons. The ufe of the match is, to receive the fire from the powder in the chamber of the mortar, in order to light the fuze : the {hell being put in the mortar with the fuze uppermoft, and exaftly in the centre, fprinkle over it a little meal-powder, and it will be ready to be fired. Fuzes made of wood muft be longer than thofe of paper, and not bored quite through, but left folid about half an inch at bottom ; and when ufed faw them oft' to a proper length, meafuring the charge from the cup at top. 96 To make Tourbillons.—Having filled fome cafes with-Tourbd- in about one diameter and a half, drive in a ladleful of l0115, clay j then pinch the ends clofe, and drive them down with a mallet. When done, find the centre of gravity of each cafe j where the nail and flick are tied which 4 A 2 ftiould 556 Varieties ftiould be half an inch broad at the middle, and run ^tfon rt'C"3 little narrower to the ends: thefe flicks muft have t -1- ; their ends turned upwards, fo that the cafes may turn horizontally on their centres : at the oppofite fides of the cafes, at each end, bore a hole clofe to the clay with a gimblet, the lize of the neck of a common cafe of the fame nature : from thefe holes draw a line round the cafe, and at the under part of the cafe bore a hole with the fame gimblet, within half a diameter of each line towards the centre ; then from one hole to the other draw a right line. Divide this line into three equal parts 5 and at X and Y (fig. 35.) bore a hole ; then from thefe holes to the other two lead a quick- match, over which pafte a thin paper. Fig. 36. repre- fents a tourbillon as it fliould lie to be fired, with a leader from one fide hole A to the other B. When tourbillons are fired lay them on a fmooth table, with their flicks downwards, and bum the leader through the middle with a portfire. They Ihould fpin three or four feconds on the table before they rife, which is about the time the compofition will be burning from the fide holes to thofe at bottom. To tourbillons may be fixed reports in this manner : In the centre of the cafe at top make a fmall hole, and in the middle of the report make another j then place them together, and tie on the report, and with a fingle paper fecure it from fire : this done, the tourbillon is completed. By this method you may fix on tourbil¬ lons fmall cones of flars, rains, &c. but be careful not to load them too much. One eighth of an inch will be enough for the thicknefs of the flicks, and their length equal to that of the cafes. Aigrettes. Mortars to throw aigrettes are generadly made of pafleboard, of the fame thicknefs as balloon mortars, and two diameters and a half long in the infide from the top of the foot : the foot muft be made of elm without a chamber, but flat at top, and in the fame proportion as thofe for balloon mortars ; thefe mortars muft alfo be bound round with a cord: fometimes eight or nine of thefe mortars, of about three or four inches diameter, are bound all together, fo as to appear but one : but when they are made for this purpofe, the bottom of the foot muft be of the fame diameter as the mortars, and only half a diameter high. The mortars being bound well together, fix them on a heavy folid block of wood. To load thefe mortars, firft put on the infide bottom of each a piece of paper, and on it fpread one ounce and a ' half of meal and com powder mixed; then tie the fer- pents up in parcels with quickmatch, and put them in the mc!*tar with their mouths downwards ; but take care the parcels do not fit too tight in the mortars, and that all the ferpenls have been well primed with powder wetted with fpirit of wine. On the top of the ferpents in each mortar lay fome paper or tow; then carry a leader from one mortar to the other all round, and then from all the outfide mortars into that in the middle : thefe leaders muft be put between the cafes and the fides of the mortar, down to the porvder at bottom : in the centre of the middle mortar fix a fire pump, or bril¬ liant fountain, which muft be open at bottom, and long enough to project out of the mouth of the mortar ; then pafte paper on the tops of all the mortars. Mortars thus prepared are called a nejl of ferpents, as reprefented by fig. 37. When thefe mortars are to be fired, light the fire-pump C, which when confumed will Chap. II. communicate to all the mortars at once by means of Varieties the leaders. For mortars of 8, 9, or 10 inches diame-ot ^nftruc- ter, the ferpents ftrould be made in one and two ounce non- . cafes fix or feven inches long, and fired by a leader brought out of the mouth of the mortar, and turned down the outfide, and the end of it covered with paper, to prevent the fparks of the other -works from letting it on fire. For a fix-inch mortar, let the quantity of powder for firing be two ounces j for an eight-inch, two ounces and three quarters \ and for a ten-inch, three ounces and three quarters. Care muft be taken in thefe, as well as fmall mortars, not to put the ferpents in too tight, for fear of burfting the mortars. Thefe mortars may be loaded with ftars, crackers, &c. If the mortars, when loaded, are fent to any diftance, or liable to be much moved, the firing powder Ihould be fecured from getting amongft the ferpents, w;hich would endanger the mortars, as well as hurt their per¬ formance. To prevent this, load the mortars thus: Firft put in the firing pow'der, and fpread it equally about j then cut a round piece of blue touch-paper, equal to the exterior diameter of the mortar, and draw on it a circle equal to the interior diameter of the mor¬ tar, and notch it all round as far as that circle : then pafte that part which is notched, and put it down the mortar clofe to the powder, and flick the palled edge to the mortar : this wall keep the powder always fmooth at bottom, fo that it may be moved or carried anywhere without receiving damage. The large fingle mortars are called pots des aigrettes. Pots des Brins are formed of pafteboard, and muft be Pots dea rolled pretty thick. They are ufually made three orbrins. four inches diameter, and four diameters long; and pinched wuth a neck at one end, like common cafes. A number of thefe are placed on a plank thus : Having fixed on a plank two rows of wmoden pegs, cut in the bottom of the plank a groove the whole length under each row of pegs j then, through the centre of each peg, bore a hole down to the groove at bottom, and on every peg fix and glue a pot, wdiofe mouth muft fit tight on the peg *, through all the holes run a quick match, one end of which muft go into the pot, and the other into the groove, wdiich muft have a match laid in it from end to end, and covered with paper, fo that when light¬ ed at one end it may difcharge the wdiole almoft inllan- taneoully : in all the pots put about one ounce of meal and corn powTder ; then in fome put ftars, and in others rains, fnakes, ferpents, crackers, &c. wdien they are all loaded, pafte paper over their mouths. Two or three hundred of thefe pots being fired together make a very pretty fhowq by affording fo great a variety of fires. Fig. 38. is a range of pots des brins, with a leader A, by which they are fired. Pots des Sauciflbns are generally fired out of large mortars without chambers, the fame as thofe for aigrettes, faucifibns, only fomewhat ftronger. Sauciffons are made of one and twm ounce cafes, five or fix inches long, and choked in the fame manner as ferpents. Half the number which the mortar contains muft be driven one diame¬ ter and a half with compofitio-n, and the other half two diameters, fo that when fired they may give two volleys of reports. But if the mortars are very ftrong, and will bear a fufficient charge to throw7 the fauciffons very high, you may make three volleys of reports, by divid¬ ing the number of cafes into three parts, and making a difference PYROTECHNY. Chap. i®o Single ver¬ tical wheels. II. P Y R O T Varieties difference in the height of the charge. After they are of Conftruc-gUg^ pinch and tie them at top of the charge almoft tlon’ clofe 5 only leaving a fmall vent to communicate the fire to the upper part of the cafe, which mult be filled with corn-powder very near the top 5 then pinch the end quite clofe, and tie it: after this is done, bind the cafe very tight with waxed packthread, from the choke at top of the compofition to the end of the cafe } this will make the cafe very ftrong in that part, and caufe the report to be very loud, bauciffons fhould be roued a little thicker of paper than the common proportion. When they are to be put in the mortar, they mull be primed in their mouths, and fired by a cafe of brilliant fire fixed in their centre. The charge for thefe mortars fhould be one-fixth or one-eighth more than for pots dcs aigrettes ot the fame diameter. There are different forts of vertical wheels ; fome ha¬ ving their fells of a circular form, others of an hexagonal, odtagonal, or decagonal form, or of any number of fides, according to the length of the cafes you defign for the wheel: the fpokes being fixed in the nave, nail flips of tin, with their edges turned up, fo as to form grooves for the cafes to lie in, from the end of one fpoke to that of another; then tie the cafes in the grooves head to tail, in the fame manner as thofe on the horizontal water¬ wheel, fo that the cafes fucceffively taking fire from one another, will keep the wheel in an equal rotation. Two of thefe wheels are very often fired together, one on each fide of a building ; and both lighted at the fame time, and all the cafes filled alike, to make them keep time together j as they will, if made by the following di¬ rections : In all the cafes of both wheels, except the firft, on each wheel drive two or three ladiesful of flow fire, in any part of the cafes j but be careful to ram the fame quantity in each cafe, and in the end of one of the cafes, on each wheel, you may ram one ladleful of dead-fire compofition, which muft be very lightly driven •, you may alfo make many changes of fire by this method. Let the hole in the nave of the wheel be lined with brafs, and made to turn on a fmooth iron fpindle. On the end of this fpindle let there be a nut, to fcrew off and on j when you have put the wheel on the fpindle, fcrew on the nut, which will keep the wheel from^ fly¬ ing off. Let the mouth of the firft cafe be a little raifed. See fig. 39. Vertical wheels are made from ten inches to three feet diameter, and the fize of the cafes muft differ accordingly } four-ounce cafes wall do for wheels of 14 or 16 inches diameter, which is the proportion ge¬ nerally ufed. The beft wood for wheels of all forts is a light and dry beech. Horizontal wheels are beft when their fells are made circular ; in the middle of the top of the na\e muft be a pintle, turned out of the fame piece as the nave, two inches long, and equal in diameter to the bore of one of the cafes of the wheel : there muft be a hole bored up the centre of the nave, within half an inch of the top of the pintle. The wheel being made, nail at the end of each fpoke (of wdiich there fhould be fix or eight) a piece of wood, wnth a groove cut in it to receive the cafe. Fix thefe pieces in fuch a manner that half the cafes may incline upwards and half downwards, and that, when they are tied on, their heads and tails may come very nearly together 3 from the tail of one cafe to the tor Horizontal wheels. E C H N Y. 557 mouth of the other carry a leader, which ihould be fe- Varieties cured with pafted paper. Befides thefe pipes, it will be of Conftruc- neceffary to put a little meal-powder within the pafted . ^ paper, to blow off the pipe, that there may be no ob- ftruftion to the fire from the cafes. By means of thefe pipes the cafes will fucceffively take fire, burning one upwards and the other downwards. On the pintle fix a cafe of the fame fort as thofe on the wheel 3 this cafe muft; be fired by a leader from the mouth of the laft cafe on the wheel, which cafe muft play downwards : inftead of a common cafe in the middle, you may put a cafe of Chinefe fire, long enough to burn as long as two or three- of the cafes on the wheel. Horizontal wheels are often fired two at a time, and made to keep time like vertical wheels, only they are made without any flow or dead fire 3 10 or 12 inches plate wull be enough for the diameter of wheels with fixcCGCLIV, fpokes. Fig. 40. reprefents a wheel on fire, with the Fig. 40. firft cafe burning. ioj Spiral wheels, are only double horizontal wheels, and Spiral made thus : The nave muft be about fix inches long,wlieel?* and rather thicker than the Angle fort 3 inftead of the pintle at top, make a hole for the cafe to be fixed in, and two fets of fpokes, one fet near the top of the nave, and the other near the bottom. At the end of each fpoke cut a groove wherein you tie the cafes, there be¬ ing no fell 3 the fpokes ffiould not be more than twm inches and a half long from the naves, fo that the wheel may not be more than eight or nine inches diameter; the cafes are placed in fuch a manner, that thofe at top play down, and thofe at bottom play up, but let the third or fourth cafe play horizontally. The cafe in the middle may begin with any of the others: fix fpokes will be enough for each fet, fo that the wheel may con- fift of 12 cafes, befides that on the top : the cafes fix inches each. I03 Plural wheels are made to turn horizontally, and to plural confift of three fets of fpokes, placed fix at top, fix at wheels, bottom, and four in the middle, which laft muft be a little ftiorter than the reft : let the diameter of the wheel be 10 inches 3 the cafes muft be tied on the ends of the fpokes in grooves cut on purpofe, or in pieces of wood nailed on the ends of the fpokes, with grooves cut in them as ufual: in clothing thefe wheels, make the up¬ per fet of cafes play obliquely downwards, the bottom fet obliquely upwards, and the middle fet horizontally. In placing the leaders, they muft be managed fo that the cafes may burn thus, viz. firft up, then dowm, then ho¬ rizontal, and fo on with the reft. But another change may be made, by driving in the end of the eighth cafe two or three ladiesful of 1W fire, to burn till the vdreel has flopped its courfe 3 then let the other cafes be fixed the contrary way, which will make the wheel run back again : for the cafe at top you may put a fmall gerbe 3 and let the cafes on the fpokes be ffrort, and fill¬ ed with a ftrong brilliant charge. I0^ Illuminatedfpiral wheel.—Firft have a circular hori- Illuminated zontal wheel made two feet diameter, with a hole quite fpiral through the nave 3 then take three thin pieces of deal, whec's> three feet long each, and three-fourths of an inch broad each : one end of each of thefe pieces nail to the fell of the wheel, at an equal diftance from one another, and the other end nail to a block with a hole in its bottom, which muft be perpendicular to that in the block of the wheel, but not fo large. The wheel being thus made, have pouble fpiral wheel. jo6 Balloon wheels. 107 Frailoni wheels. have a hoop planed down very thin and flat; then nail one end of it into the „fell of the wheel, and wind it round the three Hicks in a fpiral line from the wheel to the block at top : on the top of this block fix a cafe of Clunefe fire j on the wheel you may place any number of cafes, which muft incline downwards, and burn two at a time. If the wheel fhould confift of ten cafes, you may let the illuminations and Chinefe fire begin with the fecond cafes. Jfhe fpindle for this wheel muft be a little longer than the cone, and made very fmooth at top, on which the upper block is to turn, and the whole weight of the wheel to reft. See fig. 41. Double fpiral wheel.—For this wheel the block, or nave, muft be as long as the height of the worms, or fpiral lines, but muft be made very thin, and as light as pofTible. In this block muft be fixed feveral fpokes, which muft diminifh in length, from the wheel to the top, fo as not to exceed the furface of a cone of the fame height, lo the ends of thefe fpokes nail the wrorms, which muft crofs each other feveral times : clothe thefe wwms with illuminations, the fame as thofe on the fingle wheels} but the horizontal wheel you may clothe as you like. At top of the worm place a cafe of fpur-fire, or an amber light, fee fig. 42. This figure is fhow-n without leaders, to prevent a confufion of lines. Balloon wheels are made to turn horizontally : they muft be made two feet diameter, without any fpokes *, and very ftrong, with any number of fides. On the top of a wheel range and fix in pots, three inches diameter and feven inches high each, as many of thefe as there -are cafes on the w heel: near the bottom of each pot make a fmall vent; into each of thefe vents carry a leader from the tail of each cafe ; load fome of the pots with ftars, and fome with ferpents, crackers, &c. As the wheels turn, the pots will fucceflively be fired, and throw into the air a great variety of fires. For fruiloni wheels firft have a nave made nine inches long and three in diameter: near the bottom of this nave fix eight fpokes, with a hole in the end of each, large enough to receive a two or four ounce cafe : each of thefe fpokes may be 14 inches long from the block. Near the top of this block fix eight more of the fame fpokes, exactly over the others, but not fo long by two inches. As this wheel is to run horizontally, all the cafes in the fpokes muft play obliquely upwards, and all thofe in the fpokes at bottom obliquely dowmvards. This being done, have a fmall horizontal wheel made with eight fpokes, each five inches long from the block: on the top of this wheel place a cafe of brilliant fire : all the cafes on this w-heel muft play in an oblique di- reftion dowmvards, and burn tw-o at a time, and thofe on the large wheel four at a time; that is, tw-o of thofe in the top fet of {pokes, and two of thole in the bottom let of fpokes. The four firft cafes on the large wheel, and the two firft on the fmall, muft be fired at the fame time, and the brilliant fire at top at the beginning of the laft cafes. The cafes of the wheels may be filled w-ith a gray charge. When thefe wheels are completed, you muft have a ftrong iron fpindle, made four feet fix inches long,^ and fixed perpendicularly on the top of a ftand : on this put the large wheel, whofe nave muft have a hole quite through from the bottom to the top. This hole .muft be large enough to turn eafily round the bettom of P Y R Q T E C H N Y. Chap. II. the fpindle, at which place there muft be a ftioulder, to ^ arieties keep the wheel from touching the fland : at the top of0* the fpindle put the fmall wheel, and join it to a large , tlon- f one with a leader, in order that they may be fired both together. Cafcades off re are made of any fize ; but one made Cafcades of according to the dimenfions of that fliown in fig. 43.fire, will be large enough for eight-ounce cafes. Let tire diftance. from A to B be three feet; from B to G two feet fix inches ; and from C to D two feet-, and let the crofs piece at A be four feet long : then from each end of this piece draw a line to D 5 then make the other crofs. pieces fo long as to come within thofe lines. The top piece D may be of any length, fo as to hold the cafes, at a little diftance from each other j all the crofs pieces are fixed horizontally, and fupported by brackets; the bottom crofs piece Ihould be about one foot fix inches broad in the middle, the lecond one foot, the third nine inches, and the top piece four inches: the cafes may be made of any length, but muft be filled with a brilliant charge. On tire edges of the crofs pieces muft be nailed bits of wood, with a groove cut in each piece, large enough for a cafe to lie in. Thefe bits of w'ood are fixed fo as to incline downwards, and that the fire from one tier of cafes may play over that of the other. All the cafes being tied fart on, carry lead¬ ers from one to the other ; and let there be a pipe hung from the mouth of one of the cafes, covered at the end with a fingle paper, which you burn to fire the cafcade. IC The Fire Tree.— To make a fire tree, as {hown by Fire tree. %• 44- y°u muft firft have a piece of wood fix feet long, and three inches fquare; then at E, nine inches from the top, make a hole in the front, and in each fide; or, inftead of holes, you may fix fhort pegs, to fit the infide of the cafes. At F, nine inches from E, fix three more pegs ; at G, one foot nine inches from F, fix three pegs; at H, nine inches from G, fix three pegs; at I, nine inches from H, fix three pegs, inclining downwards; but all the other pegs muft incline upwards, that the cafes may have the fame inclination as is feen in the figure : then at top place a four-inch mortar, loaded with ftars, rains, or crackers. In the middle of this mortar place a cafe filled ivith any fort of charge, but let it be fired with the other cafes : a brilliant charge will do for all the cafes; but the mortar may be made of any diameter, and the tree of any fize; and on it any number of cafes, provided they are placed in the manner def-nbed. Chinefe Fountains.—To make a Chinefe fountain, you muft have a perpendicular piece of wood feven feet long and two inches and a half fquare. Sixteen inches from the top, fix on the front a crofs piece one inch thick, and two and a half broad, -with the broad fide up¬ wards ; below this, fix three more pieces of the fame width and thicknefs, at fixteen inches from each other; let the bottom rail be five feet long, and the others of fuch a length as to allow the fire-pumps to ftand in the middle of the intervals of each other. The pyra¬ mid being thus made, fix in the holes made in the bot¬ tom rail five fire pumps, at equal diftances; on the fe¬ cond rail, place four pumps ; on the third, three ; on the fourth, two; and on the top of the port, one; but place them all to incline a little forwards, that, when they throw out the ftars, they may not ftrike againft the 5 Chap. II. Varieties the crofs rails. Having fixed your fire-pumps, clothe of Cotiftnrc- them with leaders, fo that they may all be fired toge- . . ti^n' ther. See fig. 45. x 11 Of illuminated Globes with horizontal Wheels.—The IUuinira‘ed hoops for thefe globes may be made of wood, tin, or globes with iron wire, about two feet in diameter. For a fingle vmeels'tdl ta^e tw0 ^°0P?» tie them together, one within the other, at right angles •, then have a horizon¬ tal wheel made, whofe diameter mull be a little wi¬ der than the globe, and its nave fix inches long) on the top of which the globe is fixed, fo as to ftand three or four inches from the wheel: on this wheel you may put any number of cafes, filled with what charge you pleafe j but let two of them burn at a time : they may be placed horizontally, or to incline downwards, juft as you choofe. Now, when the wheel is clothed, fix on the hoops as many illuminations as will ftand within two inches and a half of each other : fallen theie on the hoops with fmall iron binding wire ; and when they are all on, put on the pipes of communication, which mull be fo managed as to light them all with the fecond or third cafe on the wheel. The fpindle on which the globe is to run muft go through the block of the wheel, up to the infide of the top of the globe; where muft be fix¬ ed a bit of brafs, or iron, with a hole in it to receive the point of the fpindle, on which the whole weight of the wheel is to bear, as in fig. 46. which repreients a globe on its fpindle. By this method may be made a crown, which is done by having the hoops bent in the form of a crown. Sometimes globes and crowns are managed fo as to ftand Hill, and the wdieel only to turn round 5 but when you would have the globe or crown to ftand Hill, and the w’heel to run by itfelf, the block of the wheel muft not be fo long, nor the fpindle any longer than juft to raife the globe a little above the wheels j and the wheel cafes and illumination muft be- 11.2 gin together. Dodeeahe- The Dodecahedron.—§0 called becaufe it nearly re- dron. prefents a twelve-fided figure, is made thus : Firft have a ball turned out of fome hard wood, 14 inches diame¬ ter : divide its furface into 14 equal parts, from wftuch bore holes one inch and a half diameter, perpendicular to the centre, fo that they may all meet in the middle : then let there be turned in the infide of each hole a fe¬ male fcrew *, and to all the holes but one muft be made a round fpoke five feet long, with four inches of the fcrew at one end to fit the holes; then in the fcrew’-end of all the fpokes bore a hole, five inches up, which muft be bored flanting, fo as to come out at one fide, a little above the fcrew; from which cut a fmall groove along the fpoke, within fix inches of the other end, wdrere make another hole through to the other fide of the fpoke. In this end fix a fpindle, on wdiich put a fmall wheel of three or four fides, each fide fix or feven inches long •, thefe fides muft have grooves cut in them, large enough to receive a two or four ounce cafe. When thefe wheels are clothed, put them on the fpindles, and at the end of each fpindle put a nut to keep the wheel from falling off. The wheels being thus fixed, carry a pipe from the mouth of the firft cafe on each wheel, through the hole in the fide of the fpoke, and from thence along the groove, and through the other hole, fo as to hang out at the fcrew-end about an inch. The fpokes being all prepared in this manner, you muft have a poft, on vvhich you intend to fire the work, with an 559 iron fcrew in the top of it, to fit one of the holes in Varieties the ball: on the fcrew fix the ball j then in the top Conftruc- hole of the ball put a little meal-powder, and fome , tuJ1‘ loofe quick-match : then fcrew in all the fpokes ; and v in one fide of the ball bore a hole, in which put a lea¬ der, and fecure it at the end ; and the work will be rea¬ dy to be fired. By the leader the powder and match in the centre is fired, which will light the match at the ends of the fpokes all at once, whereby all the wheels will be lighted at once. There may be an addition to this piece, by fixing a fmall globe on each wheel, or one on the top w'heel only. A gray charge will be proper for the wheel cafes. X1^ The Yew 1 ree of brilliant Tire is reprefented by Yew tree of fig. 47. as it appears when burning'. Firft, let A be an brilliant upright piece of wood, four feet long, two inchesfire- broad, and one thick : at top of the piece, on the flat fide, fix a hoop 14 inches diameter ; and round its edge and front place illuminations, and in the centre a five- pointed ftar; then at E, which is one foot and a half from the edge of the hoop, place two cafes of brilliant fire, one on each fide \ thefe cafes Ihould be one foot long each : below thefe fix two more cafes of the fame fize, and at fuch a diftance that their mouths may al- moli meet them at top : then clofe to the ends of thefe fix twm more of the fame cafes ; they muft ftand parallel to them at E. The cafes being thus fixed, clothe them with leaders j fo that they, with the illuminations and ftars at top, may all take fire together. 114. Stars with Points for regulated Pieces, &c.—Thefe Stars with ftars are made of different iizes, according to the work f)01IU'c:‘ for which they are intended 5 they are made with cafes from one ounce to one pound, but in general with four ounce-cafes, four or five inches long : the cafe muft bs rolled with pafte, and twice as thick as that of a rocket of the fame bore. Having rolled a cafe, pinch one end of it quite clofe: then drive in half a diameter of clay ; and when the cafe is dry, fill it with compofition two or three inches to the length of the cafes with which it is to burn : at top of the charge drive fome clay j as the ends of thefe cafes are feldom pinched, they would be liable to take fire. Having filled a cafe, di¬ vide the circumference of it at the pinched end clofe to the clay into five equal parts ; then bore five holes with a gimblet, about the fize of the neck of a common four-ounce cafe, into the compofition : from one hole to the other carry a quick-match, and fecure it with pa¬ per : this paper muft be put on in the manner of that on the end of wheel-cafes, fo that the hollow part, which projeifts from the end of the cafe, may ferve to receive a leader from any other work, to give fire to the points of the ftars. Thefe ftars may be made with any number of points. Fixed Sun with a tranfparent Face.—To make a fun tMxed'fun of the beft kind, there ftiould be two rows of cafes, as in with a fig. 48. which will ihow a double glory, and make the tran*Parent rays ftrong and full. The frame or fun-wheel, muft be tace' made thus : Have a circular flat nave made very flrong, 12 inches diameter: to this fix fix ftrong flat fpokes, A,B,C,D,E,F. On the front of thefe fix a circular fell, five feet diameter; within which fix another fell, the length of one of the fun-cafes lefs in diameter ; within this fix a third fell, whofe diameter muft be lefs than the fecond by the length of one cafe and one-third. The wheel being made, divide the fells into fo many equal parts PYROTECHNY. 56° Varieties parts as tliere are to be cafes (which may be done from of Con (true- to ^ . at gadi divifion fix a flat iron ftaple j thefe ■ t‘°n' ftaples mufl; be made to fit the cafes, to hold them faft on the wheel; let the ftaples be fo placed, that one row of cales may lie in the middle of the intervals of the other. In the centre of the block of the fun drive a fpindle, on which put a fmall hexagonal wheel, whofe cates' muft be filled with the fame charge as the cafes of the fun : two cafes of this wheel muft burn at a time, and begin with them on the fells. Having fixed on all the cales, carry pipes of communication from one to the other, as vou fee in the figure, and Irom one fide oi the fun to the wheel in the middle, and Irom thence to the other fide of the fun. Thefe leaders will hold the wheel fteady while the lun is fixing up, and will alfo be a fure method of lighting both cafes of the wheel together. A fun thus made is called a brilliant fun, becaufe the wrood work is entirely covered with fire from the wheel in the middle, fo that there appears nothing but fparks of brilliant fire ; but if you w-ould have a tranfparent face in the centre, you muft have one made of pafteboard of any fize. The method of making a face is, by cutting out the eyes, nofe, and mouth, for the fparks of the wdieel to appear through ; but inftead of this face, you may have one painted on oiled paper, or Perfian filk, {trained tight on a hoop •, which hoop muft be fupported by three or four pieces of wire at fix inches diftance from the wheel in the centre, fo that the light of it may illuminate the face. By this method may be Ihown in the front of a fun, Vivat Rex, cut in pafteboard, or Apollo painted on filk ; but, for a fmall colledtion, a fun with a fingle glory, and a w heel in front, will be moft fuitable. Half pound cafes, filled ten inches with compofition, will be a good fize for a fun of five feet diameter ; but, if larger, the cafes muft 116 be greater in proportion. Three ver- Three Vertical Wheels illuminated, ’which turn on their tical wheels ow;2 ]$aves vpon a horizontal Table.—A plan of this is illuminated.^ j^et D be a fir table three feet in diameter : this table muft be fixed horizontally on the top of a poft } on this poll muft be a perpendicular iron fpindle, which muft come through the centre of the table : then let A, B, C, be three fpokes joined to a triangular flat piece of wood, in the middle of which make a hole to fit eafily over the fpindle : let E, F, G, be pieces of wood, four or five inches long each, and twm inches fquare, fixed on the under fides of the fpokes 5 in thefe pieces make holes lengthwife to receive the thin p&rt of the blocks of the wheels, which, when in, are prevented from coming out by a fmall iron pin being run through the end of each. K, L, M, are three vertical oftagonal wheels, 18 inches diameter each : the blocks of thefe wheels muft be long enough for three or four inches to reft on the table •, round which part drive a number of (harp points of wire, which muft not project out of the blocks more than i-i6th of an inch : the ufe of thefe points is, that, wdren the blocks run round, they will ftick in the table, and help the wheels forward : if the naves are made of ftrong wood, one inch will be enough for the diameter of the thin part, which Ihould be made to turn eafily in the holes ©f the pieces E, F, G. On the front of the wheels make four or five circles of ftrong ware, or flat hoops, and tie on them as many il¬ luminations as they will hold at two inches diftant from Chap. II. each other : inftead of circles, you may make fpiral Varieties lines, clothed with illuminations, at the fame diftance01 Conftruc- from each other as thofe on the hoops. When illumi- tl"n' t nations are fixed on a fpiral line in the front of a wheel, they muft be placed a little on the flant, the contrary way from that in which the wheel runs ; the cafes for thefe wheels may be filled with any coloured charge, but muft burn only one at a time. The wheels being thus prepared, you muft have a globe, crown, or fpiral wheel, to put on the fpindie in the middle of the table : this fpindle fliould be juft long enough to raife the wheel of the globe, crown, or fpi¬ ral wheel, fo high that its fire may play over the three vertical wheels : by this means their fires will not be confufed, nor will the wheels receive any damage from the fire of each other. In clothing this work, let the leaders be fo managed, that all the wheels may light to¬ gether, and the illuminations after twro cafes of each wheel are burned. _ uy Illuminated works are much admired by the Italians, Illuminated and indeed are a great addition to a collection of wmrks; chandelier, in a grand exhibition an illuminated piece ftiould be fir¬ ed after every two or three w-heels, or fixed pieces of common and brilliant fires j and likewife illuminated works may be made cheap, quick, and eafy. To make an illuminated chandelier, you muft firft have one made of thin w7ood (fee fig. 50-)* chan¬ delier being made, bore in the front of the branches, and in the body, and alfo in the crown at top, as many holes for illuminations as they will contain at three inches diftance from each other : in thefe holes put il¬ luminations filled with white, blue, or brilliant charge. Having fixed in the port-fires, clothe them with leaders, fo that the chandelier and crown may light together. The fmall circles on this figure reprefent the mouths of the illuminations, which muft projedl ftraight from the front. 118 To make a flaming ftar with brilliant wheels, you muft Flaming firft have made a circular piece of ftrong wood about one ftms with inch thick and two feet diameter : round this block fix eight points, two feet fix inches long each •, four of theie points muft be ftraight and four flaming ; thefe points be¬ ing joined on very ftrong, and even with the furface of the block, nail tin or pafteboard on their edges, from the block to the end of each, where they mull be joined : this tin muft projeft in front eight inches, and be joined where they meet at the block; round the front of the block fix four pieces of thick iron wire, eight inches long each, equally diftant from each other : this being done, cut a piece of pafteboard round, two feet diameter, and draw on it a ftar, as may be feen in fig. 51. Cut -r> out this ftar, and on the back of it pafte oiled paper j then paint each point half red and half yellow, length- wife p but the body of the ftar muft be left'open, where¬ in muft run a brilliant wheel, made thus : Have a light block turned nine inches long : at eacn end of it fix fix fpokes 5 at the end of each fpoke put a two ounce cafe of brilliant fire : the length of thefe cafes muft be in proportion to the wheel, and the diameter of the wheel Vvflien the cafes are on muft be a little lefs than the dia¬ meter of the body of the fmall ftar : the cafes on the fpokes in front muft have their mouths incline outwards, and thofe on the infide fpokes muft be placed fb as to form a vertical circle of fire. When you place the leaders, carry the firft pipe from the tail of one of the cafes PYROTECHNY. Chap. 1x9 J’rojedled regulated piece with mutations. Fig- 53- Plate CCCCLV II. P Y R O T Varieties cafes in front to the mouth of one of the infide cafes, °fCt an(j t0 the bottom port, with its mouth non' facing the packthread which holds up the ftand ; fo that when this cafe is lighted, it will burn the packthread, and let the wheel fall forward, by which means it will become vertical: then from the laft cafe of the wheel, carry a leader into the barrel nest the fun, which will begin as foon as the wheel is burnt out. Grand volute illuminated with a projeSled wheel in front.—Firit have two hoops made of llrong ipon wire, one of fix feet diameter, and one of four feet two inches 5 thefe hoops muft be joined to fcrolls A, A, A, &c. as i*n fig. 54. Thefe fcrolls mutt be made of the fame fort of wire as the hoops } on thefe fcrolls tie, with iron¬ binding wire, as many illuminating port-fires as they ■will hold, at two inches diitance ; clothe thefe port-fires with leaders, fo that they may all take fire together.— Then let C be a circular wheel of four fpokes, three feet fix inches diameter ; and on its fell tie as many four ounce cafes, head to tail, as will complete the circle, only allowing a fufficient difiance between the cafes, that the~fire may pafs free ; which may be done by cut¬ ting the upper part of the end of each cafe a little ihelv- ing: on each fpoke fix a four ounce cafe, about three inches from the fell of th^e wheel: thefe cafes are to burn one at a time, and the firft of them to begin with thofe on the fell, of which four are to burn at a time ; fo that the wheel will laft no longer than one-fourth of the cafes on the fell, -which in number ftiould be 16 or 20. On the front of the wheel form a fpiral line with ftrong wire, on which tie port-fires, placing them on a llant, with their mouths to face the fame -way as the cafes on the wheel : all thefe port-fires muft be fired with the fecond cafes of the wheel. Let D, D, D, &c. be fpokes of wood, all made to ferew into a block in the centre ; each of thefe fpokes may be in length about four feet fix inches ; in the top of each fix a fpindle, and on each fpindle put a fpiral wheel of eight fpokes, fuch as E, E, E, &c. The blocks of thefe wheels muft have a hole at top for the centre cafe, and the fpindle muft have nuts ferewed on their ends ; which nuts fhould fit in the holes at top of the blocks, fo that all the wheels muft be put on before you fix in the centre cafes : as fome of thele wheels, from their fituation, wall not bear on the nut, it will be neceflary to have fmooth flioulders made on the fpindles for the blocks to run on. The cafes of thefe -wheels are to burn double ; and the method of fir¬ ing them, is by carrying a leader from each down the fpokes into the block in the centre, as in the dodecahe¬ dron, but the centre cafe of each wheel muft begin with the two laft cafes as ufual. It is to be obferved, that the large circular wheel in front muft have a tin barrel on its block, into which a pipe muft be carried from one of the fecond cafes on the wheel; this pipe being met by another from the large block, in which the eight fpokes are ferewed, will fire all the fpiral wheels and the illuminating port fires at the fame time. The cafes of the projefled wheel may be filled with a white charge, j2I and thofe of the fpiral wheels with a gray charge. Moon and Let fig. 55. be a fnlooth circular board fix feet dia- feven ftars. meter : out of the middle of it cut a circular piece 1 2 -F'g- 55- or 14 inches diameter ; and over the vacancy put white Perfian filk, on whicb paint a moon’s face : then let I, I, I, &c. be ftars, each four or five inches diameter, cut out with five points, and covered with oiled filk ; on 563 the front of the large circular board draw a feven-point- Varieties ed ftar, as large as the circle will allow j then on the0^ ton^ruc" lines which form this ftar, bore holes, wherein fix point- tl°tl' .. ed ftars. When this calei s to be fired, it mull be fixed upon the front of a poft, on a fpindle, with a wheel of brilliant fire behind the face of the moon ; fo that, while the wheel burns, the moon and liars will appear tranf- parent : and when the wheel has burnt out, they will difappear, and the large ftar in front, which is formed of pointed ftars, will begin, being lighted by a pipe of communication from the laft cafe of the vertical wheel, behind the moon \ this pipe muft be managed in the lame manner as thofe in regulated pieces. 123 Double cone-wheel illuminated.—This piece is repre-®0Ul)*e. . fented by fig. 56. Let A be a ftrong decagonal or ten- iPu^ina-6 fided wheel, two feet fix inches diameter ; then on each ted. fide of it fix a cone B and C : thefe cones are to confilt Fig $6. of a number of hoops, fupported by three or four pieces of wood, in the manner of the fpiral wheels. Let the height of each cone be three feet fix inches 5 and on all the hoops tie port-fires horizontally, with their mouths outwards, and clothe the wdreel with eight-ounce cafes, all to play horizontally, two at a time : the cones may be fired with the nrft or fecond cafes. The fpindle for this piece muft go through both the cones, and rife three feet above the point of the cone at top ; fb that its length will be 10 feet four inches from the top of the poft H, in which it is fixed, allowing four inches for the thick- nefs of the block of the wheel. The whole weight of the wheel and cones muft bear on a thoulder in the foindle, on which the block of the wheel muft turn.— Near the top of the fpindle muft be a hole in the front, into which fcreuT a fmall fpindle, after the-cones are on : then on this fmall fpindle fix a fun D, compofed of fix- teen nine inch four-ounce cafes of brilliant fire ; which cafes muft not be placed on a fell, but only ftuck into a block of fix inches diameter : then in the front of this fan muft be a circular vertical wheel, 16 inches diameter j on the front of this wheel form with iron-wire a fpiral line, and clothe it with illuminations after the ufual me¬ thod. As this wheel is not to be fired till the cones are burnt out, the method of firing it is this : Let the hole in the block, at the top of the uppermoft cone, be a lit¬ tle larger than the fpindle which pafles through it. Then, from the firft cafe of the vertical wheel before the fun, carry a leader dowm the fide of the fpindle to the top of the block of the horizontal wheel, on w’hich muft be a tin barrel: then this leader being met by another brought from the end of the laft cafe of the horizontal wheel, wall give fire to the vertical wheel as foon as the cones are extinguifhed : but the fun D muft not be fired till the vertical wheel is quite burned out. 124 Cafes for fire pumps are made as thofe for tourbil- Fire pumps. Ions; only they are parted, inftead of being rolled dry. Having rolled and dried the cafes, fill them : firft put in a little meal-powder, and then a ftar j on which ram lightly a ladleful or twx) of compofition, then a little meal-pow-der, and on that a ftar, then again coinpofi- tion ; and fo on till the cafes are filled. Stars for fire pumps ftiould not be round j but muft be made either fquare, or flat and circular, with a hole through the mid¬ dle : the quantity of powder for throwing the ftars muft increafe near the top of the cafe j for, if much powder be put at the bottom, it will burft the cafe. The ftars muft differ in fize in this manner : Let the ftar which is 4 B 2 put 125 Vertical fcroli wheel. Fig' 57- T26 Fire globe 5^4 P Y R O T Varieties pufc in firft be about a quarter lefs than the bore of the ^ 'tionmC'Cak ’ hut let the next liar be a little larger, and the .■ third liar a little larger than the fecond, and fo on : let them increafe in diameter till within two of the top of the cafe, which two mult fit in tight. As the loading of fire-pumps is rather difficult, it will be neceffary to make two or three trials before depending on their per¬ formance : when you fill a number of pumps, take care not to put in each an equal quantity of charge between the liars, fo that when they are fired, they may not throw up too many liars together. Cafes for fire-pumps ffiould be made very ftrong, and rolled on four or eight ounce formers, io or 12 inches long each. A vertical fcroll wheel may be made of any diameter, but mull be conltructed as in fig. 57. to do which proceed thus: Have a block made of a moderate fize, in which fix four flat fpokes, and on them fix a flat circular fell of wood ; round the front of this fell place port-fires; then on the front of the fpokes form a fcroll, either with a hoop or ftrong iron wire ; on this fcroll tie cafes of bril¬ liant fire, in proportion to the wheel, head to tail, as in the figure. When you fire this wheel, light the firft cafe near the fell j then, a^ the cafes fire fuccefllvely, the circle of fire will gradually diminifh : but whether the illuminations on the fell begin with the fcroll or not, is immaterial. N. B. This wheel may be put in the front of a re¬ gulated piece, or fired by itfelf, occafionally. There are two forts of jire-globes ; one with projefted cafes 5 the other with the cafes concealed. For the latter have a globe made of wood, of any diameter, and divide the furface of it into 14 equal parts, and at each divifion bore a hole perpendicular to the centre : thefe holes muft be in proportion to the cafes intended to be ufed : in every hole, except one, put a cafe filled with brilliant or any other charge, and let the mouths of the cafes be even with the furface of the globe 5 then cut in the globe a groove, from the mouth of one cafe to the other, for leaders, which muft be carried from cafe to cafe, fo that they may all be fired together j this done, cover the globe with a Angle paper, and paint it. Thefe globes may be ufed to ornament a building. Fire-globes with projeded cafes are mafle thus : the globe being made with 14 holes bored in it as ufual, fix in every hole except one, a cafe, and let each cafe pro- fed from the globe two-thirds of its length ; then clothe all the cafes with leaders, fo that they may all take fire at the fame time. Fire-globes are fupported by a pintle, made to fit the hole in which there is no cafe. Nothing adds more to the appearance of fire-works works^o^e ^an P^ac^ng them properly } though this chiefly depends exhibited' on t^ie judgement of the maker. The following are the rules generally obferved, whether the rvorks are to be fired on a building or on Hands : if they are a double fet, place one wheel of a fort on each fide of the build¬ ing -y and next to each of them, towards the centre, place a fixed piece, then wheels, and fo on •, leaving a fufficient diftance between them for the fire to play from one without burning the other. Having fixed feme of the works thus in front, place the reft behind them, in the centre of their intervals : The largeft piece, which is generally a regulated or 'iranfparent piece, muft be placed in the centre of the building, and behind it a fun, which muft always Hand above all the other works. A h.Ule before the building, or Hands, place the large 127 Method of } rockets E c H N y. Chap. II. gerbes j and at the back of the works fix marroon bat- Varieties teries, pots des aigrettes, pots des brins, pots des faucijjbns,^ Conftruc- air-balloons, and flights of rockets ; the rocket Hands Uon* j may be fixed behind, or anywhere elfe, fo as not to be in the way of the works. Single colle&ions are fired on ftands 5 which are made in the fame manner as theodolite ftands, only the top part muft be long or ffiort occafionally : thefe ftands may be fixed up very loon without much trouble. I he following order of Firing will ferve as a fpecimen of the Flan to be purfued in an exhibition of Fire- works. 1. Two fignal 2. Six Iky 3. Twm honorary 4. Four caduceus 6." \ Two | fpirar1} wheels aiuniinated 7* J C. tranfparent ftars 8. A line rocket of five changes 9. Four tourbillons 10. 1 f horizontal wheels II • | lair balloons illuminated 12. ^ Two <| Chinefe fountains I3- | regulating pieces of four mutations each 14* J ^pots des aigrettes 15- Three large gerbes 16. A flight of rockets 17* 7 T ’ 5 balloon wffieels 18. v'° £ cafcades of brilliant fire 19. Twelve flcy-rockets 20. C f illuminated yew trees 21 • 1 1 air-balloons of ferpents and two compound 22. Four tourbillons 23. 7 Two -f Fruiloni wheels 24* S L illuminated globes with horizontal wheels 25. One pot des faucijjbns 26. Twro plural wffieels 27. Marroon battery 28. Two chandeliers illuminated 29. Range of pots des brins 30. Twelve Iky-rockets 31. Two yewT-trees of fire 3 2. Neft of ferpents 33. Two double cones illuminated 34. Regulating piece of feven mutations, viz. 1. Vertical wheel illuminated 2. Golden glory 3. Otftagon vertical wheel 4. Porcupine’s quills 5. Crofs fires 6. Star-piece with brilliant rays 7. Six vertical wheels 35. Brilliant fun 36. Large flight of rockets. When water-works are to be exhibited, divide them into feveral fets, and fire one fet after every fifth or fixth change of land and air wmrks. Obferve this rule in firing a double fet of works : Always begin with fky- rockets, then two moveable pieces, then two fixed pieces, and fo on ; ending with a large flight of rockets, or a marroon battery : if a Angle colleftion, fire a fixed piece after every wheel or twTo, and now and then feme air and water-works. Chap. II. P Y R O 7 Varieties Fig. 58. reprtfents a fountain of 30 rockets. Let A of Conftrue- be a perpendicular poll, 16 feet high from the ground, 1 tl°'1' . and four inches fquare. Let the rail, or crofs piece C, xsS be one foot fix inches long, three inches broad, and one Fountain of thick. The rail D, at bottom, muft be fix feet long, p rockets. one f00t broad, and one inch thick. F and G are the ls'5S’ two fides which ferve to fupply the rails D, E, H, I, C: thefe fides are one foot broad at bottom, and cut in the front with a regular (lope, to three inches at top ; but their back edges mutt be parallel with the front of the pots A. The breadth of the rails E, H, I, will be de¬ termined by the breadth of the fides : all the rails muft be fixed at two feet diftance from each other, and at right angles with the pots. Having placed the rails thus, bore in the bottom rail 10 holes, at equal diftances, large enough to receive the Hick of a one-pound rock¬ et : in the back edge of this rail cut a groove from one end to the other, fit to contain a quick-match *, then cut a groove in the top of the rail, from the edge of each hole, into the groove in the back : in the fame manner cut in the fecond rail, E, eight holes and grooves 5 in the third rail, H, fix holes and grooves 5 in the fourth rail, I, four holes and grooves ; and in the top rail, two holes and grooves. B, a rail with holes in it to guide the ends of the rocket flicks: this rail mufl be fixed fix feet from the rail D. The fountain frame being thus made, prepare the rockets thus : Tie round the mouth of each apiece of thin paper, large enough to go twice round, and to proje£l about an inch and a half from the mouth of the rocket, which muft be rubbed with wTet meal- powder ; in the mouth of each rocket put a leader, which fecure well with the paper that projects from the mouth of the cafe : thefe leaders muft be carried into the grooves in the back of the rails, in which lay a quick-match from one end to the other, and cover it with parted paper : holes muft be made in the rail D, to receive the ends of the flicks of the rockets in the rail E, and fo on to the fourth rail; fo that the flicks of the rockets at top may go through all the rails. The rockets being fo prepared, fix a gerbe, or white flower- pot, on each rail, before the poll, with its mouth inclining a little forwards : thefe gerbes muft be lighted all at once. Behind or be¬ fore each gerbe, fix a cafe of brilliant or flow fire : thefe cafes muft be filled fo that they may burn out one after the other, to regulate the fountain ; which may be done by carrying a leader from the end of each flow or bril¬ liant fire, into the groove in the back of each rail. Dif¬ ferent fixed rockets may be ufed in thefe fountains: but it will be bell to fill the heads of the rockets on each rail with different forts of things, in this manner; thofe at top with crackers, the next with rains, the third with ferpents, the fourth with tailed liars, and the laft flight svith common or brilliant ftars. Film tree. The piece called a palm tree, though made of com¬ mon fires, and of a Ample conftrucftion, has a very plea- fing effect •, from the fires interfedlirig fo often, that Fig. 59. they refemble the branches of trees. Let A (fig. 59.) be a perpendicular port, of any thicknefs, fo that it be fufficiently ftrong to hold the cafes ; let the diftance from B to C be two feet fix inches, and from C to D two feet fix inches, and let the length of each crofs- piece be two feet j on each end of each fix a five-point¬ ed liar: then fix, on pegs made for the purpofe, twelve- inch half-pound cafes of brilliant fire, as in the figure,. E C H N Y. S6S All the cafes and ftars mufl be fired at once. This Varieties piece fhould be fixed high from the ground. 04 Conftmc- A/i illuminated pyramid, voitk Archimedian fcrews, a t‘°n' . globe, and vertical fun, may be of any fize. One made I30 according to the dimenfions of fig. 60. will be of a good Illuminated proportion, whole height is 21 feet; from C to D, fix Pyramid- feet} from E to F, nine feet: the fpace between the ^'p rails muft be fix inches, and the rails as thin as poftible : CCCGLVI. in all the rails flick portfires at four inches diftance. - I he Archimedian fcrews, G, K, are nothing more than double fpiral wheels, with the cafes placed on their wheels horizontally inftead of obliquely. The vertical fun, I, need not confiil of more than 12 rays, to form a fingle glory. The globe at top mufl be made in pro¬ portion to the pyramid ; which being prepared accord¬ ing to the preceding dire&ions* place the leaders fo that all the illuminating portfires, fcrews, globe, and fun, may take fire together. The pyramid muft be fupport- ed by the two fides, and by a fupport brought from a pole, which muft be placed two feet from the back of the pyramid, that the wheels may run freely. T~l A rofe-piece may be ufed for a mutation of a regu-Rofe piece lated piece, or fired by itfelf: it makes the befl appear- ai?d fun* ance when made large ; if its exterior diameter be fix F,s- 6l* feet,, it will be of a good fize. Fig. 61. fliows the man¬ ner in which it appears before it is fired. Let the outer fell be made of wood, and fupported by four wooden fpokes: all the other parts, on which the illuminations are fixed, muft be made of ftrong iron wire: on the outer fell place as many half-pound cafes of brilliant charge as you think proper, but the more the better ; for the nearer the cafes are placed, the ftronger will be the rays: the illuminations fhould be placed within three inches of each other : they muft all be fired toge¬ ther, and burn fome time before the fun is lighted ; which may be done by carrying a leader from the mid¬ dle of one of the illuminations, to the mouth of one of the fun cafes. ^ Fig. 62. reprefents an illuminatedfar. Let the diame- Trantpa- ter from A to B be two feet, and from C to D feven rent ftars feet. Firft make a ftrong circular back or body of the wlth,'Ilurn " flar, two feet diameter, to which fix the illuminated rays : in the centre of the front of the body fix a fpindle, on which put a double triangular wheel, fix inches dia¬ meter, clothed with two ounce cafes of brilliant charge: the cafes on this wheel muft burn but one at a time. Round the edge of the body nail a hoop made of thin wood or tinl this hoop muft projefl in front fix or feven inches : in this hoop cut three or four holes to let out- the fmoke from the wheel. The liar and garter may be cut out of ftrong pafteboard or tin, made in this manner : Cut a round piece of pafteboard or tin, two feet diameter, on which draw a ftar, and cut it out; then over the vacancy pafte Perfian filk ; paint the let¬ ters yellow j four of the rays yellow, and four red ; the crofs in the middle may be painted half red and half yellow, or yellow and blue. This tranfparent ftar muft; be faftened to the wooden hoop by a Icrew, made fo as to take off" and on ; the illuminated rays are made of thin wood, with tin fockets fixed on their fides within four inches of each other ; in thefe fockets Hick illumi¬ nating portfires ; behind the point of each ray fix a half- pound cafe of gray, black, or Chinefe fire. N, B, The. illuminated rays are-to.be lighted at the. famo 566 nated table ftar. Fi|. P Y R O T Varieties fame time as tlie triangular wheel, or after it is burnt ot Cc)rftmc-ou^ . w]1;cj1 1Tiay he done by a tin barrel being fixed to . uo"' , the wheel, after the manner of thofe in the regulated pieces. Into this barrel carry a leader from the illumi¬ nated rays, through the back ol the ftar; and this lead¬ er muft be met by another, brought from the tail of the 133 laft cafe on the wheel. Tranfpa- Fig. 63. reprefents a tob/e/far, whofe diameter, from rentillumi- £ to F, is 1 2 feet: and from E to I, four feet. This proportion, obierved on each fide, will make the centre frame four feet fquare : in this fquare fix a tranlparent ftar, as in the figure. This ftar may be painted blue, and its rays made as thofe of the flaming ftars deferibed before. The wheel for this ftar may be compofed of different coloured fires, with a charge or two of flow fire ; the wheels a, a, a, a, may be clothed with any pumber of cafes, fo that the ftar-wheel confift of the fame : the illuminating portfires, which muft be placed very near each other on the frames, muft be fo managed as to burn as long as the wheels, and lighted at the 134 fame time. Regulated 77/es of communication, which may be vfed under water, muft be a little thicker in the paper than thofe for land. Having rolled a fufficient number of pipes, and kept them till dry, wafh them over with drying oil, and fet them to dry 5 but when you oil them, leave about an inch and a half at each end dry, for joints ; as if they were oiled all over, when you come to join them, the pafte would not flick where the paper is greafy : after the leaders are joined, and the pafte dry, oil the joints. Thefe pipes will lie many hours under water, without receiving any damage. To make horizontal wheels for the water, firft get a large wooden bowl without a handle j then have an eight-fided wheel made of a flat board 18 inches diame¬ ter, fo that the length of each fide may be near feven inches: in all the fides cut a groove for the cafes to lie in. This^wheel being made, nail it on the top of the bowl \ then take four eight-ounce cafes, filled with a proper charge, each about fix inches in length. Now, to clothe the wheel with thefe cafes, get fome whitilh- brown paper, and cut it into flips four or five inches broad and feven or eight long : thefe flips being palled all over on one fide, take one of the cafes, and roll one of the flips of paper about an inch and a half on its end, fo that there will remain about two inches and a half of the paper hollow from the end of the cafe : tie this cafe on one of the fides of the wheel, near the corners of which muft be holes bored, through which put the pack¬ thread to tie the cafes : having tied on the firft cafe at the neck and end, put a little meal-powder in the hol¬ low paper 5 then pafte a flip of paper on the encfof an¬ other cafe, the head of which put into the hollow paper on the firll, allowing a fufficient diftance from the tail E C H N Y. 557 of one to the head of the other for the palled paper to Aquatic bend without tearing : tie on the fecond cafe as you did Fireworks, the firll : and fo on with the reft, except the lall, which ‘—-"V"—^ mull be clofed at the end, unlefs it is to communicate to any thing on the top of the wheel, fuch as fire-pumps or brilliant fires, fixed in holes cut in the wheel, and fired by the lall or fecond cafe, as the fancy diredls : fix, eight, or any number, may be placed on the top of the wheel, provided they be not too heavy for the bowl. Before tying on the cafes, cut the upper part of all their ends, except the lall, a little Ihelving, that the fire from one may play over the other, without being ob- llrufted by the cafe. Wheel-cafes have no clay drove in their ends, nor pinched, but are always left open, only the lalt, or thofe which are not to lead fire, which mull be well fecured. For water mines you muft have a bowl with a wheel Water3 on it, made in the fame manner as the water-wheel j on- mines, ly in its middle there muft be a hole, of the fame diame¬ ter as that of the intended mine. Thefe mines are tin pots, with ftrong bottoms, and a little more than two diameters in length : the mine muft be fixed in the hole in the wheel, with its bottom refting on the bowl j then loaded with ferpents, crackers, ftars, fmall water-roc¬ kets, Sec. in the fame manner as pots of aigrettes ; but in their centre fix a cafe of Chinefe fire, or a fmall gerbe, which muft be lighted at the beginning of the laft cafe on the wheel. Thefe wheels are to be clothed as ufual. ’ „ Bawls for water-globes muft be very large, and the Fire*gk)bes wheels on them of ten fides : on each fide nail a piece for the wa-» of wood four inches long j and on the outfide of eachter’ piece cut a groove, wide enough to receive about one- fourth of the thicknefs of a four-ounce cafe : thefe pieces of wood muft be nailed in the middle of each face of the wheel, and fixed in an oblique direSlion, fo that the fire from the cafes may incline upwards : the wheel being thus prepared, tie in each groove a four-ounce cafe filled with a gray charge ; then carry a leader from the tail of one cafe to the mouth of the other. _ Globes for thefe wheels are made of two tin hoops, with their edges outwards, fixed one within the other, at right angles. The diameter of thefe hoops muft be rather lefs than that of the wheel. Having made the globe, drive in the centre of a wheel an iron fpindle, which muft Hand perpendicular, and its length four or fix inches more than the diameter of the globe. This fpindle ferves for an axis, on which is fixed the globe, which muft Hand four or fix inches from the wheel: round one fide of each hoop muft be foldered little bits of tin, two inches and a half diftance from each other ; which pieces muft be two inches in length each, and only faftened at one end, the other ends be¬ ing left loofe, to turn round the fmall portfires, and hold them on : thefe portfires muft be made of fuch a length as will laft out the cales on the wheel. There need not be any portfires at the bottom of the globe within four inches of the fpindle > as they would have no effe£l, but to burn the wheel: all the portfires muft be placed per¬ pendicularly from the centre of the globe, with their mouths outwards *, and muft be clothed with leaders, fo as all to take fire with the fecond cafe of the wheel j and the cafes jpuft burn two at a time, one oppolite the other. When two cafes of a wheel begin together, two will . 5-68 Aquatic will end together ; therefore the two oppofite end cafes ■ ireyor^s' mufl: have their ends pinched and fecured from fire. The method of firing fuch wheels is, by carrying a leader from the mouth of one of the firfl cafes to that of the 145 other and the leader being burnt through the middle, Odoriferous will give fire to both at the fame time, loon^ Odoriferous water balloons are made in the fame man¬ ner as air-balloons, but very thin of paper, and in dia¬ meter one inch and three-fourths, with a vent of half an inch diameter. The Ihells being made, and quite dry, fill them with any of the following compofitions, which muft be rammed in tight: thefe balloons muft be fired at the vent, and put into a bowl of water. Odo¬ riferous works are generally fired in rooms. Compojition I. Saltpetre two ounces, flour of fulphur one ounce, camphor half an ounce, yellow amber half an ounce, charcoal-dull three-fourths of an ounce, fait of benjamin half an ounce, all powdered very fine and well mixed. II. Saltpetre 12 ounces, meal-powder three ounces, frankincenfe one ounce, myrrh half an ounce, camphor half an ounce, charcoal three ounces, all moiftened with the oil of fpike. III. Saltpetre two ounces, fulphur half an ounce, an¬ timony half an ounce, amber half an ounce, cedar rafp- ings one-fourth of an ounce, all mixed with the oil of rofes and a few drops of bergamot. IV. Saltpetre four ounces, fulphur one ounce, faw- duft of juniper half an ounce, faw-duft of cyprefs one ounce, camphor one-fourth of an ounce, myrrh two drams, dried rofemary one-fourth of an ounce, all moift¬ ened a little with the oil of rofes. N. JB. Water-rockets may be made with any of the above compofitions, wfith a little alteration, to make them weaker or ftronger, according to the fize of the 145 cafes. A fea^fight Having procured four or five fmall fhips, of two or fliips and^ l^rec feet length, make a number of fmall reports, a fire-fliip. which are to ferve for guns. Of thefe range as many as you pleafe on each fide of the upper decks j then at the head and ftern of each fhip fix a two-ounce cafe, eight inches long, filled with a flow portfire compofition j but take care to place it in fuch a manner that the fire may fall in the water, and not burn the rigging : in thefe cafes bore holes at unequal diftances from one another, but make as many in each cafe as half the number of re¬ ports, fo that one cafe may fire the guns on one fide, and the other thofe on the oppofite. The method of firing the guns is, by carrying a leader from the holes in the cafes to the reports on the decks j you muft make thefe leaders very fmall, and be careful in calculating the burning of the flow fire in the regulating cafes, that more than two guns be not fired at a time. When you would have a broadfide given, let a leader be carried to a cracker, placed on the outfide of the ftiip; which cracker muft be tied loofe, or the reports will be too flow7: in all the fliips put artificial guns at the port¬ holes ("a). Having filled and bored holes in two portfires for Chap. IL regulating the guns in one flap, make all the reft exaft- Aquatic ly the fame $ then, when you begin the engagement, Fneworka. light one (hip firft, and fet it a failing, and fo on with Y " ^ the reft, fending them out fingly, which wrill make them fire regularly, at different times, without confufion 5 for the time between the firing of each gun will be equal to that of lighting the flow fires. The fire-ftiip may be of any fize ; and need not be very good, for it is always loft in the aftion. To pre¬ pare a fliip for this purpofe, make a portfire equal in fize with thofe in the other Ihips, and place it at the ftern j in every port place a large portfire, filled with a very ftrong compofition. and painted in imitation of a gun, and let them all be fired at once by a leader from the flow fire, wathin two or three diameters of its bottom j all along both fides, on the top of the upper deck, lay ftar-compofition about half an inch thick and one broad, which muft be wetted with thin fize, then primed w7ith meal-powder, and fecured from fire by palling paper over it; in the place w7here you lay this compofition, drive fome little tacks wfith flat heads, to hold it fall to the deck : this muft be fired juft after the fliam guns, and w7hen burning will Ihow a flame all round the fliip : at the head take up the decks, and put in,a tin mortar loaded with crackers, which mortar muft be fired by a pipe from the end of the flow7 fire $ the firing of this mortar will fink the fliip, and make a pretty conclufion. The regulating portfire of this ftiip muft be lighted at the fame time with the firft fighting fliip. Having prepared all the (hips for fighting, we fliall next proceed wfith the management of them when on the w7ater. At one end of the pond, juft under the fur- face of the water, fix two running blocks, at what di- ftance you choofe the fliips fliould fight 5 and at the other end of the pond, oppofite to each of thefe blocks, under the water, fix a double block; then on the land, by each of the double blocks, place two fmall wfindlaf- fes j round one of them turn one end of a fmall cord, and put the other end through one of the blocks j then carry it through the fingle one at the oppofite end of the pond, and bring it back through the double block again, and round the other windlafs : to this cord, near the double block, tie as many fmall firings as half the number of the fliips, at any diftance; but thefe firings muft not be more than two feet long each : make fall; the loofe end of each to a fliip, juft under her bow fprit; for if tied to the keel, or too near the w7ater, it will overfet the ftiip. Half the fliips being thus prepared, near the other double block fix tw7o more wfindlaffes, to wfliich faften a cord, and to it tie the other half of the fliips as before : when you fire the fliips, pull in the cord with one of the wfindlaffes, to get all the fliips together j and when you have fet fire to the firft, turn that wind¬ lafs which draws them out, and fo on wfith the reft, till they are all out in the middle of the pond j then, by turn¬ ing the other wfindlafs, you will draw them back again ; by which method you may make them change fides, and tack about backwards and forwards at pleafure. For the fire-fliip fix the blocks and wfindlaffes between the others: PYROTECHNY. (a) Reports for thefe and fimilar occafions are made, by filling fmall cartridges with grained powder 5 pinch¬ ing them clofe at each end, and, when ufed, boring a hole in the fide, to which is placed a match or leader for firing them. 4 PVR O T ft (’ H NT Y IM.ilr (’rf’fMVlI Ci'CCl lil P YU O TK <' II X Y ; Pi/it t. r// rr . // *9 /?t f ^/'ft* '/. Plate C CC CLIV. F YR O T E C H N Y S^.44. ________ '’""I -n;... |«| •//'/ v n ■ //a /^x/ru/ftfet 'feet/ < Jr / y/i :C/ / I / v_jf M nr \\ % -- — v fl / iQ [Lk 1 t wammm I '■ T Yfi O T E C TI N Y r‘ ^ \' y T f rf^—ji vSt— \ * JSSrP x^a \ # / ■ ■ ’ /■Sr'r'// f-'S/v // . // *r/] r_j m./fi/o/-'/r,-//. '••••'755; : vH TYUO TE CHET. Elate CCCCEV1L. ( Chap. II. Aquatic Firewerks. 147 To fire fky- rockets un¬ der water. 148 Neptune in his chariot. Fig. 70. 149 Swans and ducks, in water. others j fo that when Hie fails out, fhe will be between the other (hips : you mull; not let this fhip advance till the guns at her ports take fire. To fire Jhy-rockets under water, you mull have ftands made as ufual, only the rails muft be placed flat inftead of edgewife, and have holes in them for the rocket- flicks to go through 5 for if they were hung upon hooks, the motion of the water would throw them off: the flands being made, if the pond is deep enough, fink them at the fides fo deep, that, when the rockets are in, their heads may juft appear above the furface of the water •, to the mouth of each rocket fix a leader, which put through the hole with the ftick ; then a little above the water muft be a board, fupported by the ftand, and placed along one fide of the rockets ; then the ends of the leaders are turned up through holes made in this board, exa£lly oppofite the rockets. By this means you may fire them fingly or all at once. Rockets may be fired by this method in the middle of a pond, by a Neptune, a fwan, a water-wheel, or any thing elfe you choofe. To reprefent Neptune in his chariot, you muft have a Neptune (made of wood, or bafket work) as big as life, fixed on a float large enough to bear his weight ; on which muft be two horfes heads and necks, fo as to feem fwimming, as fhown by fig. 70. For the wheels of the chariot, there muft be two vertical wheels of black fire, and on Neptune’s head a horizontal wheel of brilliant fire, with all its cafes, to play upwards. When this wheel is made, cover it with paper or pafteboard, cut and painted like Neptune’s coronet; then let the trident be made without prongs, but inffead of them, fix three cafes of a weak gray charge, and on each horfe’s head put an eight ounce cafe of brilliant fire, and on the month of each fix a ftiort cafe, of the fame diameter, filled with the white-flame compofition enough to laft out all the cafes on the wheels : thefe fnort cafes muft be open at bottom, that they may light the brilliant fires •, for the horfes eyes put fmall portfires, and in each noftril put a fmall cafe half filled with gray change, and the reft with portfire compofition. If Neptune is to give fire to any building on the wa¬ ter ; at his firft fetting out, the wheels of the chariot, and that on his head, with the white flames on the horfes heads, and the portfires in their eyes and noftrils, muft all be lighted at once ; then from the bottom of the white flames carry a leader to the trident. As Nep¬ tune is to advance by the help of a block and cord, you muft manage it fo as not to let him turn about, till the brilliant fires on the horfes and the trident begin •, for it is by the fire from the horfes (which plays almoft upright) that the building, or work, is lighted ; which muft be thus prepared. From the mouth of the cafe which is to be firft fired, hang fome loofe quick-match to receive the fire from the horfes. When Neptune is only to be fliowm by himfelf, without fetting fire to any other works, let the white flames on the horfes be very ftiort, and not to laft longer than one cafe of each wheel, and let two cafes of each wheel burn at a time. If you wrould have fw’ans or ducks difeharge roc¬ kets into the water, they muft be made hollow, and of paper, and filled wdth fmall wTater rockets, with fome blowing-powder to throw them out: but if this is not done, they may be made of wood, which will laft many times. Having made and painted fome fwans, fix them Vox.. XVII. Part II. PYROTECH N Y. 569 on floats: then in the places rvhere their eyres (hould be, Optical bore holes twro inches deep, inclining downwards, au q Agnations of wide enough to receive a fmall portfire ; the pottfire . cafes for this purpofe muft be made of brafs, twro inches long, and filled with a flow bright charge. In the mid¬ dle of one of thefe cafes make a little hole ; then put the portfire in the eye-hole of the fwran, leaving about half an inch to projeft out *, and in the other eye put. another portfire, with a hole made in it : then in the neck of the fwan, within two inches of one of the eyes, bore a hole flantwife, to meet that in the portfire •, in this hole put a leader, and carry it to a water-rocket, that muft be fixed under the tail with its mouth upwards. On the top ot the head place two one-ounce cafes, four inches long each, drove with brilliant fire ; one of thefe cafes muft incline forwards, and the other backwards: thefe muft be lighted at the fame time as the water-roc¬ ket ; to do wxhich, bore a hole between them in the top of the fwan’s head, down to the hole in the portfire, to which carry a leader: if the fwan is filled with rockets, they muft: be fired by a pipe from the end of the water- rocket under the tail. When you fet the fwan a fwim¬ ming, light the two eyes. zco To make a fire-fountain for the water, firft have a Water fire- float made of wood, three feet diameter ; then in the !ountain,• middle fix a round perpendicular poll, four feet high, and twTo inches diameter j round this poll fix three cir¬ cular wheels made of thin wood, without any fpokes. The largeft of thefe wheels muft be placed within two or three inches of the float, and muft be nearly of the fame diameter. The fecond wheel muft he two feet two inches diameter, and fixed at two feet diftance from the firft. The third wheel muft be one foot four inches dia¬ meter, and fixed within fix inches of the top of the poft ; the wheels being fixed, take 18 four or eight-ounce cafes of brilliant fire, and place them round the firft wheel with their mouths outwards, and inclining down¬ wards; on the fecond wheel place 13 cafes of the fame, and in the fame manner as thofe on the firft on the third, place eight more of thefe cafes, in the fame man¬ ner as before, and on the top of the poft fix a gerbe ; then clothe all the cafes with leaders, fo that both they and the gerbe may take fire at the fame time. Before firing this w-ork, try it in the water to fee whether the float is properly made, fo as to keep the fountain up- riSht- , . . . . i5r As the artificial fire-wmrks which w-e have deferibed, Opticaliml- require confiderable caution in their preparation and ma-tationsof nagement, and are attended with great expence, at- fire-works, tempts have been made to imitate fome of the more fimple kinds by optical delufion, and to give to the ob- jefts reprefented the appearance of moving fire, though they be really fixed, and no fire be employed. Thefe attempts have been tolerably fuccefsful 5 and by means of this invention, a fpe&acle of artificial fire-works may be apparently exhibited at a trifling expence ; and if the pieces employed are conftrutted with ingenuity, and wdth a proper attention to the rules of perfpe&ive, while in viewing them we employ glaffes which magnify the objefts, and prevent them from being too diftinftly feen, a very agreeable illufion will be produced. The artificial fire-works imitated with moft fuccefs by this invention, are fixed funs, gerbes, and jets of fire, cafcades, globes, pyramids, and columns, moveable around their axes. To reprefent a gerbe of fire, take 4 C paper 57° Optical paper blackened on both Tides, and very opaque; and Imitationsof tlelineated on a piece of white paper the figure , 1 " JI * • 0f a gerbe of fire, apply it to the black paper, and with the point of a very lliarp penknife make feveral llafhes Fig. 71, (Plate CCCCLVII. fig. 71.) in it, as 3, 5, or 7, pro¬ ceeding from the origin of the gerbe : thefe lines muft not be continued, but cut through at unequal intervals. Pierce thefe intervals with unequal holes made with a pinking iron, in order to reprelent the fparks of fuch a gerbe. In ihort, you muft endeavour to paint, by thefe lines and holes, the well known effedt of the fire of in¬ flamed gunpowder, when it iffues through a fmall aper¬ ture. According to the fame principles, you may delineate the cafcades (fig. 72.) and jets of fire which you are de- firous of introducing into this exhibition, which is pure¬ ly optical ; and thofe jets of fire which proceed from the radii of funs, either fixed or moveable. It may ea- fily be conceived, that in this operation tafte muft be the guide. If you are defirous of reprefenting globes, pyramids, or revolving columns, draw the outlines of them on pa¬ per, and then cut them out in a helical form ; that is, eyt out fpirals with the point of a penknife, and of a fize proportioned to that of the piece. It is to be obferved alfo, that as thefe different pieces have different colours, they may be eafily imitated by pafting on the back of the paper, cut as here deferibed, very fine filk paper coloured in the proper manner. As jets, for example, when loaded with Chinefe fire, give a reddifh light, you mull pafte to the back of thefe jets tranfparent paper, flightly tinged with red ; and pro¬ ceed in the fame manner in regard to the other colours by which the different fire-works are diltinguifhed. When thefe preparations have been made, the next thing is to give motion, or the appearance of motion, to this fire, which may be done two ways, according to circumftances. If a jet of fire, for example, is to be renrefented, prick unequal holes, and at unequal diftances from each Other, in a band of paper, fig. 73. and then move this band, making it afeend between a hght and the above jet ; the rays of light which efcape through the holes of the moveable paper will exhibit the appearance of fpaiks rifing into the air. It is to be obferved that one part of the paper muft be whole; that another muft be pierced with holes thinly fcattered ; that in another place they muft be very clofe, and then moderately fo : by thefe means it will reprefent thofe fudden jets of fire obferved in fire-works. To reprefent a cafcade, the paper pierced with holes, inftead of moving upwards, muft be made to defeend. This motion may be eafily produced by means of two rollers, on one of which the paper is rolled up, while it is unrolled from the other. Suns are attended with fome more difficulty ; becaufe in theft it is neceftary to reprefent fire, proceeding from the centre to the circumference. The artifice for this purpofe is as follows. On ftrong paper deferibe a circle, equal in diameter to the fun which you are defirous to exhibit, or even Ibmewhat larger ; then trace out on this circle two fpi¬ rals, at the diftance of a line or half a line from each other, and open the interval between them with a pen- kifife, in fuch a manner, that the paper may be cut Chap. I!. from the circumference, decreafing in breadth to a cer- Optical tain diftance from the centre, fig. 74. : cut the remain- Imkationsof remainder of the circle into fpirals of the fame kind, Firewc'rk5* open and clofe alternately; then cement the paper circle “l-'y kJ to a fmall iron hoop, fupported by two pieces of iron, crofting each other in its centre, and adjuft the whole to a fmall machine, which will fuffer it to revolve round its centre. If this moveable paper circle, cut in this man¬ ner, be placed before the reprefentation of your fun, with a light behind it, as foon as it is made to move towards that fide to which the convexity of the fpirals is turned, the luminous fpirals, or thofe which afford a paffage to the light, will give, on the image of the radii or jets of fire of your fun, the appearance of fire in continual motion, as if undulating from the centre to the circum¬ ference. The appearance of motion may be given to columns, pyramids, and globes, cut through in the manner above deferibed, by moving in a vertical dire&ion a band of paper cut through into apertures, inclined at an angle rather different from that of the fpirals. By thefe means the ipeflators will fuppofe that they fee fire continually circulating and afeending along the fpirals ; and thus will be produced an optical illufion, in confequence cf which the columns or pyramids will feem to revolve. We have thus briefly explained the principle on which artificial fire-works may be imitated ; and as the tafte of the artift may fuggeft to him many circumftances which may improve the reprefentation, and render the illufion itronger, we fhall not enlarge further on the fubjeef, but (hall conclude this article with a few obfervations on illuminated prints and drawings, which are fome- times introduced as accompaniments in thefe imitations of artificial fire-works. The mode of preparing thefe illuminations is thus de¬ feribed in Hutton’s tranllation of Montucla’s Recrea¬ tions. Take fome prints reprefenting a caftle, or palace, &c. ; and having coloured them properly, cement paper to the back of them, in fuch a manner that they ftiall be only femitranfparent; then, with pinking irons of different fizes, prick fmall holes in the places and' on the lines where the lamps are generally placed, as along the fides of the windows, on the cornices or balu- ftrades, &c. But care muft be taken to make thefe holes fmaller and clofer, according to the perfpeefive di¬ minution of the figure. With other irons of a larger fize, cut out, in other places, fome ftronger lights, fo as to renrefent fire-pots, &c. Cut out alfo the panes in fome of the windows, and cement to the back of them tranfparent paper of a green or red colour,, to reprefent curtains drawn before them, and concealing an illumi¬ nated apartment. When the print is cut in this manner, place it in the front of a fort of fmall theatre, flrongly illuminated from the back part, and look at it through a convex glafs »f a pretty long focus, like that ufed in thofe final] machines called optical boxes. If the rules of perfpec- tive have been properly obferved in the prints, and if the lights and fhades have been diftributed with tafte, this fpeflacle will be highly agreeable. Before difmiffing this fubjecl, it may not be improper Mana’ge, to point out the moft effe&ual means of relieving ihofement oi burns, to which fire-workers are fo much expofed. !?urns trQIE When the burn is firft received, and before bliftersfiie WOrlsfc arife, the belt applications are oil of turpentine, frong Spirit pVrotechny. Chap. II. P Y R O T E C H N fpirits, rcElijied fpirit of wine, or camphorated Jpirit, ter muft be with which linen rags muft be wetted and kept moift on the part till the pain abates. It no other remedy can be procured, immerfing the part for a long time in cold water will often afford great relief. When thefe means have been negledled, and blitters arife, if thefe are fmall, they thould not be opened ; but if large, the wa- Y. let out, and the fore covered with rags, fpread with a mixture of linfeed oil and lime water, in the proportion of one part of the former to three of the latter. We muft remark, however, that in all cafes of extenfive burns, or where fome very delicate part is in¬ jured, fpeedy recourfe ftiould be had to medical aflift- ance. S7r Manage¬ ment at' Burns. P Y R PYROTICS, in Medicine, cauftics, or remedies either actually or potentially hot } and which accord¬ ingly will burn the ftefti, and faiie an efchar. See Cau¬ sticity. PYRftHICHA, in antiquity, a kind of exercife on horfeback, or a feigned combat, for the exercife of the cavalry. It was thus called from its inventor Pyrrhichus, or Pyrrhus of Cydonia, wdio firft taught the Cretans to march in meafure and cadence to battle, and to ob- ferve the pace of the Pyrrhic foot.—Others derive the name from Pyrrhus the fon of Achilles, who infti- tuted this exercife at the oblequies of his father.—- Ariftotle fays, that it was Achilles himfelf who invent¬ ed it. The Romans alfo called it ludus Trojanus, “ the Tro¬ jan game and Aulus Gellius, decurfus.—It is doubt- lefs this exercife that we fee reprefented on medals by two cavaliers in front running with lances, and the word decurfio in the exergum. PYRRHICHIUS, in the Greek and Latin poetry, a foot confifting of two fyllables, both fhort ;—as, Deus.— Among the ancients this foot is alfo called pe- riambus ; by others hegernona. PYRRHO, a Greek philafopher, born at Elis in Peloponnefus, flourifhed about 300 B. C. He was the difciple of Anaxarchus, whom he accompanied as far as India, where he converfed with the Brachmans and Gymnofophifts. He had made painting his profeffion before he devoted himfelf to the ftudy of philofophy. He eftablithed a feft wbofe fundamental principle was, That there is nothing true 01 falfe, right or wrong, honeft or difhoneft, juft or unjuft ; or that there is no ftandard of any thing beyond law or cuftom, and that uncertainty and doubt belong to every thing. From this continual feeking after truth and never finding it, the fe£t obtained the name of Sceptics or Pyrrhonians. from the founder, who is laid to have acted upon his own principles, and to have carried his feepticifm to fuch a ridiculous extreme, that his friends were obliged to accompany him wherever he -went, that he might not be run over by carriages, or fall down precipices. If this was true, it was not without reafon that he was ranked among thofe whofe intellects were difturbed by intenfe ftudy. But it is treaied by a modern writer as a mere calumny invented by the dogmatifts; and we are ftrongly inclined to be of his opinion, (fee Scep¬ tics). Pyrrho died about the 90th year oi his age, when his memory was honoured with a ftatue at A- thens, and a monument ereCted to him in his own country. P Y T PYRRHUS, the name of two kings of Epirus. pyrriiU(S See Epirus. [| PYRUS, the PEAR-TREE. See Botany Index; and Pythagoras. for the culture of this fruit fee Gardening. For an ac- y count of the proceffes followed in making perry, fee A- griculture. PYTHAGORAS, a celebrated philofopher of an-^ tiquity, refpeCting the time and place of whofe birth the learned are much divided. Eratofthenes afferts, (• Dijfcrt. that in the 48th Olympiad *, when he was very young, on the Ep.^ . he was a victor at the Olympic games. Hence Dr °I Bentley f determines the date of his birth to be the 4th pytiag^ J year of the 43d Olympiad ; whilft Lloyd J, who denies ras. that the Olympic victor was the fame perfon with the § Two Dif- philofopher, places it about the 3d year of the 48th Q.Jertations lympiad. Mr Dad well § differs from both, and wiftres to fix the birth of Pythagoras in the 4th year of the and-Py- 5 2d Olympiad. Of the arguments of thefe learned writers, Le Clerc has given a fummary in the Bibliothequc Choifee, tom. x. p. 81. &c. and from a review of the whole, it would appear that he was not born earlier than the 4th year of the 43d Olympiad, or later than the 4th year of the 5 id j but in what particular year of that period his birth took place, cannot with any degree of certainty be afeertained. It is generally believed that he was born in the iiland of Samos, and that he flourilhed about 500 years before Chrift, in the time of Tarquin the laft king of Rome*. His father Mne- if Tufc. farchus, who is thought by fome to have been a lapidary, Quejt. and by others a merchant of Tyre, appears to have been hk-1V' a man of Tome diftinClion, and to have beftowed upon I' his fon the beft education. Jamblicusf relates a number of wonderful ftories re-1. yit -py, fpeding Pythagoras?s defeent from Jupiter, his birth, thag, n.6. and early life ; and reprefents him even in his youth as a prodigy of wifdcm and manly ferioul’nefs. But moft of thefe idle tales confute themfelves, afford nothing of importance to be depended upon, and only prove the credulity, careleffnefs, and prejudice of their author. Of his childhood and early education we know nothing, ex¬ cept that he was firft inftrufted in his own country by Creophilus, and afterwards in Scyrus by Pherecydes. (fee Pherecydes). According to the cuftom of the times he was made acquainted with poetry and mufic ; eloquence and aftronomy became his private ftudies, and in gymnaftic exercifes he often bore the palm for ftrength and dexterity. He firft diftinguifhed himfelf in Greece at the Olympic games, where, befide gaining the prize, he is faid to have excited the higheft admira¬ tion by the elegance and dignity of his perfon, and the brilliancy of his underftanding. 4 C 2 Soon P Y T r 572 ] P Y T Pythagoras Soon after his appearance at thefe games, Pythagoras commenced his travels in queft of knowledge. He firft vifit-ed Egypt, where, through the interelf of Polycrates tyrant of Samos, he obtained the patronage of Amafis king of Egypt, by whofe influence, combined with his own afl'iduity, patience, and perfeverance, he at length gained the confidence of the priefts ; from whom he Jearned their facred myfteries, theology, and the wdiole fyftem of fymbolical learning. In Egypt, too, he be¬ came acquainted with geometry and the true folar fyftem 5 and, before he left that country, made him- lelf mafter of all the learning for which it was fo famed among the nations of antiquity. He afterwards vifited Perfia and Chaldea, where from the Magi he learnt divination, the interpreting ot dreams, and aftronomy. He is likewife laid to have travelled into India, to have converfed with the Gym- nofophifts, and to have acquired from them a knowledge of the philofophy and literature of the eaft ; and fuch was his ardour in the purfuit of fcience, that in quell of * ^**-it, we are told by Cirero *, he croffed many feas, and lib. iv. travelled on foot through many barbarous nations. After Pythagoras had fpent many years in gathering information on every fubjefl, efpecially refpefling the nature of the gods, the rites of religion, and the immor¬ tality ol the human foul, he returned to his native iftand, • and attempted to make his knowledge ufeful by inllitu- ting a fchool for the inftruflion of his countrymen. Failing of fuccefs in this laudable undertaking, be re¬ paired to Delos, where he pretended to receive moral dogmas from the prieftefs of Apollo, He alfo vifited Crete, where he was initiated into the moil facred my¬ fteries of Greece. He went likewife to Sparta and Elis, and again aflifted at the Olympic games 5 where in the public aflembly he was faluted with the title of fophiji or wife man, which he declined for one mote humble. See Philology, N° t. and Philosophy, N° 1. He returned to Samos enriched with mythological learning and myfterious rites, and again inllituted a fchool. His myfterious fymbols and oracular precepts made this attempt more fuccefsful than the former had been ; but meeting wdth fome oppofition, or being de- teftecl in fome pious frauds, he fuddenly left Samos, re¬ tired to Magna Grecia, and fettled at Crotona. Here he founded the Italic feft (fee Philosophy, N° 20.) 5 and his mental and perfonal accomplilhments, the fame of his diftant travels, and his Olympic crown, foon procured him numerous pupils. His bold and manly eloquence and graceful delivery attrafted the moll difiblute, and produced a remarkable change in the morals of the people of Crotona. His influence xvas increafed by the regularity of his own example, and its conformity to his precepts. He punftually at¬ tended the temples of the gods, and paid his devotions at an early hour ; he lived upon the pureft and moft innocent food, clothed himfelf like the priefts of Egypt, and by his continual purifications and regular offerings appeared to be fuperior in fanftity to the reft of man¬ kind. He endeavoured to affuage the paftions af his fcholars with verfes and numbers, and made a praflice of compofing his own mind every morning, by playing on his harp, and fmging along with it the pseans of Thales. To avoid the temptations of eafe and the feduflions of idlenels, bodily exercifes alfo made a confiderable part of Pythagoras his difcipline. —v—w At Crotona he had a public fchool for the general benefit of the people, in which he taught them their duty, praifing virtue and condemning vice ; and parti¬ cularly inftrufting them in the duties of focial life. Befide this, he had a college in his own houfe, which he denominated x-oivofitoy, in which there were two claftes of ftudents, viz. who were alfo called aufcul- tantes, and nrwri^iKot. 'The former of thefe were proba¬ tioners, and were kept under a long examen. A ft- lence of five years was impofed upon them; which A- puleius thinks was intended to teach them modefty and attention ; but Clemens Alexandrinus thinks it was for the purpofe of abftrafting their minds from fenfible objefts, and inuring them to the pure contemplation of the Deity. The latter clafs of fcholars were called genuini, perfecti, mathematici, and, by way of eminence, Pythagoreans. They alone were admitted to the know¬ ledge of the arcana and depths of Pythagoric difcipline,. and were taught the ufe of ciphers and hieroglyphic writings. Clemens obferves, that thefe orders correfponded very exaftly to thofe among the Hebrew’s : for in the fchoois of the prophets there were two claffes, viz. the fons of the prophets, who wrere the fcholars, and the doflors or mafters, who were alfo called perfeBi; and among the Levites, the novices or tyros, who had their quinquen¬ nial exercifes, by way of preparation. Laftly, even among the profclytes there were two orders •, exotemci, or profelytes of the gate ; and intrinfeci or perfeBi, profelytes of the covenant. He adds, it is highly pro¬ bable, that Pythagoras himfelf had been a profelyte of the gate, if not of the covenant. Gale endeavours to prove that Pythagoras borrowed his philofophy from, that of the Jewrs 5 to this end producing the authorities of many of the fathers and ancient authors, and even, pointing out the tracks and footfteps of Mofes in feveral parts of Pythagoras’s doftrine. But w7e believe the learned author was milled by the Chriftian Platonifts. The authority of Pythagoras among his pupils was fo great, that it w'as even deemed a crime to difpute his w7ord \ and their arguments wrere confidered as in¬ fallibly convincing, if they could enforce them by add¬ ing, that “ the mafter faid fo f an expreffion which af¬ terwards became proverbial in jurare in verba magijiri. This influence over his fchool wTas foon extended to the wmrld, and even his pupils themfelves divided the ap- plaufe and approbation of the people with their mafter ^ and the rules and legiflators of all the principal towns of Greece, Sicily, and Italy, boafted of being the dif- ciples of Pythagoras. To give more weight to his exhortations, as fome writers mention, Pythagoras re¬ tired into a fubterraneous cave, where bis mother fent him intelligence of every thing w hich happened during his abfence. After a certain number of months he again re-appeared on the earth with a grim and ghaltly countenance, and declared in the affembly of the people that he was returned from hell. From fimilar exag¬ gerations it has been afferted that he appeared at the Olympic games with a golden thigh, and that he could write in letters of blood whatever he pleafed on a look- ing-glafs *, and that by fetting it oppofite to the moon, W'hen full, all the charaflers which were on the glafs became P Y T [ 57.-! 3 P Y T Pythagoras, became legible on the moon’s dife. They alfo relate, v"—that by fome magical words he tamed a bear, flopped the flight of an eagle, and appeared on the fame day and at the fame initant in the cities of Crotona and Me- tapontum, &c. At length his lingular doftrines, and perhaps his flrenuoufly afferting the rights of the people againft their tyrannical governors, excited a fpirit of jealoufy, and railed a powerful party againll him 5 which foon became fb outrageous as to oblige him to fly for his life. His friends fled to Rhegium 5 and he himfelf, af¬ ter being refufed protection by the Locrians, tied to Metapontum, where he was obliged to take refuge in the temple of the mufes, and where it is faid he died of hunger about 497 years before Chrift. Refpetting the time, place, and manner of his death, however, there are various opinions, and many think it uncertain when, where, or in what manner, he ended his days. After his death his followers paid the fame refpebt to him as was paid to the immortal gods; they erefted flatues in honour ©f him, converted his houfe at Cro¬ tona into a temple of Ceres, appealed to him as a deity, and fwore by his name. Pythagoras married Theano of Crotona, or, accord¬ ing to others, of Crete, by whom he had two fbns, Te- hmges and Mnefarchus, 'who, after his death, took care of his fchool. He is faid alfo to have had a daughter called Damo. Whether he left any writings behind him is difputed. It feems probable, however, that he left none, and that fuch as went under his name were written by fome of his followers. The golden verfes which Hierocles illu- flrated with a commentary, have been aferibed to Epi- charraus or Empedocles, and contain a brief fummary of his popular doftrines. From this circumftance, and from the myfterious fecrecy with which he taught, our information concerning his doftrine and philofophy is very uncertain, and cannot always be depended on. The purpofe of philofophy, according to the fyftem of Pythagoras, is to free the mind from incumbrances, and to raife it to the contemplation of immutable truth and the knowledge of divine and fpiritual objedls. To bring the mind to this Rate of perfection is a work of lome difficulty, and requires a variety of intermediate Reps. Mathematical fcience was with him the firR Rep to wifdom, becaufe it inures the mind to contem¬ plation, and takes a middle courfe between corporeal and incorporeal beings. The whole fcience he divided into two parts, numbers and magnitude; and each of thefe he fubdivided into two others, the former into arithme¬ tic and tnufic, and the latter into magnitude at rejl and in motion ; the former of which comprehends geometry, and the latter ajironomy. Arithmetic he confidered as the noblefl fcience, and an acquaintance with numbers as the higheR good. He confidered numbers as the princi¬ ples of everything •, and divided them into fcientific and intelligible. Scientific number is the produefion of the powers involved in unity, and its return to the fame ; number is not infinite, but is the fource of that infinite divifibility into equal parts which is the property of all bodies. Intelligible numbers are thofe which exiRed in the divine mind before all things. They are the mo¬ del or archetype of the world, and the caufe of the ef- ience of beings. Of the Monad. Duad, Triad, Tetrad, and Decad, various explanations have been given by Pythagoras, various authors; but nothing certain or important is v known of them. In all probability, numbers were ufed by Pythagoras as fymbolical reprefentations of the firR principles and forms ol nature, and efpecially of thofe eternal and immutable effences which Plato denominated ideas $ and in this cale the Monad was the fimple root from which he conceived numbers to proceed, and as fuch, analogous to the fimple effence of deity j from whence, according to his fyltem, the various properties of nature proceed. % Mufic followed numbers, and was ufeful in raifing^ the mind above the dominion of the paffions. Pytha¬ goras confidered it as a fcience to be reduced to mathe¬ matical principles and proportions, and is faid to have diicovered the mufical chords from the circumfiance of feveral men facceflively flriking witn hammers a piece ^ of heated iron upon an anvil. This Rory Dr Burney * r f djfcredits 5. but allows, from the uniform teflimony of vol. i. J writers ancient and modern, that he invented the/bzr-p. 441. monical canon or monochord, (fee Monochord). The mufic of the fpheres, of which every one has heard, was a mofi fanciful doftrine of Pythagoras. It was pro¬ duced, he imagined, by the planets linking on the ether through which in their motion they palled ; and he con¬ fidered their mufical proportions as exact, and their har¬ mony perfect. Pythagoras, as we have already feen, learned geome¬ try in Egypt 5 but by invefiigating many new theorems, and by digefling its principles, he reduced it to a more regular fcience. A geometrical point, which he defines to be a monad, or unity with pofition, he fays corre- fponds to unity in arithmetic, a line to two, a fuperfi- cies to three, and a folid to four. He difeovered fe¬ veral of the propofitions of Euclid ; and on dilcovering the 47th of book ifl, he is faid to have offered a heca¬ tomb to the gods ; but as he was averfe to animal fa- crifices, this affertion is furely falfe. His great progrefs in aflronomical fcience has been mentioned elfewhere. See Astronomy, N° ii, 22. and Philosophy, N° 15, 16. Wifdorri, according to Pythagoras, is converfant with thofe obiects which are naturally immutable, eternal, and incorruptible j and its end is to affimilate the hu¬ man mind to the divine, and to qualify us to join the affembly of the gods. A£!ive and moral philofophy preferibes rules and nrecepts for the condufl of life, and leads us to the pra&ice of public and private virtue.— On thefe heads many of his precepts were excellent, and fome of them were whimfical and ufelefs. Theoreti¬ cal philofophy treats of nature and its origin, and is, according to Pythagoras, the higheR object of Rudy. It included all the profound myfleries which he taught, of which but little is now known. God he confiders as the univerfal mind, diffufed through all things, and the felf-moving principle of all things [xvTttA.ararg.oi Trxvrav), and of whom every human foul is a portion*.* Cicero d'e It is very probable, that he conceived of the Deity as a Sene^- fubtle fire, eternal, aflive, and intelligent j which is not jI inconfiRent with the idea of incorporeality, as the an¬ cients underRood that term. This Deity was primarily combined with the chaotic mafs of paffive matter, but he had the power of feparating himfelf, and fince the reparation he has remained diflinfl. The learned Cud- worth . p Y T . . r 57+ ' vtua^0'as' contends, that Pythagoras maintained a trinity of * Sat. iii. 56* hypolfafes in the divine nature, fimilar to the Platonic triad (fee Platonism). We cannot fay that his argu¬ ments appear to have much force ; but we think the con- clufion which he wuflies to eftabliih extremely probable, as Plato certainly drew his doflrine from fome of the countries which Pythagoras had vifited before him. Subordinate to the Deity there w'ere in the Pytha¬ gorean creed three orders of intelligences, gods, demons, and heroes, of different degrees of excellence and digni¬ ty. Thefe, together wuth the human foul, were confi- dered as emanations from the Deity, the particles of fubtle ether affuming a groffer clothing the farther they receded from the fountain. Hierocles defines a hero to be a rational mind united with a luminous body. God himfelf was reprefeixed under the notion of mo¬ nad, and the fubo.-dinate intelligences as numbers de¬ rived from and included in unity. Man is confidered as confifting of an elementary nature, and a divine or rational foul. His loul, a felf-moving principle, is com- pofed of two parts; the rational, feated in the brain 5 and the irrational, including the pafifions, in the heart. In both thefe refpecis he participates with the brutes, whom the temperament of their body, &c. allow’s not to aft rationally. The fenfitive foul periihes ; the other affumes an ethereal vehicle, and paffes to the region of the dead, till fent back to the earth to inhabit fome other body, brutal or human. See Metempsychosis. It was unquetlionably this notion which led Pythago¬ ras and his followers to deny themfelves the ufe of fielh, and to be fo peculiarly merciful to animals of every de- fcription. Some authors, however, fay, that fifth and beans, the ufe of which he alfo forbade, were prohibited, becaufe he fuppofed .them to have been produced from the fame putrified matter, from which, at the creation of the w’orld, man was formed. Of the fymbols of Pythagoras little is knowm. Thev have been religioufiy concealed ; and though they have awakened much curiofity, and occafioned many ingeni¬ ous conjeftures, they ffill appear to us dark and tri¬ fling. As a fpecimen we give the following : “ Adore the found of the whifpering wind. Stir not the fire with a fword. Turn afide from an edged tool. Pafs not over a balance. Setting out on a journey, turn not back, for the furies will return with you. Breed no¬ thing that hath crooked talons. Receive not a (wal¬ low into your houfe. Took not in a mirror by the light of a candle. At a facrifice pare not your nails. Eat not the heart or brain. Tafte not that which hath fallen from the table. Break not bread. Sleep not at noon. When it thunders touch the earth. Pluck not a crow. Roaft not that which has been boiled. Sail not on the ground. Plant not a palm. Breed a cock, but do not facrifice it, for it is facred to the fun and moon. Plant mallows in thy garden, but eat them not. Abftain from beans.” I he following precepts are more important: “ Dif- courfe not of Pythagorean doftrines without light. Above all things govern your tongue. Engrave not the image of God in a ring. Quit not your Ration with¬ out the command of your general. Remember that the paths of virtue and of vice refemble the letter Y. To this fymbol Perfius refers *, when he fays, ] P Y T Et libi qiue Samios diduxit litera ram&s, Surgentem dcxtro monjlravit limite colletn. J nere has the Samian Y’s inftruftive make Python. Pointed the road thy doubtful foot Ihould take j 1 There warn’d thy raw and yet unpraftis’d youth, To tread the rifing right-hand path of truth. Tne fcantinefs and uncertainty of our information refpefting Pythagoras, renders a regular and complete account of his lite and doftrines impoflible. A mo¬ dern author f- of profound erudition, pronounces him f Ancient to have been unquejiionably the wifeft man that ever \x.Meta^hy. ved, if his mafters the Egyptian priefts muff not be ex--^"' cepted. This is faying a great deal too much \ but that he was one of the moil diftinguifhed philofophers of antiquity, or, as Cicero expreffes it, vir prajlanti fapientia, appears very evident j and his moral charac¬ ter^ has never been impeached. The myfterious air which he threw over his doftrines, and the apparent inanity of fome of his fymbols, have indeed fubjefted him to the charge of impofture, and perhaps the charge is not wholly groundlefs : but when we confider the age in which he lived, and the nature of the people with whom he had to deal, who would in all probabi¬ lity have refilled more open innovations, even this will not appear fo blameable as at firft fight we are apt to think it; and it is worthy of notice, that the worft fto- ries of this kind have come down to us in a very que- ftionable ffiape, and with much probability appear to be falfe. PYIHAGOREANS, a feft of ancient philofophers, fo called from being the followers of Pythagoras. See the preceding article. P^ i Id I A,, the prieftefs of Apollo at Delphi, by whom he delivered oracles. She was fo called from Pythius, a name of that god, which is faid to have been given him on account of his viftory over the ferpent Python. The Pythia was at firft required to be a young girl, but in later times flie was a wToman of 50 years of age. The firff and moft famous Pythia was Phemonoe. O- racles were at firff delivered by her in hexameter verfe. All the pythias were to be pure virgins, and all of them delivered their oracles with great enthufiafm and violent agitations. See Oracle and Delphi. P^ I iff IAN games, in Grecian antiquity, fports inftituted near Delphos in honour of Apollo, on account of his flaying the ferpent Python. See Apollo.— Ihefe games, at their firff inffitution, were celebrated only once in nine years ; but afterwards every fifth year, from the number of the Parnaflian nymphs who came to congratulate Apollo, and to make him prc- fents on his viftory. The viftor was crowned with gar¬ lands. PYTHON, in fabulous hiffory, a monffrous ferpent, produced by the earth after Deucalion’s deluge. Juno being exafperated at Latona, who w^as beloved by Jupi¬ ter, commanded this ferpent to deftroy her ; but flying from the purfuit of the monfter, (he efcaped to Delos, where ftie was delivered of Diana and Apollo ; the latter of whom at length deftroyed Python with his arrows, in memory of which viftory the Pythian games were infti- tuted. See Apollo. Q- 3 QUA [ 575 ] QUA Q. ,, <)r tfee 16th letter and j 2th confonant of Quadi. cur alphabet 5 but is not to be found either in <■ y-. ■ the Greek, old Latin, or Saxon alphabets j and in¬ deed fome would entirely exclude it, pretending that •k ought to be ufed wherever this occurs. However, as it is formed in the voice in a different manner, it is un¬ doubtedly a diftindf letter : for, in exprefling this found, the cheeks are contrafted, and the lips, particularly the under one, are put into a canular form, for the paflage of the breath. I he q is never founded alone, but in conjundfion rvith u, as in quality, quejlion, quite, quote, &c. and never ends any Englifh word. As a numeral, O Hands for 500; and with a dafh over it, thus t,>j for 500,000. Ufed as an abbreviature q fignifies quantity, or quan¬ tum. Thus, among phyficians, q. pi. is quantum placet, x. e. “ as much as you pleafe” of a thing j and q.f is quantum fufficit, i. e. “ as much as is neceflary.” Q. E. U. among mathematicians, is quod cnat demotijlrandum, i. e. “ which was to be demonftrated and p. E. F. is quod erat faciendum, i. e. “ which w'as to ^be done.” O. D. among grammarians is quad diclum, i. e. “ as if it t\eie laid j” or, “ as who fliould lay.-’ In the notes of the ancients, (^) Hands for Quintus, or ®uintius; Q.B.V. for quod bene vert at ; O. S. b. S. for qiue fupra feripta /tint; Q. M. for -ffiintus Mu tins, or quomodo; Quint, for dffntiliux ; and Omef. for qiuejlor. PJJAB, in Ichlh[ology, the name of a Ruffian fifh, which is laid to be at firit a tadpole, then a frog, and at I aft a fhh. Dr IMounfey, who made many inquiries concerning thefe pretended changes, confiders them all f.s fabulous. He had opportunity of feeing the fifh it- felf, and found that they {pawned" like other filhes, and grew in fize, without any appearances to juflify the re¬ port. He adds, that they delight in very clear water, in rivers with fandy or flony bottoms, and are never found in Handing lakes, or in rivers palfng through marflies or moffy grounds, where frogs choofe mofl to be. QUABES, are a free people of Africa, inhabiting the fouthern banks of the river SeHos, and between that and Sierra Leona. They are under the prote&ion of the emperor of Manow. OUACEIA, or quagga. See Equus, Mammalia Index. Marc- QUACHILTO, in Ornithology, is the name of a grnnje'i very beautiful Brafilian bird, called alfo yacaenintii and Hift. Bra- porphyria Americanus. It is of a fine blackiih purple JlL colour, variegated with white j its beak is white while young, but becomes red as it grows older, and has a naked fpace at its bafis, refemhling in fome fort the coot; its legs are of a yellowifh green ; it lives about the waters, and feeds on fifir, yet is a very well tailed bird. It imitates the crowing of a common cock, and makes its mufic early in the morning. QUACK, among phyficians, the fame with empiric. See Empiric. QUADI, (Tacitus) j a people of Germany, fituated to the fouth-eaH or the mountains of Bohemia, on the Qaadrage- banks of the Danube, and extending as far as the river bima Marus, or March, running by Moravia, which country M they occupied. Quadrant. ^ PUADilAGESIMA, a denomination given to lent, from its confifling of 40 days. See Lent. QUADRANGLE, in Geometry, the fame with a quadrilateral figure, or one confifting of four Hides and four angles. QUADRANS, the quarter or fourth part of any thing, particularly the as, or pound. Quadrans, in Englifh money, the fourth part of a penny. Before the reign of Edward I. the fmalleil com was n fieri mg, or penny, marked with a crofs j by the guidance 01 which a penny might be cut into halves for a halfpenny, or into quarters or four parts for far¬ things ; till, to avoid the fraud of unequal cuttings, that king coined halfpence and farthings in diltindt round pieces. QUADRANT, in Geometry, the arch of a circle, containing 90°, or the fourth part of the entire peri¬ phery. Sometimes alfo the fpace or area, included between this arch and two radii drawn Tom the centre to each extremity thereof, is called a quadrant, or, more pro¬ perly, a quadrantal fpace, as being a quarter of an en¬ tire circle. Quadrant, alfo denotes a mathematical inHrument, of great ufe in aHronomy and navigation, for taking the altitudes of the fun and Hars, as alio for taking angles in furveying, &c. _This inHrument is varioufiy contrived, and furnifhed with different apparatus, according to the various ufes it. is intended for j but they all have this in common, that they confifl of a quarter of a circle, whofe limb is divided into 90°. Some have a plummet fufpended from the centre, and are furnifhed with fights to look through. I he principal and moH ufeful quadrants are the com¬ mon furveying quadrant, aflronomical quadrant, Adams’s- quadrant, Cole’s quadrant, Gunter’s quadrant, Hadley’s quadrant, horodi&ical quadrant, Sutton’s or Collins’s quadrant, and the finical quadrant, &c. Of each of which in order. 1. The common furveying quadrant, is made of brafs, woo_d,. or any other folid fubHance 5 the limb of which is divided into 90°, and each of thefe farther divided into as many equal parts as the fpace will allow, either diagonally or otherwife. On one of the femidiameters are fitted two moveable fights 5 and to the centre is fometimes alfo fixed a label, or moveable index, bearing two other fights; but in lieu of thefe laff fights there is fometimes fitted a telefcope : alfo from the centre there is hung a thread with a plummet | and on the under fide or face of the inHrument is fitted a ball and focket, by means of which it may be put into any p0- Ution. The general ufe of it is for taking angles in a vertical plane, comprehended under right lines going ixom> QUA [57 Quadrant, from the centre of the inftrument, one of which is ho- rizontal, and the other is direfted to fome vifible point. But befides the parts already defcribed, there is fre¬ quently added on the face, near the centre, a kind of compartment, called the quadrat, or geometricalfquare. See Quadrat. This quadrant may be ufed in different fituations : for obferving heights or depths, its plane muff be difpof- ed perpendicularly to the horizon j but to take horizon¬ tal diftances, its plane is difpofed parallel thereto. Again, heights and diftances may be taken two wTays, viz. by means of the fixed fights and plummet, or by the label : As to which, and the manner of meafuring angles, fee Geomrtry and Mensuration. 2. The aftronomical quadrant is a large one, ufually made of brafs, or wooden bars faced with iron plates ; having its limb nicely divided, either diagonally or otherwife, into degrees, minutes, and feconds ; and fur- niihed with two telefcopes, one fixed on the fide of the quadrant, and the other moveable about the centre, by means of the fcrew. There are alfo dented wheels which ferve to direft the inftrument to any objedt or phenomenon.—The ufe of this curious inftrument, in taking obfervations of the fun, planets, and fixed ftars, is obvious j for being turned horizontally upon its axis, by means of the telefcope, till the objedf is feen through the -moveable telefcope, then the degrees, &c. cut by the index give the altitude required. See Astronomy Index. 3. Cole’s quadrant is a very ufeful inftrument invent¬ ed by Mr Benjamin Cole. It confifts of fix parts, viz. Plate the ftaff AB (fig. 1.) j the quadrantal arch DE ; three fccceLvin. vanes A, B, C 5 and the vernier FG. The ftaff is a Gg- *• bar of wTood about two feet long, an inch and a quarter broad, and of a fufficient thicknefs to prevent it from bending or warping. The quadrantal arch is alfo of wood ; and is divided into degrees, and third-parts of a degree, to a radius of about nine inches ; to its ex¬ tremities are fitted two radii, which meet in the centre of4 the quadrant by a pin, round which it eafily moves. The fight-vane A is a thin piece of brafs, almoft two inches in height and one broad, placed perpendicularly on the end of the ftaff A, by the help of two fcrews paffmg through its foot. Through the middle of this vane is drilled a fmall hole, through which the coinci¬ dence or meeting of the horizon and folar fpot is to be viewed. The horizon vane B is about an inch broad, and two inches and a half high, having a flit cut through it of near an inch long and a quarter of an inch broad ; this vane is fixed in the centre-pin of the inftrument, in a perpendicular pofition, by the help of two fcrews pal¬ ling through its foot, whereby its pofition with refpecl to the fight-vane is always the fame, their angles of in¬ clination being equal to 45 degrees. The ftiade-vane C is compofed of two brafs plates. The one, which ierves as an arm, is about four inches and a half long, and three quarters of an inch broad, being pinned at one end to the upper limb of the quadrant by a fcrew, about which it has a fmall motion ; the other end lies in the arch, and the lower edge of the arm is dire&ed to the middle of the centre-pin \ the other plate, which is properly the vane, is about two inches long, being fixed perpendicularly to the other plate, at about half an inch diftance from that end next the arch ; this vane may be ufed either by its fhade or by the folar fpot 2 6 ] q U A caft by a convex lens placed therein. And, becaufe the Qnadrant. wood-work is often apt to warp or twill, therefore this ’ ■1 f vane may be rectified by the help of a fcrew, fo that the wrarping of the inftrument may occafion no error in the obfervation, which is performed in the following man¬ ner : Set the line G on the vernier again!! a degree on the upper limb of the quadrant, and turn the fcrew on the backfide of the limb forward or backward, till the hole in the fight-vane, the centre of the glafs, and the funk fpot in the horizon-vane, lie in a right line. To find the fun’s altitude by this inftrument : Turn your back to the fun, holding the inftrument by the ftaff with your right hand, fo that it be in a vertical plane pafling through the fun ; apply your eye to the fight-vane, looking through that and the horizon-vane till you fee the horizon ; with the left hand Hide the quadrantal arch upwards, until the folar fpot or fnade, caft by the ftiade-vane, fall diredtly on the fpot or flit in the horizon-vane j then will that part of the quad¬ rantal arch, which is raifed above G or S (according as the obfervation refpedled either the folar fpot or ftiade) ftrow the altitude of the fun at that time. But if the meridian altitude be required, the obfervation muft be continued $ and as the fun approaches the meridian, the fea wrill appear through the horizon-vane, and then is the obfervation finifhed ; and the degrees and mi¬ nutes, counted as before, will give the fun’s meridian altitude : or the degrees counted from the lower limb upwards will give the zenith-diftance. 4. Adams’s quadrant differs only from Cole’s qua¬ drant in having an horizontal vane, with the upper part of the limb lengthened ; fo that the glafs, which caffs the folar fpot on the horizon-vane, is at the fame diftance from the horizon-vane as the fight-vane at the end of the index. 5. Gunter’s quadrant, fo called from its inventor Ed¬ mund Gunter, befides the ufual apparatus of other quadrants, has a ftereographical projetlion of the fphere on the plane of the equinoctial. It has alfo a kalendar of the months, next to the divifions of the limb. life of Gunter’s quadrant. 1. To find the fun’s me¬ ridian altitude for any given day, or the day of the month for any given meridian altitude. Lay the thread to the day of the month in the fcale next the limb 5 and the degree it cuts in the limb is the fun’s meridian al¬ titude. Thus the thread, being laid on the 15th of May, cuts 590 30', the altitude fought; and, contrari- ly, the thread, being fet to the meridian altitude, Ihows the day of the month. 2. To find the hour of the day. Having put the bead, which Aides on the thread, to the fun’s place in the ecliptic, obferve the fun’s alti¬ tude by the quadrant 5 then, if the thread be laid over the fame in the limb, the bead will fall upon the hour requln d. Thus fuppofe on the 10th of April, the fun being then in the beginning of Taurus, I obferve the fun’s altitude by the quadrant to be 36° 5 I place the bead to the beginning of Taurus in the ecliptic, and lay the thread over 36° of the limb 5 and find the bead to fall on the hour-line marked three and nine ; ac¬ cordingly the hour is either nine in the morning or three in the afternoon. Again, laying the bead on the hour given, having firft redtified or put it to the fun’s place, the degree cut by the thread on the limb gives the alti¬ tude. Note, the bead may be redified otherwife, by bringing QUA [5 Quadrant, bringing the thread to the day of the month, and the “ bead to the hour-line of 1 2. 3. To find the fun’s decli¬ nation from his place given, and contrariwife. Set the bead to the fun’s place in the ecliptic, move the thread to the line of declination, and the bead will cut the degree of declination required. Contrarily, the bead being adjufted to a given declination, and the thread moved to the ecliptic, the bead will cut the fun’s place. 4. .} he lun’s place being given, to find his right afcen- fion, or contrarily. Lay the thread on the lun’s place in the ecliptic, and the degree it cuts on the limb is the right afcenfion lought. Contrarily, laying the thread on the right afcenfion, it cuts the fun’s place in the ecliptic. 3. The fun’s altitude being given, to find his azimuth, and contrariwife. Rectify the bead for the time, as in the fecond article, and obferve the fun’s al¬ titude : bring the thread to the complement of that al¬ titude j thus the bead will give the azimuth fought, among the azimuth lines. 6. To find the hour of the •night from feme of the five liars laid down on the qua¬ drant. (1.) Put the bead to the liar you would ob¬ ferve, and find how many hours it is off the meridian, by article 2. (2.) Then, fr6m the right afcenfion of the liar, fubtraft the fun’s right afcenfion converted in¬ to hours, and mark the difference 5 which difference, added to the obferved hour of the liar from the meri¬ dian, fhows how many hours the fun is gone from the meridian, which is the hour of the night. Suppofe on the 15th of May the fun is in the 4th degree of Ge- rnini, I fet the bead to Ardlurus j and, obferving his al¬ titude, find him to be in the well about $2° high, and the bead to fall on the hour-line of two in the afternoon ; then will the hour be 11 hours 50 minutes pad noon, or 10 minutes Ihcrt of midnight : for 62°, the fun’s right afeention, converted into time, makes four hours eight minutes j which, fubtradled from 13 hours 58 mi¬ nutes, the right afcenfion of Arfturus, the remainder •will be nine hours 50 minutes ; which added to two hours, the obferved dillance of Arfturus from the me¬ ridian, lhowTs the hour of the night to be 11 hours 50 minutes. T he mural quadrant has been already deferibed under the article Astronomy. It is a moll important inllru- ment, and has been much improved by Mr Ramfden, who has dillinguilhed himfelf by the accuracy of his di- vifions, and by the manner in which he finilhes the planes by working them in a vertical pofition. He places the plumb-line behind the inllrument, that there may be no necefiity for removing it when we take an oblervation near the zenith. His manner of fufpending the glafs, and that of throwing light on the objedl-glafs and on the divifions at the fame time, are new, and im¬ provements that deferve to be noticed. Thofe of eight feet, which he has made for the obfervatories of Padua and Vilna, have been examined by Dr Malkelyne ; and the greatell error does not exceed tw'o feconds and a half. '1 hat of the fame fize for the obfervatory of Milan is in a very advanced Hate. The mural quadrant, of fix feet, at Blenheim, in a moll admirable inllrument. It is fixed to four pillars, which turn on two pivots, fo . that it may be put to the north and to the fouth in one minute. It was for this inllrument Mr Ramfden in¬ vented a method ol redlifying the arc of 90 degrees, on which an able allronomer had ftarted Ibme difficulties j but by means of an horizontal line and a plumb-line, Vol. XVII. Part II. 77 1 Q U A forming a kind of crofs, without touching the circle, he Ihowed him that there was not an error of a fingie fecond in the 90 degrees ; and that the difference was occafioned by a mural quadrant of Bird, in which the arc of 90 degrees was too great by feveral feconds, and wnich had never been rectified by fo nice a method as that of Mr Ramfden. But the quadrant is not the inllrument which Hands highelt in Mr Ramfden’s opinion ; it is the complete circle : and he has demonllrated to M. de la Lande, that the former mull be laid afide, if we would arrive at the utmolt exadlnefs of which an obfervation is capable. His principal reafons are : 1. The leaft variation id the centre is perceived by the two diametrically oppofile points. 2. The circle being worked on the turn, the furface is always of the greatell accuracy, which it is impoffible to obtain in the quadrant. 3. We may al¬ ways have two meafures of the fame arc, which will ferve for the verification of each other. 4. The firft point of the divifion may be verified every day with the utmolt facility. 5. The dilatation of the metal is uni¬ form, and cannot produce any error. 6. This inflru- ment is a meridian glafs at the fame time. 7. It alio becomes a moveable azimuth circle by adding a hori¬ zontal circle beneath its axis, and then gives the refrac¬ tions independent of the menfuration of time. 6. Hadley’s quadrant is an inllrument of vail utility both in navigation and pradtical allronomv. It derives its name from Mr Hadley, who firlt publiffied an ac¬ count of it, though the firlt thought originated with the celebrated Dr Hooke, and was completed by Sir Ifaac Newton (fee Astronomy, N° 32. and alfo N° j 7. and 22.). The utility of this quadrant arifes from the accuracy and precifion with which it enables us to de¬ termine the latitude and longitude ; and to it is naviga¬ tion much indebted for the very great and rapid advances it has made of late years. It is eafy to manage, and of extenfive ufe, requiring no peculiar Iteadinels of hand, nor any fuch fixed balls as is neceflary to other afiro- nomical inllruments. It is ufed as an inllrument for taking angles in maritime furveying, and with equal fa¬ cility at the mall head as upon the deck, by which its fphere of oblervation is much extended ; for fuppofing many iflands to be vifible from the malt head, and only one from deck, no ufeful obfervation can be made by any other inllrument. But by this, angles may be ta¬ ken at the mail head from the one vifible object with great exadtnefs ; and further, taking angles from heights, as hills, or a Ihip mall’s head, is almolt the only way of deferibing exadlly the figure and extent of fhoals. It has been objefted to the ufe of this inllrument for furveying, that it does notmeafure the horizontal angles, by which alone a plan can be laid down. This objection, however true in theory, may be reduced in pra£tice by a little caution 5 and Mr Adams has given very good di¬ rections for doing fo. Notwithftanding, hoxvever, the manifelt fuperiority of this inftrument over thofe that were in ufe at the time of its publication, it was many years before the failors could be perfuaded to adopt it, and lay afide their imperfeCt and inaccurate inllruments j fo great is the difficulty to remove prejudice', and emancipate the mind from the flavery of opinion. No inltrument has undergone, fince the original invention, more changes 4 I) than Cb'.'Hlranf. QUA [ 578 ] QUA Quadrant, than the quadrant of Hadley 5 of the various altera- l— v-”-" tions, many had no better foundation than the caprice of the makers, who by thefe attempts have often ren¬ dered the inftrument more complicated in conftru&ion, and more difficult in ufe, than it was in its original hate. It is an effential property of this inftrument, derived from the laws of rededfion, that half degrees on the arc anfwer to whole ones in the angles meafured : hence an odlant, or the eighth part of a circle, or 45 degrees on the arch, ferves to meafure 90 degrees ; and fextants will meafure an angular diftance of 120 degrees, though the iwch of the inftrument is no more than 60 degrees. It is from this property that foreigners term that in¬ ftrument an oBatit, which we ufually call a quadrant, and wffiich in effedl it is. This property reduces in¬ deed conuderably the bulk of the inftrument : but at the fame time it calls for the utmoft accuracy in the divifions, as every error on the arch is doubled in the obfervation. Another eflential, and indeed an invaluable, proper¬ ty of this inftrument, whereby it is rendered peculiarly advantageous in marine obfervations, is, that it is not liable to be difturbed by the fliip’s motion ; for provided the mariner can fee diftindtly the two objedls in the field of his inftrument, no motion nor vacillation of the ffiip will injure his obfervation. Thirdly, the errors to which it is liable are readily dif- covered and eafily rectified, while the application and ufe of it is facile and plain. To find whether the two fur faces of any one of the reflefting glafles be parallel, apply your eye at one end of it, and obferve the image of fome object refledfted veiy obliquely from it; if that image appear fingle, and well-defined about the edges, it is a proof that the furfaces are parallel : on the contrary, if the edge of the reflefted images appear milled, as if it threw a fhadow from it, or feparated like two edges, it is a proof that the tivo furfaces of the glafs are inclined to each other : if the image in the fpeculum, particularly if that image be the fun, be viewed through a fmall te- lefcope, the examination will be more perfeft. To find whether the furface of a reflecting glafs be plane. Choofe two diftant objefts, nearly on a level with each other : hold the inftrument in an horizontal pofition, vierv the left-hand objeft direftly through the tranfparent part of the horizon-glafs, and move the in- dey till the reflected image of the other is feen below it in' the filvered part ; make the two images unite juft at the line of feparation, then turn the inftrument round ftorvly on its own plane, fo as to make the united images move along the line of feparation of the horizon-glafs. If the images continue united without recedingTrom each other, or varying their refpeClive pofition, the refleCling fuiface is a good plane. To find if the two furfaces of a red or darkening glafs are parallel and perfeClly plane. This muft be done by means of the fun when it is near the meridian, in the fol¬ lowing manner : hold the fextant vertically, and direft the fight to fome obieCl in the horizon, or between you and the Iky, under the fun ; turn down the red glafs and move the index till the refleCled image of the fun is in eontaCl with the objeCl feen direClly : fix then the index, and turn the red glafs round in its fquare frame ; view ffie fun’s image andobjeCt immediately, and if the fun’s image is neither raifed nor deprefled, but continues in Quadrant, contaft with the objeCt below, as before, then the fur-v— faces of the darkening glafs are true. For a more particular defeription of Hadley’s qua¬ drant, and the mode of ufing it, fee Navigation, Book II. chap. i. This inftrument has undergone feveral improvements fince its firft invention, and among thefe improvers muft be ranked Mr Ramfden. He found that the effential parts of the quadrant had not a fufficient degree of fo- lidity ; the friCtion at the centre vras too great, and in general the alidada might be moved feveral minutes without any change in the pofition of the mirror j the divifions were commonly very inaccurate, and Mr Ramf¬ den found that Abbe de la Caille did not exceed the truth in eftimating at five minutes the error to which an obferver was liable in taking the diftance between the moon and a ftar 5 an error capable of producing a miftake of 50 leagues in the longitude. On this ac¬ count Mr Ramfden changed the principle of conftruc- tion of the centre, and made the inftrument in fuch a manner as never to give an error of more than half a minute *, and he has now brought them to fuch a de¬ gree of perfection as to warrant it not more than fix leconds in a quadrant of fifteen inches. Since the time of having improved them, Mr Ramfden has conftruCted an immenfe number 5 and in feveral which have been carried to the Eaft Indies and America, the deficiency has been found no greater at their return than it had been determined by examinations before their being ta¬ ken out. Mr Ramfden has made them from 15 inches to an inch and a half, in the latter of which the minutes are eafily diftinguiffiable j but he prefers for general ufe thofe of 10 inches, as being more eafily handled than the greater, and at the fame time capable of equal ac¬ curacy. See Sextant. A. great improvement wras alfo made in the con- ftruCtion of this quadrant by Mr Peter Dollond, fa¬ mous for his invention of achromatic telefcopes. The glaffes of the quadrants ftxould be perfeCt planes, and have their furfaces perfectly parallel to one another. By a praClice of feveral years, Mr Dollond found out me¬ thods of grinding them of this form to great exaCt- nefs } but the advantage which fliould have arifen from the goodnefs of the glaffes was often defeated by the index-glafs being bent by the frame which contains it. To prevent this, Mr Dollond contrived the frame fo, that the glafs lies on three points, and the part that prefles on the front of the glafs has alfo three points op- pofite to the former. Thefe points are made to confine the glafs by three ferews at the back, aCting direCtly oppofite to the points between which the glafs is pla¬ ced. The principal improvements, however, are in the methods of adjufting the glafles, particularly for the back-obfervation. The method formerly praCtifed for adjufting that part of the inftrument by means of the oppofite horizons at fea, was attended with fo many difficulties that it was fcarcely ever ufed : for fo little de¬ pendence could be placed on the obfervations taken this way, that the beft Hadley’s fextants made for the purpofe of obferving the diftances of the moon from the fun or fixed ftars have been always made without the horizon-glafs for the back-obfervation j for want of which, many valuable obfervations of the fun and moon have been loft, when their diftance exceeded 120 de¬ grees.. QUA t 579 ] Quadrant, grees. To make the adjuftment of the back-obferva- tion eafy and exaft, he applied an index to the back horizon-glafs, by which it may be moved in a parallel pofition to the index-glafs, in order to give it the two ad- juftments in the fame manner as the fore-horizon-glafs is adjufted. Then, by moving the index to which the back-horizon-glafs is fixed exaftly 90 degrees (which is known by the divifions made for that purpofe), the glafs will thereby be fet at right angles to the index- glafs, and will be properly adjufted for ufe j and the obfervations may be made with the fame accuracy by this as by the fore-obfervation. To adjuft the horizon- glafles in the perpendicular pofition to the plane of the inftrument, he contrived to move each of them by a fingle fcrew, which goes though the frame of the qua¬ drant, and is turned by means of a milled head at the back j which may be done by the obferver while he is looking at the objedl. To thefe improvements alfo he added a method, invented by Dr Mafkelyne, of pla¬ cing darkening-glaffes behind the horizon-glafles. Thefe, which ferve for darkening the objeft feen by diredt vifion, in adjufting the inftrument by the fun or moon, he placed in fuch a manner as to be turned behind the fore horizon-glafs, or behind the back horizon-glafs : there are three of thefe glaffes of different degrees of darknefs. We have been the more particular in our defcription and ufe of Hadley’s quadrant, as it is undoubtedly the beft hitherto invented. 7. Horodiftical quadrant, a pretty commodious in¬ ftrument, fo called from its ufe in telling the hour of the day.—Its conftruftion is this : From the centre of Fig. 3« the quadrant, C, fig. 3. whofe limb AB is divided into 90°, defcribe feven concentric circles at intervals at pleafure; and to thefe add the figns of the zodiac, in the order reprefented in the figure. Then applying a ruler to the centre C and the limb AB, mark upon the feveral parallels the degrees correfponding to the altitude of the fun when therein, for the given hours j conneft the points belonging to the fame hour with a curve line, to which add the number of the hour. To the radius CA fit a couple of fights, and to the centre of the quadrant C tie a thread with a plummet, and upon the thread a bead to Aide. If now the thread be brought to the parallel wherein the fun is, and the qua¬ drant diredled to the fun, till a vifual ray pafs through the fights, the bead will fhow the hour *, for the plum¬ met, in this fituation, cuts all the parallels in the de¬ grees correfponding to the fun’s altitude. Since the bead is in the parallel which the fun defcribes, and through the degrees of altitude to which the fun is ele¬ vated every hour there pafs hour lines, the bead muft Ihow the prefent hour. Some reprefent the hour-lines by arches of circles, or even by ftraight lines, and that without any fenfible error. Fig. 4. Sutton’s or Collins’s quadrant (fig. 4.) is a ftereo- graphic proje&ion of one quarter of the fphere be¬ tween the tropics, upon the plane of the ecliptic, the eye being in its north pole : it is fitted to the latitude of London. The lines running from the right hand to the left are parallels of altitude ; and thofe crofting them are azimuths. The leffer of the two circles, bounding the projection, is one-fourth of the tropic of Capricorn j the greater is one-fourth of that of Cancer. The ttvo ecliptics are drawn from a point on the left QUA edge of the quadrant, with the characters of the figns Qua I rant, upon them ; and the two horizons are drawn from the “ v fame point. The limb is divided both into degrees and time } and, by having the fun’s altitude, the hour of the day may be found here to a minute. The qua- drantal arches next the centre contain the kalendar of months j and under them, in another arch, is the fun’s declination. On the projection are placed feveral of the moft noted fixed ftars between the tropics ; and the next below the projection is the quadrant and line of ftiadows. To find the time of the fun’s rifing or fet- ting, his amplitude, his azimuth, hour of the day, &c. by this quadrant: lay the thread over the day and the month, and bring the bead to the proper ecliptic, either of fummer or winter, according to the feafon, which is called reSlifijing ; then, moving the thread, bring the bead to the horizon, in which cafe the thread wdll cut the limb in the time of the fun’s rifing or fetting before or after fix ; and at the fame time the bead will cut the horizon in the degrees of the fun’s amplitude.—Again, obferving the fun’s altitude w;.h the quadrant, and fup- pofing it found 450 on the fifth of May, lay the thread over the fifth of May, bring the bead to the fummer ecliptic, and carry it to the parallel of altitude 450 ; in which cafe the thread will cut the limb at 550 15', and the hour will be feen among the hour-lines to be either 41' paft nine in the morning, or 19' paft two in the af¬ ternoon.—Laftly, the bead among the azimuths (hows the fun’s diftance from the fouth 50° 41'. But note, that if the fun’s altitude be lefs than what it is at fix o’clock, the operation muft be performed among thofe parallels above the upper horizon, the head being recti¬ fied to the winter ecliptic. 9. Sinical quadrant (fig. 5.) confifts of feveral con- Fig. 5, centric quadrantal arches, divided into eight equal parts by radii, with parallel right lines crofting each other at right angles. Now any one of the arches, as BC, may reprefent a quadrant of any great circle of the fphere, but is chiefly ufed for the horizon or meridian. If then BC be taken for a quadrant of the horizon, either of the fides, as AB, may reprefent the meridian 5 and the other fide, AC, will reprefent a parallel, or line of eaft and weft : and all the other lines, parallel to AB, will be alfo meridians j and all thofe parallel to AC, eaft and weft lines, or parallels.—Again, the eight fpa- ces into which the arches are divided by the radii, repre¬ fent the eight points of the compafs in a quarter of the horizon j each containing 11° 15’. The arch BC is likewife divided into po*3, and each degree fubdivided into 12, diagonal-wife. To the centre is fixed a thread, which, being laid over any degree of the quadrant, ferves to divide the horizon. If the finical quadrant be taken for a fourth part of the meridian, one fide thereof, AB, may be taken for the common radius of the meridian and equator 5 and then the other, AC, will be half the axis of the world. The degrees of the circumference, BC, will reprefent degrees of latitude 5 and the parallels to the fide AB, sffumed from every point of latitude to the axis AC, will be radii of the parallels of latitude, as likewife the fine complement of thofe latitudes. Suppofe, then, it be required to find th© degrees of longitude contained in 83 of the leffer leagues in the parallel of 48° ; lay the thread over 48° of latitude on the circumference, and count thence the 8 2 leagues on 4D 2 AB, QUA [ 580 ] QUA Quid rant. AB, beginning at A j this will terminate in H, allovv- v " ing every imall interval four leagues. Then tracing out the parallel HE, from the point H to the thread ; the part AE of the thread fhows that 125 greater or equi- noftial leagues make 6o° 15'j and therefore that the 83 leffer leagues AH, which make the difference of longitude of the courfe, and are equal to the radius of the parallel HE, make 6o° 15' of the faid parallel. It the (hip fails an oblique courfe, fuch courfe, be¬ tides the north and fouth greater leagues, gives leffer leagues ealterly and wefterly, to be reduced to degrees of longitude of the equator. But thefe leagues being made neither on the parallel of departure, nor on that of arrival, but in all the intermediate ones, we muff find a mean'proportional parallel between them. To find this, we have on the inftrument a fcaie of crofs la¬ titudes. Suppofe then it were required to find a mean parallel between the parallels of 40° and 6o° j with your compaffes take the middle between the 40th and 60th degree on this fcaie : the middle point will termi¬ nate againff the 51ft degrge, which is the mean parallel required. The principal ufe of the finical quadrant is to form triangles upon, fimilar to thofe made by a Ihip’s way with the meridians and parallels •, the fides of which triangles are meafured by the equal intervals between the concentric quadrants and the lines N and S, E and W : and every fifth line and arch is made deeper than the reft. Now, fuppofe a fhip to have failed 150 leagues north-eaft, one fourth north, which is the third point, and makes an angle of 330 44' with the north part of the meridian : here are given the courfe and diftance failed, by which a triangle may be formed on the in¬ ftrument fimilar to that made by the (hip’s courfe and hence the unknown parts of the triangle may be found. Thus, fuppofing the centre A to reprefent the place of departure, count, by means of the concentric circles along the point the (hip failed on, viz. AD, 150 leagues : then in the triangle AED, fimilar to that of the Ihip’s courfe, find AEnrdifference of latitude, and DE— dif¬ ference of longitude, which muft be reduced according to the parallel of latitude come to. 7ig. 10. Gunner’s quadrant (fig. 6.), fometimes called gunner's fquare, is that ufed for elevating and pointing cannon, mortars, &c. and confifts of two branches ei¬ ther of brafs or wood, between which is a quadrantal arch divided into 90 degrees, beginning from the (liorter branch, and furnithed wuth a thread and plummet, as reprefented in the figure.—The ufe of the gunner’s quadrant is extremely eafy; for if the longeft branch be placed in the mouth of the piece, and it be elevated till the plummet cut the degree neceffary to hit a propo- fed objeft, the thing is done. Sometimes on one of the furfaces of the long branch are noted the divifion of dia¬ meters and weights of iron bullets, as alfo the bores of pieces. Quadrant of Altitude, is an appendage of the arti¬ ficial globe, confiding of a lamina, or (lip of brafs, the length of a quadrant of one of the great circles of the globe, and graduated. At the end, where the divifion terminates, is a nut rivetted on, and furnifhed with a fcrew, by means whereof the inftrument is fitted on the meridian, and moveable round upon the rivet to all points of the horizon.—-Its ufe is to ferve as a fcaie in meaiuring altitudes, amplitudes, azimuths, See. See A- Ouadr'antal STRONG MY. ' j| OUADRANTAL, in Antiquity, the name of a Qi1:ulra' veiiel in ufe among the Romans for the meafuring of t tu‘ . liquids. It was at nrft called amphora ; and afterwards quadrantal, from its form, which was fquare every way like a die. It capacity was 80 lurae, or pounds of waiter, wmch made 4^ (extaries, tw'o urnae, or eight congii. QUADRAT, a mathematical inftrument, called al'fo a Geometrical Square, and Line of Shadows: it is fre¬ quently an additional member on the face of the com¬ mon quadrant, as alio on thofe of Gunter’s and Sutton’s quadrants. UuaDRat, in Printing, a piece of metal ufed to fill up the void {paces between words, Sec. There are qua¬ drats of different fizes} as m-quadrats, n-quadrats, &c. which are reipedtively of the dimenfions of thefe letters, only lower, that they may not receive the ink. {Quadratic equations, in Algebra, thofe W'herein the unknown quantity is of two dimeniions, or railed to the lecond power. See Algebra. ^HJADRATRIX, in Geometry, a mechanical line, by means whereof we can find right lines equal to the circumference of circles, or other curves, and their fe¬ ver al parts. QUADRATURE, in Geometry, denotes the fqua- ring, or reducing a figure to a iquare. 1 hus, the find¬ ing of a fquare, which {hall contain juft as much fur- face or area as a circle, an ellipiis, a^ triangle, &c. is the quadrature of a circle, ellipfis, &c. The quadra¬ ture, efpecially among the ancient mathematicians, w as a great poftulatum. The quadrature of rectilineal fi¬ gures is eafily found, for it is merely the finding their areas or (iirjaces, 1, e. their (quares } for the fquares of equal areas are eafily found by only extracting the roots of the areas thus found. The quadrature of curvilinear fpaces is of more difficult inveftigation j and in this re- fpect extremely little w7as done by the ancients, except the finding the quadrature of the parabola by Archimedes. In 1657, Sir Paul Neil, Lord Brouncker, and Sir Chrif- topher Wren, geometiically demonftrated the equality of fome curvilinear fpaces to reCtilinear fpaces; and foon after the like was proved both at home and abroad of other curves, and it was afterwards brought under an analytical calculus ; the firft fpecimen of wftiich was given to the public in 1688 by Mercator, in a demon- ftration of Lord Brouncker’s quadrature of the hyper¬ bola, by Dr Wallis’s reduCfion of a fraCtion into an infi¬ nite feries by divifion. Sir Ifaac Newton, however, had before difeovered a method of attaining the quan¬ tity of all quadruple curves analytically by his fluxions before 1668. It is difputed between Sir Chriftopher Wren and Mr Huygens which of them firft; difeovered the quadrature of any determinate cycloidal fpace. Mr Leibnitz afterwards found that of another fpace j and in 1669 Bernoulli difeovered the quadrature of an infinity of cycloidal fpaces both fegments and feftors, &c. See Squaring the Circle. Quadrature, in AJlronomy, that afpeft of the moon when ftie is 90° diftant from the fun ; or when (he is in a middle point of her orbit, between the points of con- junClion and oppofition, namely, in the firft and third quarters. See Astronomy Index. QUADRAT US, Plate CCCCLVm Q UARTEB. - 'llitf-tfrulhG’ QUA [ 5 Quadratus Q^UADRATUS, in Anatorwj^^xv^xciz given to feve- il. ral mufcles on account of their fquare figure. See A- CWtUM NATOMY, Table of the Mufcles. OUADREL, in Building, a kind of artificial ftone, fij called from its being perfectly fquare. The quadrels are made of a chalky earth, &c. and dried in the (hade for two years. Thefe were formerly in great requeft among the- Italian architects. QUADRIGA, v\ Antiquity, a car or chariot drawn by four horfes. On the reverfes of medals, we fre¬ quently fee the emperor or Victory in a quadriga, hold¬ ing the reins of the horfes; whence thele coins are, among the curious, called nurnmi quadrigati, and vtclo- riati. QUADRILATERAL, in Geometry, a figure whofe perimeter confilts of four tides and four angles j whence it is alfo called a quadrang Aar figure. OJJ ADRILLE, a little troop or company of cava¬ liers, pompoully drefled, and mounted for the perform¬ ance of caroufals, jutts, tournaments, runnings at the ring, and other gallant divertifements. Quadrille, a game played by four perfons, -with 40 cards •, which are the remains of a pack after the four tens, nines, and eights are difcarded; thefe are dealt three, and three, and one round four, to the right hand player ; and the trump is made by him that plays with or wdthout calling-,• by naming fpades, clubs, dia¬ monds, or hearts, and the fuit named is trumps. If the perfon who names the trump fliould miftake, and fay fpades inftead of clubs, or it he name two fuits, the firll named is the trump. In this game the order of the cards, according to their natural value, is as follows : of hearts and diamonds, king, queen, knave, ace, deuce, three, four, five, fix, fieven ; in all 10 : of fpades and clubs, king, queen, knave, fieven, fix, five, four, three, deuce ; in all 9. The reafon why the ace of fpades and ace of clubs are not mentioned, is, becaufe they are always trumps in whatever fuit that is played. The ace of fpades being always the firft, and the ace of clubs the third trump, for the cards ranked according to their value when trumps ttand in the fol¬ lowing order. Hearts and diamonds, SPADILL, or the ace of fpades ; MANILL, the feventh of the two red fuits; Basto, the ace of clubs ; PONTO, the ace of hearts and diamonds ; king, queen, knave, deuce, three, four, five, fix ; in all 12. Spades and clubs, SPADILL, the ace of fpades, MANILL, the deuce of fpades and clubs, basto the ace of clubs, king, queen, knave, feven, fix, five, four, three in all \ 1. It is here to be obferved, that the card which is manill and the fecond trump, is always the lowed; in its fuit when not trumps ; and that the ace of hearts or dia¬ monds, which when trump is above the king, is below the knave when not trump. There are three matadors 5 fpadill, manill, and ha¬ llo •, the privilege of which is, that when the player has no other trumps but them, and trumps are led, he is not obliged to play them, but may play what card he thinks proper, provided, however, that the trump led is of an inferior rank 5 but if fpadill fliould be led, 81 ] QUA he that has manill or bado only is obliged to play it 5 Quadrille, it is the fame of manill bado, with refpefl to the fupe- ^ v rior matadore always forcing the inferior. Though there are properly but three matadores, neverthelefs, ail thofe trumps which follow7 the three fird without interruption, are likewife called matadores} but the three fird only enjoy the privilege above mentioned. Each perfon is to play as he judges mod convenient for his own game. He is not to encourage his friend to play •, but each perfon ought to know what to do when it is his turn to play. The dakes confid of feven equal mils or contrats, as they are fometimes called, coruprifing the ten counters and fidies, wdiich are given to each player. A mil is equal to ten fidi, and each fdi to ten counters: the value of the fifli is according to the players agreement, as alio the number of tours, which are generally fixed at ten, and marked by turning the corners of a card. If the cards ihould happen not to be deal right, or that there ihouid be two cards of the fame fort, as two deuces of fpades, for example, there mud be a new deal) provided it is difeovered before the cards are all played. The cards mud likewife be dealt over again in cafe a card is turned in dealing, as it mighti be of prejudice to him w7ho dioukl have it ; and of courfe if there diould be feveral cards turned. There is no penalty for dealing wrong, he who does fa mud only deal again. When each player has got his ten cards, he that is on the right hand of the dealer, after examining his game, and finding his hand fit to play, aiks if they play ; or if he has not a good hand, he pafles, and fo the fecond, third, and fourth. All the four may pafs; but he that has fpadill, after having diowm or named it, is obliged to play by calling a king. Whether the deal is played in this manner, or that one of the players has afked leave, nobody choofing to play without calling, the elded hand mud begin the play, fird na¬ ming the fuit, and the king which he calls •, he who w ins the trick plays anpther card, and fo of the red till the game is finhhed. The tricks then are counted } and if the ombre, that is, he who dands the game, has to¬ gether with him who is the king called, fix tricks, they have w'on and are paid the game, the confolafion, and the matadores, if they have them, and divide what is up¬ on the game, and the beads if there are any. But if they make only five tricks, it is a remife, and they are beaded, what goes upon the game, paying to the other players the confolation and the matadores. If the tricks are equally divided betwdxt them, they are likewife bead¬ ed } and if they make only four tricks between them, it is a remife } if they make lefs they lofe codill (a), and in that cafe they pay to their adverfaries what they diould have received if they had won •, that is, the game, the confolation, and the matadores, if they have them, and are beaded what is upon the game : they who win codill, divide the dakes. The bead and every thing elfe that is paid, is paid equally betwixt the two lofers ; one half by him that calls, and the other half by him that is called, as well in cale of codill as a re¬ mife ; (a) Coddl is when thofe who defend the pool make more tricks than they who dand the game 3 which is call-, ed winning the codill. QUA ,<^nadnile. mlfe • unleis the ombre does not make three tricks, in ~~v~ which cafe he that is called is not only exempted from paying half the beaft, but alfo the game, the conlblation, and the matadores if there are any, which the ombre in that cafe pays alone; and as well in cafe of a codill as a remiie. Ihis is done in order to oblige players not to play games that are unreafonable. There is ne- verthelefs, one cafe in which if the ombre makes only one trick, he is not beafted alone, and that is, when not having a good hand he paffes, and all the other players have pafled likewife; he having Ipadill is obliged to play. Here it would be unjuit to oblige him to make three or four tricks ; in this cafe, therefore, he that is called pays one half of the lofings. For which reafon he that has fpadill with a bad hand, Ihould pafs, that if he is afterwards obliged to play by calling a king (which is called forced fpadillf he may not be beafted alone. He that has once paffed cannot be admitted to play; and he that has aflced leave cannot refufe to play, unlefs any one fliould offer to play without call- ing. . He that has four kings, may call a queen to one of his kings, except that which is trump. He that wants one or more kings, may call one of thofe kings j but in that cafe, he muft make fix tricks alone, and confe- quently he wins or lofes alone. The king of that fuit in which he plays cannot be called. No one ftieuld play out of his turn, although he is not beafted for fo doing. If he who is not the eldeft hand has the king called, and plays fpadill, manill, or bafto, or even the king called in order to fhow that he is the friend, ha¬ ving other kings that he fears the ombre fhould trump, he is not to be allowed to go for the vole; he is even beafted, if ft appears to be done with that intent. It is not permitted to (how a hand though codill may al¬ ready be won ; that it may be feen whether the ombre is beafted alone. If the ombre or his friend ftiows their cards before they have made fix tricks, thinking that they have made them, and there appears a poffi- bility of preventing their making them, the other players can oblige them to play their cards as they think proper. A player need only name his fuit when he plays, without calling a king. He who plays without calling muft make fix tricks alone to wrin •, for all the other players are united againft him, and they are to do what they can to prevent his winning. He who plays with¬ out calling, is admitted to play in preference to him who w'ould play with calling ; however, if he that has aflced leave will play without calling, he has the pre¬ ference of the other who would force him. Thefe are the two methods of play without calling that are called forced. .As he who plays without calling does not divide the winnings with any perfon, he confequently, when he lofes, pays all by himfelf: if he lofes by remife he is beafted, and pays each of the other players the confo- lation, the fans appeller (which is commonly, but im- properly, called the jans prendre}, and the matadores if there are any j if he lofes codill he is likewife beaft- ed and pays to each player w'hat he w^ould have re¬ ceived from each if he had won. They who win co¬ dill divide what there is; and if there are any coun¬ ters remaining^ they belong to him of the three who ihall have fpadill or the higheft trump the next deal. It 4 t 582 ] Qua is the fame with regard to him who calls one of his own kings, he wins alone or lofes alone as in the other cafe, except the fans appeller, which he does not pay if he lofes, or receive if he wins, although he plays alone. If he plays fans appeller, though he may have a fure game, he is obliged to name his fuit j which if he ne- glecfts to do, and ftiows his cards, and fays “ I play fans appeller j” in that cafe either of the other players can oblige him to play in what fuit he pleafes, although he fhould not have one trump in that fuit. He who has afked leave is not permitted to play fans appeller, unlefs he is forced 5 in which cafe, as was faid before, he has the preference of the other that forces him. A player is not obliged to trump when he has none of the fuit led, nor play a higher card in that fuit if he has it, being at his option although he is the laft player, and the trick fhould belong to the ombre j but he is obliged to play in the fuit led if he can, other- wife he renounces. If he feparates a card from his game and fliows it, he is obliged to play it, if by not doing it the game may be prejudiced, or if he can give any intelligence to his friend} but efpecially if it Ihould be a matadore.—He that plays fans appeller, or by calling himfelf, is not fubjett to this law. He may turn the tricks made by the other players, and count what has been played as often as it is his turn to play, but not otherwife. If inftead of turning a player’s tricks, he turns and fee his game, or fhow's it to the other players, he is beafted, together with him whofe cards he turned j and each of them muft pay one half of the beaft. If any one renounces, he is beafted as often as he has renounced and it is dete&ed ; but a renounce is not made till the trick is turned. If the renounce is difco- vered before the deal is finifhed, and has been detrimen¬ tal to the game, the cards muft be taken up again, and the game replayed from that trick where the renounce was made 5 but if the cards are all played, the beaft is ftill made, and the cards muft not be replayed ; except there fhould be feveral renounces in the fame deal : then they are to be played again, unlefs the cards fhould be mixed. . If feveral beafts are made in the fame deal, they all go together, unlefs it is otherwife agreed at the beginning of the party •, and when there are feveral beafts, the greateft always goes firft. A great advantage accrues from being eldeft hand at quadrille, which often renders it very difagreeable to the reft of the players, being obliged to pafs with a good hand unlefs they choofe to play alone ; and when it hap¬ pens that the eldeft hand having afked leave, the fecond player has three matadores, feveral trumps in back, and all fmall cards, he cannot then even play alone; and having no chance of being called, he muft pafs with this good hand. On account of which, this method has been thought expedient to remedy this defeft of the game ; each player having an opportunity of availing himfelf of the goodnefs of his game, by adding to the ufual method of playing the game that of the media- teur, and the favourite fuit. The firft thing to be obferved is that of drawing for places, which is done in this manner: One of the players takes four cards; a king, a queen, a knave, and an ace ; each player draw's one of thefe cards; and commonly he w'ho comes in laft, draw's firft. The per¬ fon Quadrille. > QUA Quadrille, fon who draws the king fits where he pleafes, the queen ^ at r^^lt hand, the knave next the queen, and the « - ■ ace on the left of the king. The king draws the fa¬ vourite fuit. I he number of cards and perfons is the fame at this game as the other, and is played in the fame manner. I he favourite fuit is determined by drawing a card out of the pack, and is of the fame fuit, during the whole party, of the card fo drawn. A king is the mediateur, which is demanded of the others by one of the players, who has a hand he ex¬ perts to make five tricks of; and through the affiftance of this king he can play alone and make fix tricks. In return for the king received, he gives what card he thinks proper with a filh ; but muft give two filh if it is in the favourite fuit. He who alks by calling in the favourite fuit, has the preference to him who alks by calling in another; he who alks with the mediateur, has the preference to him who alks by calling in the favou¬ rite fuit, and by playing alone is obliged to make fix tricks t© wdn. He who alks with the mediateur in the favourite fuit, has the preference to him who alks with the mediateur in any other fuit, and is obliged to play alone, and to make fix tricks. If fans prendre is played in any other fuit than the fa¬ vourite, he who plays it has the preference to him who alks only, or with the mediateur, or even he who plays in the favourite fuit with the mediateur; and the fans prendre in the favourite fuit has the preference to all other players whatever. The only difference between this method of playing the game and the other is, that when one of the players demands the mediateur he is obliged to play alone, and to make fix tricks, as if he played fans prendre. In this cafe he fhould judge from the ftrength of his hand, whe¬ ther the aid of the king will enable him to play alone or not. With the mediateur and without the favourite fuit it is played in this manner. The game is marked and played the fame as in common, except that a filh extra¬ ordinary is given to him who plays the mediateur, and to him who plays fans prendre ; that is, he who wins the mediateur receives 13 counters from each; and if be lofes by remife he pays 12 to each j and 13 if by codill. The winner of fans prendre receives 17 counters from each ; and if by remife he lofes, he pays 16 to each, and 17 if by codill. The vole with the mediateur receives one filli only, as at common quadrille. The beafts are alfo the fame as the common game. The laft game is generally played double, and is called paulans; but for thofe who choofe to play a higher game, they may play the double colour, wdiich is called the Turk, and is double of the favourite fuit. There is alfo a higher game than this, called the anode, which is paying whatever is agreed to him who happens to hold the two aces in his hand. We have omitted many things refpefting the mode of marking the game, and playing the vole, becaufe thefe are different in different cafes, and are to be learn¬ ed only by praftice. I'he game itfelf is a very infe- rior one ; but he rvho wdlhes to know more of it, may confult Hoyle’s games improved by James Beaufort, Efq. from which we have, with very little alteration, taken this article. QUADRIPARTITION, the dividing by four, or QUA into four equal parts. Hence comes the term quadri- Quadru- partite, the fourth part, or fomething divided into four. Pe(*s QJJADRUPEDS, in Zoo/o^y ; thofe animals which nJail have four limbs or legs proceeding from the trunk of , * their body. See Mammalia. QUADRUPLE, four-fold, or fomething taken four times, or multiplied by four, on which account it is the converfe of quadripartition. QUriESTOR, fee Questor. QUAGGA, or Quacha. See Equus, Mammalia Index. QUAIL. See Tetrao, Ornithology Index. Quails are to be taken by means of the call during their whole wmoing time, which lafts from April to Auguft. The proper times for ufing the call are at fuhrifing, at nine o’clock in the morning, at three in the afternoon, and at funfet j for thefe are the natural times of the quail’s calling. The notes of the cock and hen quail are very different; and the fportfman who expedis to fucceed in the taking them muff be expert in both : for when the cock calls, the anfw-er is to be made in the hen’s note ; and when the hen calls, the anfw-er is to be made in the cock’s. By this means they will come up to the perfon, fo that he may, with great eafe, throw the net over them and take them. If a cock-quail be fingle, on hearing the hen’s note he will immediately come 5 but if he have a hen already with him, he will not forfake her. Sometimes, though only one quail an- fwers to the call, there will three or four come up 5 and then it is beft to have patience, and not run to take up the firft, but flay till they are all entangled, as they will loon be. The quail is a neat cleanly bird, and will not run much into dirty or wet places : in dew^y mornings, they will often fly inftead of running to the call ; and in this cafe, it is belt to let them go over the net, if it fo hap¬ pens that they fly higher than its top 5 and the fportf. man then changing fides, and calling again, the bird will come back, and then wall probably be taken in the net. The calls are to be made of a fmall leather purfe, about two fingers wide, and four fingers long, and made in the Ihape of a pear ; this is to be fluffed half¬ full of horfe-hair, and at the end of it is to be placed a fmall whiffle, made of the bone of a rabbit’s leg, or fome other Rich bone : this is to be about two inches long, and the end formed like a flageolet, with a little foft wax. This is to be the end faffened into the purfe ; the other is to be doled up with the fame w’ax, only that a hole is to be opened with a pin, to make it give a diftinct and clear found. To make this found, it is to be held full in the palm of the hand, with one of the fingers placed over the top of the wax \ then the purfe is to be preffed, and the finger is to fliake over the middle of it, to modulate the found it gives into a fort of fliake. This is the moft ufeful call; for it imitates the note of the hen quail, and feldom fails to bring a cock to the net if there be one near the place. The call that imitates the note of the cock, and is ufed to bring the hen to him, is to be about four inches long, and above an inch thick *, it is to be made of a piece of wire turned round and curled, and covered with leather ; and one end of it muft be clofed up with a piece of flat wood, about the middle of wdiich there muft r 583 i Quail, Quakers. * See Month, Rev. Sept I793»art S' QUA [ 58+ ] , O' U A . . mu ft be a fmall thread or ftrap of leather, and at the which is a praife to them that do well; which is a pro- Quakers, other end is to be placed the fame fort of pipe, made teftion to them that do well, and not the evil 5 and <-—v— of bone, as is ufed in the other call. The noife is made fuch foldiers as are put in place no falfe accufers muft by opening and doling the fpiral, and gives the fame be, no violence muft do, but be content with their found that the cock does when he gives the hen a fignal wages: and that magiftrate bears not the fword in vain, that he is near her. fr°m under the occafion of that fword do I feek to bring QUAKERS, a religious fociety, which took its rife people : my weapons are not carnal but fpiritual, and in England about the middle of the 17th century, and tmj kingdom is not of this world; therefore with carnal rapidly found its way into other countries in Europe, weapon I do not fight, but am from thofe things dead, and into the Englilh fettlements in North America.— from him who is not of this world, called of the world The members of this fociety, we believe, called them- by the name of G- F: and this I am ready to feal with felves at firft feelers, from their feeling the truth ; but my blood 5 this I am moved tp give forth for the truth’s after the fociety was formed, they affumed the appella- fake, who a witnefs Hands againft all unnghteoufnefs, tion of friends. The name of 'quakers was given to and all ungodlinefs, who a fufferer is for the righteous them by their enemies 5 and though an epithet of re- feed’s fake, waiting for the redemption of it, who a proach, feems to be ftamped upon them indelibly. Their crown that is mortal feeks not, for that fadeth away j founder is generallv believed to have been George Fox, but in the light dwells which comprehends that crown, an illiterate fhoemaker (fee George Fox), but this opi- which light is the condemnation of all luch, in which nion has been lately controverted. An ingenious wri- light I witnefs the crown that is immortal, which fades ter * having found, or fancied, a fimilaritv of fentiments not away fiom him who to all your fouls is a miend, among the ancient Druids and modern Quakers, feems for eftablifhing of righteoufnefs, and clearing the land to think that Fox muft have been nothing more than a of evil doers, and a witnefs againft all the wicked m- tool employed by certain deifts to pave the way for their ventions of man, and muiderer s plots, which anfwer fyftem of natural religion, by allegorizing the diflin- fhall be with the light in all your confidences, which guiftiing articles of the Chriftian faith. makes no covenant with death •, to which light in you It muft be confeffed, for experience will not allow7 it sll I fpeak, and am clear, G. F. who a new name hath, to be denied, that extremes in religion are very apt to which the world know7s not.” (a). beget each other ; and if the deifts alluded to reafoned The Quakers, however, did not long entruft the de- from this fad, they could not have pitched upon a tool fence of their principles to fuch fenfelefs enthufiafts as fitter for their purpofe than George Fox. From his George Fox: They were joined by a number of learned, works ftill extant, he appears to have been one of the ingenious, and pious men, who new7 modelled . tueir moft extravagant and abfurd enthufiafts that ever lived, creed 5 and though they did not bring it to what is ge- and to have fancied himfelf, in his apoftolic charafter, nerally deemed the Chriftian ftandard, they fo reformed fomething infinitelv fuperior to man. In a book called it as that its tenets do not fhock common feme, noi the News coming out of the North, (p. 15.) he fays of him- duties preferibed fcandalize a man of piety. The chief felf, “ I am the Door that ever was, the fame Cbrift of thefe reformers were George Keith, the celebrated yefterday, to-dav, and for ever And in the intro- Penn, and our countryman Barclay. Keith was indeed duiiftion to his Battle door for Teachers and Profe/fors, excommunicated for the liberties which he took with he fays, “ All languages are to me no more than dull, the great apoftle ", but we have not a doubt out his wri- w;ho was before languages were.” But one of the moft tings contributed to the moderation oi Penn, and to extraordinary and'blafphemous things that he ever the elegant and mafterly apology of Barclay. From wrote, is an anfwer to the Proteaor, w7ho had required that apology we fekaed the fummary of their opinions him to promife not to difturb his government as then which was given in the former edition of this work; eftabliftied. It is as follows: but they have lately publifhed fuch a fummary them- “ I who am of the world called G : F : doth deny felves, of which the reader will be pleafed with the fol- the carrying or drawing any carnal fword againft any, lowing abftraft : or againft thee O: C: or any man, in the prefence of I hey tell us, that about the beginning of the the Lord I declare it, God is my witnefs, by whom I 17th century, a number of men, diffatisfied with all vim moved to give tb s forth for the truthjs fake, from the modes of religious worfhip then known in the him whom the world calls G: Fox, who is the fon of world, withdrew from the communion of every vi- God, who is fent to ftand a witnefs againft all violence fible church to feek the Lord in retirement. Among and againft the works of darknefs, and to turn the peo- thefe was their honourable elder George ^ Fox, whp pie from darknefs to light, and to bring them from the being quickened by the immediate touches of di- occafion of the war and from the occafion of the magi- vine love, could not fatisfy his apprehenfions of duty ftrates fword, which is a terror to the evil doer, which to God without directing tne people where to find a£is contrary to the light of the Lord Jefus Chri/l; the like conlolation and inftrudtion. In the courfe of (a) We have tranCcribed this letter from the theological works of Mr Leflie, where it is preferved in its original form. The Quakers, after the death of their apoftle, expunged from their edition of it the words which we have printed in Italics ; afhamed, as we hope, of the hlafphemy imputed to them : but that Mr Leflie’s copy is authen¬ tic, is thus attefted bv two of the friends, who faw Fox deliver it to the proteftor’s mellenger : “ We are witneftes of this teftimony, whofe names in the flelh are, 1 h°- Adam, ■2 Rob. Craven, * QUA [ 585 Quakers, his travels, he met with many feeking perfons in cir- —v cumftances fimilar to his own, and thefe readily recei¬ ved his teftimony. They then give us a fliort account of their fufferings and different fettlements 5 and with a degree of candour w’hich does them infinite credit, they vindicate Charles II. from the character of a perfe- cutor ; acknowledging, that though they fuffered much during his reign, he gave as little countenance as he could to the feverities of the legiflature. They even tell us, that he exerted his influence to refcue their friends from the unprovoked and cruel perfecutions of the New England fanatics ; and they fpeak with be¬ coming gratitude of the different a£!s paffed in their fa¬ vour during the reigns of William and Mary, and George I. They then proceed to give us the following account of their doftrine : “ We agree with other profeifors of the Chriftian name, in the belief in one eternal God, the Creator and Preferver of the univerfe ; and in Jefus Chrill his Son, the Mefliah, and Mediator of the new covenant (Heb. xii. 24). “ When wre fpeak of the gracious difplay of the love of God to mankind, in the miraculous conception, birth, life, miracles, death, refurreftion, and afcenfion of our Saviour, we prefer the ufe of fuch terms as we find in Scripture •, and, contented with that knowledge which divine wifdom hath feen meet to reveal, we attempt not to explain thofe myfteries which remain under the veil j neverthelefs, we acknowledge and aflert the divinity of Chrift, who is the wifdom and power of God unto falva- tion (T Cor. i. 24). “ To Chrift alone we give the title of the Word of God (John i. 1.) and not to the Scriptures 5 although W7e highly efteem thefe facred writings, in fubordination to the Spirit (2 Pet. i. 21.), from which they wTere gi¬ ven forth 5 and we hold, with the apoftle Paul, that they are able to make wife unto falvation, through faith which is in Chrift Jefus (2 Tim. iii. 15.). “ We reverence thofe moft excellent precepts which are recorded in Scripture to have been delivered by our great Lord, and we firmly believe that they are prafti- cable, and binding on every Chriftian ; and that in the life to come every man will be rewarded according to his works (Mat. xvi. 27.). And farther, it is our be¬ lief, that, in order to enable mankind to put in practice thefe facred precepts, many of which are contradiftory to the unregenerate will of man (John i. 9.), every man coming into the world is endued with a meafure of the light, grace, or good Spirit of Chrift ; by which, as it is attended to, he is enabled to diftinguiih good from evil, and to correft the diforderly paffions and corrupt propenfities of his nature,which mere reafon is alto¬ gether infufficient to overcome. For all that belongs to man is fallible, within the reach of temptation 5 but this divine grace, which comes by Him who hath over¬ come the world (John xvi. 33.) is, to thofe who hum¬ bly and fincerely feek it, an all-futficient and prefent help in time of need. By this the fnares of the enemy are detefted, his allurements avoided, and deliverance is experienced through faith in its effectual opera- jion; whereby the foul is tranflated out of the king¬ dom of darknefs, and from under the power of Satan, into the marvellous light and kingdom of the Son of God. “ Being thus perfuaded that man, v.ithout the Spirit Vox, XVIL Part II. ] QUA of Chrift inwardly revealed, can do nothing to the glo- Quakers, ry of God, or to effedt his own falvation ; we think this '-■"“'“v"" "- influence ei’pecially neceffary to the performance of the higheft adt of which the human mind is capable, even the worfhip of the Father of lights and of fpirits, in fpirit and in truth; therefore we confider as obftruc- tions to pure w'orfliip, all forms which divert the at¬ tention of the mind from the fecrct influence of this undfion from the Holy One (1 John ii. 20, 27.). Yet, although true worfhip is not confined to time and place, we think it incumbent on Chriftians to meet often to¬ gether (Heb. x. 25.) in teftimony of their dependence on the heavenly Father, and for a renewal of their fpi- ritual ftrength : neverthelefs, in the performance of wor¬ fhip, we dare not depend, for our acceptance with Him, on a formal repetition of the words and experiences of others 5 but we believe it to be our duty to ceafe from the adlivity of the imagination, and to wait in filence to have a true fight of our condition beftowed upon us : believing even a Angle figb (Rom. viii. 26.) arifing from fuch a fenfe of our infirmities, and of the need we have of divine help, to be more acceptable to God, than any performances, however fpecious, which originate in the will of man. “ From what has been laid refpedfing worfhip, it fol¬ lows, that the miniftry we approve muft have its ori¬ gin from the fame fource : for that which is needful for a man’s own diredlion, and for his acceptance with God (Jer. xxiii. 30, to 32.), muft be eminently fo to enable him to be helpful to others. Accordingly, wre believe the renewed afliftance of the light and powrer of Chrift to be indifpenfably neceffary for all true miniftry; and that this holy influence is not at our command, or to be procured by ftudy, but is the free gift of God to his chofen and devoted fervants.—From hence arifes our teftimony againft preaching for hire, and in contradic¬ tion to Chrift’s pofitive command, “ Freely ye have re¬ ceived, freely give” (Mat. x. 8.) ; and hence our con- fcientious refufal to fupport fuch miniftry by tithes or other means. “ As wre dare not encourage any miniftry but that w’hich we believe to fpring from the influence of the Holy Spirit, fo neither dare we attempt to reftrain this influence to perfons of any condition in life, or to the male fex alone j but, as male and female are one in Chrift, we allow fuch of the female fex as we believe to be endued with a right qualification for the mini¬ ftry, to exercife their gifts for the general edification of the church : and this liberty we efteem to be a pecu¬ liar mark of the gofpel difpenfation, as foretold by the prophet Joel (Joel ii. 28, 29.), and noticed by the apof¬ tle Peter ("Afts ii. 16, 17.). “ There are twro ceremonies in ufe amongft moft pro- feffors of the Chriftian name ; Water-baptifm, and what is termed the Lord’s Supper. The firft of thefe is gene¬ rally efteemed the effential means of iuitiation into the church of Chrift 5 and the latter of maintaining commu¬ nion with him. But as w’e have been convinced, that nothing ihort of his redeeming pow’er, inwardly reveal¬ ed, can fet the foul free from the thraldom of fin, by this powrer alone we believe falvation to be effected. We hold that as there is one Lord and one faith (Eph. iv. 5.), fo his baptifm is one in nature and operation ; that nothing thort of it can make us living members of his myftical body ; and that the baptifm with water, admi- 4 niftered QUA Quakers, niftered by Ins fore-runner John, belonged, as the latter —r-— confefled, to an inferior and decreahng difpenfation (John iii. 30.). “ With refpeft to the other rite, rve believe that communion between Chrill and his church is not main- taiiied by that nor any other external performance, but only by a real participation of his divine nature (2 Pet. i. 4.) through faith j that this is the fupper alluded to in the Revelation (Rev. iii. 20.), “ Behold I Rand at the door and knock, if any man hear my voice, and open the door, I will come in to him, and will fup with him, and he with me and that where the lubRance is attained, it is unneceffary to attend to the fliadow, which doth not confer grace, and concerning which opinions fo different, and animofities fo violent, have arifen. “ Now, as we thus believe that the grace of God, which comes by Jefus Chrifl, is alone fufficient for fal- vation, we can neither admit that it is conferred on a few only, whilft others are lelt without it; nor, thus, af- ferting its univerfality, can we limit its operation to a partial cleanfing of the loul from fin, even in this life. We entertain worthier notions both of the power and goodnefs of our heavenly Father, and believe that he deth vouchfafe to affift the obedient to experience a to¬ tal furrender of the natural will to the guidance of his pure unerring Spirit; through -whole renewed affiffance they are enabled to bring forth fruits unto holinefs, and to Rand perfect in their prefent rank (Mat. v. 48.; Eph. iv. 13. ; Col. iv. 1 2.). “ There are not many of our tenets more generally known than our teftimony againR oaths and againR war. With refpeft to the former of thefe, we abide literally by ChriR’s pofitive injunction, delivered in his fermon on the mount, “ Swear not at all” (Mat. v. * See 34-) *• From the fame facied collection of the moR excellent precepts cf moial and religious duty, from the example of our Lord himfelf (Mat. ch. v. 39, 44, &c, eh. xxvi. 52, 53.; Luke xxii. 51 ; John xviii. 11.), and from the correfpondent convictions of his Spirit in our hearts, we are confirmed in the belief that wars and fightings are, in their origin and effcCts, utterly repug¬ nant to the Gofpel, which Rill breathes peace and good¬ will to men. We alfo are clearly of the judgment, that if the benevolence of the Gofpel were generally preva¬ lent in the minds of men, it would effectually prevent them from oppreffing, much mere from enflaving, their brethren, (of whatever colour or complexion), for whom, as for themfelves, Chrifl died ; and would even influence their conduCt in their treatment of the brute creation, which would no longer groan the viClims of their ava¬ rice, and of their falfe ideas of pleafuie. “ Some of our tenets have in former times, as hath been fliown, fubjeCted our friends to much fuffering from government, though to the falutary purpofes of govern¬ ment our principles are a fecurity. They inculcate fubmiffion to the laws in all cafes wherein confcience is not violated. But we hold, that as ChriR’s kingdom is not of this world, it is not the bufinefs of the civil magiflrate to interfere in matters of religion; but to QUA maintain tire external peace and good order of the com- Quakers, munity. We therefore think perfecution, even in the—' fmalleft degree, unwarrantable. We arc careful in re¬ quiring our members not to be concerned in illicit trade, nor in any manner to defraud the revenue. “ It is well known that the fociety, from its firfl ap¬ pearance, has dilufed thofe names of the months and days which, having been given in honour of the heroes or falfe gods of the heathens, originated in their flat¬ tery or luperflition ; and the cuflom of fpeaking to a Angle perfon in the plural number (b), as having ari¬ fen alfo from motives of adulation. Compliments, fu- peifluity of apparel and furniture, outward Rrows of re¬ joicing and mourning, and obfervation of days and times, we efieem to be incompatible with the fimplicity and fincerity of a Chriflian life; and public diverfions, gaming, and other vain amufements of the world, we cannot but condemn. They are a wafle of that time which is given us for nobler purpofes, and divert the attention of the mind from the lober duties of life, and from the reproofs of inflruefion, by which we are guided to an everlafling inheritance. “ To conclude, although we have exhibited the feve- ral tenets which diftinguifh our religious fociety, as objedfs of our belief, yet we are fenfible that a true and living faith is not produced in the mind of man by his own effort; but is the free gift of God (Eph. ii. 8.) in Chrifl Jefus, nouriflied and increafed by the progref- five operation of his fpirit in our hearts, and our pro¬ portionate obedience (John vii. 17.). Therefore, al¬ though, for the prefervation of the teflimonies given us to bear, and for the peace and good order of the fo¬ ciety, we deem it neceffary that thofe who are admit¬ ted into memberfliip with us, fliould be previoufly con¬ vinced of thofe dodlrines which wre efleem effential; yet we require no formal fubfeription to any articles, either as the condition of memberfliip, or to qualify for the fervice of the church. We prefer the judging of men by their fruits, in a dependence on the aid of Him w-ho, by his prophet, hath promifed to be “ a fpirit of judgment to him that fitteth in judgment” (Ifaiah xxviii. 6.). Without this, there is a danger of re¬ ceiving numbers into outward communion, without any addition to that fpiritual fheepfold, whereof our bleffed Lord declared himfelf to be both the door and the fhepherd (John x. 7, 11.), that is, fr.ch as know7 his voice, and follow him in the paths of obe¬ dience.” Such are the do&rines of this people as wz find them flated in a fmall pamphlet lately prefented by themfelves to the public ; and in the fame tratfl they give the fol¬ lowing account of their difeipline. “ In the prablice of difciplinc, we think it indifpen- fable that the order recommended by Chrift himfelf be invariably obferved : (Matth. xviii. 13. to 17.). ‘ If thy brother fliall trefpafs againft thee, go and tell him his fault between thee and him alone : if he fliall hear thee, thou haft gained thy brother ; but if he will not hear thee, then take writh thee one or two more, that in the mouth of twro or three witneffes every w*ord may be C 586 ] (b) Speaking of this cuflom, Fox fays: “ When the Lord fent me into the w7orld, he forbade me to put off my hat to any ) and I was required to t/iee and thou all men and women.” Journal, p. 24. Q, U A Quake is. be'eflablifliecl j and if he iliall negle£l to hear them, tell v it unto the church.’ “ To efleet the falutary purpofes of difcipline, meet¬ ings were appointed, at an early period of the fociety, which, from the times of their being held, were called quarterly meetings. It was afterwards found expedient to divide the diftriets of thole meetings, and to meet more often j whence a role monthly meetings, fubordinate to thofe held quarterly. At length, in 1669, a yearly meeting was eftabhlhed, to fuperintend, athit, and pro¬ vide, rules for the whole 5 previous to which, general meetings had been occafionally held. “ A monthly meeting is uiually compofed of feveral particular congregations, fituated within a convenient dittance of each other. Its bufinefs is to provide for the fubflilence of their poor, and for the education of their offspring : to judge of the fincerity and fitnefs of perfons appearing to be convinced of the religious prin¬ ciples of the fociety, and defiling to be admitted into memberihip ; to excite due attention to the difeharge of religious and moral duty ; and to deal with difor- derly members. Monthly meetings alfo grant to fuch of their members as remove into other monthly meetings, certificates of their memberfliip and condufl 3 without which they cannot gain memberfliip in fuch meetings. Each monthly meeting is required to appoint certain perfons under the name of overfeers, who are to take care that the rules of our difcipline be put in practice 3 and when any cafe of complaint or diiorderly conduft comes to their knowledge, to fee that private admoni¬ tion, agreeable to the gofpel rule before mentioned, be given previoufly to its being laid before the monthly meeting. “ When a cafe is introduced, it is ufual for a fmall committee to be appointed to vifit the offender, to en¬ deavour to convince him of his error, and to induce him to forfake and condemn it. If they fucceed, the perfon is by minute declared to have made fatisfadlion for the offence 3 if not, he is difowned as a member of the fo¬ ciety. “ In difputes between individuals, it has long been the decided judgment of the fociety that its members fliould ■not fue each other at law. It therefore enjoins all to end their differences by fpeedy and impartial arbitration, agreeable to rules laid down. If any refufe to adopt this mode, or, having adopted it, to fubmit to the award, it is the direftion of the yearly meeting that fuch be dif¬ owned. “ To monthly meetings alfo belongs the allowing of marriages 3 for our fociety hath always fcrupled to ac¬ knowledge the excluflve authority of the priefts in the folemnization of marriage. Thofe who intend to mar¬ ry, appear together and propofe their intention to the monthly meeting 3 and if not attended by their parents or guardians, produce a written certificate of their con- fent, fignecNn the prefence of witneffes. The meeting then appoints a committee to inquire whether they are clear of other engagements refpefting marriage 3 and if at a fubfequent meeting, to which the parties alfo QUA come and declare the continuance of their intention, no Quakers* objections are reported, they have the meeting’s con- v J fent to folemnize their intended marriage. This is done in a public meeting for worlhip 3 towards the dole whereof the parties itand up, and folemnly take each other for hulband and wife. A certificate of the proceedings is then publicly read, and figned by the parties, and afterwards by the relations and others as witnefles. Of fuch certificates the monthly meeting keeps a record 3 as alfo of the births and burials of its members. A certificate of the date, of the name of the infant, and of its parents, figned by thofe prefent at the birth, is the fubjeCl of one of thefe lart-men- tioned records 3 and an order for the interment, coun- terfigned by the grave-maker, of the other. The naming of children is without ceremony. Burials are alfo conduced in a fimple manner. The body, follow¬ ed by the relations and friends, is fometimes, previoufiy to interment, carried to a meeting 3 and at the grave a paufe is generally made 3 on both which occafions it frequently falls out that one or more friends prefent have fomewhat to exprefs for the edification of thofe who at¬ tend 3 but no religious rile is confidered as an effential part of burial. “ Several monthly meetings compofe a quarterly meet¬ ing. At the quarterly meeting are produced written anfwers from the monthly meetings, to certain queries refpeCling the conduft of their members, and the meet¬ ing’s care over them. The accounts thus received are digefte.d into one, which is fent, alfo in the form of an¬ fwers to queries, by reprefentatives, to the yearly meet¬ ing.—Appeals from the judgment of monthly meetings are brought to the quarterly meetings ; whole bufinefs alio it is to afliit in any difficult cafe, or where remiffnefs appears in the care of the monthly-meetings over the in¬ dividuals who compofe them. “ The yearly meeting has the general fuperintendance of the fociety in the country in which it is eftabliffied (0)3 and therefore, as the accounts which it receives dif- cover the Hate of inferior meetings, as particular exi¬ gencies require, or as the meeting is impreffed with a fenfe of duty, it gives forth its advice, makes fuch regulations as appear to be requifite, or excites to the obfervance of thofe already made 3 and fometimes appoints committees to vifit thofe quarterly meetings which appear to be in need of immediate help. Ap¬ peals from the judgment of quarterly meetings 1 re here finally determined 3 and a brotherly correfpon- dence, by epiilles, is maintained with other yearly meet- ings. “ In this place it is proper to add, that as we believe women may be rightly called to the work of the mini- ftry, we alfo think, that to them belongs a {bare in the lupport of our Chriftian difcipline 3 and that fome parts of it, wherein their own fex is concerned, devolve on them with peculiar propriety. Accordingly they have monthly, quarterly, and yearly meetings of their own fex, held at the fame time and in the fame place with thofe of the men 3 but feparately, and without the power 4 E 2 of L 537 1 (c) There are feven yearly meetings, viz. ill, London, to which come reprefentatives from Ireland 3 2d, New- England; 3d, New-York 3 4th, Pennfylvania and New-Jerfey ; 5th, Maryland 3 6th, Virginia ; 7th, the Carolinas and Georgia.” QUA [ 588 ] QUA Quakers, of making rules : and it may be remarked, that during the perfecutions, which in the laft: century occafioned the imprifonment of fo many of the men, the care of the poor often fell on the women, and was by them fatisfac- torily adminiftered. “ In order that thofe who are in the fituation of mi- niders may have the tender fympathy and counfel of thofe of either fex, wrho, by their experience in the work of religion, are qualified for that fervice the monthly meetings are advifed to feleft fuch, under the denomination of elders. Thefe, and minifters approved by their monthly meetings (d), have meetings peculiar to themfelves, called meetings of minifters and elders ; in wThich they have an opportunity of exciting each other to a difcharge of their feveral duties, and of ex¬ tending advice to thofe wdro may appear weak, without any needlefs expofure. Thefe meetings are generally held in the compafs of each monthly, quarterly, and yearly meeting. They are condufted by rules pre- fcribed by the yearly meeting, and have no authority to make any alteration or addition to them. The members of them unite with their brethren in the meetings for dif- cipline, and are equally accountable to the latter for their conduct. “ It is to a meeting of this kind held in London, called the fecond-day morning-meeting, that the revifal of manufcripts concerning our principles, previoufty to publication, is intrufted by the yearly meeting held in London } and alfo the granting, in the intervals of the yearly meeting, certificates of approbation to fuch mi- nifters as are concerned to travel in the work of the miniftry in foreign parts. When a vifit of this kind doth not extend beyond Great Britain, a certifi¬ cate from the monthly meeting of which the mini- fter is a member is fufficient •, if to Ireland, the con¬ currence of the quarterly meeting is alfo required. Regulations of fimilar tendency obtain in other yearly meetings. “ The yearly meeting held in London, in the year 1675, appointed a meeting to be held in that city, for the purpofe of advifing and aflifting in cafes of fuffer- ing for confcience fake, which hath continued with great ufe to the fociety to this day. It is compofed of friends under the name of correfpondents, chofen by the feveral quarterly meetings, and who refide in or near the city. The fame meetings alfo appoint mem¬ bers of their own in the country as correfpondents, who are to join their brethren in London on emergency. The names of all thefe correfpondents, previous to their being recorded as fuch, are fubmitted to the approba¬ tion of the yearly meeting. Thofe of the men who are approved minifters are alfo members of this meeting, which is called the meeting tor fujferings ; a name arifing from its original purpofe, which is not yet become en¬ tirely obfolete. “ The yearly meeting has intrufted the meeting for fufferings with the care of printing and diftributing books, and with the management of its flock j and Quakers, confidered as a Handing committee of the yearly Quality, meeting, it hath a general care of whatever may arife, '-“■“v——* during the intervals of that meeting, affedling the focie¬ ty, and requiring immediate attention : particularly of thofe circumftances which may occafion an application to government. “ There is not in any of the meetings which have been mentioned any prefident, as we believe that Di¬ vine Wifdom alone ought to prefide ) nor hath any mem¬ ber a right to claim pre-eminence over the reft. The office of clerk, with a few exceptions, is undertaken voluntarily by fohre member j as is alfo the keeping of the records. Where thefe are very voluminous, and require a houfe for their depofite (as is the cafe in London, where the general records of the fociety in Great Britain are kept), a clerk is hired to have the care of them ; but except a few clerks of this kind, and perfons who have the care of meeting houfes, none receive any ftipend or gratuity for their fervices in our religious fociety.” It is remarkable, that all the fettlements of the Eu¬ ropeans in America, except the Quaker fettlement of Pennfylvania, were made by force of arms, with very lit¬ tle regard to any prior title in the natives. The kings of Spain, Portugal, France, and Britain, together with the States of Holland, then the only maritime powers, gave grants of fuch parts of America as their people could lay hold on, ftudying only to avoid interference with their European neighbours. But Mr Penn, being a Quaker, did not think his power from King Cha. II. a fufficient title to the country fince called Pennfylvania: He therefore aflembled the fachems or princes then in that country, and purchafed from them the extent of land that he wanted. The government of this province is moftly in the hands of the Quakers, who never have any quarrels with the natives. When they defire to ex¬ tend their fettlements, they purchafe newr lands of the fachen>s, never taking any thing from them by force. How unlike is this condudl to that of the Spaniards, who murdered millions of the natives of Mexico, Terra Fir- ma, Peru, Chili, &c. QUALITY is a wwd which, as ufed in philofophi- Quality cal difquifitions, cannot be explained by any periphrafis. charadle- That which is expreffed by it muft be brought into the nzed by immediate view of the fenfes or intelledl, and the name AnftotIe* properly applied, or he who is a ftranger to the word will never be made to comprehend its meaning. Ari- ftotle, who treated it as a general conception, fecond in order among the ten predicaments or categories (fee Ca¬ tegory), gives feveral charafters of it; but though they are all in fome refpedts juft, no man could from them, without other affiftance, learn what quality is. Thus he tells us *, y.d\u. to ttowv, ETrideyshti # Prced. ed. to uctXXov x.ou to yitIov too TTOttt. And again, 'Opoicc Sylb. p. 44- « ccvoy.oicc xd\c& fiovcts ras? ‘TtoioTxlu.’; MyiTcti o/aoiov slwe# 45* fkg&i ovx. ier\i net]' uXM, ov^ev, n xcttf 0 ttoiov icrjiy. When (d) u Phofe who oelieve themfelves required to fpeak in meetings for worlhip, are not immediately acknow¬ ledged as minifters by their monthly meetings 5 but time is taken for judgment, that the meeting may be fatisfied of their call and qualification. It will alfo fometimes happen, that fuch as are not approved, will obtrude themfelves rtS_ minifters, to. the grief of their brethren} but much forbearance is ufed towards thefe, before the difapprobation of the meeting is publicly teftified.” Quality. QUA [5 When a man comprehends, by means of his fenfes and intellect, what it is which the word quality denotes, he will indeed perceive that the full: of thefe characters is applicable to fome qualities and not to others; that the fecond is more applicable to quantity than to quality; and that it is only the third which can with propriety be confidered as the general charafteriftic of this predi¬ cament. Thus when we have learned by our fenfe of fight that whitenefs is a quality of fnow, and blacknefs of coal j and by means of obfervation and retleClion, that wifclom is a quality of one man and folly of another—we muft admit that the fenfible quality of the fnow is con- trarq to that of the coal, and the intellectual quality of wifdom contrary to that of folly. There is, however, no contrariety between voifdom and whitenefs or black- fiefs, nor between hardnefs or foftnefs and any particular colour; for fenfible and intellectual qualities can never be compared •, and it is not eafy, if poffible, to make a comparifon between qualities perceptible only by diffe¬ rent fenfes : Nay, among qualities perceptible by the fame fenfe, wye often meet with a difference where there is no contrariety } for though the figure of a cube is dif¬ ferent from that of a fphere, and the figure of a fquare from that of a circle, the fphere is not contrary to the cube, nor the circle to the fquare. His fecond chara&eriftic of this genus is Hill lefs pro¬ per than the firlt. It is indeed true that fome qualities admit of intenfion and remiffion ; for fnow is whiter than paper, and one wroman is handfomer than another •, but of the fpecies of quality called figure wye cannot predi¬ cate either more or lefs. A crown-piece may have as much of the circular quality in it as the plane of the equator, and a mulket-bullet as much of the fplierical quality as the orb of the fun. It is indeed a property of all quantity to admit of intenfion and remiffion ; and therefore this ought to have been given as the charac¬ ter not of the fecond but of the third category. See Quantity. That it is only from a comparifon of their qualities that things are denominated like or unlike, or that one thing cannot referable another but m fome quality, is in¬ deed a juft obfervation. We know nothing direftly but qualities fenfible and intelleClual (fee Metaphysics, N° 149, 150, 151, and 227); and as thefe have no re- femblance to each other, we conclude that body or mat¬ ter, the fubjeCI of the former, is a being unlike mind, the fubjeCt of the latter. Even of bodies themfelves we can fay, that one is like or unlike another only by vir¬ tue of their qualities. A ball of ivory refembles a ball of fnow in its figure and colour, but not in its coldnefs or hardnefs ; a ball of lead may refemble a ball of fnow in its figure and coldnefs, but not in its colour ; and a cube of ivory refembles not a ball of lead either in figure, co¬ lour, or coldnefs. The mind of a brute refembles that of a man in its porvers of fenfation and perception, but does not refemble it in the powers of volition and reafoning ; or at leaft the refemblance, in this latter inftance, is very flight. All bodies refemble one another in being folid and extended, and all minds in being more or lefs a£tive. Likenefs or unlikenefs therefore is the univerfal charaCreriftic of the category quality. Im 'orta'it Ariftotle has other fpeculations refpefting quality, diftindtiotis which are worthy of notice. He diftinguifhes between of quality, qualities which are effential and thofe which are acciden¬ tal j between qualities which are natural and thofe Nothing known but qualities. 39 ] QUA which are acquired; and he fpeaks of the qualities of Quality. capacity and thofe of completion. Extenfion and figure m general are qualities effential to all bodies : but a parti¬ cular extenfion, fuch as an inch or an ell, and a particu¬ lar figure, fuch as a cube or a fphere, are qualities acci¬ dental to bodies. Among the natural qualities of glafs it is one to tranfmit objedls of vifion j but to enlarge thefe objects is an adventitious or acquired quality. The fame quality may be natural in one fubftanee, as attrac¬ tion in the magnet j and acquired in another, as the fame attraftion in the magnetic bar. Docility may be called a quality natural to the mind of man, feience an acquired one. To underftand what he means by quali¬ ties of capacity and completion, it may be fufficient to ob- ferve that every piece of iron has the qualities of a ra¬ zor in capacity, becaufe it may be converted into fteel, and formed into a razor: when it is fo formed, it has, in the language of this fage, the quality of a razor in completion. Among the qualities of capacity and comple¬ tion, the moft important, and what may lead to intereft- ing fpeculations, is the reafoning faculty of man. A capacity of reafoning is effential to the human mmd } but the completion of this capacity or adlual reafoning is not, otherwife infants and perfons afleep would be ex¬ cluded from the human fpecies. 4 Mr Locke has puzzled his readers, and perhaps him-overl°0ked felf, with a queftion refpefting the fpecies of an idiot^ bocke. or changeling, whom he pronounces to be fomething between a man and a brute *. It is not often that we * Book iv. feel ourfelves inclined to regret Locke’s ignorance ofeh. 4. § 13,. Ariftotle’s diftindftions •, but wTe cannot help thinking, ^ that had the Britilh philofopher attended to the Stagy- rite’s account of qualities in capacity and qualities in completion, this perplexing queftion would never have been ftarted. It is juftly obferved in the Eflay on Hu¬ man Underftanding, that of real effences we know no¬ thing : but that every man feletfts a certain number of qualities which he has always perceived united in certain beings 5 and forming thefe into one complex conception, gives to this conception a fpecific name, which he ap¬ plies to every being in which he finds thofe qualities 5 united. This is undoubtedly the procefs of the mind in Strange forming genera and fpecies 5 and as the excellent author c“r’1^ ^ refufes the name of man to the changeling, it is obvious qp^ver- that the complex conception, to which he gives that fight, name, muft imply rationality or the actual cxercife of rea- fon. But this limitation will exclude many beings from the fpecies man, whom Mr Locke certainly confidered as men and women. Not to mention infants and perfons in found fleep, how fhall we clafs thofe wrho, after having lived 30 or 40 years in the full exercife of reafon, have been fuddenly or by degrees deprived of it by fome dif- order in the brain ? From Marlb’rough’s eyes the ftreams of dotage flow ; And Swift expires a driveller and a fliow. Johnson. But were the hero and the wit in thofe deplorable cir- cumftances excluded from the human fpecies, and clafled between men and brutes ? No furely ; they were both acknowledged to be men, becaufe they were known to have the quality of reafon in what Arillotle would have called capacity. Their dotage and drivelling originated from fome diforder in their bodies, probably in the re¬ gion of the brain •, and Locke himfelf contends that no defeat in body is fufficient to degrade a perfon from the rank ( QUA [ 590 ] QUA Quality rank of manhood. Again, lunatics have the exercife of is one dedicated to thofe men who, as the Chinefe Quango ^ i' reafon, except at new and fuil moon. Are thefe un- pretend, difcovered the fecret of rendering themfelves jl ping-fou*. haPPy beings fometimes men and fometirnes a fpecies by immortal. ^ ° Quantity. ' themfelves between men and brutes? QUANGSI, a province of China, bounded on the ~~*v ' .6 It appears, therefore, that not the aBual cxercife of north by Koe-Tcheau and Hu-Qriang j on the ealt, by his d Uf reafor!’ but reason in capacity, ought to be included in Yunan and Quantong j on the loutk, by the fame and ti-ineTe". t5ie comPIex conception to which we give the fpecinc Tonquin ; and on the weft, by Yun-nan. It produces fpefling name otman, as fome of the greateft men that ever lived great plenty of rice, being watered by feveral large ri- the human have been during parts of their lives deprived of the vers 5 and containing 10,000,000 of inhabitants. The ipecies. power of aBual reafoning. . This, however, it will be fouthern part is a flat country, and well cultivated 5 but laid, doesmot remove the difficulty; for the occafional the northern is full of mountains covered with trees. It exercife of reafon in lunatics, and the great exertions of contains mines of all forts ; and there is a gold-mine it in Inch men as Swift and Marlborough, fhow that lately opened. The capital town is Quie linp. they had it in capacity tX all times ; whereas we have no A very lingular tree, fays Grolier, grows in this evidence that changelings have even a capacity of rea- province ; inftead of pith, it contains a foft pulp, which foning at any time, lince they never do a rational aftion, yields a kind of flour : the bread made of it is faid to nor ever utter a lentence to the purpofe. That we have no direB and yta/ikW evidence of the minds of change¬ lings being capable of reafoning, were they fupplied with proper organs, muff be granted ; but the probabi¬ lities of their being fo are many and great. \Ve know by experience that the a final exercife of reafon may be interrupted by an occalional and accidental preffure on the brain : and therefore we cannot doubt but that if this preflure were rendered permanent by any wrong configuration of the Ikull given to it in the womb, or in the a£I of being born into the world, an infant, with a mind capable of reafoning by means of proper organs, would by this accident be rendered, through the whole of life, an idiot or changeling. That idiotifm is caufed by fuch accidents, and is not the quality of an inferior mind occafionally given to a human body, will at leaft ^ feem probable from the following confiderations. True doc- It does not appear that an animal body can Jive and trine. move but while it is adiuated by fome mind. Whence then does the unborn infant derive its mind ? It muft be either immediately from God, or ex traduce from its parents ; but if the mind of man be immaterial, it can¬ not be ex traduce. Now, as idiots are very few in num¬ ber when compared with the rational part of the human fpecies, and as God in the government of this world adls not by partial but by general laws ; we muft con¬ clude that the law which he has eftablilhed refpedfting the union of mind and matter, is, that human bodies Ihall be animated with minds endowed with a capacity of reafcning, and that thofe who never exert this capa¬ city are prevented by fome fuch accident ‘as we have affigned. For a further account of qualities, why they are fup- pofed to inhere in fome fubjeel, together with the ufual diftindlion between the primary and fecondary qualities of matter, fee Metaphysics, Part II. chap. i. Chemical QUALITIES, thofe qualities principally intro¬ duced by means of chemical experiments, as fumigation, amalgamation, cupellation, volatilization, precipitation, &c. Quality, is .alfo ufed for a kind of title given to certain perfons, in regard of their territories, figniories, or other pretenfions. OUANGA. See Capra. QUANG-fing-fou, a city in China, is fituated in the northern part of the province of Pe-tcheli, between the provinces of Chang-tong and Ho-nan, and has nine cities of the third clafs dependent on it; all its plains 3re well watered' by rivers. Among its temples, there 3 be exceedingly good. Betides paroquets, hedgehogs, porcupines, and rhinocerofes, a prodigious number of wild animals, curious birds, and uncommon infe&s, are found here. This province contains 12 villages of the firft clafs, and 80. of the fecond and third. QUANG-tong, a province of China, bounded on the eaft by Kiang-ii and Fokien ; on the fouth, bv the ocean ; and on the weft, by Tonquin. This province is diverfified by valleys and mountains ; and yields two crops of corn in a year. It abounds in gold, jewels, fiik, pearls, tin, quickfilver, fugar, brafs, iron, fteel, faitpetre, ebony, and feveral forts of odoriferous wood ; befides fruits of all forts proper to the climate. They have a prodigious number of duck«, whofe eggs they hatch in ovens ; and a tree, whofe wood is remarkably hard and heavy, and thence called iron-wood. The mountains are covered with a fort of ofiers which creep along the ground, and of which they make bafkets, hurdles, matts, and ropes. Although the climate of this province is warm, the air is pure, and the people are robuft Hud healthy. They are very induftrious; and it muft be allowed that they poffefs in an eminent degree the talents of imitation : if they are only Ihown any of our European works, they execute others like them with the moft furprifing exaft- nefs. This province buffered much during the civil wars ; but at prefent it is one of the moft flourilhing in the empire ; and, as it is at a great diftance from court, its government is one of the moft important. This province is divided into ten diftrifls, which con¬ tain ten cities of the firft clafs, and 84 of the fecond and third. Canton is the capital town. T QUANTITY, as explained by the great Englifli Quantity, lexicographer, is that property of any thing which may be increafed or diminhhed. This interpretation of the word is certainly juft, and for the purpoies of com¬ mon converfation it is fufficiently determinate; but the man of fcience may expeft to fftid in a work like ours a definition of the thing fignified. This, however, can¬ not be given him. A logical definition ccnfifts of the genus under which the thing defined is ranked, and the fpecijic difference (fee Logic, N° 20, &c.j ; but quan¬ tity is ranked under no genus. In that fchool where fuch definitions were melt valued, it was confidered as one of the ten categories, or general conceptions, under whicli all the objefts of human apprehenfion were muf- tered, like foldiers in an army (fee Category and Phi¬ losophy, N0 22.). On this account, even Ariftotle himfelf, QUA (Niar.tky. himfelf, who delighted in definitions, and was not eafi- 1 v ly deterred from a favourite purfuit, coold not confift- di-'-Ae- entl7 h*8 owu ru^es attempt to define quantity. He nzed by characterizes it, however, in feveral parts of his works : Ariftotle. and particularly in the 15th chapter of the 4th book of his metaphyfics, where he gives the following account oi the three firft categories : T»v]x pnv w p-ix v ovcna. ceioiX 0 a/v *1 Trairtl',; f-tix rex rfs, to ttotov w. “ .Things are the fame of which the substance is one \fimilar, of which the quality is one ; equal, of which the quan- t 591 1 QUA which it has performed, have procured it a moil refpeft- Quantity,, able place in the circle of the Iciences. Ingenious men -v—-"' have availed themfelves of this pre-eminence of mathe¬ matics, and have endeavoured to procure refpeft for their difquiiitions on other fubjeCls, by prefenting them to the public as branches of mathematical fcience, and therefore fufceptible of that accuracy and certainty which are its peculiar boaft. Our moral affe&ions, our fenfations, our intelleftual powers, are all fufceptible of augmentation and diminution, are conceivable as greater * Freed. p. 34. edit. tity is one. Again, he tells us*, that the chief charac- » and lefs when Hated together, and are familiarly Ipoken Sylb. The fubjeft of mathe¬ matical rea¬ soning. teriftic of quantity is, that it may be denominated eequal and unequal. That any man can become wifer by reading fuch de- feriptions as thefe, none but an idolater of Ariitotle will fiippofe. There is, indeed, no periphrafis by which we can explain what is meant by quantity to thole who have not previoufly formed fuch a notion.— All that can be done by making the attempt is only to fettle language, by Hating exaftly the cafes in which we ufe this word in the greatcH conformity to general cullom; for there is a laxnefs or carelefsnefs of expref- fion in the language of moll men, and our notions are frequently communicated by fpeech in a w7ay by no means precife } fo that it is often a great chance that the notions excited in the mind of the hearer are not exadt counterparts of thofe in the mind of the fpeaker. The underHandings of men differ in nothing more re¬ markably than in their power of abHradl’on, and of ra¬ pidly iorming conceptions fo general and fimple as not to by clogged with diHinguiiliing circumfiances, which may be different in different minds while uttering and hearing the fame words : and it is of great confequence to a man of fcientific habits, either to cultivate, ifpofi- ffble, tins talent, or to fuperfede its ufe, by Hudioufiy forming to himfell notions of the moH important univer- fals in his own courfe of contemplation, by careful ab- Itraclion of every thing extraneous. His language by this means becomes doubly inllruflive by its extreme precifion \ and he will even judge with greater certainty of notions intended to be communicated by the more fio- venly language of another perfon. We cannot fay that there is much ambiguity in the general ufe of the term quantity : But here, as in all other cafes, a love of refinement, of novelty, and fre¬ quently of vanity, and the wifh of appearing ingenious and original, have made men take advantage of even the finall latitude with which the carelefs ufe of the word will furnifh them, to amufe themfelves and the public by giving the appearance of fcience to empty founds. Mathematics is undoubtedly employed in difeovering and Hating many relations of quantity ; and it is in this category alone that any thing is contemplated by the mathematician, whether in geometry, arithmetic, or al¬ gebra. Hence mathematics has been called the fcience of quantity. The firnplicity of the objefl of the ma¬ thematician’s contemplation, and the unparalleled di- flinflnefs wuth which he can perceive its modifications, have enabled him to eref! a body of fcience, eminent not only for its certainty, but alfo for the great length to which he can carry his reafonings without danger of error} and the intimate connection w7hich this fcience has with the arts of life, and the important fervices of as admitting of degrees of comparifon. We perfectly well underflood when we lay that one pain, heat, grief, kindnefs, is greater than another 5 and as this is the diflinguithing charaCteriflic of quantity, and as quantity is the fubjeCt of mathematical difcuffion, we fuppole that thefe fubjeCts may be treated mathemati¬ cally. Accordingly, a very celebrated and excellent philosopher* has faid, among many things of the fame * Fran-t kind, that the greatnefs of a favour is in the compound ratio oi the fervice performed and the dig-' Jn' nity ol the performer, and in the inverfe ratio of the me-Which is rit and rank of the receiver j that the value of a cha-‘mProPe,dy racier is in the compound ratio of the talents and virtue, !ntroc*uce^ &-c. ; and he has delivered a number of formal propo' filionson the mofl interefling queflions in morals, couch- 1 J ^ ed in this mathematical language, and even expreffed.by algebraic formulae. But this is mere play, and conveys no inflruClion. We underfland the words •, they con¬ tain no ablurdity; and in as far as they have a fenfe, we believe the propofitions to be true. But they give no greater precifion to our fentiments than the more ufual exprefiions would do. If we attend clofely to the meaning of any one of fuch propofitions, we fliall find that it only- expreffes fome vague and indiflinCt notions of degrees of thofe emoti©ns, fentiments, or qualities, which would be jafl as well conceived by means of the expreffions of ordinary language 5 and that it is only by a fort of analogy or refemblance that this mathema¬ tical language conveys any notions whatever of the fub- The objeCl of contemplation to the mathematician is The ma¬ nat whatever is fufceptible of greater and lefs, but what themati- is meafurable •, and mathematics is not the fcience ofcian con" magnitude, in its mofl abftra&ed and general accepta- onT^ouan tion, but of magnitude which can be meafured. It is, titles that"' indeed the SCIENCE of MEASURE, and whatever is are mea- treated in the way of menfuration is treated mathema-^urab*e- tic ally. Now, in the difeourfe of ordinary life and ordinary men, many things are called quantities which we cannot of elo not meafure. This is the cafe in the inftances already given of the affections of the mind, pleafure, pain, beauty, wifdom, honour, &c. We do not fay that they are incapable of meafure ; but we have not yet been able to meafure them, nor do we think of meafuring them when we fpeak rationally and ufefully about them. We therefore do not confider them mathematically ; nor can w'e introduce mathema¬ tical precifion into our difeuflions of thefe fubjeCts till we can, aim aClually do, meafure them. Pei Tons who are precife in their expreflion will even avoid fuch phrafes on thefe fubjefts as fuppofe, or ftriClly exprefs, fuch meafurement. We ftiould be much embarraffed how to anfvver the queftion, How much pain docs the tooth¬ ache give you juft now} and how much is it eafier fince yefteiday } QUA 'pjantny. ^ yefterday ? Yet the anfwer (if we had a meafure) * Would be as eafy as to the queftion, How many guineas did you win at cards ? or how much land have you bought ? Nay, though we fay familiarly, “ I know well how much fuch a misfortune would affecl you,” and are underftood when we fay it, it wmuld he aukward language to fay, “ I know wyell the quantity of your grief.” It is in vain, therefore, to expedl mathematical preciiion in our difcourfe or conceptions of quantities in the mod abflrafted fenfe. Such precifon is confined to quantity which may be and is meafured (a). It is only trifling with the imagination when we employ ma¬ thematical language on fubjedls which have not this pro¬ perty. It will therefore be of fome fervice in fcience to dif- criminate quantities in this view j to point out what are 6 lufceptible of meafure, and w7hat are not. Meafuring What is nleafuring ? It is one of thefe two things: It is fixplaixed. either finding out fome known magnitude of the thing meafured, which we can demonftrate to be equal to it } or to find a knowm magnitude of it, which being ta¬ ken fo many times {hall be equal to it. The geometer meafures the contents of a parabolic fpace when he ex¬ hibits a parallelogram of known dimenfions, and demon- ilrates that this parallelogram is equal to the parabolic {pace. In like manner, he meafures the folid contents of an infinitely extended hyperbolic fpindle, when he exhibits a cone of known dimenfions, and demonftrates that three of thefe cones are equal to the fpindle. In this procefs it will be found that he a&ually fub- divides the quantity to be meafured into parts of which it confifts, and dates thefe parts as aflually making up the quantity, fpecifying each, and adigning its boun¬ daries. He goes on with it, piece by piece, demon- drating the refpeftive equalities as he goes along, till he has exhauded the figure, or confidered all its parts.—- When he meafures by means of a fubmultiple, as w'hen he {hows the furface of a fphere to be equal to four of its great circles, he dops, after having demondrated the equality of one of thefe circles to one part of the fur- face : then he demondrates that there are other three parts, each of which is precifely equal to the one he has minutely confidered. In this part of the procefs he exprefsly adigns the whole furface into its didinft por¬ tions, of which he demondrates the equality. But there is another kind of geometrical meafurement which proceeds on a very different principle. The geo¬ meter conceives a certain individual portion of his figure, whether line, angle, furface, or folid, as known in re- fpeft to its dimenfions. Tie conceives this to be lifted from its place, and again laid down on the adjoining part of the figure, and that it is equal to the part which it now covers j and therefore that this part together with the fird is double of the fird : he lifts it again, and lays it down on the next adjoining part, and affirms that this, added to the twro former, make up a quantity tri¬ ple of the fird. He goes on in this way, making fimi- QUA lar inferences, till he can demondrate that he has in this Quantity, manner covered the whole figure by twenty applications, '"“""v ~ } and that his moveable figure will cover no more ; and he affirms that the figure is twenty times the part em¬ ployed. This mode is precifely fimilar to the manner of prac¬ tical meafurement in common life : we apply a foot-rule fucceffively to two lines, and find that 30 applications exhaud the one, while it requires 35 to exhaud the other. We fay therefore, that the one line is 30 and Euclid’s the other 35 feet long j and that thefe two lines are to fourth pro. each other in the ratio of 30 to 35. Having meafured i101*111011, two fliorter lines by a fimilar application of a dick of an inch long 30 times to the one and 35 times to the other, we fay that the ratio of the two fird lines is the fame wfith that of the two lad. Euclid has taken this method of demondrating the fourth propofition of the fird book of his celebrated elements. But all this procefs is a fiflion of the mind, and it is the fiftion of an impoffibility. It is even inconceivable, that is, we cannot in imagination make this application of one figure to another j and wye prefume to fay, that, if the elements of geometry cannot be demondrated in fome other way, the fcience has not that title to pure, abdraft, and infallible knowledge, wffiich is ufually al¬ lowed it. We cannot fuppofe one of the triangles lifted and laid on the other, without fuppofing it lomething different from a triangle in abjlracio. The individuality of fuch a triangle confilts folely in its being in the pre- cife place where it is, and in occupying that portion of fpace. If we could diftindUy conceive otherwife, wye fhould perceive that, when wye have lifted the triangle from its place, and applied it to the other, it is gone from its former place, and that there is no longer a tri¬ angle there. This is inconceivable, and fpace has al¬ ways been acknowledged to be immoveable. There is therefore fome logical defeft in Euclid’s demondration. We apprehend that he is labouring to demondrate, or rather illudrate, a fimple apprehenfion. This indeed is the utmod that can be done in any demondration (fee Metaphysics, N° 82.) : but the mode by which he guides the mind to the apprehenfion of the truth of his fourth propofition is not confident either with pure mathematics or with the laws of corporeal nature. The real procefs, as laid down by him, feems to be this. We fuppofe fomething different from the abdrafl tri¬ angle } fome thing that, in conjunflion with other pro¬ perties, has the property of being triangular, with cer¬ tain dimenfions of two of its fides and the included an¬ gle. It has avowedly another property, not eflential to, and not contained in, the abdraft notion of a triangle, viz. mobility. We alfo fuppofe it permanent in ffiape and dimenfions, or that although, during its motion, it does not occupy the fame [pace, it continues, and all its parts, to occupy an equal fpace. In ffiort, our concep¬ tion is very mixed, and does not perceptibly differ from our conception of a triangular piece of matter, where the [ 592 1 (a) To talk intelligibly of the quantity of a pain, we diould have fome dandard by which to meafure it; fome known degree of it fo well afeertained, that all men, when talking of it, flrould mean the fame thing.— And we ffiould be able to compare other degrees of pain with this, fo as to perceive didinftly, not only whether they exceed or fall ffiort of it, but alfo how much, or in what proportion; whether bv an half, or a fifth, or a tenth. Reid. 1 Q u A [ 593 Quantity, the triangle is not the fubjeft, but an adjunct, a quali- “—v- ty. And when we luppofe the application made, v.e are not in fadl fuppohng two abflradt triangles to coin- cide. This we cannot do with any thing like diftinft- nels ; for our diftindl conception now is, not that of tw o triangles coinciding, but of one triangle being now ex- aclly occupied by that moveable thing which formerly occupied the other. In Ihort, it is a vulgar meafurement, reftridkd by fuppofitions which are inadmiflible in all attual meafurements in the prefent univerfe, in which no moveable material thing is known to be permanent, either in Ihape or magnitude. This is an undeniable confequence of the principle of univerfal gravitation, and the compreffibility of every kind of tangible matter with which we are acquainted. Remove the brafs rule but one inch from its place ; its gravitation to the earth and to the reft of the univerfe is immediately changed, and its dimenfions change of con- lequence. A change of temperature will produce a fimi- lar effedt; and this is attended to and confidered in all nice menfurations. We do the beft we can to allure our- felves that our rule always occupies a fenfibly equal fpace; and we mud be contented with chances of error which we can neither perceive nor remove. We might (were this a proper place) take notice of fome other logical defedts in the reafoning of this cele¬ brated propolition : but they are belide our prefent pur- pofe of explaining the different modes of mathematical meafurement, with the view of difcovering that circum- llance in wrhich they all agree, and which (if the only 8 one) mud therefore be the charadferidic of menfuration. We think that the only circumdance in wrhich all modes of menfuration agree, or the only notion that is found in them all, is, that the quantity is conceived as confiding of parts, didinguifliable from each other, and feparated by affignable boundaries; fo that they are at once conceived feparately and jointly. We venture to aifert that no quantity is diredtly meafured which we cannot conceive in this way, and that fuch quantities only are the immediate objedls of mathematical contem¬ plation, and fhoald be didinguidied by a generic name. Let them be called Mathematical quantities. Extension, Duration, Number, and Proportion, have this charadferidic, and they are the only quantities which have it. Any perfon will be convinced of the fird aflertion by attending to his own thoughts when con¬ templating thefe notions. He will find that he conceives every one of them as made up of its own parts, which are didinguidiable from each other, and have alfign- «ible boundaries, and that it is only in confequence of involving this conception that they can be added to or fubtradled from each other 5 that they can be multi¬ plied, divided, and conceived in any proportion to each other. He may perhaps find considerable difficulty in acqui¬ ring perfedfly didindl notions of the menfurability, and the accuracy of the modes of menfuration. He will find that the way in which he meafures duration is very fimi- lar to that in which he meafures fpace or extenfion. He does not know, or does not attend to, any thing which hinders the brafs foot-rule in his hand from con¬ tinuing to occupy equal fpaces during his ufe of it, in meafuring the diilance of two bodies. In like manner he felecls an event which nature or art can repeat con¬ tinually, and in which the circumftances which contri- Vol> XVII. Part II, Tiie cha- rafteriltic notion of meni'ura- tion. 1 QUA bute to its acccmplifhment are invariably the fame, or Quantity, their variations and their effedls are infenfible. He con-"y-”*—-’ eludes that it will always occupy an equal portion of time for its accomplifitment, or always lafi: an equal time.. 1 hen, obferving that, during the event whole duration he willies to meafure, this ftandard event is ac- complifhed 29-3- times, and that it is repeated 365k times during the accomplilhmcnt of another event, he affirms that the durations of thefe are in the ratio of 29*- *-° 3^5t* ^ thus (and with the fame logical defedl as in the meafuring a line by a brafs rod) that the aftro- nomer meafures the celeftial revolutions by means of the rotation of the earth round its axis, or by the vibrations of a pendulum. We are indebted for moft of the preceding obferva- tions to Dr Pieid, the celebrated author of the Inquiry into the Human Mind on the Principles of Common Senfe, and of the Effays on the Intelleftual and A&ive Powers of Man. He has publilhed a differtation on this fubjeft in the 45th volume of the Philofophical 1 rantaefions, N° 489, which we recommend to our philofophical readers as a performance eminent for pre- cifion and acutenefs. If we prefume to differ from him in any trivial circumftance, it is wfith that de¬ ference and refped wffiich is due to his talents and his worth. • • ^ Dr Held juftly obferves, that as nothing has proper- Characters tion which has not either extenfion, duration, or num-^ ber, the characters of mathematical quantity may be re-matlta/, ftriCted to thefe three. He calls them proper quanti-^"1 U ties, and all others he calls improper. We believe that, in the ulmofl: precifion of the Englifh language, this denomination is very appofite, and that the word quantity, derived from quantum, always fuppofes mea- 10 furement : But the word is frequently ufed in cafes Other where its original is not kept in view, and we ufe other ciu; i tities words as fynonymous with it, wfiien all menfuration, whether poffible or not, is out of our thoughts. Accor- "deiedraal ding to praCtice, therefore, the jus et norma loquendi, thematical- there feems to be no impropriety in giving this name,ty* in our language at leaft, to whatever can be conceived as great or little. There is no impropriety in faying that the pain occafioned by the ftone is greater than that of the toothache j and when we fearch for the category to which the affertion may be referred, we cannot find any other than quantity. We may be allowed therefore to fay, with almoft all our fcientific countrymen, that every thing is conceivable in refpeCt of quantity which w?e can think or fpeak of as greater and lefs 5 and that this no¬ tion is the charaClerittic of quantity as a genus, wffiile meafurablenefs is the charaCleriftic of mathematical quan¬ tity as a fpecies. But do wre not meafure many quantities, and confider them mathematically, which have not this charaCleriftic of being made up of their own diftinguiffiable parts ? What elfe is the employment of the mechanician, wffien fpeaking of velocities, forces, attractions, repulfions, magnetic influence, chemical affinity, &c. &c. ? Are not thefe mathematical feiences ? And if the precifion and certainty of mathematics arife from the nature of their fpecific objeCt, are not all the claims of the me¬ chanician and phyfical aftronomer ill-founded preten- fions ? Thefe queftions require and deferve a ferious anfwer. It is moft certain that we confider the notions wffiicli are expreffed by thefe terms velocity, force, denfity, and 4 F the Velocity, force, den- fity, how meafured. Q u A Quantity, the like, as fufceptible of meafure, and them mathematically. Some of thele terras are nothing but names for rela- . tions of meafurable quantity, and only require a little re- deftion to Ihow themfelves fuch. Velocity is one of thefe. It is only a name expreffing a relation between the fpace defcribed by a moving body and the time which elapfes during its defcription. Certain moderate rates of motion are familiar to us. What greatly ex¬ ceeds this, fuch as the fight of a bird wrhen compared with our walking, excites our attention, and this excefs gets a name. A motion not fo rapid as we are familiar with, or as we with, alfo gets a name ; becaufe in this the excefs or defedt may intereft us. We wilh for the flight of the hawk j wTe chide the tardy pace of our mef- lenger : but it is fcientific curiofity which firft confiders this relation as a feparate objedl of contemplation, and the philofopher mult have a name for it. He has not formed a new one, but makes ufe of a wrard of common language, wThofe natural meaning is the combination of a great fpace with a flrort time. Having once appro¬ priated it, in his fcientific vocabulary, to this very ge¬ neral ufe, it lofes with him its true fignification. Tardi¬ ly would have done juft as well, though its true mean¬ ing is diametrically oppofite \ and there is no greater impropriety in faying the tardity of a cannon bullet than in faying the velocity of the hour-hand of a watch. Ve¬ locity is a quality or affection of motion, the notion of which includes the notions of fpace and duration (two mathematical quantities), and no other. It does not therefore exprefs a mathematical quantity itfelf, but a relation, a combination of two mathematical quantities of different kinds j and as it is meafurable in the quan¬ tities fo combined, its meafure muft be a unit of its own kind, that is, an unit of fpace as combined with an unit >«f time. Density is another word of the fame kind, expref- fmg a combination of fpace with number. Denfce arbo- res means trees Handing at a fmall diftance from each other 5 and the wrard is ufed in the fame fenfe when we fay that quickfilver is denier than wTater. The expref- fion always fuggefts to the reflefting mind the notions of particles and their diftances. We are indeed fo habi¬ tuated to complicated views of things, that we can fee j-emote connexions with aftonilhing rapidity ; and a very few circumftances are fufficient for leading forward the mind in a train of inveftigation. Common difcourfe is a moft wonderful inftance of this. It is in this way that we fay, that we found by weighing them that in¬ flammable air had not the fixth part of the denfity of common air. Suppofing all matter to confift of equal atoms equally heavy, and knowing that the weight of a bladder of air is the fum of the weights of all the atoms, and alfo knowing that the vicinity of the atoms is in a certain proportion of the number contained in a given bulk, we affirm that common air is more than fix times denfer than inflammable air; but this rapid decifion is entirely the effeX of habit, which makes us familiar with certain groups of conceptions, and we inftantan- eoufly diftinguiih them from others, and thus think and difcourfe rationally. The Latin language employs the word frequens to exprefs both the combination of fpace and number, and that of time and number. There are perhaps a few more words which exprefs combinations of mathematical quantities of different &nds j and the correfponding ideas or notions arc there- [ 59+ 1 QUA confider fore proper and immediate fubjeXs of mathematical dif- Quantity, cuflion : But there are many words which are expreflive v ' } of things, or at leaft of notions, to which this way of confidering them will not apply. All thofe affeXions or qualities of external bodies, by which they are conceived to aX on each other, are of this kind : Impulsive EORCE, WEIGHT, CENTRIPETAL AND CENTRIFUGAL FORCE, MAGNETICAL, ELECTRICAL, CHEMICAL AT. TRACTIONS AND REPULSIONS } in ffiort, all that we confider as the immediate caufes of natural phenome¬ na. Thefe we familiarly meafure, and confider mathe¬ matically. 12 What was faid on this fubjeX in the article Physics Forcesmea» will give us clear conceptions of this procefs of the t^e mind. Thefe forces or caules are not immediate objeXs^ of contemplation, and are known only by and in the phenomena which we confider as their effeXs. The phenomenon is not only the indication of the agency of any caufe, and the charaXeriftic of its kind, but the meafure of its degree. The neceffary circumftances in this train of human thought are, ift, The notion of the force as fomething fufceptible of augmentation and dimi¬ nution. 2d, The notion of an infeparable connexion of the force with the effeX produced, and of every de¬ gree of the one with a correfponding degree of the other. From thefe is formed the notion that the phenomenon or effeX is the proper meafure of the force or caufe. All this is ftriXly logical. But when w7e are confidering thefe fubjeXs mathe¬ matically, the immediate objeXs of our contemplation are not the forces w’hich we are thus treating. It is not their relations w'hich we perceive, and which wre combine w'ith fuch complication of circumftances and certainty of inference as are known in all other fci- ences: by no means; they are the phenomena only, which are fubjeXs of purely mathematical dilcuffion. They are motions, which involve only the notions of fpace and time j and when wre have finiffied an accurate mathematical inveftigation, and make our affirmation concerning the forces, wTe are certain of its truth, be¬ caufe we Juppofe the forces to have the proportions and relations, and no other, which w7e obferve in the pheno¬ mena. Thus, after having demonftrated, by the geo¬ metrical comparifon of the lines and angles and furfaces of an ellipfe, that the momentary defleXion of the moon from the tangent of her orbit is the 3600th part of the fimultaneous defleXion of a ftone from the tangent of its parabolic path •, Newton affirms, that the force by which a particle of the moon is retained in her orbit is the 3600th part of the weight of a particle of the ftone ; and having farther ftrown, from faX and obfervation, that thefe momentary defleXions are inverfely as the fquares of the diftances from the centre of the earth, he affirms, that all this is produced by a force which varies its intenfity in this manner. Now all this inveftigation proceeds on the two fuppo- fitions mentioned above, and the meafures of the forces are in faX the meafures of the phenomena. The whole of phyfical aftronomy, and indeed the whole of mecha¬ nical philofophy, might be taught and underftood, with¬ out ever introducing the wrord force, or the notion wdiich it is fuppofed to exprefs : for our mathematical reafonings are really about the phenomena, which are fubjeXs pure¬ ly mathematical. * The precifion, therefore, that w?e prefume to affirm to attend thefe inveftigations, arifes entirely from the meafurable Q u A r S9S 1 QUA tQuantity, meafureable nature of the quantities which are the real pie, &c. the effefbarenine times, 16 times, &c. greater* v objeas of our contemplation, and the fuitablenefs and and, in fhort, are proportional, not to the’ velocity but propriety of the meafures which we adopt in our com- to its fquare. This obfervation had been made before parifons. _ by Dr Hooke, who has enumerated a prodigious variety Since, then, the phenomena are the iTnmediate tub- of important cafes in which this proportion5 of eftba is jeas of our diicuffion, and the operating powers are on- obferved. Leibnitz, therefore, affirmed, that the force ly inferences from the phenomena confidered as effeas, inherent in a moving body is proportional to the fquare / the quantity afcribed to them muft alfo be an inference of the velocity. from the quantity of the effea, or of fome circumftance It is evident that a body, moving with the fame ve¬ in the effea. 1 he meafure, therefore, of the caufe, or locity, has the fame inherent force, whether this be em- natural power or force, cannot be one of its own parts 5 ployed to move another body, to bend fprings, to rife in for the whole and the part are equally unperceived by oppofition to gravity, or to penetrate a mafs of foft mat- us. Our meafure, therefore, muff be a meafure of fome ter. Therefore thefe meafures, which are fo widely dif- interefting part, or of the only interefting part of the ferent, while each is agreeable to a numerous clafs of phenomenon. It is therefore in a manner arbitrary, and fafts, are not meafures of this fomething inherent in the depends chiefly on the intereft we take in the phenome- moving body which we call its force, but are the mea- non. It muft, however, be fettled with precifion, fo that hires of its exertions when modified according to the all men in ufing it may mean the fame thing. It muft circumftances of the cafe j or, to fpeak ftill more cau- be fettled, therefore,by the defcription of that part or cir- tioufly and fecurely, they are the meafures of certain cumftance of the phenomenon which js chara&eriftic of claffes of phenomena confequent on the a&ion of a mo- of the natural power. This defcription is the definition ving body. It is in vain, therefore, to attempt to fup- 13 of the meafure. port either of them by a demonftration. The meafure Meafures Thus Newton affumes as his meafure of the centri- itfelf is nothing but a definition. The Cartefian calls Betd force. petal. Porce’ t!le momentary deviation from uniform that a double force which produces a double velocity ' rectilineal motion. Others, and fometimes Newton in the body on which it a£ts. The Leibnitzian calls himfeff, affumes the momentary change of velocity, which that a quadruple force which makes a quadruple pene- again is meafured by twice this deviation. Thefe mea- tration. The reafonings of both in the demonftration of fures, being thus feleCted, are always proper in a mathe- a propofition in dynamics may be the fame, as alfo the tnatical fenfe j and if ftriCtly adhered to, can never lead refult, though expreffed in different numbers, us into any paralogifm. They may, however, be phyfi- But the two meafures are far from being equally pro- cally wrong; there may not be that indiffoluble con- per : for the Leibnitzian meafure obliges us to do conti- neftion between the phenomenon and the fuppofed caufe. nual violence to the common ufe of words. When two But this is no mathematical error, nor does it invalidate bodies moving in oppofite directions meet, flrike each any of our mathematical inferences : it only makes them other, and ftop, all men will fay that their forces are ufelefs for explaining the phenomenon by the principle equal, becaufe they have the beft teft of equality which which we adopted j but it prepares a modification of the we can devife. Or when two bodies in motion ftrike phenomenon for fome more fortunate application of phy- the parts of a machine, fiich as the oppofite arms of a le- fical principles. . rer, and are thus brought completely to reft, w'e and all Requifites . All that can be defired in the definitions or deferip- men will pronounce their mutual energies by the inter- meafm-e t*°nS t^ePe. mea^ures *s> that they may not deviate vention of the machine to be equal. Now, in all thefe ures- from the ordinary ufe of the terms, becaufe this would cafes, it is well known that a perfeCt equality is found in always create confufion, and occafion miftakes. Dr the produ&s of the quantities of matter and velocity. Reid has given an example of an impropriety of this Thus a ball of two pounds, moving with the velocity kind, which has been the fubjeCl of much debate among of four feet in a fecond, will ftop a ball of eight pounds the writers on natural philofophy. We mean the mea- moving with the velocity of one foot per fecond.* But fure of the force inherent in a body in motion. Def- the followers of Leibnitz fay, that the force of the firft cartes, and all the writers of his time, affumed the ve- ball is four times that of the fecond. locity produced in a body as the meafure of the force All parties are agreed in calling gravity a uniform which produces it; and obferving that a body, in con- or invariable accelerating force; and the definition fequence of its being in motion, produces changes in which they give of fuch a force is, that it always pro- the ftate or motion of other bodies, and that thefe duces the fame acceleration, that is, equal accelerations changes are in the proportion of the velocity of the in equal times, and therefore produces augmentations of 15 changing body, they afferted that there is in a moving velocity proportionable to the times in which they are Controver- body a Vis insita, an INHERENT FORCE, and that this produced. The only effe phenomenon adduced in fupport of the Leibnitzian doc¬ trine, (howing them to be immediate confcquences of the aftion of a force meafured by the velocity which it produces or extinguifhes. There it appears that the heights to which bodies will rile in oppofition to the uniform aCtion of gravity are as the fquares of the initial- velocities : So are the depths to which they will pene¬ trate uniformly refilling matter : So is the number of eqiral fprings which they will bend to the fame degree, &c. &c. &c. We have had frequent oecafion to men¬ tion this propofition as the moft ex ten lively ufeful of all Newton’s difeoveries. It is this which gives the imme¬ diate application of mechanical principles to the expla¬ nation of natural phenomena. It is inceffantly employed QUA [ 597 ] QUA Quantity, in every problem by the very peiTons who hold by the Quaran- ot]ler mcafare of forces, although fuch condufl is virtu- i , 1:i'ie' ally giving up that meaiure. They all adopt, in every rnvefligation the two theorems an&fs — vv; both of which flip pole an accelerating force _/’proportional to the velocity v which it produces by its uniform adtion during the time i, and the theorem j fs — v* is the 39th 1. Princip. and is the confervatio virium viva- rum. This famous difpute (the only one in the circle of mathematical fcieuce) has led us fomewhat aiide. But we have little more to remark with refpect to meafurable quantity. We cannot fay what varieties of quantity are fufceptible of itrift meaiure, or that it is impoffible to give accurate meafures of every thing fufceptible of aug¬ mentation and diminution. We affirm, however, with confidence, that pain, pleafure, joy, &c. are not made op of their oven parts, which can be contemplated fepa- rately : but they may chance to be ailbciated by na¬ ture with fomething that is meafurable; and we may one day ‘be able to affign their degrees with as much pre- cifion as tve now afcertain the degrees of warmth by the expanfion of the fluid in the thermometer. There is one fenfe in which they may all be meaiured, viz numeri¬ cally, as Newton mealures denfity, vis matrix, &c. We can conceive the pain of each of a dozen men to be the lame. Then it is evident that the pain of eight of thefe men is to that of the remaining four as two to one •, but from fuch menfuration we do not forefee any benefit likely to ariie. Quantity, in Grammar, an affection of a fyllable, whereby its meafure, or the time wherein it is pronoun¬ ced, is afcertained ; or that which determines the fylla¬ ble to be long or fhort. Quantity is alfo the objeft of profody, and diftin- guifhes verfe from profe ; and the economy and arrange¬ ment of quantities, that is, the diftribution of long and Ihort fyllables, makes what we call the number. See Poetry, Part 111. The quantities are ufed to be diiTinguifhed, among grammarians, by the characters v, fhort, as per ; and ", long, as ros. There is' alfo a common, variable, or du¬ bious quantity ; that is, fyllables that are at one time ta¬ ken for fhort ones, and at another time for long ones j as the firlt fyllable in Atlas, patres, &c. QUARANTINE, is a trial which fhips muft un¬ dergo when fufpedted of a peftilential infection. It may be ordered by the king, with advice of the privy- council, at fuch times, and under fuch regulations, as he judges proper. Ships ordered on quarantine muft repair to the place appointed, and muft continue there during the time prefcribed (generallv fix weeks) ■, and muft have no intercourfe with the fhore, except- for neceflfary provifions, which are conveyed wuh every poflible precaution. When the time is expired, and the goods opened and expofed to the air as direfted, if there be no appearance of infection, they are admitted to port. Ships infeifted with the peftilence muft proceed to St Helen’s Pool, in the Scilly i(lands, and give notice of their ' tuation to the cuftomhoufe officers, and wait till the king’s pleafure be known. Perfons giving falfe information to avoid performing quarantine; or refilling to go to tho place appointed, or efcaping, alfo officers appointed to fee quarantine per- Quarks, formed, deferring their office, neglefling their duty, or Quarr es- ^ giving a falle certificate, fuffer death as felons. Y" " * Goods from Turkey, or the Levant, may not be land¬ ed without licenfe from the king, or certificate that they have been landed and aired at iome foreign port. See Plague. Q_U ARLES, Francis, the fon of James Quarles clerk to the boaid of green cloth, and purveyor to Queen Elifabeth, was born in 1592. He was educated ar Cambridge j oceanic a member of Lincoln’s Inn ; and w’as for tome time cup-bearer to the queen of Bohe¬ mia, and chronoioger to the city of London. It was probably on the ruin of her affairs that he went to Ire¬ land as fecretary to Archbiihop Uiher ; but the troubles in that kingdom forcing lura to return, and not find¬ ing affairs more at peace in England, fomc difquiets he met with were thought to have haftened his death, which happened in 1644. His works both in profe and verle are numerous, and were formerly in great eueem, particularly ins Divine Emblems : bat the ob- folete quaintnels of his ftyle has caufed them to fall into neglect, excepting among particular claffes of readers. ]jean]ev't “ The memory of Quarles, fays a late author, has \szoxv [deEi Beau. branded with more than common abufe, and he feems to ties of An- have been cenfured merely from the want of being read. clent ^’g- If his poetry failed to gain him friends and readers, his piety thould at leaft have fecured him peace' and good¬ will. He too often, no doubt, miftook the enthu- fialin of devotion for the infpiration of fancy j to mix the waters of Jordan and Helicon in the lame cup, was referved for the hand of Milton •, and for him, and him only, to find the bays of Mount Olivet equally verdant with thofe of Parnaffus. Yet, as the effuiions of a real poetical mind, however thwarted by unto- wardnefs of fubjecl, will be leldom rendered totally abortive, we find in Quarles original imagery, ftriking fenriment, fertility of expreflion, and happy combina¬ tions 5 together with a compreffion of ftyle that me¬ rits the obfervation of the writers of verfe. Grofs de¬ ficiencies of judgement, and the infelicity of his fubjedts, concurred in ruining him. Perhaps 110 circumftance whatever can give a more complete idea of Quarles’s degradation than a late edition of his Emblems ; the following paffage is extradled from the preface : ‘ Mr Francis Quarles, the author of the Emblems that go under his name, was a man of the moft exemplary piety, and had a deep infight into the myfteries of our holy religion. But, for all that, the book itfelf is written in fo old a language, that many parts of it are fcarce intelligible in the prefent age •, many of his phrafes are fo affedled, that no perfon, who has any tafte for read¬ ing, can perufe them with the leaft degree of pleafure; many of his expreffions are harfh. and fometimes whole lives are included in a parenthefis, by which the mind of the reader is diverted from the principal ohjedL His Latin mottoes under each cut can be of no fervice to an ordinary reader, becauie he cannot underhand them. In order, therefore, to accommodate the public with an edition of Quarles’s Emblems properly modernifed, this work was undertaken.’ Such an exhibition of Quarles is chaining Columbus to an oar, or making John Duke of Marlborough a train-band corporal.” QUARRIES, a name commonly given to an ex¬ traordinary cavern under the city of Paris, the exiffi. cnce QUA Quames. cncc of which is known to few even of the inhabitants, and many ox thofe wdio have heard of it confider the whole as an idle ftory. Mr White vifited this cavern in 1784, having, with many others, obtained leave (which is very cautioufly granted) to infpeft it, accompanied by guides with torches. He gives the following account of it in the fecond volume of the Manchelter Tranfac. tions. “ At the entrance by the Obfervatoire Royal, the path is narrow for a confiderable way j but foon we en¬ tered large and fpacious ftreets, all marked with names, the fame as in the city $ different advertifements and bills were found, as we proceeded, parted on the walls, fo that it had every appearance of a large town fwal- lowed up in the earth. “ The general height of the roof is about nine or ten feet ; but in fome parts not lefs than 30 and even 40. In many places there is a liquor continually dropping from it, wTich congeals immediately, and forms a fpecies of tranfparent ftone, but not fo fine and clear as rock cryftal. As we continued our peregrination, we thought ourfelves in no fmall danger from the roof, which we found but indifferently propped in fome places with wood much decayed. Under the houfes, and many of the ftreets, however, it feemed to be tolerably fecured by immenfe ftones fet in mortar ; in other parts, where there are only fields or gardens above it, it was totally unfupported for a confiderable fpace, the roof being perfectly level, or a plane piece of rock. After tra- verfing about twro miles, we again defcended about 20 Heps, and here found fome workmen in a very cold and • damp place, propping up a moft dangerous part, which they were fearful would give way every moment. The path here is not more than three feet in width, and the loof fo low, that we were obliged t© ftoop confiderably. “ On walking fome little diftance farther, we entered into a kind of faloon cut out of the rock, and faid to be exa&ly under the Eglife de St Jacques. This was illu¬ minated with great tafte, occafioned an agreeable fur- prife, and made us all ample amends for the danger and difficulty rve had juft before gone through. At one end was a reprefentation in miniature of fome of the principal forts in the Indies, with the fortifications, draw-bridges, &c. Cannons were planted with a couple of foldiers to each ready to fire. Centinels were placed in different parts of the garrifon, particularly before the governor’s houfe ; and a regiment of armed men was drawn up in another place with their general in the front. The whole was made up of a kind of clay which the place affords, was ingenioufly contrived, and the light that was thrown upon it gave it a very pretty effeft. On the other fide of this hall was a long table fet out with cold tongues, bread, and butter, and fome of the beft Burgundy I ever drank. Now every thing was hilarity and mirth j our fears were entirely difpelled, and the danger we dreaded the moment before was now no longer thought of. In fhort, we were all in good fpints again, and proceeded on our journey about twTo miles farther, when our guides judged it prudent for us to afeend, as we were then got to the fteps which lead up to the town. \Ve here found ourfelves fafe at the Val de Grace, near to the Englifh Benediaine convent, without the leaft accident having happened to any one of the party. We imagined we had walked about two French leagues, and were abfent from the fur face of the earth betwixt four and five hours. 1 *98 ] QUA “ 1 here were formerly feveral openings into the quarries, but the two I have mentioned, viz. the Obfer- vatory and the Val de Grace, are, I believe, the only ones left 5 and thefe the infpetrtors keep conftantly lock¬ ed, and rarely open them, except to ftrangers particu¬ larly introduced, and to workmen who are always em¬ ployed in fome part by the king. The police thought it a neceffary precaution to fecure all the entrances into this cavern, from its having been formerly inhabit¬ ed by a famous gang of robbers, who infefted the coun¬ try for many miles round the city of Paris. “ As to the origin of this quarry, I could not, on the ftridteft inquiry, learn any thing fatisfadtory j and the only account I know publiftied is the following contain¬ ed in the Tableaux de Paris, nouvelle edition, torne pre¬ mier, chapitre yne, page lime. “ For the firft building of Paris it was neceffary to get the ftone in the environs 5 and the confumption of it was very confiderable. As Paris was enlarged, the fuburbs were infenfibly built on the ancient quarries, fo that all that you fee without is effentially wanting in the earth for the foundation of the city : hence proceed the frightful cavities which are at this time found under the houfes in feveral quarters. They ft and upon abyf- fes. It would not require a Very violent ftiock to throw back the ftones to the place fronf whence they have been raifed with fo much difficulty. Eight men being fwal- lowed up in a gulf of 150 feet deep, and fome other lefs known accidents, excited at length the vigilance of the police and the government, and, in fadl, the build¬ ings of feveral quarters have been privately propped up/ and by this means a fupport given to thefe obfeure fub- terraneous places which they before wranted. “ iUl the fuburbs of St James’s, Harp-ftreet, and even the ftreet of Tournon, ftand upon the ancient quarries 5 and pillars have been erefted to fupport the weight of the houfes. What a fubjeft for reflexions, in confidering this great city formed and fupported by means abfolutely contrary ! Thefe towers, thefe fteeples, the arched roofs of thefe temples, are fo many figns to tell the eye that what we now fee in the air is wanting under our feet.” QUARRY, a place under ground, out of which are got xharble, freeftone, flate, limeftone, or other matters proper for building. See Strata. Some limeftone quarries in Fife are highly worthy the attention of the curious, on account of an amazing mixture of organized marine produXions found in them. One of this kind wras opened about the year 1759, at a farm called Enderteel, in the neighbourhood of Kirkal- dy, belonging to General St Clair. The flakes of the ftone, wTich are of unequal thick- nefs, moft: of them from eight to ten inches, lie hori¬ zontally, dipping towards the fea. Each of thefe flakes, when broken, prefents to our view an amazing colleXion of petrified fea bodies, as the bones of fifties, ftalks of fea-weed, vaft quantities of ftiells, fuch as are commonly found on thofe coafts, befides feveral others of very uncommon figures. In fome places the ftiells are fo numerous, that little elfe is to be feen but prodigious clufters or concretions of them. In the uppermoft ftratum the fliells are fo entire, that the outer cruft or plate may be feraped off with the finger 5 and the ftalks of the fca-weed have a darkifli colour, not that gloffy whitenefs which they have in the heart of Quarry. 1 QUA Qii.irry. of the quarry. The fmalleft rays or vein# of the (hells c are deeply indented on the ftone, like the impreffion cl0n of a feal upon wax. In (hort, no fpot at the bottom of the ocean could exhibit a greater quantity of fea- bodies than are to be found in this folid rock; for we have the fkeletons of feveral fifties, the antenna or feelers of lobfters, the roots and (talks of fea-rveeds, with the very capfula which contain the feed. The place where all thefe curiofities are found is on an eminence about an Englifti mile from the fea; and as the ground is pretty deep the whole way, it may be 200 feet higher at lead. There are two or three things to be remarked here. I. That among all the bodies we have mentioned, there are none but what are fpecifically heavier than •water. This holds fo conftantly true, that the fea-weed, which floats in water when the plant is entire, has been dripped of the broad leaves, which make it buoyant, before it has been lodged here. 2. The (hells have been all empty ; for the double ones, as thofe of the flat kind, are always found (ingle, or with one fide only. 3. The rock feems to have been gradually deferted by the fea, and for a long time, wafhed with the tides \ for the up¬ per furface is all eaten, and hollowed in many places like an honey-comb, jud as we obferve in flat rocks expofed every tide to the accefs and recefs of the waters. See the article Sea. Quarry, or Quarrel, among glaziers, a pane of glafs cut in a diamond form. Quarries are of two kinds, fquare and long 5 each of which are of different fizes, exprefled by the number of the pieces that make a foot of glafs, viz. eighths, tenths, eighteenths, and twentieths : but all the fizes are cut to the fame angles, the acute angle in the fquare quarrels being 770 19', and 67° 21' in the long ones. Quarry, among hunters, is fometimes ufed for a part of the entrails of the bead taken, given by way of re¬ ward to the hounds. Quarry, in falconry, is the game which the hawk is in purfuit of, or has killed. QUART, a meafure of capacity, being the fourth part of fome other meafure. The Englifti quart is the fourth part of the gallon, and contains two pints. The quart of the Romans was the fourth part of their congius. The French have various quarts, befides their quart or pot confiding of tivo pints, and are diflinguifhed by the whole of which they are quar¬ ters ; as quart de muid, and quart de boijfeau. QUARTAN, a meafure containing the fourth part of fome other meafure. Quartan, a fpecies of intermitting fever. See Me¬ dicine Index. QU AR T AT ION, is an operation by which the quantity of one thing is made equal to a fourth part of the quantity of another thing. Thus when gold alloyed with filver is to be parted, we are obliged to facilitate the action of the aquafortis, by reducing the quantity of the former of thefe metals to one fourth part of the whole mafs; which is done by (ufficiently increafing the quantity of the filver, if it be neceffary. This operation is called quartatwn, and is preparatory to the parting ; and even many authors extend this name to the opera¬ tion of parting. See Ores, Ana/yjis of. t 599 1 QUA QUARTER, the fourth part of any thing, the frac- Quarter; tional expreflion for which is v— Quarter, in weights, is generally ufed for the fourth part of an hundred weight avoirdupois, or 28 lb. & E > Ufed as the name of a dry meafure, quarter is the fourth part of a ton in weight, or eight buftiels. Quarter, a term in the manege. To work from quarter to quarter, is to ride a horfe three times in upon the fird of the four lines of a (quare } then changing your hand, to ride him three times upon the fecond: and (o-to the third and fourth j always changing hands, and obferving the fame order. Quarters, with refpeft to the parts of a horfe, is ufed in various fenfes: thus the (boulders and fore-legs are called the fore-quarters, and the hips and hinder-legs the hind quarters. The quarters of a horfe’s foot are the (ides of the coffin, comprehending between the toe and the heel; the inner quarters are thofe oppofite to one another, facing from one foot to the other j and thefe are always weaker than the outfde quarters, which lie on the external Tides of the coffin. Falfe quarters, are a cleft in the horn of a horfe’s hoof, extending from the coronet to the (hoe. A horfe is faid to be quarter-cqfl when for any diforder in the coffin we are obliged to cut one of the quarters of the hoof. Quarter, in Afronomij, the fourth part of the moon’s period : thus, from the new moon to the quadrature is the firft quarter; from this to full moon, the fecond quarter, &c. Quarter, in Hera/dnj, is applied to the parts or members of the firfl: divifion of a coat that is quartered, or divided into four quarters. Franc QUARTER, in Heraldry, is a quarter (ingle or alone j which is to poffefs one fourth part of the field. It makes one of the honourable ordinaries of a coat. QUARTER of a Ship, that part of a (hip’s fide which lies towards the (fern •, or which is comprehended be¬ tween the aftmofl: end of the main chains and the (ides of the (fern, where it is terminated by the quarter- pieces. Although the lines by which the quarter and bow of a (hip, with refpedl to her length, are only imagi¬ nary, yet experience appears fufficiently to have afcer- tained their limits : fo that if we were to divide the (hip’s (ides into five equal portions, the names of each fpace would be readily enough expreffed. Thus the firft, from the (fern, would be the quarter ; the fecond, abaft the midftiips j the third, the midfhips ; the fourth, before the midftiips; and the fifth, the bow. Whether thefe divifions, which in reality are fomewhat arbitrary, are altogether improper, may be readily difcovered by referring to the mutual fituation or approach of two ad¬ jacent veffels. The enemy boarded us on the larboard fide ! . Whereabouts ? Abaft the midftiips, before the midftiips, &c. Fig. 1. reprefents a geometrical elevation of a quar- Plate ter of a 74 gun (hip. A the keel, with a the falfe keel ccccrvur. beneath it.. B the ftern-’poft. DD the quarter-gallety, Fi^ u with'its balluftrades and windows. EE the quarter- pieces, which limit and form the outlines of the ftern. F the taffarel, or upper pieces of the ftern. FG the profile of the ftern, with its galleries, FI the gun-ports of; QUA [ 6 Quarter, of the lower deck j h the gun-ports of the upper and U~"V ” quarter-deck. 1 the after-part of the mizen channel. K the wing tranfom. KG the lower counter. LB the ftation of the deck tranfom. L£) the after-part of the main-wale. DR the after-part of the channel-wale, pa¬ rallel to the main-wale. SU the iheer-rail, parallel to both wales. T t the rudder. A t F the rake of the item. P i i the drift-rails. TU the after-part of the load water line; h k l the curve of the feveral decks correfponding to thofe reprefented in the head. See the article Head. As the marks, by which veffels of different conftruc- tions are diltinguilhed from each other, are generally more confpicuous on the ftern or quarter than any other part, we have reprefented fome of the quarters, which affurae the moft different fhapes, and form the greateft Fig. 2. 3.4. con trait with each other. Fig. 2. (hows the ftern and 5- 6- 7* quarter of a Dutch flight. Fig. 3. the ftern and quar¬ ter of a cat. Fig. 4. is the ftern and quarter of a com¬ mon galley. Fig 5. exhibits the quarter of a firft-rate galley, otherwife called a galleajje. Fig. 6. the quarter of a Dutch dogger, or galliot. Fig. 7. reprefents the ftern and quarter of a floop of war. The quarters of all other fhips have a near affinity to thofe above exhibited. Thus all fhxps of the line, and Eaft-Indiamen, are formed with a quarter little differing from the principal figure in this plate. Xebecs have quarters nearly relembling thofe of galeaffes, only fome- what higher. Hagboats and pinks approach the figure of cats, the former being a little broader in the ftern, and the latter a little narrower ; and the fterns and quar¬ ters of cats feem to be derived from thofe of fly-boats. The fterns of Dutch doggers and galliots are indeed lin¬ gular, and like thofe of no other modern veffel : they have neverthelefs a great refemblance to the fhips of the ancient Grecians, as reprefented in medals and other monuments of antiquity. On the QUARTER, may be defined an arch of the ho¬ rizon, contained betwen the line prolonged from the ftiip’s ftern and any diftant objeff, as land, fliips, &c. Thus if the {hip’s keel lies on an eaft and weft line, the ftern being weftward, any diftant objeft perceived on the north-weft or fouth weft, is faid to be on the lar¬ board or itarboard quarter. QUARTER-Bill, a roll, or lift, containing the diffe¬ rent stations, to which all the officers and crew of the Ihip are quartered in the time of battle, and the names of all the perfons appointed to thofe ftations. See Quarters. ’Quarter-Mq/ler, an officer, generally a lieute¬ nant, whofe principal bufinefs is to look after the quarters of the foldiers, their clothing, bread, am¬ munition, firing, &c. Every regiment of foot and ar¬ tillery has a quarter-mafter, and every troop of horfe one, who are only warrant-officers, except in the Blues. QUARTER-Majfer-General, is a confiderable officer in the army ■, and ftiould be a man of great judgment and experience, and well Ikilled in geography. His duty is to mark the marches and encampments of an army : he ffiould know the country perfe&ly well, with its rivers, plains, marfties, woods, mountains, de¬ files, paffages, &c. even to the fmalleft brook. Prior to a march, he receives the order and route from the commanding general, and appoints a place for the o ] 0 U A quarter-mafters of the army to meet him next morning, Quarter, with whom he marches to the next camp ; where being come, and having viewed the ground, he marks out to the regimental quarter-mailers the ground allowed each regiment for their camp : he choofes the head-quarters, •and appoints the villages lor the generals of the army’s quarters : he appoints a proper place for the encamp¬ ment of the train of artillery: he condudls foraging parties, as likewife the troops to cover them againlt af- faults, and has ;■ lhare in regulating the winter-quarters and cantonments. QUARTER Netting, a fort of net-work, extended along the rails on the upper part of a Ihip’s quarter. In a fhip of war thefe are -always double, being fupported by iron cranes, placed at proper diltances. The inter¬ val is fome times filled with cork, or old fails; but chief¬ ly with the hammocks of the labors, fo as to form a pa¬ rapet to prevent the execution of the enemy’s fmallarms in battle. OyARTER-SeJJions, a general court held quarterly by RiackJI. the juftices of peace of each county. This court is Comment. appointed by flat. 1 Hen. V. c. 4. to be in the firftvoi-1V- week after Michaelmas-day •, the firft week after the1" 2'1‘ Epiphany $ the firft week after the clofe of Eafter 5 and in the week after the tranllation of Saint Thomas a Becket, or the 7th of July. 'J he court is held before two or more juftices of the peace, one of whom mult be of the quorum. The jurifdidfion of this court by 34 Fid. III. c. 1. extends te the trying and. determining of all felonies and trefpaffes whatfoever, though they feldom, if ever, try any greater offence than imall fe¬ lonies within the benefit of clergy, their commiffion providing, that if any cafe of difficulty arifes, they lhall not proceed to judgment, but in the prefence of one of the iuftices of the courts of king’s benca or common pleas, or one of the judges of affize. And therefore murderers and other capital felons are ufu- ally remitted for a more folemn trial to the affizes. They cannot alfo try any new7 created offence, without exprefs power given them by the ftatute which creates it. But there are many offences, and particular mat¬ ters, which by particular flatutes belong properly to this jurifdiftion, and ought to be profecuted in this court j as, the fmaller mifdemeanors againft the public or commonwealth, not amounting to felony, and efpe- ciaily offences relating to the game, highways, alehoufes, baftard children, the fettlement and provifion for the poor, vagrants, fervants wages, apprentices, and popifh recufants. Some of thele are proceeded upon by in¬ dictment, and others in a fummary way .by motion and order thereupon ; which order may, tor the moft part, unlefs guarded againft by particular flatutes, be remo¬ ved into the court of king’s bench, by writ of certiorari facias, and be there either quaff ed or ccnfirmed. The records or rolls of the feffions are committed to the cuf- tody of a fpecial officer, denominated the cttfos rctu- lorutn. In moft corporation towns there are quarter-lef- ficns kept before ji ftices of their ow n, within their re- fpeCHve limits, which have exaCUy the fame authority as the general quarter-feffions of the county, except in very few inftances: one of the moft confiderable of which is the matter of appeals from orders of removal of the poor, which, though they be from the orders of corporation juftices, mnft be to the feffions of the county, by 8 and 9 Will. III. c. 30. In both corpo¬ rations Quarter- Staff; Quarters. QUA [ 60 rations and counties at large, there is fometimes kept a fpecial or petty feffion, by a few juftices, for difpatch- , ing fmaller bufmefs in the neighbourhood between the times of the general fefTions, as for licenfing ale- houfes, pafling the accounts of parith-officers, and the like. ARTER-Staff, a long ftaff borne by forefters, park- keepers, &c. as a badge of their office, and occafionally ufed as a weapon. QUARTERS, a name given at fea to the feveral fta- tions wrhere the officers and crew of a ffiip of war are pofted in action. See Naval Tactics. The number of men appointed to manage the ar¬ tillery is always in proportion to the nature of the guns, and the number and condition of the ffiip’s crew. They are, in general, as follow, when the ihip is well manned, fo as to fight both fides at once oc¬ cafionally : Pounder. To a 42 32 24 18 12 No. of men. 6 5 4 3 No. of men. Pounder. 15 To a 9 13 6 11 4 9 3 7 This number, to which is often added a boy to bring powder to every gun, may be occafionally reduced, and the guns neverthelefs well managed. The number of men appointed to the fmall arms, on board his Ma- jelty’s ilups and Hoops of war, by order of the admiralty, are. Rate of the fh!p. ift 2d 3d of 80 guns —of 70 guns 4th of 60 guns 4th of 50 guns 5th 6th Sloops of war No. of men to the fmall arms. 150 120 100 80 70 - 60 50 40 30 The lieutenants are ufually Rationed to command the different batteries, and diredd their efforts againff the enemy. The mailer fuperintends the movements of the fhip, and whatever relates to the fails. The boat- fwain, and a fufficient number of men, are Rationed to repair the damaged rigging *, and the gunner and car¬ penter, wherever neceffary, according to their refpe£live offices. The marines are generally quartered on the poop and forecafile, or gang-way, under the dire&ion of their officers •, although, on fome occafions, they af- fifi at the great guns, particularly in dillant cannon¬ ading. Quarters, at a liege, the encampment upon one of the principal paffages round a place befieged, to pre¬ vent relief and convoys. Head Quarters of an Army, the place where the commander in chief has his quarters. The quarters of generals of horfe are, if poffible, in villages behind the right and left wings, and the generals of foot are often in the fame place : but the commander in chief Ihould be near the centre of the army. QUARTERS of Rcf cfhment, the place or places where Vox.. XVII. Part II. Quaffia. 1 3 QUA troops that hare-been much haraffed are put to recover Quarts themfelves during fome part of the campaign. Intrenched Quarters, a place fortified with a ditch and parapet to fecure a body of troops. Winter QUARTERS, fometimes means the fpace of time included between leaving the camp and taking the field j but more properly the places where the troops are quartered during the winter. The firR bulinefs, after the army is in winter-quar¬ ters, is to form the chain of troops to cover the quarters well: which is done either behind a river, under cover of a range of Rrong poRs, or under the proteftion of fortified towns. Huffars are very ufeful on this fer- It ffiould be obferved, as an invariable maxim, in winter-quarters, that your regiments be difpofed in brigades, to be always under the eye of a general offi¬ cer ; and, if poffible, let the regiments be fo diflri- buted, as to be each under the command of its own chief. QUARTILE, an afpe and put the roots he has prun- tive running mercury are found near the lurface of the “ ■ ' ed off into fand or mould, where they will keep until earth, that the black Haves often colledt it in good quan- he has leifure to cut them into proper lengths for plant- titles, and fell it for a trifling price to the apothecaries ing *, he Will likewiie keep them in the fame way until but none of thefe mines have ever been worked or taken planted. ^ notice of by the owners. Gold naturally amalgamated “ The great advantage of my plan is : firft, that in with mercury is likewife met with in the neighbourhood cafe any one has raifed from haws a thorn with remark- of that place 5 and it is laid that almoft all the gold ably large piickles, of vigorous growth, or pofTeffing mines of that country are worked out by limply walking any other qualification requifite to make a good fence, them out with running water, after reducing into pow^- he may propagate it far better and fooner, from roots, der the hard ores, which are fbmetimes imbedded in than any other way. Secondly, in three years he may quartzofe and rocky matrices. raife from roots a better plant than can in fix years be In the duchy of Deux Fonts and in the Lower Au- i'abed from haws, and with double the quantity of Aria the quickiiiver flows from a fchifiofe or ftony ma- rools ", my three-year-old fpecimen would have been trice, and is probably, fays Mr Kirwan, mixed with half as big again, had I not been obliged to move all fome other metal, as its globules are not perfe&ly fphe- my cuttings the fecond year after they were planted. rical. The mines of Friuli are all in limiiar beds or “ It would not be a bad way, in order to get roots, to ftrata. The metal is likewife found vilibly diffufed plant a hedge in any convenient place, and on each fide through mafles of clay or very heavy ftone, of a w'hite, trench the ground two yards wide, and tw’o grafts deep; red, or blue colour ; of which laft kind are the mines of from which, every two or three years, a large quantity Spain, fome of Idria, and of Sicily. Mafcagni found of roots might be obtained, by trenching the ground fluid quickfilver, as well as native cinnabar and mineral over again, and cutting away what roots w'ere found, ethiops, near the lake of Travale in the duchy of Sien- which would all be young and of a proper thicknefs.” na ; but the quantity was fo fmall as not to be worth QUICKLIME, a general name for all calcarous fub- the expence of working. On the other hand, the fol- fiances when deprived of their fixed air ; fuch as chalk, lowing mines afford profits to the owners after clearing limeftone, oyfter-fiiells, &c calcined. See Lime, ChiT- all expences, viz. thofe at Kremnitz in Flungary ; at MISERY, for an account of the properties and combina- Horowitz in Bohemia ; Zorge in Saxony; W olfiteim, tions of lime. Stahlberg, and Moefchfeld in the Palatinate. Mercury QUICKSILVER, or Mercury, one of the metals, is alfo brought from Japan in the Eail Indies ; but the and fo fufible that it cannot be icduced to a foil’d fiate greateft part of what is fold in Europe as Japan cinna- but at a degree of cold, equal to 40 below o of Fahren- bar is faid to be manufactured in Holland, heit’s thermometer. For the method of extracting Lemery, Pomet, and others, lay down fome external quickfilver from its ore, &c. fee ORES, ReduEiion of. marks by which thofe places are diitinguilhed where lor the various preparations, &c. fee Chemistry and there are mines of quickfilver, viz. thick vapours like Materia Medica Index; and for the natural hiftory of clouds arifing in the months of April and May; the the ores of quickfilver or mercury, fee Mineralogy plants being much larger and greener than in other Index. places : the trees leldom bearing flowTers or fruit, and Mines of quickfilver are very rare, infomuch that, ac- putting forth their leaves more flowly than in other cording to the calculations of Hoffman, there is 50 times places; but, according to Neumann, thefe marks are more gold got every year out of the mines than mercury far from being certain. They are not met with in all and its ores. But Dr Lewis, in his notes upon Newmann, places where there is quickfilver, and are obferved in fays, that Cramer fufpefts that Hoffman only meant five places where there is none. Abundance of thefe cloudy times inftead of 50 ; but neither the Latin nor the Eng- exhalations are met with in the Hariz forett in Ger- lifh edition of this author expreffes any fuch thought; on many, though no mercury has ever been found there; the contrary, he adopts the fame opinion ; and only adds, to winch we may add, that through vaft quantities of that mercury is much more frequently met with than is mercurial ores are found at Almaden in Spain, none of commonly believed ; but being fo volatile in the fire, it the above-mentioned indications are there to be met often flies off in the roafting of ores, and efcapes the at- with. tention of metallurgifts. Native mercury was formerly fought from the mines According to NewTmann, the mines of Idria have pro- of Idria with great avidity by the alchemifts for the pur- duced at the rate of 231,778 pounds weight of mercury pofe of making gold ; and others have {bowed as ridi- per annum ; but thofe of Almaden in Spain produce culous an attachment to the Hungarian cinnabar, flip- much more. The chemifts of Dijon inform us, that pofing it to be impregnated with gold ; nay, we are in- their annual produce is five or fix thoufand quintals, or formed by Newmann, that not only the cinnabar, anti- between five and fix hundred thoufand pounds weight. monyf and copper of Hungary, but even the vine trees In the year 1717 there were upwards of 2,500,000 of that country were thought to be impregnated with pounds of quickfilver fent from them to Mexico, for the the precious metal. Not many yeai'S ago a French che- amalgamation of the gold and filver ores of that coun- miff advertifed that he had obtained a confiderable quan- try. tity of gold from the allies of vine twigs and ftems, as At Guan^avelica in Brafil the annual produce of the well as of the garden foil where they grew : but the mines, according to Bomare, amounts to one million of falfehood of thefe affertions was demonffrated by the pounds, which are carried overland to Lima, thence to count de Lauragais to the fatisfadfion of the Royal Aca- Arica, and laftiy to Potofi for the fame purpofe. demy of Sciences. Befldes thefe mines there are others in Brafil near The redudlion of mercury into a folid flate, fo that it Qm; ufts. Q U I [608 Quickfilvei' it might be employed like filver, was another favourite 1 alchemical purfuit. But all procefles and operations of this kind, fays Newmann, if they have mercury in them, are no other than hard amalgams. When melted lead or tin are juft becoming conliftent after fufion, if a flick be thruft into the metal, and the hole filled with quick- filver, as loon as the whole is cold, the mercury is found folid. Macquer informs us, that mercury becomes equal¬ ly folid by being expofed to the fumes of lead. Mau¬ rice Huffman, as quoted by Newmann, even gives a pro- ceis for reducing mercury, thus coagulated, to a ftale of malleability, viz. by repeatedly melting and quenching it in linfeed oil. Thus, he tells us, we obtain a metal which can be formed into rings and other utenfils. But here the mercury is entirely diflipated by the repeated fufions, and nothing but the original lead is left. Wal- lerius, after mentioning ftrong foap-leys, or cauftic lixi¬ vium, and fome other liquors proper for fixing quick- filver, tells us, that by means of a certain gradatory wa¬ ter, the compofition of which he learned from Creuling dc Aureo Ve/lere, he could make a coagulum of mercury whenever he pleafed, of fuch confiftency that great part of it would refill cupellation 5 but what this gradatory water was, he has not thought proper to lay before the public. QUICK-match, among artillery men, a kind of combuftible preparation formed of three cotton ftrands drawn into length, and dipped in a boiling compofi. tion of white-wine vinegar, faltpetre, and mealed pow¬ der. After this immerfion it is taken out hot, and laid in a trough where fome mealed powder, moiftened with fpirits of wine, is thoroughly incorporated into the twills of the cotton, by rolling it about therein. Thus pre¬ pared, they are taken out feparately, and drawn through mealed powder ; then hung upon a line and dried, by which they are fit for immediate fervice. QUID pro quo, in Law, q. d. “ what for what,” denotes the giving one thing of value for another j or the mutual confideration and performance of both par¬ ties to a contra£l. Quib pro quo, or Qui pro quo, is alfo ufed in phyfic to exprefs a miftake in the phyfician’s bill, where quid is wrote for quo, i. e. one thing for another ; or of the apothecary in reading quid for quo, and giving the pa¬ tient the wrong medicine. Hence the term is in the ge¬ neral extended to all blunders or miftakes committed in medicine, either in the prefeription, the preparation, or application of remedies. QUIDDITY, quidditas, a barbarous term ufed in the fchools for ejjence. The name is derived hence, that it is by the eflence of a thing that it is a tale quid, fuch a quid, or thing, and not another. Hence what is effential to a thing is faid to be quiddative. QUIETISTS, a religious febl, famous towards the clofe of the lafl century. 1 hey were fo called from a K-ind of abfolute reft and inadtion, which they fuppofed the. foul to be in when arrived at that Hate of perfedlion which they called the unitive life ; in which Hate they imagined the foul wholly employed in contemplating its God, to whofe influence it was entirely fubmiflive ; fo that he could turn and drive it where and how he would. In this.ftate, the foul no longer needs prayers, hymns, &c. being laid, as it were, in the bofom and between the arms of its God, in whom it is in a manner fwallow- ed up. ] QUI Molinos, a Spanifh prieft, is the reputed author of (hretift*. Quictifm j though the Illuminati in Spain had certain- ly taught fomething like it before. The fentiments of Molinos were contained in a book which he publifhed at Rome in the year 1681, under the title of the Spi¬ ritual Guide; for which he was call into prifon in 1685, and where he publicly renounced the errors of which he was accufed. This folemn recantation, how¬ ever, was followed by a fentence of perpetual imprifon- ment, and he died in prifon in the year 1696. Moli¬ nos had numerous difciples in Italy, Spain, France, and the Netherlands. One of the principal patrons and propagators of Quietifm in France was Marie Bouvi- eres de la Mothe Guyon, a woman of falhion, remark¬ able for goodnefs of heart and regularity of manners j but of an unfettled temper, and lubjefl to be drawn away by the feduftion of a warm and unbridled fancy. She derived all ideas of religion from the feelings of her own heart, and deferibed its nature to others as Ihe felt it herfelf. Accordingly her religious fentiments made a great noife in the year 1687 ; and they were de¬ clared unfound, after accurate inveftigation, by feveral men of eminent piety and learning, and profeffedly con¬ futed, in the year 1697, ^7 ^ celebrated Boffuet. Hence arofe a controverly of greater moment between the prelate laft mentioned and Fenelon archbilhop of Gambray, who feemed difpofed to favour the fyftem of Guyon, and who in 1697 publilhed a book contSining feveral of her tenets. Fenelon’s book, by means of Boffuet, was condemned in the year 1699, by Innocent XII. and the fentence of condemnation was read by Fe¬ nelon himfelf at Cambray, who exhorted the people to refpedl and obey the papal decree. Notwithftanding this feeming acquiefcence, the archbilhop perfifted to the end of his days in the fentiments, which, in obedi¬ ence to the order of the pope, he retraced and condemn¬ ed in a public manner. A fedl fimilar to this had appeared at Mount Athos in Theffaly, near the end of the 14th century, called Hefychqfis, meaning the fame with Quietifts. They were a branch of the myftics, or thofe more perfedl monks, who, by long and intenfe contemplation, endea¬ voured to arrive at a tranquillity of mind free from every degree of tumult and perturbation. In conformity to an ancient opinion of their principal doftors (who thought there rvas a celeftial light concealed in the deepeft retirements of the mind), they ufed to fit every day, during a certain fpace of time, in a folitary-corner, with their eyes eagerly and immoveably fixed upon the middle regions of the belly, or navel ; and boafted, that while they remained in this pofture, they found, in ef¬ fect, a divine light beaming forth from their foul, which diffufed through their hearts inexpreflible fenfations of pleafure and delight. To fuch as inquired what kind of light this was, they replied, by way of illuftration, that it was the glory of God, the fame celeftial radiance that furrounded Chrift during his transfiguration on the Mount. Barlaam, a monk of Calabria, from whom the Barlaamites derived their denomination, ftyled the monks who adhered to this inftitution MaJJ'alians and Euchites ; and he gave them alfo the new name of Umbilicani. Gregory Palamas, archbilhop of Theffalonica, defended their caufe againft Barlaam, who was condemned in a council held at Conftantinople in the year 1341.—See Tendon's Max. des Saints. The 4 Q, U l The IV^ahometans feem to be no Grangers to quietifm. They expound a paffage in the 17th chapter of the Ko¬ ran, viz. “ O thou foul which art at reft, return unto thy Lord, See.” of a foul which, having, by puifuing the concatenation of natural caufes, raifed itfelf to the knowledge of that being which produced them and exifts of neceflity, refts fully contented, and acquiefces in the knowledge, &c. of him, and in the contemplation of his perfection. QUILLET, Claude, an eminent Latin poet of the 17th century, was born at Chinon, in Touraine, and practifed phylic there with reputation : but ha¬ ving declared againft the pretended poffeflion of the nuns of Loudun, in a manufeript treatife, the original of which was depofited in the library of the Sorbonne, he was obliged to retire into Italy, where he became fe- cretary to the marlhal d’Eftrees, the French ambaffador at Rome. In 1655 Quillet having publiftred in Holland a Latin poem, entitled Ca/lipccdia, under the name of •Galvidius La-tus, he there inlerted fome verfes againft the cardinal Mazarine and his family ; but that cardi¬ nal making him fome gentle reproaches, he retrenched what related to the cardinal in another edition, and dedicated it to him, Mazarine having, before it was printed, given him an abbey. He died in 1661, aged 59, after having given Menage all his writings, and 500 crowns to pay the expence of printing them j but the abbe took the money and papers, and publiftr¬ ed none of them. His Cal/ipcedia, or the art of get¬ ting beautiful children, has been tranflated into Englilh verfe. QUILLS, the large feathers taken out of the end of the wing of a goofe, crow, &c. They are denomi¬ nated from the order in which they are fixed in the wing j the fecond and third quills being the beft for writing, as they have the largeft and roundeft barrels. Crow-quills are chiefly ufed for drawing. In order to harden a quill that is foft, thruft the barrel into hot aftres, ftirring it till it is foft, and then taking it out, prefs it almoft flat upon your knee wdth the back of a penknife, and afterwards reduce it to a roundnefs with your fingers. If you have a number to harden, fet wra- ter and alum over the fire, and while it is boiling put in a handful of quills, the barrels only, for a minute, and then lay them by. QUIN, James, a celebrated performer on the En- glilh ftage, w^as born at London in 1693. He was in¬ tended for the bar ; but preferring Shakefpeare to the ftatutes at large, he on the death of his father, when it was neceffary for him to do fomething for himfelf, ap¬ peared on the ftage at Drury-lane. In 1720, he firft riifplayed his comic powers in the character of Falftaflf, and foon after appeared to as great advantage in Sir John Brute 5 but it was upon Booth’s quitting the ftage that Quin appeared to full advantage, in the part of Cato He continued a favourite performer until the year 1748* when, on fome difguft between him and Mr Rich the manager, he retired to Bath, and only came up annually to aft for the benefit of his friend Ryan j until the lofs of two front teeth fpoiled his utterance for the ftage. While Mr Quin continued upon the ftage, he conftantly kept company with the greateft geniufes of the age. He was well known to Pope and Swift and the earl of Chefterfield frequently invited VOL. XVII. Part IL [ 609 1 Q U I him to his table : but there was none for whom he en¬ tertained a higher efteem than for the poet Thom- fon, the author of the Seafons, to whom he made him¬ felf knowm by an aft of generefity that does the greateft 1 honour to his charafter; and for an account of which fee our life of Thomson. Mr Quin’s judgement in the Englilh language recommended him to his royal high- nefs Frederick prince of Wales, who appointed him to inftruft his children in fpeaking and reading with a graceful propriety; and Quin being informed of the elegant manner in which his prefent Majefty delivered his firft gracious fpeech from the throne, he cried out in a kind of eeftafy, “ Ay—I taught the boy to fpeak ! ” Nor did his majefty forget his old tutor ; lor, foon after his acceftion to the throne, he gave orders, without any application being made to him, that a genteel penfion ftrould be paid to Mr Quin during his life. Mr Quin, indeed, was not in abfolute need of this royal benefac¬ tion $ for, as he wras never married, and had none but diftant relations, he lirnk 2C00I. which was half his for¬ tune, in an annuity, for which he obtained 200I. a-year j and with about 2000I. more in the funds, lived in a de¬ cent manner during the latter part of his life at Bath, from wTence he carried on a regular correfpondence with Mr Garrick, and generally paid a vifit to his friends in the metropolis once a-year, when he conftantly palled a week or two at Mr Garrick’s villa at Hampton. He died of a fever in 1766. QUINARIUS, wras a fmall Roman coin equal to half the denarius, and confequently wTorth about three¬ pence three farthings of our money. See Money. It was called quinarius, becaufe it contained the value of five afles, in the fame manner as the denarius wras named from its containing ten. QUINAUT, Philip, a celebrated French poet, born of a good family at Paris in 1635. He cultivated poetry from his infancy, and 16 dramatic pieces of his were afted between the years 1653 and 1666. In the mean time, Quinaut wras not fo much devoted to poetry but that he applied himlelf to the ftudy of the law ; and made his fortune by marrying the widow of a rich mer¬ chant to whom he had been ufeful in his profeflion. Ouinaut afterwards turned his attention to the compo- fing of operas, which w^ere fet to mufic by the famous Lully ; and Lully was charmed with a poet whefe verfes wrere not too nervous to yield to the capricious airs of mufic. He died in 1688, after having for many years enjoyed a handfome penfion from Louis XIV. : and W’e are told he w’as extremely penitent in his laft illnefs for all thofe of his compofitions which tended to infpire love and pleafure. QUINCE, in Botany. See Cydonia. QUINCUNX, in Roman antiquity, denotes any thing that confifls of five-twelfths of another } but particular¬ ly of the as. Quincunx Order, in gardening, is a plantation of trees, difpofed originally in a fquare confifting of five trees, one at each corner, and a fifth in the middle; which difpofition, repeated again and again, forms a re¬ gular grove, wTood, or wildernefs. QUINDECAGON, in Geometry, a plain figure with 15 fides and 15; angles. QUINDECEMVIRI, in Roman antiquity, a col¬ lege of 15 magiftrates, w hofe bufinefs it was to prefide 4 H over Quin II Q^iinde- cemviri. q u i Quinqfta,- nan us Quin ten ever the facrifiees. They tvere alfo the inlerpreters of the Sybil’s books 5 which, however, they never confult- ed but by an exprefs order of the lenate. OUINOUAGENABIUS, in Roman antiquity, an officer who had the command of 50 men. O UiNpUAGESiMA Sunday, Shrove Sunday, fo called as being about the 50th day before Rafter. QUIN^HJATRIA, or Ouinquatrus, was a feftival kept at Rome in honour of Minerva, which began on the 13th of March, or, as others will have it, on the 19th, and lafted five days. On the firft day they offer¬ ed lacrifices and oblations without the eftufion of blood 3 the fecond, third, and fourth, were fpent in (hows ot gladiators 3 and on the fifth day they went in proceflion through the city. Scholars had a vacation during the lolemnity, and prefented their mailers at this time with a gift or fee, called Minerval. Boys and girls ufed now to pray to the goddefs Minerva for wifdom and learning, of which Ore had the patronage. Plays were added, and difputations held, at this feali, on lubjedls of polite li¬ terature. The quinquatria were fo called, becaufe they laffed for five. days. There feerns to be a ftrong re- femblance betwixt this fedival and the panathenoea of the Greeks. QUINQUENNALIS, in Roman antiquity, a magi- .flrate in the colonies and municipal erties of that empire, who had much the fame office os the gedile at Rome. pUINQUEREMIS, in the naval architefture of the ancients, a name given to a galley which had five rows of oars. They divided their veffels in general in- * See Toly- to monocrota and polycrota*. The former had only one c>ota. t;r2 0f rowers : - t'he latter had feveral tires of them, from two or three up to 20, 36, or even 40 3 for fuch a veffei rve have an account of in the time of Philopater, which required no lefs than 4000 men to row it. Meibom has taken off from the imaginary improba¬ bility of there ever having been fuch a veffel, by redu¬ cing the enormous height fuppofed neceffary for Inch a number of rows of oars and men to work them, by find¬ ing a better way of placing the men than others had thought of. The quinqueremes of the ancients had 420 men in each 3 300 of which were rowers, and the red foidiers. The Roman fleet at Medina confided of 330 of thtfe (hips 3 and the Carthaginian, at Lilyboeum, of 330 of the fame fize. Each veffel was 1 co feet long. Thus 1 30,000 men were contained in the one, and 150,000 in the other, with the apparatus and pro- vifiems neceffary for fuch expeditions as they were intend¬ ed for. This gives fo grand an idea of the ancient na¬ val armaments, that fome have quedioned the truth of the hidory : but we find it related by Polybius, an hi- llorian too authentic to be queftloned, and who expreffes his wonder at it while he relates it. QUINQUEVIRI, in Roman antiquity, an order of five prieds, peculiarly appointed for the facrifices to the dead, or celebrating the rites of Erebus. QUINQUINA. See Cinchona, Botany and Ma¬ teria Medica Index. QUINSY, or Quinzy. See Medicine, n° 177— j83- QUINTEN, a town of France, in Bretagne, with a handfome caftle. It is feated in a valley near the ri¬ ver Guy, and near a large fored of the fame name, eight miles fouth of St Brieux, and 200 weft of Paris. It had. W. Long. 2. 40. N. Quint of¬ fence [ 610 ] q u formerly the title of a duchy. Lat. 48. 26. QUINTESSENCE, in Chemiflnj, a preparation con- fitting of the effential oil of tome vegetable fubftance, „ mixed and incorporated with {’pint ot wine. Quintessence, in Alchemy, is a myfterious term, figr ntying the fifth or lad and higheft cftence of power in a natural body.—Or when divettedof its alchemiiiical fignification, and employed to exprefs iomethmg that is intelligible, the word denotes merely the highett ftate of purification in which any body can be exhibited. Q UINTAL, the weight of loolbs. inmoft coun¬ tries, but in England it is the cwt. or 112 lbs. Quin¬ tal was formerly uled for a weight of lead, iron, or other common metal, ufually equal to 100 lbs. at fix Icores to the hundred. QUINTILE, in AJlronomy, an afpe£f of the planets when they are 72 degrees aidant from one another, or a fifth part of lire zodiac. QUINTILIANUS, Marcus Fabius, a celebrated Latin oraror, and the moil judicious critic of his time, was a native oi Calagurris, or Calahorra, in Spain 3 and was the difciple of Domnins A ter. who died in the year 59. He taught rhetoric at Rome for 20 years with great applaui'e : and not only laid down rules for fpcak¬ ing, but exhibited his eloquence at the bar. Some au¬ thors imaeine, but with little foundation, that he am- O 7 . . . . ved at the con uhhip 3 but tt is more certain that he was preceptor to the grandibns of the emperor Domitian’s fider. There is dill extant his excellent work, intitled, Injlitutiones Orator ice, which is a treatife of rhetoric in 12 books 3 where his precepts, judgment, and tade, are judly admired. Thefe inditutions were found entire by Poggius, in an old tower of the abbey of St Gal, and not in a grocer’s ihop in Germany as feme authors have afferted. There is alfo attributed to Quintilian a dia¬ logue De caujis corruptee eloquenlue ; but it is more commonly aicribed to Tacitus. The bed editions of Quintilian’s works are thofe of Mr Obreight, publithed at Strafburg in 2 vols qto, in 1698, and of M. Cap- peronier, in folio. There is an Englith tranilation by Mr Guthrie. Quintilian had a fon of the fame name, on whom he bedows great praids. This fon ought not to be con¬ founded with Quintilian the father, or rather the grand¬ father, of him who is the fnbjeft of this article, and who wrote 145 declamations. Ugolin of Parma publithed the firlt 1 36 in the 15th century 3 the nine others were publithed in 1563 by Peter Ayrault, and afterwards by Peter Pithou in 1580. There have alfo been 19 other declamations printed under the name of Quintilian the Orator ; but, in the opinion of Voffius, they were writ¬ ten neither by that orator nor his grandfather. QUINTILIANS, a feel of antient heretics, thus called from their prophetefs Quintilia. In tins feft the women were admitted to perform the faceidotal and epif- copal functions. They attributed extraordinary gifts to Eve for having fird eaten of the tree of knowledge 3 told great things of Mary the lider ol Mofes, as having been a prophetefs, &c. They added, that Philip the deacon had four daughters, who were all propheteffes, and were of their feft. In thefe affemblies it was ufual to fee the virgins entering in white robes, perfonating propheteffes. QUINTIN Quintin II Quiritff. Q U I f Cn ] Q U I ()UINTJN MATSYS, alfo called the Farrier of Ant¬ werp, famous for being transformed, by the force of love, from a blackfmith to a painter. He had followed the trade of a blackfmith and farrier for near twenty years •, when falling in love with a painter’s daughter who was very handfcme, and diiliked nothing but his trade, he quitted it, and betook himielt. to painting, in which he made very great progrefs. Ho-was a diligent and careful imitator or ordinary life, and lucceeded bet¬ ter in reprefeuling the deietts than the beauties of na¬ ture. Some hiftoiical performances of this matter deferve commendation, particularly a Defcent from the Crofs, in the cathedral at Antwerp : but his belt known pifture is that of the two Miters it) the gallery at Vv indfor. He died in 1529. QU INTIN IE, John df. la, a celebrated French gardener, born at Poidiers in 1626. Pie was brought up to the law j and acquitted himfelf fo well at the bar as to acquire the efteem of the chief magiftrate. M. Tamboneau, prefident of the chamber of accounts, en¬ gaged him to undertake the precepiorfhip of his only ton, which Quintinie executed entirely to his falisfac- tion ; applying Iris leifure hours to the fludy of writers on agriculture, ancient and modern, to which he had a ftrong inclination. He gained new lights by attending his pupil at Italy ; for all the gardens about Home be¬ ing open to him, he failed not to add praftice to his the¬ ory. On his return to Paris, M. Tamboneau gave up the management of his garden entirely to him } and puintinie applied fo clofely to it, that he became fa¬ mous all over France. Louis XIV. creeled a new of¬ fice purpofely for him, that of direclor of the royal fruit and kitchen gardens; and thefe gardens, while he lived, were the admiration of the curious. He lived to a good old age; we have not learned the time of his death ; his Hi regions for the management of Fruit and Kitchen Gardens have been much efteemed. QUINTUS CALABER, a Greek poet, who wrote a large Supplement to Homer’s Iliad, in 14 bocks, in which a relation is given of the Trojan w ar from the death of Heftor to the deftruftion of Troy. It is con- je£lured, from his ftyle and manner, that he lived in the fifth century. Nothing certain can be colle&ed either concerning his perfon or country. His poem was firit made known by Cardinal Beffanon, w7ho difeovered it in St Nicolas’s church, near Otranto in Calabria; from whence the author w'as named Quintus Calaber. It was firii publithcd at Venice by Aldus, but it is not laid in what year. QUINTUS Curtius. See CurFius. QUINZY, QuiNSEY, or Angina Pectoris. See Me¬ dicine, N° 409. QUIRE of Paper, the quantity of 24 (heels. QUIRINALIA, in antiquity, a feaft celebrated a- mong the Romans in honour of Romulus. QUIRITES. in Roman antiquity. In confequence of the agreement entered into by Romulus and latius king of the Sabines, Rome was to retain its name, taken from Romulus, and the people were to be called ^uiri¬ tes, from Cures, the principal town of the Sabines, a name ufed in all public addrefles to the Roman people. Dion. Hal. fays,' that each particular citizen was to be called Romanus, and the colleftive body of them Quirites; yet it appears by this ancient form of w'ords ufed at funerals, Ollus ^uiris letho datus ejty that each private citizen was alio called d^uiris. The origin of the word ^uirites, which was at fil'd peculiar to the Sabines, and became, in Romulus’s time, the general name of the inhabitants of Rome, has been much fought for •, and the molt probable account antiqui¬ ty gives us of it, is this : The word ^uiris, according to Plutarch and fome others, fignified, in the Sabine language, both “ a dart,” and “ a warlike deity armed with a dart.” It it uncertain whether the god gave name to the dart, or the dart to the god. But be that as it will, this Quins, or Quirinus, was either Mars or fome other god of war j and the worfhip of Qjiiris con¬ tinued in Rome all Romulus’s reign : but after his death he was honoured with the name Qgiinnus, and took the place of the god Quins. QUIRK, in a general fenfe, denotes a fubtilty or art¬ ful didindfion. Quirk, in building, a piece of ground taken out of any regular ground-plot, or door : thus, if the ground- plot were oblong or fquare, a piece taken out of a cor¬ ner to make a court or yard, &c. is called a quirk. QUI3QUALIS, a genus of plants belonging to the decandria clafs, and in the natural method ranking un¬ der the 3 id order, Veprccutce. See Botany Index. QUITO, a town of South America, in Peru (fee Pi.Ru),feated between twochains of high mountains call¬ ed Cordillera de los Andes, on much higher ground than the red of habitable Peru. It is 300 yards higher than the level of the fea according to the exacted obfervations. The town is 1600 yards long and 1200 broad, and is the feat of a bifhop. It contains about 35,000 inhabi¬ tants, one-third of whom are originally Spaniards. Among the inhabitants are fome perfons of high rank and didindtion, defeended either from the original con¬ querors, or perfons who at different times came from Spain invefted with fome lucrative pod. The number of thefe, however, is but fmall. The commonalty, be- fides Spaniards, confid of Medizos, Indians, and Ne¬ groes ; but the lad are not proportionally numerous. Merchandiies and commodities of all forts are ex¬ tremely dear, partly on account of the difficulty of bring¬ ing them. There are feveral religious communities at Quito, and two colleges or univerfities governed by Jefuits and Do¬ minicans. The principal courts held at Quito are that,,of the royal audience, which esnfifts of the prefident, who is governor of the province with regard to law affairs; four auditors, who are at the fame time civil and cri¬ minal judges } a royal fifeal, who, befides the caufes brought before the audience, takes cognizance of every thing relating to the revenue; and an odicer dyled the proteBor of the Indians, who folicits for them, and when they are injured pleads in their defence. The next is the treafury, the chief officers of which are an account¬ ant, a treafurer, and a royal fifeal. The tribunal of the Croifade, which has a commiffary, who is generally fome dignitary of the church, and a treafurer. There is alfo a treafury for the effefts of perfons deceafed : an inditution edablidied all over the Indies, for receiving the goods of thofe whofe lawful heirs are in Spain, in order to fecure them from thofe accidents t@ which they might be liable in private hands. There is like- 4 H 2 wife \ R A A [6 Quitter- wife a commiffary of the inquifition, with an alguazil- b°ne major and familiars, appointed by the inquifition of Li- Rj*ab ma. The corporation confifts of a corregidor, two - ■ ordinary alcaldes, chofen annually, and regidores. The latter fuperintend the eleftion of the alcaldes, which is attended with no finall diflurbance, the people being divided into two parties, the Creoles and Europeans. QUITTER-bone. Sec Farriery, N° 347. QUIT-RENT (quietus redd it us, i. e. “ quiet rent,”) is a certain fmall rent payable by the tenants of manors, in token of fubjeftion, and by which the tenant goes quiet and free. In ancient records it is called ’white rent becaufe paid in filver money, to diftinguilh it from rent- corn, &c. QUOIN, or Coin, on board a flriip, a wedge fa¬ ttened on the deck dole to the breech of the carriage of a gun, to keep it firm up to the (hip’s fide. Cantic quoins are ftrort three-legged quoins put between caiks to keep them fteady. Quoins, in ArchiteElure, denote the corners of brick or ilone walls. The word is particularly ufed for the ttones in the corners of brick buildings. When thefe (land out beyond the brick-work, their edges being chamfred off, they are called rujiic quoins. QUOTIDIAN, any thing which happens every day. Hence, when the paroxyfms of an ague recur every day, it is called a quotidian ague. See Medicine, N° 161—164. 2 ] R A B QUOTIDIANA deceptiva. See Medicine,Quotidiana N° 150. . _ II QUOAD hoc, is a term ufed in the pleadings and Rabat‘ . arguments of lawyers j being as much as to fay, As to this thing the law is fo and fo. QUORUM, a word frequently mentioned in our fla- tutes, and in commiflions both of juftices of the peace and others. It is thus called from the words of the commiffion, quorum A. B. ununi e()'e volumus. For an example, where a commiflion is diredted to feven per- fons, or to any three of them, whereof A. B. and C. D. are to be two} in this cafe, they a*re faid to be of the quotum, becaufe the reft cannot proceed without them: fo a juftice of the peace and quorum is one with¬ out whom the reft of the juftices in fome cafes cannot proceed. QUOTIENT, in Arithmetic, the number refulting from the divifion of a greater number by a fmaller, and which ihows how often the fmaller is contained in the greater, or hpw often the divifor is contained in the dividend. The word is formed from the Latin quo- ties ; q. d. How often is fuch a number contained in fuch another ? In divifion, as the divifor is to the dividend, fo is unity to the quotient—Thus the quotient of 12 divided by 3 is 4 ■, which is thus difpofed, 3) 12 (4 quotient. See Arithmetic. R. Ror r, a liquid confonant, being the 17th letter of 5 our alphabet. Its found is formed by a guttural extrufion of the breath vibrated through the mouth, with a fort of quivering motion of the tongue drawm from the teeth, and canulated with the tip a little ele¬ vated towards the palate. In Greek words it is fre¬ quently afpirated with an h after it, as in rhapfody, rhe¬ toric, &c. otherwife it is always followed by a vowel at the beginning of words and fyllables. In the notes of the ancients, R. or RO. fignifies Roma, R. C. Romana civitas ; R. G. C. rei gerendee caufa ; R. F. E. D. reBe facium et diBum; R. G. F. regis fdius ; R. P. res publica, or Romani principes ; and R. R. R. F. F. F. res Romana met ferro,fame,Jlamma. Ufed as a numeral, R anciently ftood for 80 ; and with a dalh over it thus R, for 80,000 ; but the Greek r, €, with a fmall mark over it, fignified 100 •, with the fame mark under it, it denoted 1000 X I0 ? thus g fignified 100,000. In the Hebrew numeration 1 de¬ noted 200: and with two horizontal points over it 1000 x 200 ; thus i — 200,000. In the preferiptions of phyficians, R or ]£> (lands for recipe, i. e. “ take.” RAAB, a town of Lower Hungary, capital of Ja- vern, with a cattle and a bifliop’s fee. It is a ftrong frontier bulwark againft the Turks, and has two bridges, one over a double ditch, and another that leads towards Alba Regalis. The furrounding country is plain, and there is nothing that feems to command it but a fmall hill at fome diftance, which is undermined and may be blown up. It wTas taken by Amurath III. with the lofs of 20,000 men *, but was furprifed foon after by Count Palfi, who killed all the Turks that were found therein. It is feated at the confluence of the rivers Rab and Rabnitz, not far from the Danube, 32 miles weft of Gran, and 55 fouth-eaft of Vienna. E. Long. 17. 25. N. Lat. 47. 48. RAB AC, a fmall port on the Arabian coaft of the Red fea, in N. Lat. 22° 35' 40", by Mr Bruce’s ac¬ count. The entry to the harbour is from the E. N. E. and is about a quarter of a mile broad. The port ex¬ tends about two miles in length to the eaftward. The mountains are about three leagues to the north, and the town about four miles north by eaft from the entrance to the harbour. The water is good, and all (hips may be fupplied here from the wells which are in the neigh¬ bourhood of the town. The country is bare and uncuL tivated j but from the appearance of it, and the frefhnefs of the water, Mr Bruce fuppofes that it fometimes rains among the mountains here, which is the more probable as it is confiderably within the tropic. RABAT, a large and handfome fea-port town of Africa, R A B [6 Rabat Africa, in the kingdom of Fez and province of Treme- R t fen. It has fine mofques and handfome palaces, and is . : feated at the mouth of the river Burrigrig, almoft in the mid-way between Fez and Tangier. W. Long. 5. 28. N. Lat. 34. 40. Raba, together with Sallee, which is oppofite to it, was formerly famous for fitting out piratical veflelsj but the late emperor Sidi Mahomet fubdued them both, and annexed them to the empire j fince which time the harbour of Rabat has been fo filled with the fand wathed in by the fea as to render it unfit to carry on fuch pira¬ cies in future. The town of Rabat, whofe walls inclofe a large fpace of ground, is defended on the fea-fide by three forts to¬ lerably wellfinilhed, which were ere£led fome little time ago by an Englifh renegade, and furnilhed with guns from Gibraltar. The houfes in general are good, and many of the inhabitants are wealthy. The Jews, who are very numerous in this place, are generally in better circumltances than thofe of Larache or Tangier, and their women are extremely beautiful. The callle, which is very extenfive, contains a ftrong building, formerly ufed by the late emperor as his prin¬ cipal treafury, and a noble terrace, which commands an extenfive profpeft of the town of Sallee, the ocean, and all the neighbouring country. There are alfo the ruins of another caftle, which is faid to have been built by Jacob Almanzor, one of their former emperors, and of which at prefent very little remains but its walls, con¬ taining within them fome very Itrong magazines for powder and naval ftores. On the outfide of thefe walls is a very high and fquare tower, handfomely built of cut ftone, and called the tower of Hajfen. From the work- manlhip of this tower, contrafted with the other build¬ ings, a very accurate idea may be formed how greatly the Moors have degenerated from their former fplendour and tafte for archite&ure. RABBETTING, in Carpentry, the planing or cut¬ ting of channels or grooves in boards, &c. In (hip-carpentry, it fignifies the letting in of the planks of the (hip into the keel *, which, in the rake and run of a (hip, is hollowed away, that the planks may join the clofer. RABBI, or Rabbins, a title which the Pharifees and doftors of the law among the Jews affumed, and literally fignifies majters or excel/ents. There were feveral gradations before they arrived at the dignity of a rabbi; which was not conferred till they had acquired the profoundeft knowledge of the law and the traditions. It does not, however, appear that there was any fixed age or previous examination neceflary ; but when a man had diftinguiihed himfelf by his (kill in the written and oral law, and paffed through the fubordinate degrees, he was faluted a rabbin by the public voice. - Among the modern Jews, for near 700 years pad, the learned men retain no other title than that of rabbi, or rabbins; they have great refpeft paid them, have the firft places or feats in their fynagogues, determine all matters of controverfy, and frequently pronounce upon civil affairs j they have even power to excommunicate the difobedient. RABBINISTS, among the modern Jews, an appel¬ lation given to the doftrine of the rabbins concerning 3 1 . 11 A B traditions, in oppofition to the Caraites j who reject all Rabelais, traditions. See Caraite. , Ral)blt. „ RABJtLAIS, Francis, a French writer famous for his facetioufnefs, was born at Chinon in Touraine about the year 1483. He was firft a Francifcan friar *, but quitting his religious habit itudied phyfic at Montpelier, where he took his dodlor’s degree. It is faid, that the chancellor du Pratt having abolifhed the privileges of the faculty of phyfic at Montpelier by a decree of the parliament, Rabelais had the addrefs to make him re¬ voke what he had done ; and that thofe who were made dodlors of that univerfity wore Rabelais’s robe, which is there held in great veneration. Some time after, he came to Rome, in quality of phyfician in ordinary to Cardinal John du Bellay archbilhop of Paris. Rabelais is faid to have ufed the freedom to jeer Pope Paul III. to his face. He had quitted his religious connexions for the fake of leading a life more agreeable to his tafte 5 but renewed them on a fecond journey to Rome, when he obtained, in 1536, a brief to qualify him for hold¬ ing ecclefiaftical benefices; and, by the intereft of his friend Cardinal John du Bellay, he was received as a fe- cular canon in the abbey of St Maur near Paris. His profound knowledge in phyfic rendered him doubly ufe- iul ; he being as ready, and at leal! as well qualified, to preferibe for the body as for the foul : but as he was a man of wit and humour, many ridiculous things are laid to his charge, of which he was quite innocent. He publifhed feveral things j but his chief performance is a ftrange incoherent romance, called the Hi/lory of Gar- gantua and Pantagruel, being a fatire Upon priefts, popes, fools, and knaves of all kinds. This work contains a wild, irregular profufion of wit, learning, obfeenity, low conceits, and arrant nonfenfe ; hence the flirewd- nefs of his fatire, in fome places where he is to be un- derftood, gains him credit for thofe where no mean¬ ing is difcoverable. Some allufions may undoubtedly have been fo temporary and local as to be now quite loft : but it is too much to conclude thus in favour of every unintelligible rhapfody ; for we are not without Englifh writers of great talents, whofe fportive geniufes have betrayed them into puerlities, no lefs incoherent at the times of writing than thofe of Rabelais appear above two centuries after. He died about 1553. RABBIT, in Zoology. See Lepus, Mammalia Index. The buck rabbits, like our boar cats, will kill the young ones if they can get at them •, and the does in the warrens prevent this, by covering their (locks, or nefts, with gravel or earth, which they clofe fo artificially up with the hinder part of their bodies, that it is hard to find them out. They never fuckle their young ones at any other time than early in the morning and late at. night ; and always, for eight or ten days, clofe up the hole at the mouth of the neft, in this careful manner, when they go out. After this they begin to leave a fmall opening, which they increafe by degrees 5 till at length, when they are about three weeks old, the mouth of the hole is left wholly open that they may go out ; for they are at that time grown big enough to take care of themfelves, and to feed on grafs. People who keep rabbits tame for profit, breed them in hutches •, but thefe mull be kept very neat and clean, elfe they will be always fubjedt to difeafes. Care mud be taken alfo to keep the bucks and does apart till the latter R A B latter bavejuil: kindled; then they are to be turned to the bucks again, and to remain with them till they fliun and run from them. The general direftion for the choofmg of tame rab¬ bits is, to pick the largeft and faireft ; but the breeder fhould remember that the Ikins of the filver-haired ones fell better than any other. The food of the tame rab¬ bits may be colewort and cabbage-leaves, carrots, parf- neps, apple-rinds, green corn, and vetches, in the time of the year ; alfo vine-leaves, grafs, fruits, oats, and oatmeal, milk-thiftles, fuw-thirties, and the like : but with thefe moift foods they muft always have a propor¬ tionable quantity of the dry foods, as hay, bread, oats, bran, and the like, oilier wile they will grow pot-bellied, and die. Bran and grains mixed together have been alfo found to be very good food. In winter they will eat hay, oats, and chaff, and thefe may be given them three times a-day ; but when they eat green things, it muft be obferved that they are not to drink at all, for it would throw them into a dropfy. At all other times a very little drink ferves their turn, but that muft always be frefh. When any green herbs or grafs are cut for their food, care muft be taken that there be no hem¬ lock among it ; for though they will eat this greedily among other things when offered to them, yet it is hidden poifon to them. Rabbits are fubjeff; to two principal infirmities. Firft, the rot, which is caufed by giving them too large a quantity of greens, or from giving them frefti gather¬ ed with the dew or rain hanging in drops upon them. Excefs of moifture always caufts this difeafe. The greens therefore are always to be given dry ; and a fuf- ficient quantity of hay, or other dry food, intermixed with them, to take up the abundant moifture of their juices. On this account the very beft food that can be given them, is the fhorteft and fweeteft hay that can be got, of which one load wall ferve 200 couples a year ; and out of this flock of 200, 200 may be eaten in the family, 200 fold in the markets, and a fufficient num¬ ber kept in cafe of accidents. The other general difeafe of thefe creatures is a fort of madnefs : this may be known by their wallowing and tumbling about with their heels upwards, and hopping in an odd manner into their boxes. This diftemper is fuppofed to be owing to the ranknefs of their feeding ; and the general cure is the keeping them low, and gi¬ ving them the prickly herb called tare thijUe to eat. The general computation of males and females is, that one buck-rabbit will fefve for nine does : ibme al¬ low ic to one buck ; but thofe who go beyond this al¬ ways fuffer for it in their breed. Wild rabbits are either to be taken by fmall cur-dogs, or by fpaniels bred up to the fport; and the places of hunting thofe who ftraggle from their burrows, is under clofe hedges or bufhes, or among corn-fields and frefli pallures. The owners ufe to courfe them with fmall greyhounds; and though they are feidom killed this way, yet they are driven back to their burrows, and are prevented from being a prey to others. The com¬ mon method is by nets called purfe-ncts, and ferrets. The ferret Is fent into the hole to fetch them out; and the purfe-net being fpread over the hole, takes them as they come out. The ferrets mouths muft be muffled, and then the rabbit gets no harm. For the more certain ta¬ king of them, it may not be improper to pitch up a hay- R A B net or two, at a imall diftance from the burrows that are intended to be hunted: thus very few of the number that are attempted will efcape. Some who. have no ferrets fmoke the rabbits out of their .holes with burning brimftone and orpiment. This certainly brings them out into the nets ; but then it is a very troublefome and offenfive method, and is very detrimental to the place, as no rabbit will for a lung time afterwards come near the burrows which have been fumed with fuch ingredients. I he following obfervations on the breeding and ma¬ nagement of rabbits and fume other animals appear to us to be of fuch importance, that we fhali give them a place in the words of the author. “ In my travels through America,” fays the author, “ I have often been furprifed that no attempt has been made to introduce, for the purpofe of propagation, that ufeful little animal, the warren rabbit, of fuch vaft im¬ portance to the hat manufaftpry of England. It is chiefly owing to the fur cf this animal that the Englilh hats are fo much efteemed abroad. It is a fa£l well known amongft the hatters, that a hat compofed of one half of coney wool, one-fixth old coat beaver, one-fixth pelt beaver, and one-fixth Vigcnia wool, will wear far pre¬ ferable to one made all of beaver, as it will keep its fliape better, feel more firm, and wear bright and black much longer. “ I he value of the coney wool, the produce of the united kingdom only, is not lefs, I will venture to fay, than .250,000!. per annum ; but the quantity is much diminiftied, owing to the banifhment and perfecution they meet with on every fide, and fo many fmall war¬ rens taken in for grain land ; in confequence of which it is time that fome protection fhould be afforded, if portable, to that important branch of Britifh manufac¬ tory (in which coney wool is ufed) from fuffering any inconvenience in the want of fo effential an article, and the accomplifhment of this grand object I conceive per¬ fectly eafy. “ General Obfervations.—When I fpeak of the war¬ ren rabbit, I have to obferve, that there are in England, as well as in moft parts of Europe, three other kinds, viz. the tame rabbit, of various colours, the fur of which -is of little value, except the white ; the fliock rabbit, which has. a long fhaggy fur of little value ; the bulh rabbit, like thofe of America, which commonly fits as a hare, and the fur of which is of a rotten inferior quality. “ To return to the warren rabbit.—There are two forts in refpedl to colour, that is, the common gray, and the filver gray, but little or no difference in refpeft to the ftrength and felting qualities of the fur. The nature of this animal is to burrow deep in fandy ground, and there live in families, nor will they fuffer one from a neighbouring family to come amongft them without a fevere conteft, in which the intruders are generally glad to retire with the lofs of part of their coat, un- lefs when purfued by an enemy, when they find protec¬ tion. “ It is fcarcely worth while for me to mention 3 thing fo generally known, viz. that rabbits, particularly thofe of the warren, are the moft prolific of all other four-footed animals in the world ; nor do I apprehend any difficulty would attend the exporting this little quadruped with fafety to any diftance, provided it was [ 6-4 ] K A B [ 615 ] RAC RaW-.it. was J^ept dry, and regularly fupplied with clean fwcet food, and a due regard to the cleanlinefs of the boxes or places of confinement. “ Twelve or fifteen pair of thefe valuable animals taken to Upper Canada, and there eticlufed within a final] fpace of ground fuitable to their nature, but fur- rifiled with a few artificial burrows at the firft by way of a nurfery, fpread over th.ofe now ufelefs plains, iflands, and peninfulas, fo well calculated to their nature, would, I will make bold to fay, the eighth year after their in¬ troduction, funddi the Britifh market with a valuable raw material, amounting to a large fum, incrtenfing every year with aftonifhing rapidity, fo as to become, in a few years, one amongft the firft of national ob¬ jects. “ It may be fuppofed by fome, that the above project: is magnified beyond poffibility, or even probability ; but the ferious attention I have paid to the fubjebt, thefe many years paft, as to all points for and againft, leaves no room to accufe myielf of being too fanguine ; for, if properly managed a few years at the firit, I cannot find a tingle thing likely to interrupt their pro- grefs. “ Some idea of the aftonilhing increafe of the rabbit may be had from the following facts : “ An old doe rabbit will bring forth young nine times in one year, and from four to ten each time 5 but to al¬ low for cafualities, ftalc the number at five each litter. In nine months ----- 45 1 he females of the firft litter will bring forth five times, the proportion of which is 2 [ females pro¬ duce - - - - - - 62 Thofe of the fecond litter four times produce 50 Ditto of ditto third ditto three ditto ditto - 37 Ditto of ditto fecond ditto two ditto ditto - 25 Total in one year from cne pair - 219 “ The third female race of the old dam, and the fe¬ cond of the firft litter, feldom breed the firft year, but are early breeders in the fpring following, when we might expect an'increafe of the whole in proportion to the firft pair, if properly attended to and protected. “ It is geneially allowed, that hares are not more than one-fourth as prolific as rabbits, not withftanding, agreeable to an experiment tried by Lord Ribblefdale, who enclofed a pair of hares for one year, the offspring ■was (as I have been credibly informed) 68 : thefe ani¬ mals could they be exported to Upper Canada with fafety, and there pro reeled within enclofures for a few years, would foon after fpread over a large extent of country : the fur is nearly as valuable as that of the rabbit. “ In that part of Upper Canada within the 4 ; degrees of north latitude, and the fouthern and weftern boun¬ daries, the climate is nearly the fame as that of Eng¬ land, a little hotter a few days in fummer, and a little colder a few days in winter, agreeable to Fahrenheit’s thermometer, which I have paid great attention to for fome years, comparing the fame with the obfervations of the Englifh. “ The increafe of moft animals appears much greater in propetion in America than in England, mankind not ex-^euted : that of fheep is very apparent to thofe that pay attention to their breeding flock, which gives me hopes, that in a few years we {hall be able to pay RaMft for our woollen cloths in wool. Finding the effeeft of H foil and climate fo falutary to fheep, &c., it may be rea- , R‘~ce‘ , fonabiy fuppofed, that rabbits will anfwer the moit fan¬ guine ex peedations, as I underftand the wool of the fheep retains all its nature the fame as in England, particu¬ larly its ftrength, and felting qualities among the hat¬ ters, which allures me that rabbit wool from thofe bred in Upper Canada will do the fame 5 and there are fome millions of acres within the latitude and boundaries which I have before deferibed, foiled to the nature of the warren rabbit 5 nor do I apprehend that the wolves, foxes, &c., of Upper Canada will be half fo defliudive as the poachers in England. “ Theguanaco, or camel {beep of South America, no doubt will be a national objeft at fome future period. 1 his is a tame, domelhc animal, very hardy, and ufed with much cruelty by the natives in travelling over the mountains with their burthens; it fliears a fleece of wool of from 2lb. to 31b., which is of dufoy red on the back ; on the fides inclined to white, and under the belly quite white; its texture is very fine, yet ftrong; its felting qualities very powerful, and is worth, when ready for ufe, from five to fifteen fhillings per pound. This ani¬ mal would no doubt thrive, and do well in England, Upper Canada, and in particular I fhould fuppofe in New Holland. “ The beaver might be propagated to great advantage in Scotland, Ireland, and northern parts of England. + It is an animal, when tamed, very familiar, and will eat bread and milk, willow flicks, elm bark, &c., and no doubt might be imported with fafety ; but as thefe two lafl-mentioned animals are not likely to be attended to immediately, I fltall fay no more refpefling them for the- prefent*.” _ ° * Tmnf of I? ABIR'IUS, C. a Roman knight, who lent an im- Sac. for en. menfe fum of money to Ptolemy Auletes king of Egypt. The monarch afterwards not only refufed to repay but even confined him, and endangered his life. Rabi-for r>us efcaped from Egypt with difficulty ; but at his re¬ turn to Rome he was accufed by the fenate df having lent money to an African prince for unlawful purpofes. He was ably defended by Cicero, and acquitted with difficulty.—There was a Latin poet of the fame name in the age of Auguflus. He wrote a poem on the viffory which the emperor had gained over Antony at AcHum. Seneca has compared him to Virgil for ele¬ gance and majefty ; but Quintilian is not fo favourable to his poetry.—And there was an architeff in the reign of Domitian called Rabtrius. He built a celebrated pa¬ lace for the emperor, of which the ruins are full feen at Rome. RACCOON. See Ursus, Mammalia Index. RACE, in genera], figriifies running with others in order to obtain a prize, either on foot, or by riding on hcrfeback, in chariots, &c. The race was one of the exercifes among the ancient Grecian games, which was performed in a courfe con¬ taining 125 paces; and thofe who contended in thefe foot-races were frequently clothed in armour. Cha¬ riot and horfe-races alfo made a part of the ancient games. Races were known in England in very early times. Fitz-Stephen, who wrote in the days of Henry II. mentions the great delight that the citizens of London RAC [ 616 ] RAC Race, took in the diverfion. But by his words, it appears not Raclne- to have been dehgned for the purpofes of gaming, but merely to have iprung from a generous emulation of ihowing a fuperior {kill in horfemanihip. Races appear to have been in vogue in the reign of Queen Elizabeth, and to have been carried to fuch ex- cefs as to injure the fortunes of the nobility. The fa¬ mous George earl of Cumberland is recorded to have wafted more of his eftate than any of his anceflors, and chielly by his extreme love to horle-races, tiltings, and other expenfive diverftons. It is probable that the parfimonious queen did not approve of it ; for races are not among the diverfions exhibited at Kennelworth by her favourite Leicefter. In the following reign, places were allotted for the fport. Croyden in the fouth, and Garterly in Yorkfhire, were celebrated courfes. Cam¬ den alfo fays, that in 1607 there were races near York, and the prize was a little golden bell. See Racing. Race, in genealogy, a lineage or extradtion continued from father to fon. See Descent. RACINE, John, a celebrated French poet, member of the French academy, treafurer of France in the gene¬ rality of Moulins, and fecretary to his majefty, was born at Ferre Milon in i 639. He had a fine genius for the belles lettres, and became one of the firft poets of the age. He produced his Thebaide when but very young, and afterward other pieces, which met with great fuccefs, though they appeared when Corneille wTas in his higheft reputation. In his career, however, he did not fail to meet with all that oppofition which envy and cabal are ever ready to fet up againft a fuperior genius. It was partly owing to a chagrin from this circumftance that he took a refolution to quit the theatre for ever ; although his genius was ftill in full vigour, being not more than 38 years of age. But he had alfo imbibed in his infancy a deep fenfe of religion *, and this, though it had been fmothered for a while by his conneftions with the theatre, and particularly with the famous aflrefs Champmelle, whom he greatly loved, and by whom he had a fon, now at length broke out, and bore down all before it. In the firft place, he refolved not only to write no more plays, but to do a rigorous penance for thofe he had written •, and he actually formed a defign of becoming a Carthufian friar. His religious direc¬ tor, however, a good deal wafer than he, advifed him to think more moderately, and to take meafures more fuit- able to his char after. He put him upon marrying, and fettling in the wrorld : with which propofal this humble and traftahle penitent complied } and immediately took to wafe the daughter of a treafurer of France for Ami¬ ens, by whom he had feven children. He had been admitted a member of the French aca¬ demy in 1673, in the room of La Mothe le Vayer de- ceafed \ but fpoiled the fpeech he made upon that oc- cafion by pronouncing it wuth too much timidity. In 1677, he was nominated with Boileau, with whom he was ever in ftrift friendlhip, to write the hiftory of Louis XIV. \ and the public expefted great things from twro writers of their diftinftion, but wrere difappointed. Boileau and Racine, after having for fome time laboured at this work, perceived that it was entirely oppofite to their genius. He fpent the latter years of his life in compofing a hiftory of the houfe of Port-Royal, the place of his education, which, however, though finely drawn up, 4 as many have afferted, has not been publilhed. Too great ienfibility, fay his friends, but more properly an impotence of ipirit, ftiortened the dajs of this poet.— Though he had converted much with the court, he had not learned the wifdom, which is ufually learned there, of difguifing his real fentiments. Having drawn up a well-reafoned and well-written memorial upon the mife- ries of the people, and the means of relieving them, he one day lent it to Madame de Maintenon to read j when the king coming in, and demanding what and whofe it wTas, commended the zeal of Racine, but difapproved of his meddling wdth things that did not concern him, and faid with an angry tone, “ Becaufe he knows how to make good verfes, does he think he knows every thing ? And wbuld he be a minifter of ftate, becaule he is a great poet ?” Thefe words hurt Racine greatly : he conceived dreadful ideas of the king’s difpleafure 5 and his chagrin and fears brought on a fever, of which he died the 2 2d of April 1699. The king, who was fenfible of his great merit, and ahvays loved him, fent often to him in his illnefs j and finding after his death that he had more glory than rich¬ es, fettled a handfome penfion upon his family.—There is nothing in the French language written with more wit and elegance than his pieces in profe. Befides his plays, feveral of his letters have been publilhed ; he alfo wrote fpiritual fongs, epigrams, See. Racine’s works were printed at Amfterdam in 1722, in 2 vols 1 2mo, and the next year a pompous edition was printed in 2 vols Racing, quarto. RACING, tire riding heats for a plate, or other pre¬ mium. See Plate. The amufement of horfe-racing, which is now fo common, was not unknown among the great nations of antiquity, nor wholly unpraftifed by our anceftors in Britain, as we have already mentioned in the article Race. In 1599, private matches between gentlemen, who were their own jockies and riders, were very common *, and in the reign of James I. public races were eftablilhed at various places, when the difeipline, and mode of preparing the horfes for running, &c. were much the fame as they are now. The moft celebrated races of that time were called bell-courfes, the prize of the conqueror being a bell : hence, perhaps, the phrafe bearing the bell, when applied to excellence, is derived. In the latter end of Charles I.’s reign, races were per¬ formed in Hyde-Park. Newmarket was alfo a place for the fame purpofe, though it was firft ufed for hunting. Racing was revived foon after the Reftoration, and much encouraged by Charles II. wTho appointed races for his ow n amufement at Dachet Mead, when he refided at Windfor. Newmarket, howrever, now became the principal place. The king attended in perfon, eftabliflr- ed a houfe for his own accommodation, and kept and entered herfes in his own name. Inftead of bells, he gave a filver bowl or cup value 100 guineas ; on which prize the exploits and pedigree of the fuccefsful horfe were generally engraved. Inftead of the cup or bowl, the royal gift is now a hundred guineas. William III. not only added to the plates, but even founded an aca¬ demy for riding ; and Queen Anne continued the boun¬ ty of her anceftors, adding feveral plates herfelf. George I. towards the end of his reign, difeontinued the plates, and gave in their room a hundred guineas. An aft. was paffed in the 13 th year of the reign of George II. for fuppreffing races by poneys and other fmall and weak horfes, R A C •Racing horfes, See. by which all matches for any prize under the value of 50I. are prohibited, under a penalty of 1 200I. to be paid by the owner of each horfe running, and 1 col. by i'uch as advertife the plate ; and by which each horfe entered to run, if five years old, is obliged to carry ten Hones ; if fix, eleven ; and if feven, twelve. • It is alfo ordained, that no perfon (hall run any horfe at a courfe unlefs it be his own, nor enter more than one horfe for the fame plate, upon pain of forfeiting the hor- fes j and alfo every horfe-race mult be begun and ended in the fame day. Horfes may run for the value of 50I. with any weight, and at any place, 13 Geo. II. cap. 19. 18 Geo. II. cap. 34. Pennant’s Britifh Zoology, vol. i. p. 6, &c. JBerrenger’s Hiltory and Art of Horfeman- fhip, vol. i. p. 185, &c. At Newmarket there are two courfes, the long and the round : the firlt is exaftly four miles and about 380 yards, i. e. 7420 yards. The fe- cond is 6640 yards. Childers, the fwifteft horfe ever known, has run the firft courfe in feven minutes and a half, and the fecond in fix minutes forty feconds j which is at the rate of more than forty-nine feet in a fecond. But all other horfes take up at leaft feven minutes and fifty feconds in completing the firft and longeft courfe, and feven minutes only in the (horteft, which is at the rate of more than forty-feven feet in a fecond. And it is com¬ monly fuppofed that thefe couriers cover, at every bound, a fpace of ground in length about twenty-four Englifh feet. Race horfes have for fome time been an objedl of taxation. RACHITIS, the Rickets. See Medicine In¬ dex. RACK, Edmund, a perfon well known in the lite¬ rary world by his attachment to, and promotion of, a- gricultural knowledge : he was a native of Norfolk, a (Quaker. His education was common, and he was ap¬ prenticed originally to a fhopkeeper : his fociety was felecl in this fituation, and by improving himfelf in learning, his converfation was enjoyed by a refpedlable acquaintance. Ele wrote many effays, poems, and let¬ ters, and fome few controverfial tradb. At length he fettled, about his 40th year, at Bath in 1775, and was loon introduced to the moft eminent literati of that -place, among whom Dr Wilfon and Mrs Macaulay highly eftcemed him for his integrity and abilities. In 1777 he publifhed Mentor’s Letters, a moral work, which has run through many editions. But this year . he gained great celebrity by his plan of an agricultural fociety, which wTas foon adopted by four counties. He ftill further advanced his fame by his papers in the Far¬ mer’s Magazine, and his communications in the Bath So¬ ciety’s papers ; a work remarkable for its ingenuity and fpirit. His laft engagement was in the Hiftory of So- merfetfhire, where the topographical parochial furveys were his. This work, in 3 vols 4to, wTas publithed in 1791, by his colleague the Reverend Mr Collinfon. • —Mr Rack died of an afthma in February 1787, aged 52. Rack, an engine of torture, furniftied with pulleys, cords, &c. for extorting confeffion from criminals.— The trial by rack is utterly unknown to the law of England : though once, when the dukes of Exeter . and Suffolk, and other minifters of Henry VI. had laid a defign to introduce the civil law into this kingdom as she rule of government •, for a beginning thereof they ^reeled a rack for torture, which was called in cjerifipi? VtU. XVII Part H. RAD the duke of Exeter’s daughter, and ftill remains in the Rad; Tower of London, where it "was occafionally ufed as II an engine of ftate, not of law, more than once in the a c ’ reign of Queen Elizabeth. But when, upon the affaf- fination of Villiers duke of Buckingham, by Felton, it was propofed in the privy council to put the aflaffin to the rack in order to difeover his accomplices ; the judges, being confulted, declared unanimoully, to their own honour and the honour of the Englifii law, that no fuch proceeding was allowable by the laws of Eng¬ land. It feems altonithing that this ufage of ad mini- ftering the torture ftiould be faid to arife from a tender- net’s to the lives of men ; and yet this is the reafon given for its introdudlion in the civil law, and its fub- fequent adoption by the French and other foreign na¬ tions, viz. becaufe the laws cannot endure that any man ftiould die upon the evidence of a falfe or even a fingle witnefs, and therefore contrived this method that inno¬ cence flrould manifeft itfelf by a ftout denial, or guilt by a plain confeflion 5 thus rating a man’s virtue by the hardinefs of his conftitution, and his guilt by the fenfi- bility of his nerves. The Marquis Beccaria, in an ex- quifite piece of raillery, has propofed this problem, with a gravity and precifion that are truly mathematical : “ The force of the mufcles and the fenfibilily of the nerves of an innocent perfon being given ; it is requi¬ red to find the degree of pain neceflary to make him confefs himfelf guilty of a given crime”. See Act of Faith, Inquisition, and Torture. Rack, a fpirituous liquor made by the Tartars pf Tongufia. This kind of rack is made of mare’s milk, which is left to be four, and afterwards diftilled twice or thrice between two earthen pots clofely flopped ; whence the liquor runs through a fmall wooden pipe. This liquor is more intoxicating than brandy diftillcd from wine. Rack, or Arack. See Arack. To Rack Wines, 'b'c. To draw them off from their lees, after having flood long enough to ebb and fettle. Hence rack-vintage is frequently ufed for the fecond voyage our wine-merchants ufed to make into France for racked wines. RACKOON, a fpecies of urfus. See Ursus, Mam¬ malia Index. RACONI, a populous town of Italy, in Piedmont, feated in a pleafant plain, on the road from Savillan to Turin, on the rivers Grana and Macra. It belongs to the prince of Carignan, who has a handfome caftle here. It is fix miles from Savillan, and fix from Carignan. E. Long. 7. 46. N. Eat. 44. 39. RADCLIFFE, Dr John, an Englifh phyfician of great eminence in his time, born at Wakefield in Vorkfhire in 1650. He was educated at Oxford, and enrolled himfelf upon the phyfical line ; but it was re¬ markable that he recommended himfelf more by his ready wit and vivacity, than by any extraordinary ac- quifitions in learning. He began to praclife at Oxford in 1675 ■, but never paid any regard to eftablifhed rules, which he cenfured whenever he thought fit, with great freedom and acrimony } and as this drew7 all the old practitioners upon him, he lived in a continual ftate of huftility with them. Neverthelefs, his reputation in- creal’ed with his experience ; fo that, before he had been two years in bufinefs, his pradlice was very extenfive among perfons of high rank. In 1684 he removed to 4 I London, t 6i7 ] R A D [ 618 ] RAG ftatklifll: London, and fettled in JBow-fireet, Covent Garden, i> where in lefs than a year he got into great employment. Rac ncr. tpe prjncefs Anne of Denmark made him her phyiician : yet nhen her hulhand and the joined the prince of Orange, Radcliffe, either not chooiing to de¬ clare himfelf, or unwilling to favour the meafures then in agitation, excufed himfelf from attending them, on the plea of the multitude of his patients. Neverthelefs, lie was often fent for to King William and other great perfonages, though he did not incline to be a courtier. He incurred fwme cenfure for his treatment of Queen Mary, who died ol tire imallpox •, and foon after loft his place about the princeis Anne, by his attachment to his bottle. He alfo totally loft the favour of King William by his uncourtly freedom ; lor, in 1699, w^en the king fhowed him his fwollen ankles, while the reft of his body was emaciated, and afked him what he thought of them? “ Why truly I would not have your majefty’s two legs for your three kingdoms,” replied Kadclifte. He continued increafing in bufinefs and infolence as long as he lived, continually at war with his brethren the phyficians ; who confidered him in no other light than that of an aftive ingenious empiric, whom conftant pradlice had at length brought to fome degree of fkill in his profeflion. He died in 1714; and if he never attempted to write any thing himlelf, has perpetuated his memory by founding a fine library at Oxford, to pre- ferve the writings of other men. RADIAL IS, the name of two mufcles in the arm. See Anatomy, Table of the Mufcles. RADIANT, in Optics, is any point of a vifiblc ob¬ ject from whence rays proceed. RADIATED FLOWERS, in Botany, are fuch as have feveral ferniflofcules fet round a difk, in form of a radiant ftar ; thofe which have no fuch rays are called (life on s flowers. RADIATION, the aft of a body emitting or dif- fufing rays of light all round as from a centre. RADICAL, in general, fomething that ferves as a bafis or foundation. Hence phyficians talk much of a radical moifture. In grammar, we give the appella¬ tion radical to primitives, in contradiftinftion to com¬ pounds aad derivatives. Algebraifts alfo fpeak of the radical fign of quantities, which is the charafter expref- ling their roots. RADICLE, that part of the feeds of all plants which upon vegetating becomes their root, and is dif- ooverable by the microfcope. See Plant. RADISH. See Raphanus, Botany Index; and for the mode of culture fee Gardening Index. RADIUS, in Geametrif, the femidiameter of a circle, or a right line drawn from the centre to the circumfe¬ rence. In Trigonometry, the radius is termed the whole fine, •r fine of 90°. See Sine. Radius, in Anatomy, the exterior bone of the arm, defeending along with the ulna from the elbow to the wrift. RADNOR, the county-town of Radnorfiiire, in South Wales. It is a fmall town, diftant from London about 1 qo miles. It is fituated near the fpringbead @f the river Somergil, in a fruitful valley at the bottom of a hill, where there are fheep grazing in abundance. It is a very ancient borough-town, whofe jurifdiftion ex¬ pends near 1 % miles round about: the government of it is veiled in a bailiff and 25 burgeiTes. Though it is the county-town, the affizes are held at Prefteign : it has one privilege, however, that is very extraordinary, befidcs that of fending one member to parliament ; and that is, it keeps a court of pleas for all aftions, with¬ out being limited to any particular fum. It was form¬ erly fenced with a wall and Itrong caftle ; but both were in a great meaiure demolilhed by Owen Glen- dower, when he affumed the title of Prince of Wales, upon the depofitkm of King Richard II. W. Long. 2. 4 5. N. Lat. 52. 10. RADNORSHIRE, a county of South Wales, is bounded on the north by Montgomeryfhire •, on the eait by Shropfhire and Herefordlhire \ on the loulh and fouth-weft by Brecknockfhire •, and on the weft by Car- diganlhire ; extending 30 miles in length and 25 in breadth. This county is divided into fix hundreds, in which are contained three market-towns, 52 pariihes, about 3160 houfes, and 19,050 inhabitants. It is feat- ed in the diocefe of Hereford, and fends two members to parliament, one for the county and one for the town of Radnor. The air of this county is in winter cold and piercing. The foil in general is but indifferent j yet fome places produce corn, particularly the eafteru and fouthern parts ; but in the northern and weftern, ■which are mountainous, the land is chiefly flocked with horned cattle, fheep, and goats. RADIX. See Root. RAFT, a fort of float, formed by an affemblage of various planks or pieces of timber, fattened together fide by fide, fo as to be conveyed more commedioufiy to any fhort diftance in a harbour or road than if they were feparate. The timber and plank with which merchant-fhips are laden, in the different parts of the Baltic fea, are attached together in this manner, in or¬ der to float them off to the ihipping. RAFTERS, in building, are pieces of timber which, Handing by pairs on the reafon or railing piece, meet in an angle at the top, and form the roof of a building. See Architecture. Rowley RAGG, a variety of whinftone or green- ftone of a d 11 Iky or dark gray colour, with many fmall Ihining cryftals, having a granular texture, and ac¬ quiring an ochry cruft by expofure to the air. RAGMAN’S roll, Reftius Ragimund’s roll, fo called from one Ragimund a legate in Scotland, who calling before him all the beneficed clergymen in that kingdom, caufed them on oath to give in the true va¬ lue of their benefices •, according to which they were afterwards taxed by the court of Rome $ and this roll, among other records, being taken from the Scots by Edward I. was redelivered to them in the beginning of the reign of Edward III. RAGOUT, or RagOO, a fauce, or feafoning, intend¬ ed to roufe the appetite when loft or languifiling. This term is alfo ufed for any high-feafoned dilh pre¬ pared of flefh, fifli, greens, or the like: by ftewing them with bacon, fait, pepper, cloves, and the like ingredients. We have ragouts of celery, of endive, afparagus, cock’s combs, giblets, craw fifli, &c. The ancients had a ragout called garum, made of the putrified guts of a certain filh kept till it diffolved into a mere fanies, which was thought fuch a dainty, that, according to Pliny, its price equalled that of the richeft perfumes. RAGSTONE, Radnor . ihire Raaout. It A I [6 RAGSTONE, a coarfe kind of fandftone which is ufed as a whetftone for coarfe cutting tools. It is found in the hills about Newcaftle, and many other parts of England, where there are large rocks of it. RAGULED, or Ragged, in Heraldry, jagged or knotted. This term is applied to a crofs formed of the trunks of two trees without their branches, of which they fnow only the flumps. Raguled differs from in¬ dented, in that the latter is regular, the former not. RAG USA, an ancient towm of Sicily, in the Val di- Noto, near the river Maulo, x 2 miles north of Modica E. Long. 14. 59. N. Lat. 37. o. RaGUSA, a city of Dalmatia, and capital of Ragu- fen. It is about two miles in circumference, is pretty well built, and ftrong by fituation, having an inaccef- fible mountain on the land-flde, and on the fide of the fea a ffrong fort. It has an archbilhop’s fee and a re¬ public, and has a doge like that of Venice, but he con- •tinues a month only in his office. It carries on a con- fiderable trade with the Turks, and is 6o miles north- weft of Scutari, and no north of Brindifi. E. Long. 18. TO. N. Lat. 42. 50. RAGUSEN, a territory of Europe in Dalmatia, lying along the coaft of the gulf of Venice, about 55 miles in length, and 20 in breadth. It was formerly a republic under the proteffion of the Turks and Vene¬ tians, but has fallen under the dominion of the French. Ragufa is the capital town. RAJA, or Rajah, the title of the Indian black princes, the remains of thofe who ruled there before the Moguls. Some of the rajas are faid to preferve their independency, efpecially in the mountainous parts 5 but moft of them pay an annual tribute to the Mogul. The Indians call them rai; the Perfians, raian, in the plural j and our travellers rajas, or ragias. Raja, the Ray-Fijh, in Ichthyology, a genus of fillies belonging to the cartilaginous order. RAIANIA, a genus of plants belonging to the di- oecia clafs ; and in the natural method ranking under the xxth order, Sarmentacce. See Botany Index. RAIETEA, one of the South fea illands, named alfo Ulietea. RAIL. See Rallus, Ornithology Index. RAILLERY, according to Dr Johnfon, means flight fatire, or fatirical merriment j and a beautiiul writer of the laft century compares it to a light which dazzles, and which does not burn. It is fometimes innocent and pleafant, and it ffiould always be fo, but it is moft fre¬ quently offenftve. Raillery is of various kinds j there is a ferious, fevere, and good-humoured raillery 5 and there is a kind which perplexes, a kind which oftend’s, and a kind wffiich pleafes. To rally well, it is abfolutely neceffary that kindnefs run through all you fay; and you muft ever preferve the charafter of a friend to fupport your pretenfions to be free with a man. Allufions to pall follies, hints to revive what a man has a mind to forget for ever, ffiould never be introduced as the fubjecfs of raillery. This is not to thruft with the {kill of fencers, but to cut with the barbarity of butchers. But it is below the character of men of humanity and good breeding to be capable of mirth, while there ig any in the company in pain and diforder. RAIN, the defcent of water from the atmofphere in the form of drops of ^ confiderable fize. By this 9 ] R A I circumftance it is diftinguifhed from dew and fog : in the former of which the drops are fo fmall that they ' are quite invifible } and in the latter, though their fize be larger, they feem to have very little more fpecific gravity than the atmofphere itfelf, and may therefore be reckoned hollowr fpherules rather than drops. Some of the more general fadts relative to the phenomena of rain have been already given under Meteorology. We {hall here add feme account of the (peculations of philofophers on the fame fubjefl, in attempting to ac¬ count for thofe phenomena. It is univerfally agreed, that rain is produced by the water previouily ablbrbed by the heat of the fun, or otherwife, from the terraqueous globe, into the atmo¬ fphere ; but very great difficulties occur when we begin to explain why the wrater, once fo elofely united with the atmofphere, begins to feparate from it. We cannot aferibe this feparation to cold, ftnee rain often takes place in very warm weather j and though we ftiould fuppofe the condenfation owing to the fuperior cold of the higher regions, yet there is a remarkable faft which will not allow us to have recourfe to this fuppofition. It is certain that the drops of rain increafe in fize con- fiderably as they defeend. On the top of a hill, for in- ftance, they will be fmall and inconfiderable, forming only a drizzling fhower 5 but at the bottom of the fame hill the drops will be excefiively large, defeending in an impetuous rain ; which ftiows that the atmofphere is difpofed to condcnfe the vapours, and aiRually does fo, as rvell where it is warm as where it is cold. For fome time the fuppofitions concerning the caufe of rain were exceedingly infufficient and unfatisfac- tory. It was imagined, that when various congeries of clouds were driven together by the agitation of the winds, they mixed, and run into one body, by which means they were condenfed into water. The coldnefs of the upper parts of the air alfo was thought to be a great means of colledling and condenfing the clouds into water; which, being heavier than the air, muft necelTarily fall down through it in the form of rain. The reafon why it falls in drops, and not in large quantities, was faid to be the refiftance of the air j whereby being broken, and divided into fmaller and fmaller parts, it at laft arrives to us in fmall drops. But tins hypothefis is entirely contrary to almoft all the phenomena : for the weather, when coldeft,' that is, in the time of fevere froft, is generally the moft ferene ; the moft violent rains alfo happen where there is little or no cold to condenfe the clouds •, and the drops of rain, inftead of being divided into fmaller and fmaller ones as they approach the earth, are plainly increafed in fize as they defeend. Dr Derham accounted for the precipitation of the drops of rain from the veficulae being full of air, and meeting with an air colder than they contained, the air they contained w^as of confequence con traded into a fmaller fpace; and confequently the -watery (hell ren¬ dered thicker, and thus fpecifically heavier, than the common atmofphere. But it has been thorvn, that the veficulae, if fuch they arc, of vapour, are not filled with air, but with fire, or heat •, and confequently, till they part with this latent heat, the vapour cannot be condenfed. Now, cold is not always fufficient to effed this, fince in the moft fevere frofts the air is very often ferene, and parts with little or ngne of its vapour 413 for R A I [ 620 ] RAT Rain. for a very confiderable time. Neither can we admit “"V“—' the winds to have any confiderable agency in this mat¬ ter, lines we find that blowing upon vapour is fo far from condenfing it, that it unites it more clofely with the air, and wind is found to be a great promoter of evaporation. According to Rohault, the great caufe of rain is the heat of the air ; which, after continuing for fome time near the earth, is raifed on high by a wind, and there thawing the fnowy villi or Hocks of half-frozen vefi- culm, reduces them to drops ; which, coalelcing, de- feend. Here, however, we ought to be informed by what means thefe veficulae are fufpended in their half- frozen ftate $ fince the thawing of them can make but little difference in their fpecific gravity, and it is cer¬ tain that they afeended through the air not in a frozen but in an aqueous Hate. Dr Clarke and others aferibe this defeent of the rain rather to an alteration of the atmofphere than of the veficuloe; and fuppofe it to arife from a diminution of the elaftic force of the air. This elafticity, which, they fay, depends chiefly or wholly upon terrene ex¬ halations, being weakened, the atmofphere finks un¬ der its burden, and the clouds fall. Now, the little veficles being once upon the defeent, will continue there¬ in, notwithftanding the increafe of refiftance they every moment meet wuth. For, as they all tend to the centre of the earth, the farther they fall, the more coalitions they wall make ; and the more coalitions, the more matter wall there be under the fame furface j the furface increafing only as the fquares, but the foli- dity as the cubes •, and the more matter under the fame furface, the lefs refiftance will there be to the fame mat¬ ter. Thus, if the cold, wind, &c. aft early enough to precipitate the afeending veficles before they are ar¬ rived at any confiderable height, the coalitions being but few, the drops will be proportionably fmall 5 and thus is formed a dew. If the vapours be more copious, and rife a little higher, wre have a mill or fog. A little higher ftill, and they produce a fmall rain if they neither meet with cold nor wind, they form a heavy thick dark fky. This hypothefis is equally un- fatisfaftory with the others; for, granting that the de¬ feent and condenfation of the vapours are owing to a di¬ minution of the atmofphere’s elafticity, by what is this diminution occafioned ? To fay that it is owing to ter¬ rene exhalations, is only folving one difficulty by ano¬ ther 5 fince we are totally unacquainted both with the nature and operation of thefe exhalations. Befides, let us fuppofe the caufe to be what it will, if it afts equally and at once upon all the vapour in the air, then all that vapour muft be precipitated at once ; and thus, inftead of gentle {honkers continuing for a confiderable length of time, we fiiould have the moft violent w^ater- ipouts, continuing only for a few minutes, or perhaps feconds, which, inftead of refrefhing the earth, wTould drown and lay wafte every thing before them. Since philofopners have admitted the eleftric fluid to fuch a large fhare in the operations of nature, al- moft all the natural phenomena have been accounted .or by the aftion of that fluid 5 and rain, among others, has been reckoned an effeft of eleftricity. But this word, unlefs it is explained, makes us no wifer than we were before •, the phenomena of artificial eleftricity having been explained on principles which could fcarce apply in any degree to the eleftricity of nature : and Ra;n- therefore all the folution we can obtain of the natural —-*v— appearances of which wre fpeak, comes to this, that rain is occafioned by a moderate eleftrification, hail and fnow by one more violent, and thunder by the moft violent of all ; but in wffiat manner this eleftrification is occa¬ fioned, has not yet been explained. The principles of eleftricity neceflary to be attended to in the folution of the phenomena under confideration are the following : 1. The eleftric fluid and folar light are the fame fub- ftances in twTo different modifications. 2. Eleftricity is the motion of the fluid when running, or attempting to run, in a continued ftream from one place to another : heat is when the fluid has no ten¬ dency but to vibrate outwards and inwards to and from a centre ; or at leaft when its ftreams converge to a point or focus. 3. The fluid afting as eleftricity, like w-ater, or any other fluid, always tends to the place where there is leaft refiftance. On thefe three principles may the phenomena of at- mofpherical eleftricity, and the defeent of rain by its means, be explained as follows : 1. The light or heat of the fun, afting in that pe¬ culiar manner which wre call heat, unites itfelf with the moifture of the earth, and forms it into vapour, which thus.becomes fpecifically lighter than air, and of confequence afeends in the atmofphere to a certain height. 2. Befides the quantity of light which is thus united to the water, and forms it into vapour, a very confider¬ able quantity enters the earth, where it affumes the na¬ ture of eleftric fluid. 3. As the earth is always full of that fluid, every quantity which enters muft difplace an equal quantity which is already there. 4. This quantity which is difplaced muft efcape ei¬ ther at a diftance from the place where the other en¬ ters, or very near it. 5. At whatever place a quantity of eleftric matter efcapes, it muft eleftrify the air above that place where it has efcaped ; and as a confiderable quantity of light muft always be reflefted from the earth into the atmofphere, where it does not combine with the aqueous vapour, wx have thence another fource of eleftricity to the air) as this quantity muft undoubt¬ edly affume the aftion of eleftric fluid, efpecially af¬ ter the aftion of the fun has ceafed. Hence the rea- fon why in ferene weather the atmofpherical eleftricity is always ftrongeft, and rather more fo in the night than in the day. 6. From thefe confiderations, wre fee an evident rea- fon why there muft commonly be a difference between the eleftricity of the earth and that of the atmofphere, excepting when an earthquake is about to enfue. The confequence of this muft be, that as the aftion of the folar light continues to bring down the eleftric matter, and the earth continues to difeharge an equal quantity of it into the atmofphere, fome part of the atmofphere muft at laft become overloaded with it, and attempt to throw it back into the earth. This attempt wall be vain, until a vent is found for the eleftricity at fome other place ; and as foon as this happens, the eleftrified atmofphere begins to throw off its fuperfluous eleftricity, and the earth to receive it. As the almofphere itfelf is R A I [62 is a bad. conduftor, and the more To the drier it is,^ the eleftric matter attacks the fmall aqueous particles which are detained in it by means of the latent heat. Ihefe being unable to bear the impetus of the fluid, throw out their latent heat, which eaflly efcapes, and thus makes a kind of vacuum in the electrified part of the atmofphere. The confequences of this are, that the aqueous par¬ ticles being driven together in large quantity, at laft become vifible, and the Iky is covered with clouds} at the fame time a wind blows againfl: thefe clouds, and, if there is no refiftance in the atmofphere, will drive them away. 7. But if the atmofphere all round the cloud is ex¬ ceedingly eleCtrified, and the earth is in no condition to receive the fuperfluous fluid excepting in tiiat place which is direCtly under the cloud, then the whole elec¬ tricity of the atmofphere for a valt way round will tend to that part only, and the cloud will be eleCtrified to an extreme degree. A wind will now blow againfl: the cloud from all quarters, more and more of the vapour will be extricated from the air by the eieClric matter, and the cloud will become darker and thicker,, at the fame time that it is in a manner ftationary, as.being aCl- ed upon by oppofite winds; though its fize is enlarged with great rapidity by the continual fupplies of vapour brought by the winds. 8. The vapours which were formerly fufpended in- vifibly by means of the latent heat are now fufpended vifibly by the eleClric fluid, which will not let them fall to the earth, until it is in a condition to re¬ ceive the eleClric matter defcending with the rain.—- It is eafy to fee, however, that thus every thing is prepared for a violent llorm of thunder and lightning as well as rain. I he furface of the earth becomes eleCfrified from the atmofphere : but when this has con¬ tinued for fome time, a zone of earth confiderably be¬ low the furface acquires an eleClricity oppofite to that of the clouds and atmofphere ; of confequence the elec¬ tricity in the cloud being violently preffed on all fides, will at laft burfl: out towards that zone where the re¬ fiftance is leaft, as explained under the article Light- jg-jNG. The vapours now having loft that which fup- ported them, will fall down in rain, if there is not a fufficient quantity of eleClric matter to keep them m the fame ftate in which they were before :. but if this happfens to be the cafe, the cloud will inftantly be charged again, while little or no rain will fall} and hence very violent thunder fometimes takes place with¬ out any rain at all, or fuch as is quite inconfiderable in quantity. 9. When the electricity is lefs violent, the rain will defeend in vaft quantity, especially after.every flafti of lightning; and great quantities of eleClric matter will thus be conveyed to the earth, infomuch that fometimes the drops have been obferved to ftnne as if tney weie on fire, which has given occafion to the reports of fiery rain having fallen on certain occafions. If the quantity of eleClric matter is fmaller, fo that the rain can. convey it all gradually to the ground, there will be rain with¬ out any thunder \ and the greater the quantity of eleClri- citv the more violent will be the rain. From this account of the caufes of rain, we may fee the reafon why in w'arm climates the rains are excef- five, and for the moft part accompanied with, thunder 5 for there the eleClricity of the atmofphere is immenfely i ] 11 a r greater than it is with us. We may alfo fee why in certain places, according to the fituation of moun¬ tains, feas, &c. the rains will be greater than in others, and likewife why fome parts of the wmrld are exempted from rain altogether; but as a particular difeuflion of thefe would necefi'arily include an explanation of the caufes and phenomena of Thunder, wTe fhall for this reafon refer the whole to be treated of under that article. Whether this theory be juft, however, it would be too affuming in us to fay. It may admit of difpute, for w^e muft grant that in the very beft fyftems, though an oc¬ currence fo frequent, the theory of rain is but very im- perfeCtly underftood. Dr Hutton, whofe fpeculations are ahvays ingenious, though generally extraordinary, and much out of the common way, has given a new theory of rain in the firft volume of the TranfaClions of the Royal Society of Edinburgh. It is well known that atmofpheric air is capable of diffolving, wdth a certain degree of heat, a given quantity of w^ater. The DoClor afeertains the ratio of the diffolving po-wer of air, in relation to water, in different degrees of heat * and (hows, that by mixing a portion of tranfparent humid warm air wdth a portion of cold air, the mixture becomes opake, and part of the w’ater will be precipitated; or, in other wmrds, the vapour wdll be condenfed into rain. The ratio which he ftates, however, does not appear to us to be fupported by experience. Whether the elec¬ tricity of the air changes in confequence of its depofiting the water diffolved in it, or the change is a caufe of this depofition, muft remain uncertain 5 but, in either viewq there muft be an agent different from heat and cold, fince the changes in thefe refpefts do not in other operations change the ftate of eleftricity. Dr Hutton fuppofes that heat and folution do not increafe by equal incre¬ ments 5 but that, in reality, if heat be fuppofed to in¬ creafe by equal increments along a ftraight line, folution will be expreffed by ordinates to a curve whofe convex fide is turned towards that line. That the power of folution is not increafed in the fame ratio wdth heat, is,, however, hypothetical, except when wre rife pretty high in the fcale, wdien its proportional increafe is a little doubtful ; and it is not, in this paper, fupported by ex¬ periment. The condenfation of the breath in air is not an obfervation in point, except in air already faturated with vapour. It can amount, in any view, to no more than this, that to render- it vifible, the heat muft be di- miniftied in a greater proportion than can be compen- fated by the power of folution in the body of air, in which the portion expired is at firft immerfed. To ex¬ plain rain from this caufe, we muft ahvays fuppofe a conftant diminution of heat to take place at the mo¬ ment of the condenfation of the vapour ; but we actu¬ ally find that the change from a ftate of vapour to the fluid ftate is attended with heat ; fo that rain muft at once oppofe its ow-n caufe, and continued rains w-ould be impoflible, w ithout calling in the aid of other caufes. From his own fyftem, Dr Hutton endeavours to ex¬ plain the regular and irregular feafons of rain, either refpeCling the generality of its appearance, or the re¬ gularity of its return. And to obviate the apparent ex¬ ceptions of the theory, from the generality of rain, he explains the proportional quantities of rain, and adds a comparative eftimate of climates, in relation to rain, with the meteorological obfervations made in our own.- climate.. 11 A I [62 climate. As liis principle is at leafl infutTicient, and we think erroneous, it would be ufelefs, even were this a proper place for it, to purfue thefe various branches, which muft partake of the errors of the fyftem. In thefe branches we ought to obferve, that there are feveral juft obfcrvations, mixed with errors, becaufe evaporation and condenfation muft at laft be the great bafis of every the¬ ory : the miilakes arife from not being aivare of all the caufes, and mifreprefenting the operation of thofe w'hich do exift. In a work entitled Thoughts on Meteorology, vol. ii. M. de Luc conftders very particularly the grand pheno¬ menon of rain, and the numerous circumftances connect¬ ed with it. He examines the feveral hypothefes with confiderable care \ but thinks them, even if admiftible, utterly infufficient to account for the formation of rain. The grand queftion in this inquiry is, what becomes of the water that rifes in vapour into the atmofphere ; or what ftate it fubfifts in there, between the time of its evaporation and its falling down again in rain. If it continues in the ftate of watery vapour, or fiich as is the immediate produCI of evaporation, it muft poffefs the diftinCHve charafters effential to that fluid : it muft make the hygrometer move towards humidity, in propor¬ tion as the vapour is more or lefs abundant in the air : on a diminution of heat, the humidity, as fhown by the hygrometer, muft increafe ; and on an increafe of the heat the humidity muft diminilh ; and the introduction of other hygrofcopic iubftances, drier than the ah, muft have the fame effeCt as an augmentation of heat. Thefe are the properties of watery vapour, on every hypolhefis of evaporation j and therefore all the water that exifts in the atmofphere without poffeffing thefe properties, is no longer vapour, but muft have changed its nature. M. de Luc fhows, that the water which forms rain, though it has ever been confidered and reafoned upon as producing humidity, does not poffefs thefe properties, and muft therefore have paffed into another ftate. As he thinks that the vapour paffes into an invifible ftate in the interval between evaporation and its falling again in rain, and that in that ftate it is not fenfible to the hy¬ grometer, he confiders the law’s of hygrology as infuffi¬ cient for explaining the formation of rain ; but he does not pretend to have difeovered the immediate caufe of the formation of clouds and rain. If it is not in the im¬ mediate produCI of evaporation that rain has its fource ; if the vapours change their nature in the atmofphere, fo as no longer to be fenfible to the hygrometer, or to the eye ; if they do not become vapour again till clouds ap¬ pear 5 and if, when the clouds are formed, no alteration is perceived in the quality of the air—we muft acknow¬ ledge it to be very probable, that the intermediate ftate of vapour is no other than air—and that the clouds do not proceed from any diftinCI fluid contained in the at¬ mofphere, but from a decompofition of a part of the air itfelf, perfectly fimilar to the reft. L appears, to us at leaft, that M. de Luc’s mode of reafoning on this fubjeft agrees better with the ph eno- inena than Dr Hutton’s. The Doftor, however, thinks differently, and publilhed anfwers to the objeCHons of M. de Luc with regard to his theory of rain j to which M. de Luc replied in a letter which was printed in the Appendix to the 81ft volume of the Monthly Review : but it would extend our article beyond its due bounds, to give a view of this controverfy. ] R A I As to the general quantity of rain that falls, and its proportion in leveral places at the lame time, and in the lame place at feveral times, we have many oblervations, journals, &.c. in the IVIemoirs of the french Academy, the Philofophical IranfaCHons, &c. Upon meafuring, then, the rain falling yearly, its depth, at a medium, and its proportion in feveral places, is found as in the follow¬ ing table : At I ownley, in Lancaffiire, obferved bv Mr Townley - - . Upminifter, in Effex, by Dr Derham Zurich, in Swifferland, by Dr Scheuchzer Pifa, in Italy, by Dr Mich. Ang. Tilii Paris, in France, by M. de la Hire Lille, in Flanders, by M. de Vauban Inchf~. 42*' J9f 32t 24 At Upminfter. 1700 19 Inch. 18 1701 1 702 1703 1704 1'/°S 23 ii 16 •°3 .69 •38 •99 .80 •93 from the Meteorological Journal of the Royal Socie- ty, kept by order of the prefident and council, it ap¬ pears that the whole quantity of rain at London, in each of the years fpecified below, was as fellows. Inches. x774 i?7i 1776 1777 1778 1779 1780 26 24 20 25 20 26 i? .328 .083 •354 •371 .772 •785 •3 i3 ihe quantity of rain in the four following years at Lon¬ don was Inches. In 1789 - - 2i .976 179° ” - 16 .0^2 1791 1792 i9 .310 .489 Proportion oj the Rain of the feveral Seafons to one ano¬ ther. 1708 Jan. Feb. Mar. April May June Depth at Pifa. Inch. 6 .41 3 -28 2 .65 1 .23 3 -33 4 -9° Half Year 2i .82 Depthat Upniirf. Inch. 2 .88 o .46 2 0.3 O .96 2 .02 2 .32 10 .67 Depthat Zurich. Inch. I .64 I .65 1 -i1 4 -69 I .91 5 -91 i? -3i 1708 July Aug. jSept. |oa. Nov. Dec. jDepth ai Pifa. Inch. O .20 2 .27 7 .21 5 -33 o .13 o .00 Half Depthat Up m inf. Inch. 1 .11 2 -94 1 .46 o .23 o .86 1 .97 lYeari'4 M 8 -57 Depthat Zurich. Inch. 3 -50 3 -15 3 -02. 2 .44 o .62 2 .62 ii -35 See Philofophical Tranfa&ions abridged, vol. iv. part ii, p. 81, &c. and alfo Meteorological Journal of the Royal Society, publilhed annually in the Philofophical Tranf- aftions. As to the ufe of rain, we may obferve, that it moi- ftens R A I [ 623 ] R A I Rain, ftens and foftcns the earth, and thus fits it for affording ■—V"—' nourifhment to plants ; by falling on high mountains, it carries down with it many particles of loofe earth, which ferve to fertilize the lurrounding valleys, and purifies the air from noxious exhalations, which tend in their return to the earth to meliorate the foil; it moderates the heat of the air } and is one means of fupplying foun¬ tains and rivers. However, vehement rains in many countries are found to be attended with barrennefs and poornefs of the lands, and nrifcarriage of the crops in the fucceeding year : and the reafon is plain j for thefe exceffrve llorms walh away the fine mould into the ri¬ vers, which carry it into the fea, and it is a long time before the land recovers itfclf again. The remedy to the famine, which fome countries are fubject to from this fort of mifchief, is the planting large orchards and groves of fuch trees as bear efculent fruit; for it is an old obfervation, that in years, when grain fucceeds word:, thefe trees produce mod fruit of all. It may partly be owing to the thorough moideningof the earth, as deep as their roots go by thefe rains, and partly to their trunks dopping part of the light mould carried down by the rains, and by this means furniihing them- felves with a coat of new earth. Preternatural RsllNS. We have numerous accounts, in the hidorians of our own as well as other countries, of preternatural rains ; fuch as the raining of bones, of dud, of blood, nay, and of living animals, as young . frogs, and the like. We are not to doubt the truth of what thofe who are authors of veracity and credit relate to us of this kind, fo far as to fuppofe that the falling of bones and dud never happened ; the whole midake is, the fuppofing them to have fallen from the clouds : but as to the blood and frogs, it is very certain that they never fell at all, but the opinion has been a mere decep¬ tion of the eyes. Men are extremely fond of the mar¬ vellous in their relations ; but the judicious reader is to examine ftrittly whatever is reported ox this kind, and is not to fuffer himfelf to be deceived. There are two natural methods by which quantities of bones and dud may fall in certain places, without their having been generated in the clouds or fallen as rain. The one is by means of hurricanes : the wind which we frequently fee tearing off the tiles of hoofes, and carrying them to confiderable didances, being equal¬ ly able to take up a quantity of bones, and drop them again at fome other place. But the other, which is much .the mod powerful, and probably the mod ufual way, is for the eruptions of volcanoes and burning mountains to tofs up, as they frequently do, a vad quantity of bones, allies, and cinders, to an immenfe height in the air : and thefe, being hurried away by the hurricanes and impetuous winds which ufually accompany thofe eruptions, and being in themfelves much lighter than common bones, as being half calcined, may eafily be thus carried to vad didances j and there falling in pla¬ ces where the inhabitants know nothing of the occafion, they cannot but be fuppofed by the vulgar to fall on them from the clouds. It is well known, that, in the great eruptions of /Etna and Vefuvius, {bowers of afhes, dud, and fmall cinders, have been feen to obfeure the air, and overfpread the furface of the fea for a great way, and cover the decks of blips ; and this at fuch a d’dance, as it biould appear fcarce conceivable that they ftiQuid have been carried to: and probably, if the ac- courtts ot all the ihowers of thefe fubdances mentioned R-i'-1’- by authors be colle&ed, they will all be found to have v fallen within Inch didances of volcanoes} and if com¬ pared as to the time of their falling, will be found to correipond in that alfo with the eruptions of thofe mountains. We have known indances of the afhes from Vefuvius having been carried thirty, nay, forty leagues, and peculiar accidents may have carried them yet far¬ ther. It is not to be fuppoied that thefe blowers of bones and dud fall for a continuance in the manner of blowers of rain, or that the fragments or pieces are as frequent as drops of water j it is fufficient that a num¬ ber of bones, or a quantity of dud, fall at once on a place, where the inhabitants can have no knowledge of the part from wdience they came, and the vulgar will not doubt their dropping from the clouds. Nay, in the canton of Berne in Swifferland, the inhabitants ac¬ counted it a miracle that it rained earth and fulphur up- pon them at a time that a fmall volcano terrified them and even while the wind was fo boiderous, and hurri¬ canes fo frequent, that they faw almod every moment the dud, land, and little bones torn up from the furface of the earth in whirlwinds, and carried to a confiderable height in the air, they never conlidered that both the fulpi mr thrown up by the volcano, and the dud, carried from their feet mud fall foon after fomewhere. It is very certain that in fame of the terrible dorms of large hail, where the haildones have been of many inches round, on breaking them there have been found what people have called Jlones in their middle; but thefe obfervers needed only to have waited the diffolving of one of thefe haildones, to have feen the done in its centre difunite alfo, it being only formed of the parti¬ cles of loofe earthy matter, which the water, exhaled by the fun’s heat, had taken up in extremely fmall mole- culae with it} and this only having ferved to give an opaque hue to the inner part of the congelation, to which the freezing of the water alone gave the apparent hard- nefs of done. The raining of blood has been ever accounted a more terrible fight and a more fatal omen than the other pre¬ ternatural rains already mentioned. It is very certain that nature forms blood nowhere but in the veffels of animals ; and therefore Ihowers of it from the clouds are by no means to be credited. Thofe who fuppofe that what has been taken for blood has been a finally feen failing through the air, have had recourfe to" Hying in¬ fers for its origin, and fuppofe it the eggs or dung of certain butterflies difeharged from them as they were high up in the air. But it feems a very wild conjec¬ ture, as we know of no butterfly whofe excrements or eggs are of fuch a colour, or whofe abode is fo high, or their flocks fo numerous, as to be the occafion of this. It is mod probable that thefe bloody waters w’ere never feen falling ; but that people feeing the danding waters blood-coloured, were affured, from their not knowing how it diould elfe happen, that it had rained blood into them. A very memorable indance of this took place at the Hague in the year 1670. Swam¬ merdam, who relates it, tells us, that one morning the whole towai w'as in an uproar on finding their lakes and ditches full of blood, as they thought ; and having been certainly full of water the night before, thev agreed it mud have raiped blood in the night: but a certain phy- fitiau. R A I r 624 ] R A I Rain, flcian went down to one of the canals, and taking home a quantity of this blood-coloured water, he examined it by the microfcope, and found that the water was water hill, and had not at all changed its colour $ but that it was full of prodigious fwarms of fmall red animals, all alive, and very nimble in their motions, whofe colour and prodigious number gave a red tinge to the whole body of the water they lived in, on a lefs accurate in- fpe£tion. The certainty that this wras the cafe, did not however perfuade the Hollanders to part with the mi¬ racle : they prudently concluded, that the hidden ap¬ pearance of fuch a number ot animals wras as great a prodigy as the raining of blood would have been $ and are allured to this day, that this portent foretold the fcene of war and deitruftion which Louis XIV. after¬ wards brought into that country, which had before en¬ joyed 40 years of uninterrupted peace. The animals which thus colour the water of lakes and ponds are the pulices arborefccntes of Sivammerdam, or the water-deas with branched horns. Thefe creatures are of a reddilh-yellow or dame colour : they live about the tides of ditches, under -weeds, and among the mud ; and are therefore the lefs viiible, except at a certain time, which is in the end or beginning of June : it is at this time that thefe little animals leave their recedes to doat loofe about the water, to meet for the propagation of their fpecies, and by that means become vifible in the colour they give the w'ater. This is vilible, more or lefs, in one part or other of almoft all Handing wa¬ ters at this feafon ) and it is always at this feafon that the bloody waters have alarmed the ignorant. The raining of frogs is a thing not lefs wonderful in the accounts of authors who love the marvellous, than thofe of blood or Hones } and this is fuppofed to happen fo often, that there are multitudes who pretend to have been eye-witneffes of it. Thefe rains of frogs always happen after very dry feafons, and are much more fre¬ quent in the hotter countries than in the cold ones. In Italy they are very frequent; and it is not uncom¬ mon to fee the flreets of Rome fwarming both with young frogs and toads in an indant in a Hrower of rain •, they hopping everyrvhere between the people’s legs as they walk, though there was not the lead appearance of them before. Nay, they have been feen to fall through the air down upon the pavements. This feems a flrong circumHance in favour of their being rained down from the clouds ; but, when Hriftly examined, it comes to nothing : for thefe frogs that are feen to fall, are always found dead, lamed, or bruifed by the fall, and never hop about as the refl ; and they are never feen to fall, except dole under the walls of houfes, from the roofs and gutters of which they have accidentally flipped down. Some people, who love to add 'o Hrange things yet ftranger, affirm that they have had the young frogs fall into their hats in the midfl of an open field } but this is idle, and wholly falfe. Others, who cannot agree to their falling from the clouds, have tried to folve the difficulty of their Hidden appearance, by fuppofing them hatched out of the egg, or fpawn, by thefe rains. Nay, fome have fuppofed them made immediately out of the dufl : but there are unanfwerable arguments againfl all thefe fuppofitions. Lquivocal generation, or the fpontaneous produdion of animals out of dufl, is now wholly exploded. The fall from the clouds muH deflroy and kill thefe tender and 1 foft-bodied animals: and they cannot be at this time Rann hatched immediately out of eggs •, becaufe the young 'v~"" frog does not make its appearance from the egg in form, but has its hinder legs enveloped in a fkin, and is what we call a tadpole ; and the young frogs are at leaft 100 times larger at the time of their appearance, than the egg from which they fliould be hatched. It is beyond a doubt, that the frogs which make their appearance at this time, were hatched and in being long before : but that the dry feafons had injured them, and kept them fluggiihly in holes or coverts \ and that all the rain does, is the enlivening them, giving them new fpirits, and calling them forth to feek new habitations, and enjoy the element they were deflined in great part to live in. Theophraftus, the greatell of all the natu- ralifls of antiquity, has affirmed the fame thing. We find that the error of fuppofing thefe creatures to fall from the clouds was as early as that author’s time ; and alfo that the truth, in regard to their appearance, was as early known ; though, in the ages fince, authors have taken care to conceal the truth, and to hand down to us the error. We find this venerable fage, in a fragment of his on the generation of animals which appear on a . hidden, bantering the opinion, and afferting that they were hatched and living long before. The world owes, however, to the accurate Signior Redi the great proof of this truth, which Theophraftus only has affirmed : for this gentleman, diffefting fome of thefe new-appear¬ ing frogs, found in their Homachs herbs and other half- digefted food } and, openly (bowing this to his credu¬ lous countrymen, alked them whether they thought that . nature, which engendered, according to their opinion, thefe animals in the clouds, had alfo been fo provident as to engender grafs there for their food and nourilh- ment ? To the raining of frogs we ought to add the raining of grafskoppers and loctjls, which have fometimes ap¬ peared in prodigious numbers, and devoured the fruits of the earth. There has not been the leaft pretence for the fuppofing that thefe animals defcended from the clouds, but that they appeared on a hidden in prodigi¬ ous numbers. The naturalift, who knows the many ac¬ cidents attending the eggs of thefe and other the like animals, cannot but know that fome feafons will prove particularly favourable to the hatching them, and the prodigious number of eggs that many infefts lay could not but every year bring us fuch abundance of the young, were they not liable to many accidents, and had not pro¬ vident nature taken care, as in many plants, to continue the fpecies by a very numerous Hock of feeds, of which perhaps not one in 500 need take root in order to con¬ tinue an equal number of plants. As it is thus alfo in regard to infedls, it cannot but happen, that if a favour¬ able feafon encourage the hatching of all thofe eggs, a very fmall number of which alone was neceffary to continue the fpecies, we muft, in fuch feafons, have a proportionate abundance of them. There appeared about 50 years ago, in London, fuch a prodigious fwarm of the little beetle called the lady-cotv, that the very pofts in the ftreets were everywhere covered with them. But thanks to the progrefs of philofophy among us, we had nobody to afiert that it rained cow-ladies, but con¬ tented ourfelves with faying that it had been a favour¬ able feafon for their eggs. The prodigious number of a fort of grub which did vaft mifchief about the lame period R A I [ ( perioJ among the corn and grafs by eating off their roots, might alfo have been fuppofed to proceed from its having rained grubs by people fond of making every¬ thing a prodigy ; but our knowledge in natural hillory affured us, that thefe were only the hexapode worms of the common hedge beetle called the cockchafer. I he raining of fijhes has been a prodigy alfo much talked of in France, where the ftreets of a town at fome difiance from Paris, after a terrible hurricane in the night, which tore up trees, blew down houfes, &c. were found in a manner covered with fillies of various fizes. Nobody here made any doubt of thefe having fallen from the clouds ; nor did the abfurdity of fifh, of five or fix inches long, being generated in the air, at all ftartle the people, or drake their belief in the miracle, till they found, upon inquiry, that a very well-flocked fiflr-pond, which flood on an eminence in the neighbourhood, had been blown dry by the hurricane, and only the great fifh left at the bottom of it, all the fmaller fry having been toffed into their flreets. Upon the whole, all the fuppofed marvellous rains have been owing to fubflances naturally produced on the earth, and either never having been in the air at all, or cnly carried thither by accident. In Silefia, after a great dearth of wheat in that coun¬ try, there happened a violent florm of wind and rain, and tire earth was afterwards covered, in many places, with fmall round feeds. The vulgar cried out that Pro¬ vidence had fent them food, and that it had rained mil¬ let : but thefe were, in reality, only the feeds of a fpe- cres of veronica, or fpeedwell, very common in that country ; and whofe feeds being juft ripe at that time, the wind had diflodged them from their capfules, and Mattered them about. In our own country, we have hiftories of rains of this marvellous kind, but all fabu- lous. It was once faid to rain wheat in Wiltfhire ; and the people were all alarmed at it as a miracle, till Mr Cole fhovved them, that what they took for wheat was only the feeds or kernels of the berries of ivy, which be¬ ing then fully ripe, the wind had diflodged from the fides of houfes, and trunks of trees, on which the ivy that produced them crept. And we even once had a raining of fifties near the coaft of Kent in a terrible hurricane, wuth thunder and lightning. The people w’ho faw fmall fprats ftrewed all about afterwards, would have it that they had fallen from the clouds ; but thofe who confidered how far the high winds have been known to carry the fea-w’ater, did not wonder that they fhould be able to carry fmall fifh with it fo fmall a part of the way. In the Philofophical T ran factions far 1782 wre have the following account of a preternatural kind of rain by Count de Gioeni : “ The morning of the 24th in- ftant there appeared here a moil lingular phenomenon. .Every place expofed to the air was found wet with a coloured cretaceous gray w^ater, which, after evapora¬ ting and filtrating away, left every place covered with it to the height of two or three lines ; and all the iron¬ work that was touched by it became rufly. “ 1 he public, inclined to the marvellous, fancied va¬ rious caufes of this rain, and began to fear for the ani¬ mals and vegetables. “In places where rain-water was ufed, they abftain- cd from it : fome fufnedling vitriolic principles to be Vol. XVII. Part II. 25 ] R A I mixed with it, and ethers predidling fome epidemical diford er. “ I hofe who had obferved the explofions of Etna 20 days and more before, were inclined to believe it origi¬ nated from one of them. “ The fliower extended from N. ^ N. E. to S. A S. W. over the fields, about 70 miles in a right line from the vertex of Etna. “ There is nothing new in volcanoes having thrown up fand, and alfo Hones, by the violent expanfive force generated within them, which fand has been carried by the ivind to diftant regions. “ But the colour and fubtilty of the matter occafion- ed doubts concerning its origin ; which increafed from the remarkable circumftance of the water in which it came incorporated ; for which reafons fome other prin¬ ciple or origin was fufpefted. “ It became, therefore, neceffary by all means to af- certain the nature of this matter, in order to be convin¬ ced of its origin, and of the effefts it might produce. This could not be done without the help of a chemical analyfis. io do this then with certainty, I endeavour¬ ed to colleft this rain from places where it -was molt pro¬ bable no heterogeneous matter would be mixed with it. I therefore chofe the plant called brajjica capitata, which having large and turned-up leaves, they contained enough of this coloured water : many of thefe I emptied into a veffel, and left the contents to fettle till the water became clear. _ “ This being feparated into another veffel, I tried it with vegetable alkaline liquors and mineral acids; but could obferve no decompofition by either. I then eva¬ porated the water in order to reunite the fubftances that might be in folution ; and touching it again with the aforefaid liquors, it Ihowed a flight effervefcence with the acids. When tried with the fyrup of violets, this became a pale green ; fo that I was perfuaded it con¬ tained a calcareous fait. With the decoftion of galls no precipitation wTas produced. “ The matter being afterwards dried in the ftiade, it appeared a very fubtile fine earth, of a cretaceous colour but inert, from having been diluted by the rain. “ I next thought of calcining it with a flow fire, and it affumed the colour of a brick. A portion of this being put into a crucible, I applied to it a ftronger heat; by which it loft almoft all its acquired colour. Again, I expofed a portion of this for a longer time to a very violent heat (from wdiich a vitrification might be ex¬ pelled) ; it rerfiained, however, quite foft, and was eafily brmfed, but returned to its original dufky co¬ lour. “ From the mofl accurate obfervations of the fmoke from the three calcinations, I could not difeover either colour or fmell that indicated any arfenical or fulphure- ous mixture. “ Haying therefore calcined this matter in three por¬ tions, with three different degrees of fire, I prefented a good magnet to each : it did not aft either on the firft or fecond ; a flight attra£lion was vifible in many places on the third : this perfuaded me, that this earth contains a martial principle in a metallic form, and not in a vi¬ triolic fubftance. “ The nature of thefe fubftances then being difeover- ed, their volcanic origin appears $ for iron, the more it 4 K is R A I [ 626 ] H A I Rain, is expofed to violent calcination, the more it is divided .Rainbow, by bie l0fs cf its phlogiilic principle j which cannot naturally happen but in the great chimney of a volcano. Calcareous fait, being a marine fait combined with a calcareous fubltance by means of violent heat, cannot be otherwife compofed than in a volcano. “ As to their dreaded effedls on animals and vegeta¬ bles, every one knows the advantageous ufe, in medi¬ cine, both of the cne and the other, and this in the fame form as they are thus prepared in the great laboratory of nature. “ Vegetable?, even in flower, do not appear in the lead macerated, which has formerly happened from on¬ ly {bowers of land. “ How this volcanic produdtion came to be mixed with water may be conceived in various ways. “ /Etna, about its middle regions, is generally fur- rounded with clouds that do not always rife above its fummit, which is 2900 paces above the level of the fea. This matter being thrown out, and defcending upon the clouds below it, may happen to mix and fall in rain with them in the ufual way. It may alio be corjedlu- red, that the thick fmoke which the volcanic matter contained might, by its rarefaftion, be carried in the atmofphere by the winds over that tra£l of countiy j and then cooling fo as to condenfe and become fpecifi- cally heavier than the air, might defcend in that colour¬ ed rain. “ I mud, however, leave to philofophers (to whom the knowledge of natural agents belongs) the examina¬ tion and explanation of Rich phenomena, confining my- felf to obfervation and chemical experiments.” Rain, a well built and fortified town of Bavaria, one of the keys of this deflorate, on the Lech, 20 miles wed of Ingollladt. N. Lat. 48. 51. E. Long. 11. 12. RAIN-Bird. ■ See CucuLUS, ORNITHOLOGY Index. RAINBOW. See Optics. In the Philofophical Tranfadions for 1793, we have the following account of two rainbows feen by the Rev. Mr Sturges. “ On the evening of the 9th of July 1792, between feven and eight o’clock, at Alverdroke, near Gofport, on the fea-coad of Hampthire, there came up, in the fouth-ead, a cloud with a thunder fhower \ while the fun {hone bright, low in the horizon to the north- Plate vveft- fcccLvin. “ In this fhower tw7o primary rainbows appeared, Fig. a AB and AC, not concentric, but touching each other at A, in the fouth part of the horizon \ with a fecon- dary bow to each, DE and DF (the lad very faint, but difcernible), which touched likewife at D. Both the primary w7ere very vivid for a confiderable time, and at different times nearly equally fo \ but the bow AB w7as mod permanent, was a larger fegment of a circle, and at lad, after the other had vanifhed, became aimed a femicircle •, the fun being near fetting. It was a perfed calm, and the fea was as fmooth as glafs. “ Lr I might venture to offer a folution of this ap¬ pearance, it w’ould be as follows. I confider the bow AB as the true one, produced by the fun itfelf j and the other, AC, as produced by the refledion of the fun from the fea, wLich, in its perfedly fmooth date, aded as a fpeculum. The diredion of the fea, between the Ifle of Wight and the land, was to the north-wTed in a l^ne with the fun, as it was then fituated. The image refleded from the w7ater, having its rays liming from a Rainbow, point lower than the real fun, and in a line coming from u—v*—' beneath the horizon, would confequently form a bow higher than the true one AB. And the ihores, by w7hich that narrow part of the lea is bounded, would be¬ fore the fun’s adual fetting intercept its rays from the furface of the water, and caufe the bow AC, wdiich I fuppofe to be produced by the refledion, to difappear before the other.” The marine or fea bow is a phenomenon vrhich may be frequently obferved in a much agitated fea, and is occaiioned by the wind fwceping part of the waves, and carrying them aloft j which when, they fall down are refraded by the fun’s rays, which paint the colours of the bow juft as in a common {bower. Thefe bows are often feen when a veffel is failing with confiderable force, and dafhing the waves around her, which are raifed paitly by the adion of the ftvip and partly by the force of the wind, and, falling down, they form a rainbow j and they are alfo often occaiioned by the dafliing of the waves againft the rocks on ftiore. In the Philofophical Tranfadions, it is obferved by F. Bourzes, that the colours of the marine rainbow are lefs lively, lefs diftind, and of ftiorter continuance, than thofe of the common bow j that there are Icarcely above two colours diftinguilhable, a dark yellow on the fide next the fun, and a pale green on the oppofite fide. But they are more numerous, there being fometimes 20 or 30 feen together. To this clai's of bows may be referred a kind of white or colourlefs rainbows, which Mentzelius and others af¬ firm to have feen at noon-day. M. Marlotte, in his fourth EJfai de Physique, fays, thefe bows are formed in mills, as the others are in fhowers; and adds, that he has feen feveral both after funrifing and in the night. The want of colours he attributes to the fmallnefs of the vapours which compofe the mift •, but perhaps it is ra¬ ther from the exceeding tenuity of the little veficulse of the vapour, which being only little watery pellicles bloated with air, the rays of light undergo but little re- fradion in paffing out of air into them ; too little to ie- parate the differently coloured rays, &:c. Hence the rays are refleded from them, compounded as they came, that is, white. Rohault mentions * coloured rainbows on * Trade de the grafs 5 formed by the refradions of the fun’s rays in Fhy/iquc. the morning dew. Rainbows have been alfo produced by the refledion of the fun from a river j and in the Philofophical Tranfadlions, vcl. 1. p. 294. we have an account of a rainbow, which mull have been formed by the exhalations from the city of London, when the fun had been fet 20 minutes, and confequently the centre of the bow was above the horizon. The colours were the fame as in the common rainbow, but fainter. It has often been made a fubjed of inquiry among the curious how there came to be no rainbow before the flood, which is thought by fome to have been the cafe from its being made a fign of the covenant which the Deity was pleafed to make with man after that event. Mr Whitehurft, in his Inquiry into the Original State and Formation of the Earth, p. 173, &c. endeavours to eftablifh it as a matter of great probability at leaft, that the antediluvian atmofphere was fo uniformly temperate as never to be fubjed to ftorms, tempefts, or rain, and of courfe it could never exhibit a rainbow. For our own part, wre cannot fee how the earth at that period could do R A t Rainbow, do without rain any more than at prefent; and it appears ^ to us from Scripture equally probable that the rainbow was feen before the flood as after it. It was then, how¬ ever, made a token of a certain covenant; and it would unqueflionably do equally well for that purpole if it had exifted before as if it had not. Lunar RAINBOW. The moon fometimes alfo exhi¬ bits the phenomenon of an iris or rainbow by the re¬ fraction of her rays in drops of rain in the night time. This phenomenon is very rare. In the Philolophical TranfaCtions for 1783, however, we have an account of three feen in one year, and all in the fame place, com¬ municated in two letters by Marmaduke lunftall, Efq. The firft was feen 27th February 1782, at Greta Bridge, Yorkfliire, between feven and eight at night, and appeared in tolerably diftinCt colours, fimilar to a folar one, but more faint: the orange colour leemed to predominate. It happened at full moon ; at which time alone they are faid to have been always feen. Though Ariflotle is faid to have obferved two, and fome others have been feen by Snellius, &c. I can only find two de- fcribed with any accuracy j viz. one by Plot, in his Hi- ftory of Oxfordthire, feen by him in (675, though with¬ out colours •, the other feen by a Derbylhire gentleman at Glapwell, near Chefterfield, defcribed by Thorefby, and inferted in N° 331. of the Philofophical Tranfac- tions : this was about Chriftmas, 1710} ant^ hiid to have had all the colours of the Iris Solaris. The night was windy •, and though there was then a drizzling rain and dark cloud, in which the rainbow was reflected, it pro¬ ved afterwards a light frofl:.,, Two others were afterwards feen by Mr 1 unftall ; one on July the 30th, about 1 x o’clock, which lafted about a quarter of an hour, without colours. The other, which appeared on Friday OCtober 18. was “ perhaps the moA extraordinary one of the kind ever feen. It was firfl: vifible about nine o’clock, and continued, though with very different degrees of brilliancy, till paft two. At firft, though a ftrongly marked bow, it was without colours •, but afterwards they were very confpicuous and vivid in the fame form as in the folar, though faint¬ er ; the red, green, and purple, were moft diftinguifh- able. About twelve it was the moft fplendid in ap¬ pearance ; its arc was confiderably a fmalier fegment of a circle than a folar ; its fouth-eaft limb firft began to fail, and a confiderable time before its final extinftion : the wind was very high, nearly due weft, moft part of the time, accompanied with a drizzling rain. It is a Angular circumftance, that three of thefe phenomena fhould have been feen in fo Ihort a time in one place, as they have been efteemed ever fince the time of x\riftotle, who is faid to have been the firft obferver of them, and faw only twro in 50 years, and fince by Plot and Thorelby, almoft the only two Englilh authors who have fpoke of them, to be exceeding rare.. They feem evidently to be occafioned by a refraClion in a cloud or turbid atmofphere, and in general are indications of ftormy and rainy weather : fo bad a feafon as the late fummer having, I believe, feldom occurred in England. Thorelby, indeed, fays, the one he obferved was fuc- ceeded by feveral days of fine ferene weather. One particular, rather lingular, in the fecond, viz. of July the 30th, was its being fix days after the full of the moon} and the laft, though of fo long a duration, was r - pence •, but was obliged to return on account of an in- feffious diftemper on board. Fie was, however, lo little afledfed by this dilappointment, that he now laid before the queen and council a propofal for, exploring the continent of North America j and in 1584 obtained a patent empowering him to pcffefs iuch countries as he (hould dikover in that part of the globe. Accordingly Mr Raleigh fitted out twro (hips at his own expence, which failed in the month of April, and returned to England about the middle of September, reporting that they had diicovered arid taken poffeflion of a fine coun¬ try called Windangocoa, to which the queen gave the name of Virginia. About this time he was defied knight of the (hire for the county of Devon, and foon after received the honour of knighthood ; and to en¬ able him to carry on his defigns abroad, the queen granted him a patent for licenfing the venders of wine throughout the kingdom. In 1585 he fent a fleet of feven (hips to Virginia, ccmmanded by his relation Sir Richard Greenville, who left a colony at Roanah of 107 perfons, under the government of Mr Lane ; and by the eftabliftiment of this colony he firft imported tobacco into England. See Nicgtiana. In the fame year Sir Wal¬ ter Raleigh obtained a grant of 12,000 acres of the forfeited lands in the county of Corke in Ireland.— About the fame time he was made fenefchal of the duchy of Cornwall, and warden of the ftanneries-; and grew into fuch favour with the queen, that even Leiceiler was jealous of his influence. In 1587, he fent another colony of 150 men to Vir¬ ginia, with a governor, Mr John White, and 12 aflifl- ants. About this time wre find our knight diftinguilh- ed by the titles of Captain of the queen's guards, and Lieutenant general of Cornwall. From this period to the year 1594, he was continually engaged in projecting new expeditions, fending fuccours to the colonies abroad, defending the kingdom from the infults of the Spani¬ ards, and tranfafting parliamentary bufinefs, with equal ability and refolution. Whilft thus employed, he was publicly charged, in a libel written by the infamous Jefuit Parfons, with being an Atheift; a groundlefs and ridiculous imputation. In 1594, he obtained from the queen a grant of the manor of Sherborne in Dor- fetfhire, where he built a magnificent heufe : but Sir Walter fell under the queen’s difpleafure on account of an intrigue wilh the daughter of Sir Nicholas Throg¬ morton, one of the maids of honour 5 however, he mar¬ ried the lady, and lived with her in great conjugal har¬ mony. [ 6*8 ] II A L [ 629 ] RAM Raleigh mony. Daring his difgrace at court, he projefted the il conquefi of Guiana in South America, and in 1595 , failed for that country j of which having taken poffel- fon, after defeating the Spaniards who were fettled theie, he returned to England the lame year, and foon after publilhed an account of his expedition. In the following year he was one of the admirals in the fuccefs- ful expedition a gain it Cadiz, under the command of Howard and the earl of Effex \ and in 1597 fehed with the fame commanders againft the Azores. Soon after thefe expeditions, we find him. affiduoufly engaged in parliamentary bufinefs, an in the office of intendant to the duke of Bouillon, prince de Turenne. The moft capital work of his writing is the Travels of Cyrus, which has been feveral times printed in Englilh. Ramsay, The Reverend James, fo juftly celebrated for his philanthropy, was born on the 25th of July 1733, at Fraferfburgh, a fmall town in the county of Aberdeen, North Britain. His defeent was honourable, being, through his father, from the Ramfays of Melrofe in Banffshire, and through his mother, from the Ogilvies of Purie in Angus. His parents were of charafters the mofl: refpe&able, but in circumftances by no means af¬ fluent. From his earliefl: years he difeovered a ferious difpofition, and a ftrong thirft for knowledge ; and af¬ ter palling through the courfe of a Scotch grammar fchool education, he was inclined to purfue the ftudies requifite to fit him for the profeffion of a clergyman j an inclination with which the wilhes of his mother, a woman of eminent piety, powerfully concurred. Seve¬ ral circumftances, however, confpired to divert him for a time from his favourite purfuit. _ Fie was educated in the epifcopal perfuafion 5 and ha¬ ving been unhappy enough to lofe his father while yet very young, he found, upon his advancing towards the Hate of manhood, that the joint fortunes of himfelf and his mother could not bear the expence of a regular edu¬ cation in either of the univerfities of Oxford er Cam¬ bridge, which he doubtlefs thought abfolutely neceffary to one who afpired to refpeftability in the church of England. Yielding therefore to necelfity, he refolved to ftudy furgery and pharmacy •, and was with this view bound apprentice to Dr Findlay, a phyfician (a) in Fra- ferlburgh. But though obliged to relinquilh for a time his favourite ftudies, he did not think ignorance excu- fable in a furgeon more than in a clergyman, or conceive that he could ever become eminent in the profeffion in which circumftances had placed him, merely by Ikill in fetting a bone or compounding a medicine. He deter¬ mined therefore, with the full approbation of his mailer, who ^nd tpotheca6 rCm°te t0WnS °f Scctland 1116 fairiC man {generally a&s in the triple capacity of phyfician, furgeon f 632 ] 2 RAM [ 633 ] R A M Ramfay. wlio very foon difcovered his talents far literature, to *”-~v make himfelf acquainted with at lead the outlines of the liberal arts and fciences $ and with this view he repaired in 1750 to the King’s College and univerfity oi Aber¬ deen, where he obtained one of the burfaries or exhibi¬ tions which are there annually bellowed upon fuch can¬ didates for them as diiplay the mod accurate knowledge of the Latin language. The fmall fum of five pounds, however (which none of thefe burfaries exceed), was dill inadequate to the expence of refidence in college j but our young dudent was loon to obtain a more valu¬ able exhibition, and to obtain it likewife by his own merit. During the long vacation he returned to his mader Dr Findlay, and was by him intruded with a very def- perate cafe in furgery, ot which his management may be laid to have laid the foundation of his future fortunes. A female fervant of one of the judges of the Court of Seffion, who, when the court was not fitting, redded in the neighbourhood of Fraferiburgh, had been fo dread¬ fully gored by a bull, that hardly any hopes were en¬ tertained of her recovery ; but Mr Ramfay, to whofe care die was entirely left, treated the wound with fuch fkilful attention, that, contrary to general expedlation, his patient recovered. This attracted the judge’s no¬ tice, who having informed himfelf of the young man’s circumltances and charadler, recommended him fo effec¬ tually to Sir Alexander Ramfay of Balmain, that he prefented him with a burfary of 15 pounds a-year, which commenced at the next fejjion or term, in the fame col- lege. Fie nowr profecuted his dudies with comfort ; and though he wTas detained in college a year longer than is ufual, being obliged, upon his acceptance of a fecond burfary, to begin his courfe anew, he always confidered this as a fortunate circumllance, becaufe it gave him the celebrated Dr Reid three years for his preceptor. To that great and amiable philofopher he fo recom¬ mended himfelf by his talents, his induftry, and his vir¬ tues, that he was honoured with his friendfhip to the day of his death. Nor was it only to his mailers that his condudl recommended him ; Sir Alexander Ramfay whom he vilited during fome of the vacations, wras fo well pleafed with hrs converfation, that he promifed him another burfary, in his gift, of 25I. a-year, to commence immediately on the expiration of that which he enjoy¬ ed. This promife he performed in the beginning of the year 1755 ; and at the felicitation of Dr Findlay, even paid the money per advance to enable the exhibitioner to travel for the purpofe of improving himfelf in his pro- feflion. Thus provided, Mr Ramfay went to London, and fludied furgery and pharmacy under the aufpices of Dr Macaulay; in whofe family he lived for two years, careffed and efleemed both by him and by his lady. Afterwards, having paffed the ufual examination at Surgeons-hall, he ferved in his medical capacity for feveral years in the royal navy j but how long he was continued in the 11a- tion of a mate, or when and by w7hom he was firfl: ap¬ pointed furgeon, wre have not been able to learn. We can fay, however, upon the bell authority, that by his humane and diligent difeharge of his duty in either Ra¬ tion, he endeared himfelf to the feamen, and acquired the efteem of his officers. Of his humanity there is indeed one memorable in- Vol. XVII. Part II, fiance, w’hich muft not be omitted. Whiift he aefed as Rairfay. furgeon of the Arundel, then commanded by Captain ^ (now7 Vice-admiral Sir Charles) Middleton, a llave-fiiip on her pallage from Africa to the Weft indies fell in with the fleet to which the Arundel belonged. An epidemical dhtemper, too common in fuch veiiels, had fwept away not only a great number of the unfortunate negroes, but alfo many of the {hip’s crew, and among others the furgeon. In this diftrefled fituation the commander of the Guinea fhip applied to the Engliffi commodore for medical afhtlance •, but not a furgeon or furgeon’s mate in the whole fleet, except Mr Ramfay, would expofe hinifelf to the contagion of fo dangerous a diftemper. Prompted, however, by his own innate benevolence, and fully authorized by his no lels bene¬ volent commander, the iurgeon of the Arundel, regard- lefs of perfonal danger, and trufiing in that God to whom mercy is more acceptable than facrifice, went on board the infedled fhip, viiited all the patients, and re¬ mained long enough to leave behind him written direc¬ tions for their future treatment. If a cup of cold water given in charity be entitled to a reward, how much more fuch an action as this ? But the rewards of Chri- flianity are not immediate. Mr Ramfay indeed efcaped the contagion ; but on his return to his own fhip, jull as he had got cn the deck, he fell and broke his thigh¬ bone ; by w7hich he was confined to his apartment for ten months, and rendered in a fmail degree lame through the remainder of his life. The fearlefs humanity which he difplayed on this occafion gained him the friendship and ellecm of Sir Chari es Middleton, which no future action of his life had the fmalleft tendency to impair 3 but the fradture of his thigh-bone and his fubfequent lamenefs determin¬ ed him to quit the navy, and once more turn his thoughts towards the church. Accordingly, while the Arundel lay at St Chriffopher’s, he opened h:s views to fome of the principal inhabitants of thatifland, by whom he was fo ftrongly recommended to the biihop of Lon¬ don, that on his coming home with Sir Charles Mid¬ dleton, who warmly joined in the recommendation, he was admitted into orders ; after which he immediate¬ ly returned to St Chrillopher’s, where he was prefent¬ ed by the governor to two redories, valued at 700I. a- year. As foon as he took poffeffion of his livings, in 1763, he married Mifs Rebecca Akers, the daughter of a planter of the heft family-connedions in the ifland, and began to regulate his houfehold on the pious plan incul¬ cated in his Ejjay on the Treatment and Converjion of the African Slaves in the Briti/h Sugar Colonies. Fie fum- moned all his own (laves daily to the prayers of the fa¬ mily, when he took an opportunity of pointing out to them their duty in the plained terms, reproving thofe that had done amifs, and commending fuch as had fhown any thing like virtue; but he confeffed that his occa- fions for reproof were more frequent than for commen¬ dation. As became his office and charader, he incul¬ cated upon others what he pradifed himfelf, and knew to be equally the duty of all. “ On his firft fettlement as a minifter in the Weft Indies, he made fome public attempts to inftrud flaves. He began to draw up fome eafy plain difeourfes for their inftrudion. He invited them to attend on Sundays, at particular hours. He appointed hours at home to inftrud; fuch fenfible flaves 4 L %s RAM [ 5.34 ] RAM Ramfay. as would of tliemfelves attend. He repeatedly exhorted -— ' their mailers to encourage Inch in their attendance. He recommended the French cuftom, of beginning and end¬ ing work by prayer. But inconceivable is the liillefT- nefs with which he was heard, and bitter was the cen- fure heaped on him in return. It was quickly fuggeft- ed, and generally believed, that he wanted to interrupt the work of Haves, to give them time, forfooth, to fay their prayers j that he aimed at the making of them Chriftians, to render them incapable of being good Haves. In one word, he flood, in opinion, a rebel con- vi£t againft the intereit and majefty of planterflrip. And- as the Jews fay, that in every punifliment, with which they have been proved, lince the bondage of Egypt, there has been an ounce of the golden calf of Horeb ^ fo might he fay, that in every inltance of prejudice (and they were not a few) with which, till within a year or two of his departure from the country, he was exercifed, there was an ounce of his fruitlefs attempts to improve the minds of Haves. In the bidding prayer, he had in- ferted a petition for the converHon of thofe perfons. But it was deemed fo difagreeable a momento, that feveral white people, on account of it, left off attending divine fervice. He was obliged to omit the prayer entirely, to try and bring them back. In ihort, neither were the Haves, at that time, defirous of being taught, nor were their makers inclined to encourage them.” That he was hurt by this negledf cannot be queHion- ed, for he had a mind benevolent, warm, and irritable ; but he Hill retained many friends amongfl: the moil wor¬ thy members of the community ; and as he was confci- ous of having done nothing more than his duty, he con- loled hijnfelf with rcflefting, that thofe are “ blefled ■whom men revile, and perfecute, and fpeak all manner of evil again!! falfely, for the fake of the gofpel.” Although his ferious fludies were now theological, lie confidered himfelf as anfwerable to God, his country, and his own family, for a proper ufe of every branch of knowledge which he pofleffed. He therefore took the charge of feveral plantations around him in the capaci¬ ty of a medical practitioner ; and attended them with unremitting diligence, and with great fuccefs. Thus he lived till the year 1777, when relinquilhing the practice of phyfic entirely, he paid a vifit to the place of his na¬ tivity, which he had not feen fince 1755. His mother, whofe latter days he had made comfortable by a hand- fome annuity, had been dead for fome years 3 but he re- tvarded all wdio had been attentive to her, or in early life ferviceable to himfelf 3 and he continued the penfion to a filter who had a numerous family, for which her hufband was unable to provide. After remaining three weeks in Scotland, and near a year in England, during which time he wras admitted into the confidence of Lord George Germaine, fecre- tary of Hate for the American department, Mr Ramfay was appointed chaplain to Admiral Barrington, then going out to take a command in the Welt Indies. Un¬ der this gallant officer, and afterwards under Lord Rod¬ ney, he was prelent at feveral engagements, where he difplayed a fortitude and zeal for the honour of his country which would not have difgraced the oldeft ad¬ miral. To the navy, indeed, he feems to have been itrongly attached 3 and he wrote, at an early period of his life, an F-.JJ'oy on the Duty and Qiia/ifications of a Sea- oficer, with fuch a knowledge of the fervice as would have done honour to the pen of the mofl: experienced Ramfay. commander. Of the firlt edition of this eflay the pro- v fits were by its benevolent author appropriated to the Magdalen and Britilh lying-in hofpitals, as thofe of the fecund and third (which laft was publilhed about the period of which we now write) were to the maritime ichool, or, in the event of its failure, to the marine fo- ciety. Although carefled by both the admirals under wThom he ferved, and having fuch influence with the latter as to be able to render eflential fervices to the Jews and other perfons wdiom he thought harlhly treated at the capture of St Euflatius, Mr Ramfay once more quitted the fea-fervice, and retired to his pafloral charge in the ifiand of St Chriftopher’s. There, however, though the former animoiities again!! him had entirely fubfided, and though his friend (hip w7as now folicited by every perfon of confequence in the ifland, he remained but a little while. Sick of the life of a planter and of the profpefl of Havery around him, he refigned his livings, bade adieu to the ifiand, and returned to England with his wife and family in the end of the year 1781. Im¬ mediately on his arrival, he was, through the intereit of his Heady friend Sir Charles Middleton, prefented to the livings of Teilon and Nettlefiead in the county of Kent. Here he was foon determined, by the advice of thofe whom he moH refpefted, to publifh an EJfay, which had been written many years before, on the Treatment and Converfion of African Slaves in the Britijh Sugar Colo¬ nies. The controverfy in which this publication invol¬ ved him, and the acrimony with which it was carried on, are fo frefii in the memory of all our readers, that no man wdio thinks of the narrow limits within w’hich our biographical articles mufi be confined, will blame us for not entering into a detail of the particulars Torrents of obloquy were poured upon the benevolent author by writers who were unfair enough to conceal their names 3 and it mufi be confefied, that his replies abounded with farcafms, which the mol! rational friends to the caufe which he fupported would not have been ferry to fee blotted from his pages. The provocation, however, which he received was great 3 and Mr Ram¬ fay, though an amiable, virtuous, and pious man, had a warmth of temper, \vhich, though not deferving of praife, will be ceniured by none who refledl on the frail¬ ties of our common nature. That the particular calumnies propagated againft him on this occafion were wholly groundlefs, it is impoffible to doubt, if we admit him to have been poffeffed of common underflanding. When fome years ago a fiory was circulated, of Swift’s ha¬ ving, when prebendary of Kilroot, been convifted be¬ fore a magiftrate of an attempt to commit a rape on the body of one of his pariftneners, it was thought a fufficient confutation of the calumny to put the retailer of it in mind, that the dean of St Patrick’s, though detefted by the moft powerful faction in the kingdom, lampooned without dread, and with great feverity, the dean of Ferns for the very crime, of wdiich, had this anecdote been true, he mufi have been confcious that all Ireland knew himfelf to be guilty ! Such condud! cannot be reconciled to common fenfe. Had Swift been a ravifirer, though he might have been penitent, and reafoned in general terms againft giving way to fuch licentious paflions, he would never have fatirifed a / RAM Machine. Ramfay,^ a particular pcrfon for the crime of which he himfelf Ramfden’s ft00d conviaed. In like manner, had Mr Ramfay been a tyrant to his own Haves, though he might have argued againll flavery in the abftraft, on the broad balls of vir¬ tue and religion, he never could have arraigned for li- milar cruelty a number ef individuals in the very iHand which witneffed his own enormities. But the melancholy part of the narrative is behind. The agitation given to his mind by thefe calumnies, and the fatigues he underwent in his endeavours to re- fcue from mifery the moll helplefs portion of the human race, contributed to fliorten a life in no common degree uieful. He had been for fome time afflicted with a pain in his ftomach, for which he was prevailed upon, though with great reluctance, to try the effefts of air and ex- ercife, by attempting a journey of 100 miles. But in London, being leized with a violent vomiting of blood, he w-as unable either to proceed or to be removed home; and in the houle of Sir Charles Middleton lie ended his days, on the 20th of July 1789, amidlt the groans of his family, and the tears of many friends.— Thus died a man, of whom it is not too much to fay, that “ the blef- hng of many that were ready to perilh came upon him for whatever be the fate of the Have-trade (fee Sla¬ very), it is certain that his writings have contributed much to meliorate the treatment of Haves. He left be¬ hind him a widow and three daughters : and his works, befides thole to which we have alluded, conlift of a vo¬ lume of Sea-fermons, preached on board his majefty’s ihip the Prince of Whies, which fliow him to have been a mailer of true pulpit-eloquence ; and a Treatife on Sig¬ nals, which Was certainly wmitten, and we think printed, though we know not whether it was ever publiflied. RAMSDEN’s Machine for Dividing Mathema¬ tical Instruments, is an invention by which thefe divifions can be performed with exceeding great accu- racy, fuch as would formerly have been deemed incre¬ dible. On difcovering the method of conlfru&ing this machine, its inventor, Mr Ramfden of Piccadilly, re¬ ceived 6151. from the commiHioners of longitude ; en- gaging himfelf to inltruct a certain number of perfons, not exceeding ten, in the method of making and ufing this machine from the 28th Odfober 1775 to 28th Oc^ tober 1777 : alfo binding himfelf to divide all odlants and fexants by the fame engine, at the rate of three Ihil- lings for each oftant, and fix fiiillings for each brafs fex- tant, with Nonius’s divifions to half minutes, for as loner time as the commiHioners Ihould think proper to let the engine remain in his pofleflion. Of this Him of 61 5I. paid to Mr Ramfden, 300I. was given him as a reward for the improvement made by him in difcovering the engine, and the remaining q r d. for his giving up the property of it to the commiHioners. The following defeription of the engine, is that given upon oath by Mr Rarofden himfelf. “ 1 his engine confifis of a large wheel of bell-metal, mpported on a mahogany Hand, having three legs which are firongly conneffed together by braces, fo as to make it perfectly Heady. On each leg of the Hand is placed a conical friction pulley, whereon the dividing-wheel relrs: to prevent the wheel from Hiding off the fridlion- pulieys, the bell-metal centre under it turns in a locket on the top of the Hand. “ The circumference of the wheel is ratched or cut f by a method which will be deferibed hereafter) into [ 635 1 RAM 2160 teeth, in which an endlefs ferew a6ts. Six fevo- Ramfdervs lutions of the ferew will move the wheel a fpace equal Machine; to one degree. - ——v-- .w Now a circle of brafs being fixed on the ferew arbor, haying its. circumference divided into 60 parts, each divifion will confequently anfwef to a motion of the wheel of 10 feconds, fix of them will be equal to a mi¬ nute, &c. “ Several different arbors of tempered fteel are truly ground into the focket in the centre of the wheel. The upper parts of the arbors that Hand above the plane are turned of various fizes, to fuit the centres of "different pieces of work to be divided. “ When any inftrument is to be divided, the centre of it is very exadlly fitted on one of thefe arbors ; and the inftrument is fixed down to the plane of the divid¬ ing wheel, by means of ferews, which fit into holes made in the radii of the wheel for that purpofe. “ I'he inftrument being thus fitted on the plane of the wheel, the frame which carries the dividing-point is connedled at one end by finger-ferews with the frame which carries the endlefs ferew ; while the other end embraces that part of the fteel arbor, which Hands above the inftrument to be divided, by an angular notch in a piece of hardened fteel; by this means both ends o^ the frame are kept perfectly fteady and free from any ftiake. “ The frame carrying the dividing-point, or tracer, is made to Aide on the frame which carries the endlefs ferew to any diftance from the centre of the wheel, as the radius of the inftruraent to be divided may require, and may be there faftened by tightening two clamps ; and the dividing-point or tracer being connected with the clamps by the double-jointed frame, admits a free and eafy motion towards or from the centre for cutting the divifions, without any lateral fhake. “ From what has been faid, it appears, that an in¬ ftrument thus fitted on the dividing-wheel may be mov¬ ed to any angle by the ferew and "divided circle on its arbor, and that this angle may be marked on the limb of the inftrument with the greateft exa&nefs by the di¬ viding-point or tracer, which can only move in a diredl line tending to the centre, and is altogether freed from thole inconveniences that attend cutting by means of a ftraight edge. I his method of drawing lines will alfo prevent any error that might arife from an expanfion or contraction of the metal during the time of divid- ing. The fciew-frame is fixed on tne top of a conical pillar, which turns freely round its axis, and alfo moves freely towards or from the centre of the wheel, fo that the ferew-frame may be entirely guided by the frame which connects it with the centre: by this means any eccentricity of the wheel and arbor would not produce any error in the dividing ; and, by a particular contri¬ vance (which will be deferibed hereafter), the ferew when preffed againft the teeth of the wheel always moves parallel to itfelf; fo that a line joining the centre of the Plate arbor and the tracer continued, will always make equalCCccLI^- angles with the ferew. plate _ “ Figure x. reprefents a perfpedive view of the en- c''CCGLx:’ Sme- , # Fig. 2. , Tig. 2. is a plan, of which fig. 3. reprelents a fee- tion on the line IT A. “ The Iarge wheel A is 45 inches in diameter, and 4 T* 2 haV Raml'len’: Machine. Fig- 3- Fig- T, 2, and 3. Fig- b Fig. 4. rig. i. & rig. 4. Fig- 4- F»g- 5* Fig- 1, 2. At 5- R A M [ 63 has ten radii, each being iupported by edge-bars, as reprefented in fig. 3. Thefe bars and radii are con- nefted by the circular ring B, 24 inches in diameter and three deep } and, for greater itrength, the whole is call in one piece in bell-metal. “ As the whole weight of the wheel A refts on its ring B, the edge-bars are deepeft where they join it ■, and from thence their depth diminithes, both towards the centre and the circumference, as reprefented in %• 3;, “ The furface of the wheel A was worked very even and flat, and its circumference turned true. The ring C, of fine brafs, was fitted very exactly on the circum¬ ference of the wheel; and was faftened thereon with ferews, which, after being ferewed as tight as poflible, were well rivetted. The face of a large chuck being turned very true and flat in the lathe, the flattened fur- face A of the wheel was faffened againfl: it with hold- fafts ; and the two furfaces and circumference of the ring C, a hole through the centre and the plane part round (b) it, and the lower edge of the ring B, were turned at the fame time. “ D is a piece of hard bell-metal, having the hole, which receives the fteel-arbor d, made very flraight and true. This bell-metal was turned very true on an arbor} and the face, which refts on the wheel at was turned very flat, fo that the fteel arbor d might ftand perpendicular to the plane of the wheel : this bell metal was faftened to the wheel by fix Heel ferews /. “ A brafs focket Z is faftened on the centre of the mahogany ftand, and receives the lower part of the bell-metal piece D, being made to touch the bell- metal in a narrow part near the mouth, to prevent any obliquity of the wdieel from bending the arbor : good fitting is by no means neegffary here j fince any fhake in this locket will produce no bad efteft, as will appear hereafter when we deferibe the cutting frame. “ The wheel w7as then put on its ftand, the lower edge of the ring B refting on the circumference of three conical friftion-pulleys W, to facilitate its mo¬ tion round its centre. The axis of one of thefe pulleys is in a line joining the centre of the wheel and the middle of the endlefs ferew, and the other two placed fo as to be at equal diftances from each other. “ F is a block of wood ftrongly faftened to one of the legs of the ftand j the piece g is ferewed to the upper fide of the block, and has half holes, in which the tranfverfe axis h turns: the half holes are kept toge¬ ther by the ferews f. 4- “ The lower extremity of the conical pillar P termi¬ nates in a cylindrical fteel-pin k, which paffes through and turns in the tranfverfe axis /i, and is confined by a cheek and ferew. “ lo the upper end of the conical pillar is faftened the frame G, in which the endlefs ferew turns : the pivots of the ferew are formed in the manner of two fruftums of cones joined by a cylinder, as reprefented at X. Thefe pivots are confined between half poles, which prefs only on the conical parts, and do not touch the cylindric parts : the half holes are kept together by ferews a, which may be tightened at any time, lo pre¬ vent the fevew from {baking in the frame. “ On the ferew-arbor is a fmall wheel of brafs K, having its outfide edge divided into 60 parts, and num- 3 6 ] "RAM bered at every 6th divifion with 1, 2, &c. to 10. The Ramfclen’s motion of this wheel is fhown by the index y on the Machine.^ ferew-frame G. Fig. 4. 8c “ H reprefents a part of the ftand, having a parallel pig. It flit in the direction towards the centre of the wheel, large enough to receive the upper part of the conical brafs pillar P, which carries the ferew and its frame : and as the refiftance, when the wheel is moved by the endlefs ferew, is againft. that fide of the flit FI which is towards the left hand, that fide of the flit is faced with brafs, and the pillar is prefled againft it by a fteel fpring on the oppofite fide : by this means the pillar is ftrongly fupported laterally, and yet the ferew may be eafily prefled from or againft the circumference of the wheel, and the pillar will turn freely on its axis to take any direction given it by the.frame L. “ At each corner of the piece I are ferews « of Fig. 4. tempered fteel, having poliihed conical points : two of them turn in conical holes in the fciew-frame near 0, and the points of the other two ferews turn in holes in the piece j the ferews f> are of fteel, which being tightened, prevent the conical pointed ferews from un¬ turning when the frame is moved. “ L is a brafs frame, which ferves to connect the end- r> 2» lefs ferew, its frame, &c. with the centre of the wheel : each arm of this frame is terminated by a fteel ferew, that may be palled through any of the holes y in the ^ piece Q, as the thickneis of work to be divided on the wheel may require, and are faftened by the finger-p;.r x ^ 3 nuts r. “ At the other end of this frame is a flat piece of tempered fteel b, wherein is an angular notch : when Fig. 6. the endlefs ferew is prefled againft the teeth on the cir¬ cumference ot the wheel, which may be done by turn- ing the finger-ferew S, to prefs againft the fpring t, 1‘ ^ this notch embraces and preffes againft the fteel arbor d. Fig. 2. This end of the frame may be railed or deprefled by mov¬ ing the prifmatic Aide u, which may be fixed at any height by the four fteel-fcrews v. Fig. r, 2, 6. “ The bottom of this Aide has a notch b, whofe Fig. 1. &. 6* plane is parallel to the endlefs-fcrew •, and by the point of the arbor d refting in this notch, this end of the Fig. 3. frame is prevented from tilting. The ferew S is pre¬ vented from unturning, by tightening the finger- I»?* nut w. “ The teeth on the circumference of the wheel were cut by the following method : “ Having confidered what number of teeth on the circumference would be moft convenient, which in this engine is 2i6d, or 360 multiplied by 6, I made two ferews of the fame dimenfions, of tempered Heel, in the manner hereafter delcribed, the interval between the threads being fuch as I knew by calculation would come within the limits of what might be turned off the circumference of the wheel : one of the ferews, which was intended for ratching or cutting the teeth, was notched acrofs the threads, fo that the ferew, when prefled againtt the edge of the wheel and turned round, cut in the manner of a law. Then having a fegment of a circle a little greater than 60 degrees, of about the lame radius with the wheel, and the circumference made true, from a very fine centre, I defcribtd an arch near the edge, and fet off the chord of 60 degrees on this arch. This fegment was put in the place of the wheel, the edge of it was ratched, and the number of revolutions Ramfdeo’s Machine. RAM [ 637 ] R revolutions and parts of the fcrew coi'itained between coincide with the fixed wire A M rig- 7- Fig. 7. Fig- 3- Fig- 1, 2, 3 the interval of the 60 degrees were counted. The radius was correifted in the proportion of 360 revolu¬ tions, which ought to have been in 60 degrees, to the number actually found ; and the radius, fo corrected, was taken in a pair of beam-compaffes : while the wheel was on the lathe, one foot of the compaffes was put in the centre, and with the other a circle was de- fcribed on the ring •, then half the depth of the threads of the fcrew being taken in dividers, was fet from this circle outwards, and another circle was defcribed cut¬ ting this point} a hollow was then turned on the edge of the wheel of the fame curvature as that of the fcrew at the bottom of the threads : the bottom of this hol¬ low was turned to the fame radius or diftance from the centre of the wheel, as the outward of the trvo circles before-mentioned. “ The wheel was now taken oft the lathe ; and the bell-metal piece 1) was fcrewed on as before directed, which after this ought not to be removed. “ From a very exaft centre a circle was defcribed on the ring C, about four-tenths of an inch within where the bottom of the teeth would come. This circle was divided with the greatell exaftnels I was capable of, firft into five parts, and each of thefe into three. Thefe parts were then bifecled four times : (that is to fay) fuppofing the whole circumference of the veheel to con¬ tain 2160 teeth, this being divided into five parts, each would contain 432 teeth; which being divided into three parts, each of them would contain 144 ; and this fpace bifedted four times would give 72, 36, iS, and 9 : there¬ fore each of the laft divifions would contain nine teeth. But, as I was apprehenfive fome error might arife from quinquefedlion and triieClion ; in order to examine the accuracy of the divifions, I defcribed another circle on the ring C, one-tenth of an inch within the former, and divided it by continual bifeftions, as 2160, 1080, 540, 270, 135, 67!, and 33-i ; and as the fixed wire (to be defcribed prefently) croffed both the circles, I could examine their agreement at every 135 revolutions; (af¬ ter ratching, could examine it at every 33^) : but, not finding any fenfible difference between the two lets of divifions, I, for ratching, made choice of the former; and, as the coincidence of the fixed wire with an inter- feflion could be more exactly determined than with a dot or divifion, I therefore made ufe of interfeftion in both circles before defcribed. “ The arms of the frame L were connefled by a thin piece of brafs of three-fourths of an inch broad, having a hole in the middle of four-tenths of an inch in diameter; acrofs this hole a filver wire was fixed exa£Hy in a line to the centre of the wheel; the coincidence of this wire with the interfeftions was examined by a lens feven- tenths of an inch focus, fixed in a tube which w'as at¬ tached to one of the arms L (a). Now a handle or winch being fixed on the end of the fcrew, the divifion marked on the end of the fcrew, the divifion marked 10 on the circle K was fet to its index, and, by means of a clamp and adjufting fcrew for that purpofe, the inter- feflion marked 1 on the circle C was fet exa&ly to the fcrew was then care- Ramfden's fully preffed againft the circumference of the wheel, by Machine.^ turning the finger-ferew S ; then, removing the clamp, I turned the fcrew by its handle nine revolutions, till the interfe£tion marked 243 came nearly to the wire ; then, unturning the finger-lcrew S, I releafed the fcrew from the wheel, and turned the wheel back till the in- terfeflion marked 2 exactly coincided with the wire, and, by means of the clamp before-mentioned, the di- vifion 10 on the circle being fet to its index, the fcrew was preffed againft the edge of the wheel by the finger- ferew S ; tftg clamps were removed, and the fcrew turn¬ ed nine revolutions till the interfeftion marked 1 nearly coincided with the fixed wire ; the fcrew wras releafed from the wheel by unturning the finger-ferew S as before, the wheel was turned back till the inter- fetftion 3 coincided with the fixed wire ; the divi- lion 10 on the circle being fet to its index, the fcrew was preffed againft the wdieel as before, and the fcrew was turned nine revolutions, till the interfe&ion 2 nearly coincided with the fixed wire, and the fcrew was releafed ; and I proceeded in this manner till the teeth were marked round the whole circumference of the wheel. This was repeated three times round, to make the impreffion of the fcrew deeper. I then ratch- ed the wdieel round continually in the fame direfticn without ever difengaging the fcrew; and, in ratching the wheel about 300 times round, the teeth were fi- nilhed. “ Now it is evident, if the circumference of the wheel was even one tooth or ten minutes greater than the fcrew would require, this error would in the firft in- ftance be reduced to Pai‘t a revolution, or two feconds and a half; and thefe errors or inequalities of the teeth were equally diftributed round the wheel at the diftance of nine teeth from each other. Now, as the fcrew in ratching had continually hold of feveral teeth at the fame time, and, thefe conftantly changing, the above-mentioned inequalities foon corrected them- felves, and the teeth were reduced to a perfect equality. The piece of brafs which carries the wire was now ta¬ ken away, and the cutting fcrew ivas alfo removed, and a plain one (hereafter defcribed) put in its place : on one end of the fcrew is a fmall brafs circle, having its edge divided into 60 equal parts, and numbered at every fixth divifion, as before-mentioned. On the other end of the fcrew is a ratchet-wheel C, having 60 teeth, covered by the hollowed circle r/, which carries twro Fig. 5. clicks that catch upon the oppofile fides of the ratchet when the fcrew is to be moved forwards. The cylin¬ der S turns on a ftrong fteel arbor F, which paffes through and is firmly fcrewed to the piece Y : this piece, for greater firmnefs, is attached to the ferew- frame G by the braces v; a fniral groove or thread F'g- 4". is cut on the outfide of the cylinder S, which ferves both for holding the ftr’ng, and alio giving motion to the lever J on its centre by means of a fteel tooth n, that works between the threads of the fpiral. To the lever is attached a ftrong fteel pin m, on which a brafs focket r turns : this focket paffes through a flit (a) The interfe£lions are marked for the fake of illuftration, though properly invifible, becaufe they lie under the brafs plate. Pi A M t 63S ] RAM Ramfden*s in tLe piece /», and may be tiglilened in any part of , Maclnne. finger.nut f this piece ferves to regu¬ late the number of revolutions of the fcrew for each tread of the treadle R. Fig. 1. “ T is a brafs box containing a fpiral llringrj a llrong gut is faftened and turned three or forr times round the circumference of this box , the gut then pafles feveral times round the cylinder S, and from thence down to the treadle R. Now7, when the treadle is prefled down, the firing pulls the cylinder S round its axis, and the clicks catching hold of the teeth bn the ratchet carry the fcrew round wdth it, till, by the tooth ti working in Fig. 4. the fpiral groove, the lever J is brought near the wheel r/, and the cylinder flopped by the fcrew-head x linking on the top of the lever J •, at the fame time the fpring is wound up by the other end of the gut palling round the box T. Now7, when the foot is taken oft' the treadle, the fpring unbending itfelf pulls back the cylinder, the Fig. x. clicks leaving the ratchet and fcrew at reft till the piece t ftrikes on the end of the piece /> : tire number of revo¬ lutions of the fcrew at each tread is limited by the num¬ ber of revolutions the cylinder is allow7ed to turn back before the flop ftrikes on the piece />. “ When tire endlefs fcrew was moved round its axis with a confiderable velocity, it would continue that mo- Fig. 1. Sc 4. tion a little after the cylinder S was flopped : to prevent this, the angular lever jj was made j that when the lever .1 comes near to flop the fcrew x, it, by a fmall chamfer, preffes dowrn the piece x of the angular lever ; this brings the other end « ol the fame lever forwards, and flops the endlefs fcrew by the Heel pin y. linking upon the top of it \ the foot of tire lever is raifed again by a fmall fpring preffing on the brace v. Fig- r, 2, 6. “ D, two clamps, connecled by the piece Aide one on each arm of the frame L, and may be fixed at plea- lure by the four finger-fcrew7s s, which prefs againft Heel fprings to avoid fpoiling the arms : the piece q is made to turn without ftiake between tw’o conical pointed fcrew’S f, which are prevented from unturning by tightening the finger-nuts N. PI g “ The piece M is made to turn on the piece q by the conical pointed fcrervsy'refting in the hollow cen¬ ters e. “ As there is frequent occafion to cut divifions on in¬ clined planes, for that purpofe the piece y, in which the tracer is fixed, has a conical axis at each end, which turns in half holes : when the tracer is fet to any inclina¬ tion, it may be fixed there by tightening the fteel fcrews /3. Defcription of the Engine bij which the endlefs fcrew of the Dividing Engine Was cut. 11 Fig. 9. reprefents this engine of its full dimenfions feen from one fide. “ Fig. 8. the upper fide of the fame as feen from a- bove. “ A reprefents a triangular bar of fteel, to which the triangular holes in the pieces B and C are accurately fitted, and may be fixed on any part of the bar by the fcrews D. “ E is a piece of fteel whereon the fcrew is intended to be cut j which, after being hardened and tempered, has its pivots turned in the form of two fruftums of cones, as reprefented in the drawings of the dividing engine (%• 5-)' Thefe pivots were exaflly fitted to the half holes F, and T, which w7ere kept together by the RamCJen4* fcrew Z. Machine, “ FI reprefents a fcrew of untempered fteel, having a , Ran‘li'-V' pivot I, which turns in the hole K. At the other end " v of the fcrew is a hollow centre, which receives the har¬ dened conical point of the fteel pin M. When this point is fufficiently prefled againft the fcrew, to prevent its fhaking, the fteel pin may be fixed by tightening the ferew's Y. “ N is a cylindric nnt, moveable on the ferew^ H j which, to prevent any (hake, may be tightened by the ferdws O. This nut is connedted with the faddle-piece P by means of the intermediate univerfal joint W, through which the arbor of the fcrew H pafles. A front view of this piece, with the fedfion acrofs the fcrew ar¬ bor, is reprelented at X. This joint is connedted with the nut by means of tw7o fteel flips S, which turn on pins between the cheeks T on the nut N. The other ends of thefe flips S turn in like manner on pins a. One axis of this joint turns in a hole in the cock b, which is fixed to the faddle-piece ; and the other turns in a hole d, made for that purpofe in the lame piece on which the cock b is fixed. By this means, ‘when the fcrew is tur¬ ned round, the faddle-piece w7ill Hide uniformly along the triangular bar A. “ K is a fmall triangular bar of well-tempered fteel, which Aides in a groove of the fame form on the faddle- piece P. The point of this bar or cutter is formed to the ftiape of the thread intended to be cut on the end¬ lefs fcrew7. When the cutter is fet to take proper hold of the intendecTfcrew, it may be fixed by tighten¬ ing the fcrew e, which prefles the tw7o pieces of brafs G upon it. “ Having meafured the circumference of the dividing- wheel, I found it would require a fcrew about one thread in a hundred coarfer than the guide-ferew H. The wheels on the guide-ferew arbor H, and that on the fteel E, on which the fcrew was to be cut, were pro¬ portioned to each other to produce that effeft, by giving the wheel L 198 teeth, and the wheel £) 200. Thefe wheels communicated with each other by means of the intermediate wheel R, wdiich alfo ferved to give the threads on the tw7o fcrews the fame direction. “ The faddle-piece P is confined on the bar A by means of the pieces g, and may be made to Aide with a proper degree of tightnefs by the fcrew7s /i.” For Ramfden’s equatorial or portable obfervatory, lee Optics, N° 89. and Astronomy, N° 364. See alfo a long account of an equatorial inftrument made by Mr Ramfden by the direttion of Sir George Shuckburgh in the Philofophical TranfacHons for 1793, art. x. p. 67. In this inftrument the circle of declinations is four feet in diameter, and may be obferved nearly to a fecond, 'I he glafs is placed between fix pillars, which form the axis of the machine, and turn round by tw7o pivots pla¬ ced on two blocks of ftone. See alfo Barometer. RAMSEY, A town of Huntingdonftiire, 68 miles north of London, and 12 north-eaft of Huntingdon. It is fituated as it were in an iftand, being everywhere encompafled with fens, except on the weft, where it is separated fromjthe terra frma by a caufeway for two miles. The neighbouring meers of Ramfey and Whitlefey, which are formed by the river Nyne, abound with fifli, efpecially eel and large pikes. It was once famous for a 4 i’late CCC( jLJX. 1\ A MS DiDiSr s A La cl, i n e. . //„/?-a/, ) - '/./A///?', " • A,r . w -‘5 II V Ram fey II Ramtrut RAM a very rich abbey, part of the gatehoufe of which is ftill Handing, and a neglefted ftalue of Ailwin 5 the epitaph on whofe tomb, which is reckoned one of the oldeft pie¬ ces of Englifh iculptnre extant, Hyles him “ kinfman of the famous King Edward, alderman of all England, and miraculous founder of this abbey.” It w-as dedicated to St Dunllan, and its abbots were mitred and fat in parliament j and fo many kings of England were bene- fadlors to, it, that its yearly rents, fays Camden, were Toool. I he town was then called Rajnfey the Rich; but by the diffoluLon of the abbey it foon became poor, and even loft its market for many years, till about 185 years ago it recovered it. It is held on Saturday, and is reckoned one of the moft plentiful and cheapeft in Eng¬ land. In the year 1721 a great number of Roman coins was found here, fuppofed to have been hid by the monks on fome incurfion of the Danes. There is a charity Ichool m the town for poor girls. W. Lonn o 10 El Lat. 52. 26. ' Ramsey, an ifland of South Wales, on the coaft of Pembrokefhire, about two miles in length, and a mile and a half broad. Near it are leveral fmall ones, known by the name of the bifhop and his clerks. It is four miles weft of St David’s, and 17 north-eaft of Milford haven. It belongs to the bifhopric of St David’s, and was in the laft age, fays Camden, famous for the death of one Ju- ftinian,, a moft holy man, who retiring hither from Brit- anny, in that age rich in faints, and devoting himfelf entirely to God, lived a long while in folitude, and be¬ ing at laft murdered by his fervant was enrolled amonp- the martyrs. , W. Long. 5. 20. N. Lat. 51. 55. Ramsey, in ,the Me of Man, to the north, a moft noted, and fpacious haven, in which the greateft fleet may ride at anchor with fafety enough from all winds but the north-eaft, and in that cafe "they need not be embayed. I his town Handing upon a beach of loofe fand, or ftiingle, is in danger, if not timely prevented, of be¬ ing waftied away by the fea. RAMSGATE, a fea-port town of Kent, in the ifte of Thanet, five miles from Margate, where a very fine pier has been lately built for the fecurity of fliips that come into the harbour, being feated near the Downs be¬ tween the north and fouth Foreland, 10 miles north-eaft of Canterbury. The town is fituated in the cove of a chalky cliff. It was formerly but an obfcure fifiling vil¬ lage, but fince the year 1688 has been improved and en¬ larged by a fuccefsful trade to Ruflia and the eaft coun¬ try. But what renders it moft; worthy of notice, and attrafts multitudes of ftrangers, is the new' harbour, which is one of the moft capacious in England, if not in Europe. It was begun in the year 1750, but delayed by various interruptions. It confifts of two piers; that to the eaft is built ivholly of Purbeck ftone, and extends itfelf into the ocean near 800 feet before it forms an an¬ gle ; its breadth on the topis 26 feet, including a ftrong parapet wall, w’hich runs along the outfide of it. The other to the weft is conftrufted of wrood as far as the low- water mark, but the reft is of ftone. The angles, of which there are five in each pier, confift of 160 feet ea: h, with oflagons at the end of 60 feet diameter, leaving an entrance of 200 feet into the harbour, the depth of which admits of a gradual increafe of 18 to 36 feet. E. Long. I. 30. N. Lat. 51. 22. RAMTRUT, a deity worftripped by the Ranazins of Hindoftan, where he has a celebrated temple at Onor. t 639 1 K A M Lie is reprefented as more relembling a monkey than a Ramrs. man. RAM US, in general, denotes a branch of any thing, as ot a tree, an artery, &c. In the anatomy of plants it means the firft or lateral branches, which go off from the petiolum, or middle rib of a leaf. The fubdivifions ot thele are called>W/; and the final divifions into the moft minute of all, are by fome called capillamenta; but both kinds are generally denominatedfnrculus. Ramus, Peter, was one of the moft famous profeffors of the 16th century. He was born in Picardy in 1 <-r 5. A thirft for learning prompted him to go to Paris when very young, and he was admitted a fervant in the col¬ lege of Navarre. Spending the day in waiting on his mailers, and the greateft part of the night in ttudy, he made fuch furprifing progrefs, that, when he took his mailer of arts degree, he offered to maintain a quite op- pofite doarine to that of Ariftotle. This railed him many enemies; and the two firlt books he publilhed, Injiitutiones Dia/ediicre, and Ariftotelicce Animadver/tonesy occafioned great difturbances in the univerfity of Paris: and the oppofition again!! him was not a little heighten- tened by his deferting the Romifti religion, and profef- fing that of the Reformed. Being thus forced to retire from Paris, he vifited the univerfities of Germany, and leceived great honours wherever he came. Lie return¬ ed to France in j 571, and loft his life miferably in the hor- nd maffacie of St Bartholomew’s day. He was a great orator, a man of univerfal learning, and endovred with veiy fine moral qualities. He publiftied many books, which Teiflier enumerates. Ramus’s merit in his oppo- fi.ion to Ariftotle, and his firmnefs in undermining his authority, is unqueftionably great. But it has been doubted, and wuth much reafon, whether he was equal¬ ly fuccefsfully in his attempts after a new logical inftitute. We have the following general outline of his plan in Dr Enfield’s Hillory of Philofophy. “ Confidering dialec¬ tics as the art of deducing conclufions from premifes, he endeavours to improve this art, by uniting it wuth that of rhetoric. Of the feveral branches of rhetoric, he con- fiders invention and difpofition as belonging equally to logic. Making Cicero his chief guide, he divides" his treat! fe on diale&ics into two parts, the firft of which treats of the invention of arguments, the fecond of judg¬ ments. Arguments he derives not only from wEat the Ariftotelians call middle terms, but from any kind of pro’.ofition, which, conne61ed with another, may ferve to prove any affertion. Of thefe he enumerates various kinds. Judgments he divides into axioms, or felf-evi- dent propofitions, diano'ia, or dedudlions by means of a feries of arguments. Both thefe he divides into various claljes j and illuftrates the whole by examples from the ancient orators and poets. “ In the logic of Ramus, many things are borrowed from Ariftotle, and only appear under new names ; and many others are derived from other Grecian lources, particularly from the dialogues of Plato, and the logic of the Stoics. The author has the merit of turning the art'of reafoning from the futile fpeculations of the fchools to forenfic and common ufe ; but his plan is defective in confining the whole dialectic art to the Angle objedl of difputation, and in omitting many things, which refpect the general culture of the underftanding and the invefti- gation of truth. Notwithftanding the defedls of his fyf- tem, we cannot, however, fubfcribe to the fevere cen- furer RAN [ 640 ] R A N Ramus Cure Xvliicli has been paiTed upon Ramus by i^ord Bacon II i and others ; for much is, we think, due to him for hav- Ran:4oipL w't^ rQ much firmnefs and perfeverance afferted the v ' natural freedom of the human underftanding. The lo¬ gic of Ramus obtained great authority in the fchools of Germany, Great Britain, Holland, and France j and long and* violent contefts arofe between his followers and thoie of the Stagy rite, till his fame vanifhed be tore that of Defcartes.” RAN, in the old Englilh writers, means open or pub¬ lic robbery, fo manifeft as not to be denied. Ran diet- tur aberta rapina qua vegan non poteji. Lamo. Leg. Canut. cap. 58. Hence it is now commonly laid of one who takes “the goods of another injurioufly and violently, that he has taken or fnatcbed all he could rap and ran. RANA, or Ranula. See Ranula. Rana, the frog } a genus of reptiles belonging to the order of amphibia. See Er.petol.ogy Index. RANAI, one of the Sandwich iiknds difcovered by Captain Cooke, is about nine miles diftant from MowEE and MOROTOI, and is lituated to the fouth-weih ol the paffage between thofe two illes. Ihe country towards the fouth is elevated and craggy 5 but the other parts of the ifland had a better appearance, and feemed to be well inhabited. It abounds in roots, inch as fweet po¬ tatoes, taro, and yams ; but produces very few7 plantains and bread fruit trees. Tne fouth point of Ranai is in the latitude of 20° 46' north, and in the longitude of 203° 8' eaft. RANCID, denotes a fatty fubftance that is become rank or mufty, or that has contradled an ill fmell by be¬ ing kept clofe. RANDIA, a genus of plants belonging to the pentan- dria clafs 3 and in the natural method ranking with thofe of which the order is doubtful. See Botany Index. RANDOLPH, Thomas, an eminent Englilh poet in the I’yth century, wras born in Northamptonlhire 1605. He was educated at Weftminfter and Cambridge, and very early dillinguilhed for his excellent genius ; for at about nine or ten years of age he wrote the Hiftory of the Incarnation of our Saviour in verfe. His fubfequent writings eftablilhed his character, and gained him the efteem and friendlhip of fome of the greateft men of that age, particularly of Ben Johnfon, who adopted him one of his fons in the mufes. He died in 1634, and was ho¬ nourably interred. He wrote, 1. The Mufes Look- ing-glafs, a comedy. 2. Amyntas, or the Impoflible Dowry, a paftoral, a&ed before the king and queen. 3. Ariftippus, or the Jovial Philofopher. 4. The Con¬ ceited Pedlar. 5. The Jealous Lovers, a comedy. 6. Random Hey for Honefty, down with Rmavery, a comedy j and feveral poems. _ _ RANDOM SHOT, in Gunnery, is a fhot made when the muzzle of a gun is railed above the hori¬ zontal line, and is not deiigued to ihoot dircclay 01 point blank. The utmoft random of any piece is about ten times as far as the bullet wall go point-blank. 1 he bullet will go fartheft when the piece is mounted to about 450 above the level range. See Gunnery and Projec¬ tiles. RANGE, in Gunnery, the path of a bullet, or the line it defcribes from the mouth of the piece to the point where it lodges. If the piece lie in a line parallel to the horizon, it is called the right or level range : if it be mounted to 430, it is faid to have the uttnojl range i all others between 00 and43° are called the inlet mediate ranges. RANGER, a fworn officer of a foreft, appointed by the king:sletters patent •, whole bufineisisto walk through his charge, to drive back the deer out of the purlieus, &c. and to prefent all trefpalfes within his jurildiction at the next foreft court. r • 1 1 RANK, the order or place affigned a perfon fuitable to his quality or merit. . Rank, is a ftraight line made by the fouhers ol a battalion or fquadron, drawn up fide by fide : this order was eftablilhed for the marches, and for regulating the different bodies of troops and officers which compofe an army. RANK and Precedence, in the army and navy, are as follow: _ Engineers RANK. Chief, as colonel } director, as lieutenant-colonel} fub-dire£tor, as major ; engineer in ordinary, as captain j engineer extraordinaiy, as captain- lieutenant fub-engineer, as lieutenant; praftitioner en¬ gineer, as enfign. . Navy Rank. Admiral, or commander in chief of his Majefty’s fleet, has the rank of a field-marlhal ; ad¬ mirals, with their flags on the main-top-maft-head, rank with generals of horfe and foot; vice-admirals, with lieutenant-generals ■, rear-admirals, as major-generals j commodores, with broad pendants, as brigadier-gene- rals y captains of poft-fhips, after three years from the date of their firft commiffion, as colonels ; other cap¬ tains, as commanding poft-lhips, as lieutenant-colonels j captains, not taking poll, as majors j lieutenants, as captains. ii Rank. Rank, / RAN [ 641 ] RAP Rank between the Army, Navy, and Governors. Army. General in Chief Generals of horfe Lieutenant-generals Major-generals Colonels Lieutenant-colonels Majors Captains Navy. Admiral in chief Admiral with a flag at the main-top-malt Vice-admirals Rear-admirals Poft-captains of3 years Poll-captains Captains Lieutenants Governors. Commander in chief of the forces in America Captain-general of provinces Lieutenant generals of provinces Lieutenant-governors and preiidents Lieutenant-governors not commanding Governors of charter colones Deputy-governors Eftablilhed by the king, 1760 Rape. Doubling of tli* RANKS, is the placing two ranks in one, frequently ufed in the manoeuvres of a regiment. RANKS and Files, are the horizontal and vertical lines f the women. But our Englifh law does not enter- Vol. XVIL Part II. tain quite fuch fublime ideas of the honour of either fex, as to lay the blame of a mutual fault upon one of the tranfgreffors only ; and therefore makes it a neceffary ingredient in the crime of rape, that it mult be againit the woman’s will. Rape was punifned by the Saxon laws, particularly thofe of King Athelflan, with death ; which was alfo agreeable to the old Gothic or Scandinavian conftitu- tion. But this was afterwards thought too hard : and in its Head another fevere, but not capital, punifhment was inflibted by William the Conqueror, viz. catiration and lofs of eyes; which continued till after BraCton wrote, in the reign of Henry III. But in order to prevent malicious accufations, it was then the law, (and, it feems, ftill continues to be fo in appeals of rape), that the woman fliould, immediately after, go to the next town, and there make difcovery to fome cre¬ dible perfons of the injury fire has fuffered ; and after¬ wards fliould acquaint the high conftable of the hun¬ dred, the coroners, and the ftieriif, with the outrage. This feems to correfpond in fome degree with the laws of Scotland and Arragon, which require that complaint mult be made within 24 hours : though afterwards by llatute Weftm. I. c. 13. the time of limitation in Eng¬ land was extended to 40 days. At prefent there is no time of limitation fixed : for, as it is ufually now punifli- ed by indictment at the fuit of the king, the maxim of law takes place, that “ nullum tempus occurrit regi but the jury will rarely give credit to a Rale complaint. During the former period alfo it was held for law, that the woman (by confent of the judge and her parents) might redeem the offender from the execution of his lenience, by accepting him for her hufband ; if he alfo was willing to agree to the exchange, but not other- wife. In the 3 Edw. I. by the Ratute WeRm. 1. c. 13. the punilhment of rape wr3s much mitigated : the of¬ fence itfelf, of ravilhing a damfel w’ithin age, (that is, twelve years old) either with her confent or without, or of any other woman againfl her will, being reduced to a trefpafs, if not profecuted by appeal within 40 days, and fubjeCting the offender only to two years imprifon- 4 ^ ment. Rape. RAP r 642 1 RAP ment, and a fine at the king’s will. Eat this lenity- being productive of the moft terrible coniequenccs, it was, in ten years afterwards, 13 Edw. I. found neceffa- rv to make the offence of forcible rape felony by ftatute Weftm. 2. c. 34. And by ftatute 18 Ekz. c. 7. it is made felony without benefit of clergy : as is alio the abominable wickednefs of carnally knowing or abufing any woman-child under the age ot ten years 5 in which cafe the content or non-confent is immaterial, as by rea- fon of her tender years the is incapable of judgment and difcretion. Sir Matthew Hale is indeed ot opinion, that fuch profligate aftions committed on an infant under the age of twelve years, the age of female difcretion by the common law, either with or without confent, amount to rape and felony 5 as well fince as before the ftatute of Queen Elizabeth : but that law has in general been held only to extend to infants under ten •, though it fhould feem that damfels between ten and twelve are ftill un¬ der the protection or the ftatute Weftm. 1. the law with refpeCt to their feduftion not having been altered by ei¬ ther of the fubfequent ftatutes. A male infant, under the age of fourteen years, is prefumed by law incapable to commit a rape, and there¬ fore it feems cannot be found guilty of it. For though in other felonies “ nialitia fupplet a^tatem yet, as to this particular fpecies of felony, the law fuppofes an im- becillity of body as well as mind. The civil law feems to fuppofe a proftitute or common harlot incapable of any injuries of this kind : not allow7- ing any punifhment for violating the chaftity of her, who hath indeed no chaftity 'At all, or at leaft hath no regard to it. But the lawr of England does not judge fb hardly of offenders, as to cut off all opportunity of retreat even from common ftrumpets, and to treat them as never capable of amendment. It therefore holds it to be felony to force even a concubine or harlot ; becaufe the woman may have forfaken that unlawful courfe of life : for, as Brafton wTell ob- ferves, “ licet meretrix fuerit antea, eerie tunc tempo- ris non fuit, cum reclamando nequitise ejus confentire noluit.” As to the material faffs requifite to be given in evi¬ dence and proved upon an indictment of rape, they are of fuch a nature, that, though neceffary to be known and fettled, for the conviftion of the guilty and prefer- vation of the innocent, and therefore are to be found in fuch criminal treatifes as difeourfe of thefe matters in delail, yet they are highly improper to be publicly dir- cuffed, except only in a court of juftice. We fliall therefore merely add upon this head a few remarks from Sir Matthew7 Hale, with regard to the competency and credibility of witneffes 5 which may, fa/vo pudore, be confidered. And, firft, the party ravifhed may give evidence upon oath, and is in law a competent wdtnefs : but the credi¬ bility of her teftimony, and how far forth flie is to be believed, muff be left to the jury upon the circumflances of faff that concur in that teftimony. For inftance: if the vvitnefs be of good fame; if (he prefently difeover- ed the offenre, and made fearch for the offender*, if the party accufed fled for it; thefe and the like are con¬ curring circumftances, which give greater probability to her evidence. But, on the other fide, if (he be of evil fame, and ftand unfupported by others; if fhe con¬ cealed the injury for any confiderable time after (he had opportunity to complain ; if the place, where the faff was alleged to be committed, w7as where it was pofliole fhe might have been heard, and (he made no outcry : thefe and the like circumftances carry a ftrong, but not conclufive, prefumplion that her teftimony is falfe or feigned. Moreover, if the rape be charged to be committed on an infant unuer 12 years of age, fhe may ftill be a competent witnefs, if fhe hath fenfe and underftand- ing to know the nature and obligations of an oath, and, even if fhe hath not, it is thought by Sir Mat¬ thew7 Hale, that fhe ought to be heard without oath, to give the court information } though that alone will not be fufficient to conviff the offender. And he is of this opinion, firft, Becaufe the nature of the offence being lecret, there may be no other poffible proof of the aftual faff} though afterwards there may be con¬ current circumftances to corroborate it, proved by other witneffes : and fecondly, Becaufe the law al¬ lows rVhat the child told her mother, or other rela¬ tions, to be given in evidence, fince the nature of the cafe admits frequently of no better proof 5 and there is n*uch more reafon for the court to hear the narra¬ tion of the child herfelf, than to receive it at fecond- hand from thofe who fwear they heard her fay fo. And indeed it feems now to be fettled, that in thele cafes infants of any age are to be heard ; and, if they have any idea of an oath, to be alfo fvvorn: it being found by experience, that infants of very tender years often give the cleareft and trueft teftimony. But in any of thefe cafes, wFeiher the child be fworn or not, it is to be wflfhed, in order to render her evidence cre¬ dible, that there flioutd be tome concurrent teftimony of time, place, and circumftances, in order to make out the faff; and that the conviction fhould not be grounded fingly on the unfupported accufation of an infant under years of difcretion. There may be there¬ fore, in many cafes of this nature, wfltneffes who are competent, that is, who may be admitted to be heard \ and yet, after being heard, may prove not to be cre¬ dible, or fuch as the jury is bound to believe. For one excellence of the trial by jury is, that the jury are triers of the credit of the witneffes, as w'ell as of the truth of the faft. “ It is true (fays this learned judge), that rape is a moft deteftable crime, and therefore ought feverely and impartially to be punifhed with death ; but it muft be remembered, that it is an accufation eafy to be made, hard to be proved, but harder to be defended by the party accufed, though innocent.” He then relates two very extraordinary cafes of malicious profecution for this crime, that had happened within his owm obfervation ; and concludes thus : “ I mention thefe inflances, that we may be the more cautious upon trials of offences of this nature, wherein the court and jury may with fo much eafe be imnofed upon, wdthout great care and vi¬ gilance *, the heinoufnefs of the offence many times tranf- portlng the judge and jury wflth fo much indignation, that they are over-haftily carried to the conviction of the perfons accufed thereof, by the confident teftimony of fometimes falfe and malicious witneffes.” RAPHAEL D’Urbino, the greateft’, moft fublime, and moft excellent painter that has appeared, fihee the revival of the fine arts, w’as the fon of an. indifferent painter named Sanzio, and was born at Urbino on Good Friday RAP [ 643 ] RAP Raphael Friday 1481. The popes Julius II. and Leo X. who || employed him, loaded him with wealth and honour j Ra^in. aiu] it is faid that Cardinal de St Bibiana had fuch a v value for him, that he offered him his niece in marriage. His genius is admired in all his pictures; his contours are free, his ordonnances magnificent, his defigns cor- redl, his figures elegant, his expreftions lively, his atti¬ tudes natural, his heads graceful; in fine, every thing is beautiful, grand, fubhme, juft, and adorned with graces. Thefe various perfediions he derived not only from his excellent abilities, but from his ftudy of anti¬ quity and anatomy; and from the friendfhip he con- tradced with Ariofto, who contributed not a little to the improvement of his tafte. His pictures are principally to be found in Italy and Paris. That of the Transfigu¬ ration, preferved at Rome in the church of St Peter Monterio, palfes for his mafterpiece. Fie had a hand- fbme perf’on, was well proportioned, and had great fweetnefs of temper j was polite, affable, and modeft. Fie, however, lived in the utmoft fplendor 5 mcft of the eminent mailers of his time were ambitious of working under him 5 and he never wrent out without a crowd of artifts and others, who followed him purely through re- fpect. Fie was not only the belt painter in the world, but perhaps the beft architedl too ; on which account Leo X. charged him with building St Peter’s church at Rome : but he was too much addidled to pleafure, which occafioned his death at 37 years of age. FJe left a great number of difciples ; among whom were Julio Rornano and John Francis Penni, who were his heirs. Many able engravers, as Raimondi, George Mantuan, and Bloe- marf, engraved after Raphael. See Painting. RAPHAIM, or Rephaim, (Mofes), a name figni- fying Giants, as they really were, and an actual people too, fituated in Bafan or Batanea, beyond Jordan, fe- parated from the Zanzummim by the liver Jabbok. Al¬ io a valley near Jerufalem •, Joihua x. RAPHANUS, Radish •, a genus of plants belong¬ ing to the tetradynamia clafs ; and in the natural me¬ thod ranking under the 39th order, Siliquofce. See Bo¬ tany Index ; and for the method of culture, fee Gar¬ dening. RAPHANIDOSIS, a punifhment inflidfed at A- thens upon adulterers. The manner of it was this: The hair was plucked off from the privities of the of¬ fenders, hot-allies laid upon the place, and a radifh or mullet thruft up his fundament, as has been mentioned under ADULTERY. To this Juvenal alludes, Sat. x. ver. 317. -djiofJam machos et mugilis intrat. Perfons who had been thus puniihed were called tw^oHclot. The word raphanrdojis is derived from “ a radifti.” RAPHIDIA, a genus of infefts, of the neuroptera order. See ENTOMOLOGY Index. RAPIER, formerly fignified a long old-fafhioned fword, fuch as thofe worn by the common foldiers : but it now denotes a fmall fword, as coniradiflinguiihed from a back-fword. RAPIN, Rene, a Jefuit and eminent French writer, was born at Tours in 1621. He taught polite litera¬ ture in the fociety of the Jefuits with great applaufe, and was juftly efteemed one of the beft Latin poets and greateft wits of his time. He died at Paris in 1687. Fie wrote, 1. A great number of Latin poems, which have rendered him famous throughout all Europe \ among which are hisHortorum libri quatuov, which is rec- R- pin koned his mafterpiece. 2. Refleflions on Eloquence, , Poetry, Hiftory, and Philofophy. 3. Companions be- tween Virgil and Homer, Demofthenes and Cicero, PIat6 and Anftotle, Thucydides and Titus Livius. 4. The FXiftory of Janfenifm. 5. Several works on reli¬ gious fubjefts. The beft edition of his Latin poems is that of Paris in 1723, in 3 vols. i2mo. Rapin de Thc’jras, Paul de, a celebrated hiftorian, was the fon of James de Rapin lord of Thoyras, and was bom at Caftres in 1661. He was educated at firit under a tutor in his father’s houfe ; and afterwards fent to Puylaurens, and thence to Samur. In 1679 he re¬ turned to his father, with a defign to apply himfelf to the ftudy of the law, and was admitted an advocate : but fome time after, reflefting that his being a Prote- ftant would prevent his advancement at the bar, he re- folved to quit the profefiion of the law, and apply him¬ felf to that of the fword ; but his father would not con- fent to it. The revocation of the edi£l of Nantes in 1685, and the death of his father, which happened two months after, made him relblve to come to England 5 but as he had no hopes of any fettlement here, his Hay was but fhort. He therefore foon after went to Hol¬ land, and lifted himfelf in the company of French vo¬ lunteers at Utrecht, commanded by M. Rapin his cou- fin-german. He attended the prince of Orange into England in 1688: and the following year the lord Kingfton made him an enfign in his regiment, with which he went into Ireland, where he gained the efteem of his officers at the fiege of Catrickfergus, and had foon a lieutenant’s commiffion. He was prefenl at the battle of the Boyne, and was ftiot through the fhouider at the fiege of Limerick. He was foon after captain of the company in which he had been enfign } but, in 1693, refigned his company to one of his brothers, ’in order to be tutor to the earl of Portland’s fon. In 1699, ^ie married Marianne Teftard ; but this marriage neither abated his care of his pupil, nor prevented his accompa¬ nying him in his travels. Having finilhed this employ¬ ment, he returned to his family, which he had fettled at the Hague ; and here he continued fome years. But as he found his family ’ncreafe, he refolved to retire to fome cheap country 5 and accordingly removed, in 1707, to Wefel, where he wrote his Hiftory of England, and fome other pieces. Though he was of a ftrong confti- tution, yet 17 years application (for fo long was he in compofing the hiftory juft mentioned) entirely ruined his health. He died in 1725. He wrote in French, I. A Differtation on the Whigs and Tories. 2. His Hiftory of England, printed at the Hague in 1726 and 1727, in 9 vols 4to, and reprinted at Trevoux in 1728, in 10 vols 4to. This laft edition is more complete than that of the Hague. It has been tranftated into Englifh, and improved with Notes, by the reverend Mr Tindal, in 2 vols folio. This performance, though the work of a foreigner, is defervedly efteemed as the fulleft and moft impartial colle&ion of Englilh political tranfaftions extant. The readers of wit and vivacity, however, may be apt to complain of him for being fometimes rather te¬ dious and dull. RAPINE, in Law, the taking away another’s goods, &c. by violence. RAPPERSWIL, a town of Swifferland, on the 4 Ma confines HAS [ 644 ] HAS Rappol- conaaes of the canton of Zurich, and of the territory of item Garter, with an old caftle. It is ftrong by fituation, R'h S<-m being feated on a neck of land which advances into the y—«. lake of Zurich, and over which there is a bridge 850 paces long. It is fubject to the cantons of Zurich and Berne. E. Long. 8. 57. N. Lat. 47. 20. RAPP0LSTE1N, a town of France in Upper Al- face, which, before the revolution, had the title of a barony. All the murtcians of Alface like wife depended upon this baron, and were obliged to pay him a certain tribute, without which they could not play upon their inftruments. F. Long. 7. 28. N. Lat. 48. 15. RAPTURE, an ecftafy or tranfport of mind. See Extasy. RARE, in Physic, Hands oppofed to denfe j and de¬ notes a body that is very porous, whofe parts are at a great diftance from one another, and which is fuppofed to contain but little matter under a large bulk. See the following article. RAREFACTION, in Physics, the a is pleafantly fituated near the fouth-wTeft end of the ifland, which is the mort level part of it. It has an extenfive and excellent garden, and is furrounded with foreft trees of confiderable mag¬ nitude ; another proof that trees will grow upon the edge of the fea, though it muft be allowed that the channel here is narrow7. Immediately behind the houfe of Rafay are'the ruins of an ancient chapel, now ufed as the family burying-place. RASCIANS, a poor oppreffed people who dw’elt on both fides of the Danube, and who, about the year 1594, being w^eary of the Turkilh thraldom, firft took 13 of their veffels upon that river ; and then drawing together a body of 15,000 men between Buda and Belgrade, twice defeated the pallia of Temefwar with a body of 14,000 Turks. They afterwards took Baczkerek, four miles from Belgrade, and the caftle of Ottadt; then laying fiege to that of Beche, on the Theyfla, the old pafha of Temefwar marched to relieve it with 11,000 men 5 but the Rafcians encountering them, flew near 10,000, and took 18 pieces of cannon. The confe- quence of this vidlory wras the redudlion of Werfetza ,« and Lutz. Then, fending to the archduke for aid and gunners, they offered to put themfelves and their coun¬ try under the emperor’s proteflion. RASOR-bill, afpecies of alca. See Alca, Orni¬ thology Index. RASOR-FiJh, a genus of Ihell-fifh. See Solen, CoN- CHOLOGY Index. RASTALL, John, a printer and mifcellaneous wri¬ ter, w7as born in London, probably about the end of the 15th century, and educated at Oxford. Returning from the univerfity, he fettled in the metropolis, and com¬ menced printer, “ then efteemed (fays Wood) a profef- flon fit for any fcholar or ingenious man.” Fie married RAT [ 645 ] RAT Raftall the fifter of Sir Thomas More, with whom, we are told, il he was very intimate, and whofe writings he ftrenuouily Rat‘ defended. From the title-page of one of his books, he appears to have lived in Cheapfide, at the fign of the Mermaid. Fie died in the year 1 536 ; and left two fons, William and John : the firft of whom became a judge in Queen Mary’s reign, and the latter a jutfice of peace. This John Raftall, the fubjeft of the prefent article, was a zealous Papift •, but Bale fays, that he changed his re¬ ligion before his death. Fie wrote, 1. Natura naturata. Pits calls it a copious (prohxa) and ingenious comedy, defcribing Europe, Alia, and Africa j with cuts. What fort of a comedy this was, is not eafy to conceive. Pro¬ bably it is a coimographical defcription, written in dia¬ logue, and therefore ftyled a co?nedy. 2. The paftyme of the people 5 the cronycks of diverfe realmys, and molt efpecially of the realm of England, brevely com¬ piled and emprinted in Cheapefyde, at the fign of the mearmaid, next Pollyfgate, cum pnvilegio, fol. 3. Ec- clefia Johannis Rqfiall, 1542, was one of the prohi¬ bited books in the reign of Flenry VIII. 4. Lcgum Anglicanarum vocabula explicata. French and Latin. Loud. 1567, 8vo. And fome other works. RASTADT, a town of Germany, in the circle of Suabia and marquifate of Baden, with a handfome caftle. It is remarkable for a treaty concluded here between the French and imperialifts in 1714; and near this place the French defeated the imperial troops in July 1796 ; in 1798 a congrefs wras held here for the conclufion of a peace between France and Germany 5 but it broke up in 1799, when, not far from Rallradt, the French plenipo¬ tentiaries, on their return, wrcre murdered by a party of Auftrian huffars. Fee France, N° 501. Raftadt is feated on the river Merg, near the Rhine. E. Long. S. 14. N. Lat. 48. 54. RASTENBURG, a fine city in Prufiia, on the Gu- ber, furrounded with a wall, and fince 1629 alfo with a rampart. It is 46 miles fouth-eaft; of Koningfberg. E. Long. 21. 30. N. Lat. 54. 20. RAT. See Mus, Mammalia Index; and for an account of the methods of deftroying rats, fee Vermin, Deflrudiion of. RAT-Ifland, a fmall detached part of the ifiand of Lundy, off the north coaft of Devon. Though noted in Donn’s map of the county, it is not worth mention here, but as giving opportunity to fubjoin a farther no¬ tice of Lundy, which ifiand w7as purchafed a few years fince by Mr Cleveland, M. P. for about 1200 guineas, who has a fmall villa on it : not more than 400 acres are cultivated : it is let altogether for 70I. a-year. The foil is good, though no trees will grow on the ifiand. It has fine fprings of water : the houfes are feven : the inhabitants, men, women, and children, do not exceed 24. The bird called murr, whofe eggs are very large and fine, the Lundy parrot, and rabbits, are the chief produce ; thefe abound, and are taken for the feathers, eggs, and fkins, principally. They have now (1794) 70 bullocks and 400 fheep, but the latter do not thrive. They pay no taxes : fithing fkiffs often call with necef- faries: the fituation is very pleafant, and the rocks around, which are large, and partly granite, are wild and romantic. It had probably more inhabitants once, as human bones have been ploughed up. It has no place of worftiip, and no public-houfe 5 but flrangers are always welcome. Eight cannon lie on the battle¬ ments on the top of a very fleep precipice, under which Ratana is a curious cavern. Lord Gow'er, Mr Benfon, and Sir J. B. Warren, K. B. have been former proprietors. See . - . Lundy. RAT- Tails, or Arrejls. See FARRIERY Index. RATAFIA, a fine fpirituous liquor, prepared from the kernels, &c. of feveral kinds of fruits, particularly of cherries and apricots. Ratafia of cherries is prepared by bruifing the cher¬ ries, and putting them into a veffel wdierein brandy has been long kept j then adding to them the kernels of cherries, with ftrawberries, fugar, cinnamon, white pep¬ per, nutmeg, cloves ; and to 20 pounds of cherries 10 quarts of brandy. The veflel is left open 10 or 12 days, and then flopped clofe for tw7o months before it be tapped. Ratafia of apricots is prepared tvro ways, viz. either by boiling the apricots in white-wine, adding to the liquor an equal quantity of brandy, -vj'ith fugar, cinnamon, mace, and the kernels of apricots; infufing the whole for eight or ten days ; then {training the li¬ quor, and putting it up for ufe : or elfe by infufing the apricots, cut in pieces, in brandy, for a day or two, pal- fing it through a {training bag, and then putting in the ufual ingredients. , RATCH, or rash, in clock-work, a fort of wheel having twelve fangs, which ferve to lift up the detents every hour, and make the clock Itrike. See Clock. RATCHETS, in a wTatch, are the Imall teeth at the bottom of the fufy, or barrel, which {tops it in winding UP* RATE, a ftandard or proportion, by vdiich either the quantity or value of a thing is adjufted. RATES, in the navy, the orders or claffes into wdiich the (hips of war are divided, according to their force and magnitude. The regulation, wdiich limits the rates of men of war to the fmalleft number poflible, feems to have been dic¬ tated by confiderations of political economy, or of that of the fimplicity of the fervice in the royal dock-yards. The Britifh fieet is accordingly diftributed into fix rates, exclufive of the inferior veffels that ufually attend on na¬ val armaments; as {loops of war, armed fiiips, bomb- ketches, fire-lhips and cutters, or fchooners command¬ ed by lieutenants. Ships of the firft rate mount 100 cannon, having 42- pounders on the lower deck, 24-pounders on the middle deck, 12-pounders on the upper deck, and 6-pounders on the quarter-deck and fore-caftle. They are manned with 850 men, including their officers, feamen, marines, and fervants. In general, the fhips of every rate, befides the cap¬ tain, have the mafter, the boatfwain, the gunner, the chaplain, the purfer, the furgeon, and the carpenter 5 all of whom, except the chaplain, have their mates or affiftants, in wFich are comprehended the fail-maker, the mafter at arms, the armourer, the captain’s clerk, the gunfmith, &c. The number of other officers is always in proportion, to the rate of the {hip. Thus a firft-rate has fix lieu¬ tenants, fix mailer’s mates, tvTeRty-four midihipmen, and five furgeon’s mates, who are confidered as gentle¬ men : befides the following petty officers ; quarter-maf- ters and their mates, fourteen ; boatfwain’s mates and yeomen, eight *, gunner’s mates and afliftants, fix 5 quar¬ ter gunners, twenty-five ) carpenter’s mates, two, befides fourteen: RAT [ 646 ] RAT fourteen affiflants ; with one fteward and fteward’s mate to the purfer. If the dimenlions of all fhips of the f^me rate were equal, it would be the fimpleit and moft perfpicuous method to collect them into one point of view in a table: but as there is no invariable rule for the general dimen¬ lions, we muft content ourfelves with but a few re¬ marks on (hips of each rate, fo as to give a general idea of the difference between them. 'Idle Viftory, one of the lafl built of our firfl: rates, is 222 feet 6 inches in length, from the head to the ftern j the length of her keel, 151 feet 3 inches ; that of her gun-deck, or lower deck, 186 feet; her extreme breadth is 51 feet 10 inches; her depth in the hold, 21 feet 6 inches ; her burden, 2162 tons; and her poop reaches 6 feet before the mizen-maft. Ships of the fecond rate carry 90 guns upon three decks, of which thofe on the lower battery are 32* pounders; thofe on the middle, 18-pounders; on the Upper deck, 12-pounders ; and thofe on the quarter¬ deck, 6 pounders, which ufually amount to four or fix. Their complement of men is 750, in which there are fix lieutenants, four mailer’s mates, 24 midfhipmen, and four furgeon’s mates, 14 quarter-mailers and their mates, eight boatfwain’s mates and yeomen, fix gunner’s mates and yeomen, with 2 2 quarter-gunners, two carpenter’s mates, with 10 affiilants, and one lleward and fteward’s mate. Ships of the third rate carry from 64 to 80 cannon, which are 31, 18, and 9 pounders. The 80-gun fhips, however, begin to groiv out of repute, and to give way to thofe of 74, 70, &c. which have only two whole batteries ; whereas the former have three, with 28 guns planted on each, the cannon of their upper deck being the fame as thole on the quarter-deck and fore-caltle of the latter, which are 9 pounders. The complement in a 74 is 650, and in a 64, 300 men ; having, in peace, four lieutenants, but in war, five; and when an admiral is aboard fix. They have three mailer’s mates, 16 midlhipmen, three furgeon’s mates, 10 quarter-mailer, and their mates, fix boatfwain’s mates and yeomen, four gunner’s mates and yeomen, with 18 quarter-gunners, one carpenter’s mate, with eight aflilknts, and one llew¬ ard and lleward’s mate under the purfer. Ships of the fourth rate irount from 60 to 50 guns, upon two decks, and the quarter-deck. The lower tier is compofed of 24-pounders, the upper tier of 12- pounders, and the cannon on the quarter-deck and fore-cafile are 6-pounders. The complement of a 50 gun fiiip is 350 men, in which there are three lieute¬ nants, two mailer’s mates, 10 midfhipmen, two fur¬ geon’s mates, eight quarter-mailers and their mates, four boatfwain’s mates and yeomen, one gunner’s mate and one yeoman, with 12 quarter-gunners, one carpen¬ ter’s mate and fix affillants, and a lleward and lleward’s mate. All veffels of war, under the fourth rate, are ufually comprehended under the general name of frigates, and never appear in the line of battle. They are di¬ vided into the 5th and 6th rates; the former mounting from 40 to 32 guns, and the latter from 28 to 20. The larged of the fifth rate have two decks of cannon, the lower battery being of 18-pounders, and that of the upper deck of 9-pounders; but thofe of 36 and 32 guns have one complete deck of guns, mounting 12- 2 pounders, befides the quarter-deck and fore-cadle, which Ratos carry 6-pounders. The complement of a Ihip of 44 ii guns is 280 men; and that of a frigate of 36 guns., Ratcen' 240 men. The fird has three, and the fecond two- v lieutenants ; and both have two mailer’s mates, fix mid- ihipmen, two furgeon’s mates, fix quarter-maders and their mates, two boatfwain’s mates, and one yeoman, one gunner’s mate and one yeoman, with xo or ix quar¬ ter-gunners, and one purler’s lleward. Frigates of the 6th rate carry 9-pounders, thcfe of 28 guns having 3 pounders on their quarter-deck, with 200 men for their complement ; and thofe of 24, 160 men : the former has two lieutenants, the latter, one ; and both have two reader’s mates, four midlhipmen, one furgeon’s mate, four quarter-mailers and their males, one boatfwain’s mate and one yeoman, one gunner’s mate and one yeoman, with fix or feven quarter-gunners, and one purfer’s deward. The Hoops of war carry from 18 to 8 cannon, the larged of which have fix-pounders ; and the fmalleil, viz. thofe of 8 or 10 guns, four-pounders. Their offi¬ cers are generally the fame as in the 6th rates, with little variation ; and their complements of men are from 1 20 to 60, in proportion to their force or magnitude. N. B. Bomb-veflels aie on the fame edablilhment as fioops ; but fire-diips and hofpital Ihips are on that of fifth rates. Nothing more evidently manifeds the great improve¬ ment of the marine art, and the degree of perfeftion to which it has arrived in Britain, than the facility of ma- naging our fird rates ; which were formerly edeemed incapable of government, unlefs in the mod favourable weather of the furnmer. Ships of the fecond rate, and thofe of the third, which have three decks, carry their fails remarkably well, and labour very little at fea. They are excellent in a general a£tion, or in cannonading a fortrefs. Thofe of the third rate, which have two tiers, are fit for the line of battle, to lead the convoys and fquadrons of Ihips of war in a61ion, and in general to fuit the different exi¬ gencies of the naval fervice. The fourth-rates may be employed on the fame occa- fions as the third-rates, and may be alfo deltined amongft the foreign colonies, or on expeditions of great di¬ dance ; fince thefe veffels are ufually excellent for keep¬ ing and fudaining the fea. Veffels of the fifth rate are too weak to differ the diock of a line of battle ; but they may be dedined to lead the convoys of merchant dfips, to proted the com¬ merce in the colonies, to cruize in different dations, to accompany fquadrons, or be fent exprefs with neceffarv intelligence and orders. The fame may be obferved of the fixth rates. The frigates, which mount from 28 to 38 guns upon one deck, with the quarter-deck, are extremely proper for cruizing againlt privateers, or for fiiort expeditions, being light, long, and ufually excellent failers. RATEEN, or Ratten, in commerce, a thick woollen duff, quilled, woven on a loom with four treddles, like ferges and other duffs that have the whale or quilling. There are fome rateens dreffed and prepa¬ red like cloths ; others left fimply in the hair and others where the hair or knap is frized. Rateens are chiefly manufadured in France, Holland, and Italy, and RAT [ 647 ] RAT Ratification are rr.oftly ufed in linings. The frize is a fort of coarfe !! rateen, and the drugget is a rateen half linen half wool- len. RATIFICATION, an a£I of approving and con¬ firming fomething done by another in our name. RATIO, in Arithmetic and Geometry, is that rela¬ tion of homogeneous things which determines the quan¬ tity of one from the quantity of another, without the in¬ tervention of a third. The numbers, lines, or quantities, A and B, being propofed, their relation one to another may be confider- ed under one of thefe two heads : 1. How much A ex¬ ceeds B, or B exceeds A ? And this is found by taking A from B, or B from A, and is called arithmetic rea- fon or ratio. 2. Or how many times, or parts of a time, A contains B, or B contains A ? and this is cal¬ led jwwe/nh reafon or ratio ; (or, as Euclid defines it, it is the mutual habitude, or refpeci, of two magnitudes of the fame kind, according to quantity ; that is, as to how often the one contains, or is contained in, the other) ; and is found by dividing A by B, or B by A. And here note, that that quantity which is referred to another quantity is called the antecedent of the ratio : and that to which the other is referred is called the con- fequent of the ratio ; as, in the ratio of A to B, A is the antecedent, and B the confequent. Therefore any quantity, as antecedent, divided by any quantity as a confequent, gives the ratio of that antecedent to the ccnfequent. Thus the ratio of A to B is but the ratio of B to A is j and, in numbers, the ratio of 12 to 4 is 12 .41 —=2, or triple ; but the ratio ot 4. to 12 is — ~ —7 4 or r 7 ” ‘ 12 3 or fubtriple. And here note, that the quantities thus compared muft be of the fame kind ; that is, fuch as by multipli¬ cation may be made to exceed one the other, or as thefe quantities are faid to have a ratio between them, which, being multiplied, may be made to exceed one another. Thus a line, how fhort foever, may be multiplied, that is, produced fo long as to exceed any given right line j and confequently thefe may be compared together, and the ratio expreffed : but as a line can never, by any multi¬ plication whatever, be made to have breadth, that is, to be made equal to a fuperficies, how frnall foever $ thefe can therefore never be compared together, and confequently have no ratio or refpeft to one another, according to quantity 5 that is, as to how often the one contains, or is contained in, the other. See Quan¬ tity. RATIOCINATION, the aft of reafoning. See Reasoning. RATION, or Rattan, in the army, a portion of ammunition, bread, drink, and forage, diftributed to each foldier in the army, for his daily fubfillence, &c. The horfs have rations of hay and oats when they can¬ not go out to forage. The rations of bread are regu¬ lated by weight. The ordinary ration of a foot fbldier is a pound and a half of bread per day. The officers have feveral rations according to their quality and the number of attendants they are obliged to keep.—When the ration is augmented on occalions of rejoicing, it is called a double ration. The {hip’s crews have alfo their 'Rationale rations or allowances of biiket, pulfe, and water, proper- tioned according to their Hock. , Ratll:-e?- < RA1IONALE, a folution or account of the princi¬ ples of fome opinion, aftion, hypolhefis, phenomenon or the like. RA1IBOR, a town of Germany, in Silefia, and ca¬ pital ol a duchy ol the fame name, with a caille. It has been twice taken by the Swedes, and is feated on the river Oder, in a country fertile in corn and fruits, 1 $ miles north-eait of Troppaw, and 142 eafi of Prague, E. Long. 22. 24. N. Lat. 50. 14. RATISBON, an ancient, large, rich, handfome, and itrong city of Germany, in Bavaria, free and im¬ perial, with a biffiop’s lee, whole biihop is a prince of the empire. It is called by the Germans Regenfburg, from the river Regens, which runs under a fine {tone bridge, and throws itlelf into the Danube below the city \ and the rivers Luber and Nab mix with it above the city. I he French call it Ratilbon, in imitation of the Latins; it hath formerly been fubjeft to the kings of Bavaria, who made it the place of their refidence ; but it was declared free by the emperor Frederick I. which does not, however, hinder the dukes of Bavaria from dividing the toll with the citizens, according to an agreement between them. Thefe princes have alfo the criminal jurifdiftion, lor which the magillrates of the city pay them homage. It is the firft city of the bench of Suabia, and contains at prefent within its walls five different free Hates of the empire 5 namely, the biihop, the abbot of St Emmeran, the abbeffes of the Low and High Munfter, and the city. The inhabitants of Ra- tiibon have the privilege not to be cited before other tri¬ bunals, urdefs for aftions above 400 florins. The lenate is compoled of 17 members, and there is a council of 10, which is charged with the government of the Hate. The citizens have a right to eleft a chief, who judges of the affairs of police. The catholics have the exercife oT their religion in the cathedral church and others, and the Lutherans in three churches which they have built. The magiftrates and officers of,the city are all Protef- tantsj and it is to be remarked, that although there are about 22 Catholic churches, yet there are very few Ca¬ tholic citizens, the magiftracy not allowing the freedom of the town to be given to Catholics living there. As this city is large, elegant, and full of magnificent houfes, it has been chofen many years for the place of holding the diet, upon account of the conveniencv, to many neighbouring princes and Hates, of fcnding'their provi- fions by land and water, without great expence. The town-houie, in the midH of which the diet meets, is ex¬ tremely magnificent. In the year 1740, however, when there was a war in Germany, the diet met at Frankfort on^ the Main, till after the death of the emperor Charles VII. Provifions are very plentiful at Rablbon in time of peace. The inhabitants have a good deal of trade the river on which it Hands being navigable, and com¬ municating with a great part of Germany. It is ^5 • miles fouth-eafl of Nuremberg, 62 north of Munich, and 103 weft: of Vienna. E .Long. 12. 5. N. Lat. 48 59* RATLINES, or, as the failors call them, ratlins, thofe lines which make the ladder fteps to go up the Ihroods and puttocks, hence called the ratlins of the Jhrouds. RATOLFZEL R A V f 648 ] R A V llatolfzel RATOLFZEL, a ftrong town of Germany, in Sua- II bia, near the weft end of the lake Conftance. It is Rtvcnna ^eaj-e(j on ^aj- part of it called Bodenfee, and belongs to the houfe of Auftria, who took it from the duke of Wirtemburg, after the battle of Nordlingen. It is 12 miles weft of the city of Conftance. It is defended by the impregnable caftle of Hohen Dwel, on an inaccel- ftble hill in the middle of a plain, the rock of which is flint, fo that a few men may hold it out againft an army. RATTLESNAKE. See Crotalus, Ophiology Index. Rattlesnake Root, See Polygala, Botany Index. RATZEBURG, or Ratzemburg, an ancient town of Germany, in the circle of Lower Saxony, and in the duchy of Lawrenburg, with a bilhop’s fee and a caf¬ tle. The town depends on the duchy of Lawenburg, and the cathedral church on that of Ratiburg. It is feated on an eminence, and almoft furrounded with a lake 2 $ miles in length and three in breadth. The duke of Lawenburg feized and fortified it in 1689, and the king of Denmark took it in 1693; but it was dif- mantled, and reftored in 1700 to the duke, who re¬ fortified it. This town has been frequently pillaged, particularly in 1552, by Francis duke of Saxe Lawen¬ burg, becaufe the canons refufed to eledl his fon Mag¬ nus their biftiop. It is nine miles fouth of Lubec. This place is noted for its excellent beer. E. Long. 10. 58. N. Lat. 53. 47. RAVA, a town of Great Poland, and capital of a palatinate of the fame name, with a fortified caftle, where they keep ftate prifoners. The houfes are built of wood, and there is a Jefuit’s college. It is feated in a morafs covered with water, wLich proceeds from the river Rava, with which it is furrounded. It is 45 miles fouth of Blolko, and 50 fouth-weft of Warfaw. The palatinate is bounded on the north by that of Blolko, on the eaft by that of Mazovia, on the foutli by that of Sandomer, and on the weft by that of Lencieza. RAVELIN, in Fortification, was anciently a flat baftion placed in the middle of a curtain j but now a detached work compofed only of two faces, which make a faliant angle without any flanks, and raifed before the counterfcarp of the place. See Fortifica¬ tion. RAVEN. See Corvus, Ornithology Index. Sea RAVEN, or corvo marine of Kongo in Africa, in Ichthyology, is about fix feet long •, but the moft lingu¬ lar circumftance appertaining to this creature is the ftone found in its head, to which the natives aferibe fome me¬ dicinal virtues, and the delicate tafte of its hard roe, which is ftill much admired, when died in the fun, and becomes as hard as a ftone. RAVENGLAS, a town of Cumberland in England, fituated between the rivers Irt and Elk, which, with the fea, encompafs three parts of it. It is a well built place, and has a good road for Ihipping, which brings it fome trade. E. Long. o. 5. N. Lat. 54 20. RAVENNA, in Ancient Geography, a noble city of Gallia Cifpadana ; a colony of Theffahans, on the Adri¬ atic, in waflies or a boggy fituation, which proved a natural fecurity to it. The heufes were all of wood, the -communication by bridges and boats, and the town kept fweet and clean by the tides carrying away the mud and 4 foil, (Strabo). Anciently it had a port at the mouth of Ravenna the Bedefis ; Auguftus added a new port, capacious to II hold a fleet, for the fecurity of the Adriatic, between, ^ l!K ‘, which and the city lay the Via Caefaris. In the lower age it was the feat of the Oftrogoths for 72 years j but being recovered by Narfes, Juitinian’s general, it be¬ came the refidence of the exarchs, magiftrates fent by the emperor from Conftantinople, for 173 years, when it was taken by the Longobards. It is ftill called Ra¬ venna, capital of Romania. The feat of the weftern or Roman empire was by Honorius tranflated to Ravenna about the year 404, and hence the country in which it flood was called Romania, in the pope’s territory. It had a very tlourilhing trade till the fea withdrew two miles from it, which has been a great detriment. The fortifications are of little importance, and the citadel is gone to ruin. It is now moft remarkable for the excel¬ lent wine produced in its neighbourhood. The maufo- leum of Theodoric is ftill to be feen, remarkable for being covered by a fingle ftone 28 feet in diameter and 15 thick. It was at Ravenna that the duke of Nemours fell, after having gained a moft decifive victory over the confederate army, in 1511. See France, N° j 29, and Modern Univerfal Hiftory, vol. xx. p. 324. &c. RAVENSBURG, a county of Germany, in Weft- phalia, bounded on the north by the biflioprics of Ofna- burg and Minden, on the eaft by Lemgow, on the fouth by the bifhopric of Paderborn, and on the w'eft by that of Munfter. It belongs to the king of Pruflia, and has its name from the caftle of Ravenfburg. The population amounts to about 81,812. Ravensburg, a free and imperial town of Ger¬ many, in Algow, in the circle of Suabia. It is well built, and the public ftru£lures are handfome. The in¬ habitants are partly Proteftants and partly papifts. It is feated on the river Chenfs, in E. Long. 9. 46. N. Lat. 47. 44. RAVET, an infeft fliaped like a may-bug, or cock¬ chafer, (fee ScARABiEUs), with which the ifland of Guadaloupe is much peftered. It has a ftinking fmell, preys upon paper, books, and furniture, and whatever they do not gnaw is difcoloured by their ordure. Thefe rally infefls, which are very numerous, and appear chiefly by night, would be intolerable, w7ere it not for a large fpider, fome of them as long as a man’s fill, which intangles them in its web, and otherwife furprifes them. On which account the inhabitants of the ifland are very careful of thefe fpiders. RAVILLIAC, Francis, the infamous aflaflin of^0^. \Jniv, Henry IV. of France, wTas a native of Angoulefme, Jiijl. vol. and at the time of his execution was about one or two P- I47* and thirty years of age. See France, N° 146, andnote A’Si'c’ Henry IV. of France. Ravilliac was the for. of parents who lived upon alms. His father was that fort of infe¬ rior retainer to the lawr, to which the vulgar give the name of a pettifogger, and his fon had been bred up in the fame way. Ravilliac had fet up a claim to an eftate, but the caufe went againft him : this difappointment af- fe6ied his mind deeply : he afterrvards taught a fchool, and, as himfelf faid, received charitable gifts, though but of a very fmall value, from the parents of thofe whom he taught j and yet his diftrefs was fo great, that he bad much ado to live. "When he was feized for the king’s murder, he was very loofely guarded j all were permitted to fpeak with him who pleafed; and it was thought R A V [ 649 1 RAY Ravilliac. tliouglit very remarkable that a Jefult flrould fay to him, v,“—“ Friend, take care, whatever you do, that you don’t charge honeft people.” He was removed next day from the houfe of Efpernon to the Conciergerie, the proper prifon of the parliament of Paris. When he was firft interrogated, he anfwered with great boldnefs, “ That he had done it, and would do it if it were to do again.” When he was told that the king, though dangeroufly wounded, was living, and might recover, he laid that he had ifruck him home, and that he was lure he was dead. In his fubfequent examinations he owned that he had long had an intention to kill the king, becaufe he fullered two religions in his kingdom ; and that he en¬ deavoured to obtain an audience of him, that he might admonilh him. He alfo faid that he underllood the king’s great armament to be again!! the pope, and that, in his opinion, to make war againlt the pope, was to make war*hgainft God. We have no diftincl account of the three Taft examinations; but he is faid to have perlifted, in the moft folemn affeverations, that he had no accom¬ plices, and that nobody had perfuaded him to the iadl. He appeared furprifed at nothing fo much as at the univerfal abhorrence of the people, which, it leems, he did not expeft. They were forced to guard him ftridtly from his fellow-prifoners, who would otherwife have murdered him. Ihe butchers of Paris delired to have him put into their hands, affirming that they would flay him alive, and that he ihould Hill live 12 days. When he was put to the torture, he broke out into horrid execrations, and always infilled that he did the fa«?/ his lubject as well as underjland it j yet, that he may preferve a proper eafe and maderlinefs of delivery, it is alio neceftary he fliould guard againd discovering too much emotion and perturbation. From this reafoning we deduce the following rule, for the tones which indicate the paffions ana emotions. “ In reading, let all your tones of expreffion be bor¬ rowed from thofe of common fpeech, but fomething more faintly charaaerifed. Let thofe tones which fig- nify any difagreeable paifion of the mind, be dill moie faint than thofe which indicate their contrary} and pre¬ ferve yourfelf fo far from being affedted with the fubje.a, as to be able to proceed through it with tnat peculiar kind of eafe and maderlinefs, which has its charms in this as well as every other art."’ We {hall conclude this feaion with the following.ob- fervation, which relates to fpeaking as well as reading. When words fall in our rvay, whole “ founds feem an echo to the fenfe,” as fquirr, bu%%, hum, rattle, hifs,jar, &c. we ought not to pronounce them in iuch a manner as to heighten the imitation, except in light and ludi¬ crous fubjefits. For indance, they ffiould not in any other cafe be founded fqmr.r.r—bu%'Z.‘Z>.‘Z,—lium m.m^ r.r.rattle, &c. On the contrary, when the imitation lies in the movement, or flow andflruBure of a whole (which frequently happens in poetry), the deli¬ very may always be allowed to give a heightening to it with the greated propriety , as in the following indan¬ ces, out of a number more which every experienced rea¬ der will quickly recoiled!. In thefe deep folitudes and awful cells, Where heavenly penflve Contemplation dwells, And ever-muflng Melancholy reigns Pope’s Eloifa to Abelard. With eafy courfe The veffels glide unlefs their fpeed be dopp’d By dead cairns, that oft he on thefe fmooth fleas. Dyer’s Fleece. Softly fweet in Lydian meafure, Soon he foollid her foul to pleafure. Dryden’s Ode on St Cecilia's day. Still II E A [ ^57 ] REA Reading. Still gathering force it fmokes, and, urg’d amain, ' ^ Whirls, leaps, and thunders dawn impetuous to the plain. Pope’s Iliady b. 13. For who to dumb forgetfulnefs a prey, This pleating anxious being ere resign’d, Left the warm precinfts of the cheerful day, Nor call one longing lingering look behind? Gray’s Elegy. Exprefiion Befides the particular tones and modifications of as to the voice above defcribed, which alwTays accompany and face and exprefs our inward agitations, nature has in thefe cafes gelture. endowed us with another language, w7hich, inftead of the ear, addreffes itfelf to the eye, thereby giving the communications of the heart a double advantage over thofe of the underftanding, and us a double chance to preferve fo ineilimable a blefling. This language is what arifes from the different, almoft involuntary, movements and configurations of the face and body in our emotions and paffions, and which, like that of tones, every one is formed to underhand by a kind of intuition. When men are in any violent agitation of mind, this co-operating expreflion (as it is called) of face and gel¬ ture is very ftrongly marked, and totally free from the mixture of any thing which has a regard to graceful- nefs, or what appearance they may make in the eyes of others. But in ordinary converfation, and where the emotions are not fo wTarm, falhionable people are perpe¬ tually infinuating, into their countenance and adlion, whatever they imagine will add to the eafe and elegance of their deportment, or imprefs on the fpe£lator an idea of their amiablenefs and breeding. Now, though the above mentioned natural organical figns of the emotions fhould accompany every thing fpoken, yet from what was obferved in the introduftory part of this article (like the tones we have juft treated upon), they fhould in reading be much lefs ftrongly expreffed, and thofe fuffer the greateft diminution that are in themfelves the moft ungainly. And as it was in the laft feflion re¬ commended to the reader to preferve himfelf as far from being affefted in all pafiionate fubje&s as to be able to keep a temperate command over the various affedlions of the voice, &c. fo under the fanftion of this fubor- dinate feeling he may accompany his delivery more fre¬ quently wdth any eafy aftion or change of face, which wrill contribute to fet off his manner, and make it agree¬ able on the principles of art. As thefe calm decorations of aftion (as wfe may call them) are not altogether natural, but have their rife from a kind of inftitution, they muft be modelled by the praftices of the polite. And though mankind dif¬ fer from one another fcarce more in any particular than in that of talents for adopting the graceful aftions of the body, and hence nothing determinate can be faid of their nature and frequency, yet even thofe, moft happily calculated to acquit themfelves wTell in their ufe, might profit by confidering that it is better greatly to abridge the difplay, than to over-do it ever fo little. For the peculiar modefty of deportment with which the inhabitants of this kingdom are endowed, makes hs in common endeavour to fuporefs many figns of an agitated mind ; and in fuch cafes the bodily ones in par¬ ticular are very fparingly ufed. We have alfo a natural and rooted diflike to any kind of affe&ation ; and to no Vol. XVII. Part II. fpecies, that wTe can recoiled!:, a greater, than to that Reading;, which is feen in a perfon who pretends to mimicry v ' ' and courtly gefture, without poffeffing the advantages and talents they require *, and of which not many people, comparatively fpeaking, have any remarkable ftiare. The inference of this is too obvious to need drawing out, and we would particularly recommend it to the con- fideration of thofe readers who think the common occur¬ rences of a newfpaper, &c. cannot be properly delivered without a good deal of elbow-room. Although it is impoflible to come to particulars in any diredlions of this kind, yet there is one article of our prefent fubjedt on which a ferviceable remark may be made. In ordinary difeourfe, when we are particu¬ larly prefiing and earned in what we fay, the eye is na¬ turally throwm upon thofe to whom we addrefs ourfelves: And in reading, a turn of this organ now and then up¬ on the hearers, when any thing very remarkable or in- terefting falls in the way, has a good effedl in gaining it a proper attention, &c. But this Ihould not be too frequently ufed ; for if fo, befides its having a tendency to confound the natural importance of different paffages, it may not be altogether agreeable to fome to have their own refledtions broken in upon by a fignal, which might be interpreted to hint at their wanting regula¬ tion. One obfervation more, and then we (hall attempt to recapitulate the fubftance of this fedtion in the form of a precept. Though it is, wdren ftridlly examined, ineon- fiftent, both in fpeaking and reading, to imitate with ac¬ tion what we are deferibing, yet as in any thing comic fuch a pradtice may fugged ideas that will accord with thofe of the fubjedt, it may there be now and then in¬ dulged in either of thefe articles. “ In a manner fimilar to that diredled with regard to tones, moderate your bodily expreflions of the figns of the emotions. And in order to fupply, as it were, this deficiency, introduce into your carriage fuch an eafy gracefulnefs, as may be confiftent with your acquire¬ ments in thefe particulars, and the neceffary dread wduch * thould ever be prefent of falling into any kind of affec¬ tation or grimace.” V. Paufes. Speech confiding of a fucceflion of di- ftindl words, muft naturally be liable (both from a kind of accident, and a difficulty there may be in be¬ ginning certain founds or portions of phrafes immedi¬ ately on the ending of certain others) to feveral final! intermiffions of voice; of which, as they can have no meaning, nothing farther need here be faid. There are, however, fome paufes, wffiich the fenfe neceflarily de¬ mands 5 and to thefe the fubftance of this fettion is cli- refted. The paufes are in part to diftinguilh the members of fentences from one another, the terminations of complete periods, and to afford an opportunity for taking breath. Befides this, they have a very graceful effect in the mo¬ dulation, on the fame account they are fo effential in mufic.—In both articles, like blank fpaces in pictures, they fet off and render moreconfpicuous whatfoever they disjoin or terminate. Were language made up of nothing but ffiort collo¬ quial fentences, thefe paufes, though they might do no harm, and would generally be graceful, would hov/ever be fuperfeded as -to ufe by the completenefs and nar- 4 O roixmtfs, REA [6 Reading, rowrtefs, as we may fay, of the meaning. But in more ~ diSfafe language, compofed of ieveral detached fen- tences, and which require fome degree of attention in order to take in the fenfe, the intermidions of voice under confideration are of the greateft lervice, by fig- nifying to the mind the progrefs and completion of the whole paffage. Now, though in extenfive and dif¬ ferently formed periods there may be members whofe completenefs of fenfe might be conceived of various de¬ grees, and hence might feem to require a fet of paufes equally numerous 5 yet, fince the fenfe does not alto¬ gether depend upon thefe intermiffions, and their ra¬ tios to one another, if capable of being properly de¬ fined, could not be accurately obferved, grammarians have ventured to conceive the whole clafs of panics as reducible to the four or five kinds now in ufe, and whole marks and ratios are well known (g) j prefu¬ ming that under the eye of Lafte, and with the afliil- ance of a particular to be next mentioned, they would not fail in all cafes to fuggeft intermillions of voice fuitable to the fenfe. But in many of theic extenfive and complex periods, rounded with 'a kind of redun¬ dancy of matter, where the full fenfe is long fufpended, and the final words are not very important, there would be fome hazard of a mifapprehenfion of the termina¬ tion, had we not more evident and infallible notice of it than that which is given by the paufe. This notice is the cadence, referred to in the fehlion on Modulation; which, as is there obferved, befides the ornamental variety it affords, appears from thefe remarks to be a very neceffary and ferviceable article in perfpicuous de¬ livery. As this cadence naturally accompanies the end of every entire fenfe, circumltanced as above-mentioned, it may fometimes fall before the femicolon, but more generally before the colon, as well as the period : For thefe marks are often found to terminate a complete fenfe $ and in thefe cafes, the relation what follows has to what went before, is fignified to the mind by the re¬ lative Ihortnefs of the flop, and the form of introdu¬ cing the additional matter. Nor can any bad confe- quence arife from thus founding dil!in£Hons on ratios of time, which it may be faid are too nice to be often rightly hit upon : for if a confufion Ihould happen be¬ tween that of the colon and period, there is perhaps fo trifling a difference between the nature of the paffages they fucceed, as to make a fmall inaccuracy of no con- fequence. And as to the refts of the femicolon and period, it will not be eafy to miftake about them, as their ratio is that of two to one. Add to this the power which the matter and introduftion of the fub- fequent paffages have to rectify any flight error here 58 ] REA made, and we {hall be fully fatisfied, that the paufes Readin*. as ufually explained, with the cadence above deferibed, ——v—■ and a proper knowledge of the language, will convey fufficient information to the underltanding of the con- firuftive nature of the paffages after which they are found. It may be obferved, that in natural fpeech, accord¬ ing to the warmth and agitation of the fpeaker, the veils are often fhort and injudicioufly proportioned, and hence that every thing thus delivered cannot be fo graceful as it might have been from a proper attention to their mag¬ nitude and effedfs. Paufes then, though chiefly fubjedfed to the fenfe are, as was remarked at the outlet, ferviceable in beautifying the modulation, &c.—And fince books are often inaccurately printed as to points, and peo¬ ple’s tafles differ fome little about their place and va¬ lue, it appears, that, “ although in reading great at¬ tention Ihould be paid to the flops, yet a greater fhould be given to the fenfe, and their correfpondent times occasionally lengthened beyond what is ulual in common fpeech j which obiervation contains all that we {ball pretend to lay down by way of rule for the management of paules in the delivery of written lan- guage. As there are two or three fpecies of writing, which have fome thing Angular in them, and with regard to the manner in which they Aiould be read, a few particular remarks feem neceffarily required, we {hall conclude this article with laying them before the reader: 1. Of Pr.AYS, and fuch like conversation-pieces!. Writings of this kind may be confidered as intended for two different purpofes ; one to unfold fubjeft matter for the exercife of theatric powers } and the other to convey amufement, merely as fable replete with pleafing inci¬ dents and charadleriflic manners. Hence there appears to be great latitude for the difplay of a conji/hnt delivery of thefe performances : for while, on one hand, a good reader of very inferior talents for mimicry may be heard with a tolerable degree of pleafure •, on the other, if any perfon is qualified to give a higher degree of life and force to the dialogue and charafters by delivering them as an adlor, he muft be fully at liberty to ftart from the confinement of a chair to a pollute and area more flut¬ ed to his abilities j and, if he be not deceived in himfelf, his hearers will be confiderable gainers by the change.—- The next article is, 2. Sermons or other orations, which in like man¬ ner may be conceived intended for a double purpofe. Firft, as matter for the difplay of oratorical powers and, fecondly, as perfuafive difeourfes, &.C. which may be (g) Suppoling the comma {,) one time, the femicolon (5) will be two; the colon (;) three, and the period (.) as alfo the marks of interrogation (?) and admiration (!) four of thefe times. The blank line (— or -—), and the breaks \)eX.-wztx\paragraphs, intimate ftill greater times; and by the fame analogy may be reckoned a double and quadruple period refpeftively. Now and then thefe blank lines are placed immediately after the ordinary points, and then they are conceived only as feparating for the eye the different natures of the matter ;—as a tjueflion from an anfwer,—precept from example,—premifes from inferences, &c. i* which cafe their import is evident. But of late fome authors have not fcrupled to confound theft; diftin£lions ; and to make a blank ferve for all the paufes univerfally, or the mark of an indefinite reft, the quantity of which is left to the determination of the reader’s tafte. A pradlice, it is imagined, too deftruftive of the intended precifion of thefe typical notice? to be much longer adopted. REA [ - the reclufe was to have every thing neceflary for the fupport of life conveyed to him through a window. If he was a prieft, he was allowed a fmall oratory, with a window, which looked into the church, through which he might make his offerings at the mafs, hear the ling- ing, and anfwer thofe w7ho fpoke to him j but this win¬ dow had curtains before it, fo that he could not be feen. He was allowed a little garden, adjoining to his cell, in which he might plant a lew herbs, and breathe a little frelh air. If he had difciples, their cells -were contigu¬ ous to his, with only a window of communication, through w'hich they conveyed neceffaries to him, and re¬ ceived his inftruftions. It a reclufe fell fick, his door might be opened for perfons to come in and afliit him, but he himfelf was not to ftir out. RECOGNITION, in Law, an acknowledgment-, a word particularly ufed in our law-books for the firft chapter of the ftatutc 1 Jac. I. by which the parlia¬ ment acknowledged, that, after the death of Oueen Elifabeth, the crown had rightfully defcended to King James. RECOGNIZANCE, in Law, is an obligation of record, %vhich a man enters into before fome court of record or magiftrate duly authorifed, with condition to do fome particular aft ; as to appear at the affixes, to keep the peace, to pay a debt, or the like. It is. in molt refpefts like another bond : the difference being chiefly this, that the bond is the creation of a frefti debt or obligation de novo, the recognizance is an ac¬ knowledgment of a former debt upon record j the form wdiereof is, “ that A. B. doth acknowledge to owe to ©ur lord the king, to the plaintiff, to C. 1). or the like, the fum of ten pounds,” with condition to be void on performance of the thing ftipulated : in w-tnch cafe the king, the plaintiff, C. D. &:c. is called the cognizee, is cm cognofcitur ; as he that enters into the recognizance is called the cognizor, is qui cognofcit. This being cer¬ tified to, or taken by the officer of fome court, is wit- neffed only by the record of that court, and not by the party’s feal: fo that it is not in ftrift propriety a deed, though the effefts of it are greater than .a common obligation ; being allowed a priority in point of pay- ment, and binding the lands of the cognizor f.om the time of enrolment on record. RECOIL, or Rebound, the ftarting backward of a fire-arm after an explofion. jMerfennus tells us, that a cannon 12 feet in length, weighing 64001b. gives a ball of 241b. an uniform velocity of 640 feet per^fe- cond. Putting, therefore, W =: 6400, w=: 14, V = 640, and v— the velocity with which the cannon recoils; tve fhall have (becaufe the momentums of tne cannon J . mV and ball are equal) W v rr mV 5 and lo v — — £1*^! = 2,4 ; that is, it would recoil at the rate of 6400 feet per fecond, if free to move. RECOLLECTION, a mode of thinking, by which ideas fought after by the mind are found and brought to view. . RECONNOITRE, in military affairs, implies to view and examine the ftate of things, in order to make Reconnoi- a report thereof. ^re Parties ordered to reconnoitre are to obferve the ^ecc][je. country and the tnemy •, to remark the routes, conve- l , niences, and inconveniences of the firft} the pofition, march, or forces of the fecond. In either cafe, they Ihould have an expert geographer, capable of taking plans readily : he ftiould be the belt mounted of the whole, in cafe the enemy happen to fcatter the efcorte, that he may fave his works and ideas. See War. RECORD, an authentic teftimony in writing, con¬ tained in rolls of parchment, and preferved in a court of record. See Court. Tna/ by RECOItDr a fpecies of trial which is ufed only in one particular inftance : and that is where a mat¬ ter of record is pleaded in any aftion, as a fine, a judg¬ ment, or the like j and the oppofite party pleads, nul ticl record, that there is no fuch matter of record exiL ting. Upon this, iffue is tendered and joined in the following form, “ and this he prays may be inquired of by the record, and the other doth the like j” and here¬ upon the party pleading the record has a day given him to bring itjin, and proclamation is made in court for him to “ bring forth the record by him in pleading alleged, or elfe he (hall be condemned and, on his failure, his antagonift lhall have judgement to recover. The trial, therefore, of this iffue, is merely by the record : for, as Sir Edward Coke obferves, a record or enrolment is a monument of fo high a nature, and importeth in itfelf fuch abfolute verity, that if it be pleaded that there is no fuchrecord, itftiall not receive’any trial by witnefs, jury, or otherwife, but only by itfelf. Thus titles of nobility, as whether earl or not earl, baron or not baron, (hail be tried by the king’s writ or patent only, which is matter of record. Alfo in cafe of an alien, whether alien friend or enemy, (hall be tried by the league or treaty between his fovereign and ours j for- every league or treaty is of record. And alfo, whether a manor be held in ancient demefne or not, (hall be tried by the record of demefday in the king’s exchequer. RECORDE, Robert, phyfician and mathematician, was defcended of a refpeftable family in Wales, and lived in the time of Henry VIII. Edward I. and Mary. The time of his birth is not exactly known, but it muff have been about the beginning of the 16th century, for he was entered of the univerfity of Oxford about Ij2j, and was elefted fellow of All Souls college in 1531'. As he made phyfic his profeflion, he went to Cambridge, where he was honoured with the degree of doftor in that faculty in 154 5, and very much efteemed by all who were acquainted with him, for his extenfive knowledge of many of the arts and fciences. He afterwards returned to Ox¬ ford, where he publicly taught arithmetic and mathema¬ tics, as he had done prior to his going to Cambridge, and that with great applaufe. It appears that he after¬ wards went to London, and was, it is faid, phyfician to Edward VI. and to Mary, to whom fome of his books are dedicated y yet he died in the king’s-bench prifon, Southwark, where he was confined for debt, in the year 1 ^58, at a very immature age. He publiflied feveral works on mathematical fubjefts, chiefly in the form of dialogue between mafter and fcho- lar, of which the following is a lift. _ The Pathway to Knowledge, containing the firft prin¬ ciples REG Recorde ciples of geometry, as they may mofte aptly be applied Recovery. U1.lto P1'a<^:ice» bothe for the ule of Inftrumentes Gecme- u—tricall and Aftronomicall, and alfo for projedion of Plattes, much neceffary for all fortes of men. Lond. 4to> I55I* The Ground of Arts, teaching the perfed worke and pradice of Arithmeticke, both in whole numbers and fradions, after a more ealie and exad forme then in former time hath been fet furth, 8vo, 1552. The Cafle of Knowledge, containing the Explica¬ tion of the Sphere both Celeitiall and Material!, and divers other things incident thereto. With fundry pleafaunt proofes and certaine newe demonftrations not written before in any vulgare woorkes. Lond. fob 1556. The Whetjlone of Witte, which is the fecond part of Arithmetike, containing the extradion of rootes; the Coflike pradice, with the rules of equation; and the woorkes of furde numbers. Lond. 410, 1557. Wood fays that he was the author of feveral pieces on phyfic, anatomy, politics, and divinity, but it is uncertain whether thefe were ever publiihed. Sher¬ burne fays that he alio publilhed Cojmographice Ifa- gogen ; that he wTrote a book, De arte faciendi horolo¬ gium, and another De ufu globorum, et de Jiatu tem- porurn, none of which we have had an opportunity of feeing. RECORDER, a perfon whom the mayor and other magiftrates of a city or corporation affociate to them, lor their better diredion in matters of juftice and proceedings in law ; on which account this perfon is generally a counfellor, or other perfon well Ikilled in the law. J&lachji. Comment. [ 664 ] REG no legal title to the land j but that he came into poffef- Rccevery. fion ol it after one Hugh Hunt had turned the demand-' ant out oi it. Ihe lublequent proceedings are made up nto a record or recovery roll, in which the writ and complaint of the demandant are firft recited : whereupon the tenant appears, and calls upon one Jacob Morland, who is fuppoled, at the original purchafe, to have war¬ ranted the title to the tenant 5 and thereupon he prays, that the faid Jacob Morland may be called in to defend* the title which he fo warranted. This is called the voucher, “ vocatio,” or calling of Jacob Morland to warranty; and Morland is called the vouchee. Upon, this Jacob Morland, the vouchee, appears, is impleaded, and defends the title. Whereupon Golding the deman¬ dant defires leave of the court to imparl, or confer with the vouchee in private j which is (as ufual) allowed him. And foon afterwards the demandant Golding returns to court} but Morland the vouchee difappears, or makes default. Whereupon judgment is given for the deman¬ dant Golding, now called the reeoverer, to recover the lands in queition againft the tenant Edwards, who is now the recoveree : and Edwards has judgment to re- covei of Jacob Morland lands of equal value, in recom- penfe for the lands fo warranted by him, and now loft by his defaultwhich is agreeable to the do&rine of warranty mentioned in the preceding chapter. This is called the recompenfe, or recovery in value. But Jacob Morland having no lands of his own, being ufually the ciier of the court, wdio, from being frequently thus vouched, is called the common vouchee, it is plain that Edw-ards has only a nominal recompenfe for the lands fo recovered againft him by Golding j which lands are now 'PU J p r j • 1 r 1 , abiolutely veiled in the faid recoverer by judgment of J Jj d*r of,L°"don V5 ^ofen by the lord mayor law, and feifin thereof is delivered by 0^ftieriff of the arid aldermen-, and as he is held to be the mouth of the city, delivers the judgment of the courts therein, and records and certifies the city-cuftoms. See London .N° 38. ’ RECOVERY, or Common Recovery, in Englilh law, a fpecies of affurance by matter of record ; concern¬ ing the original of which it mull be remarked, that com¬ mon recoveries were invented by the ecclefiaftics to elude the ftatutes of mortmain (fee T ail) ’, and afterwards encouraged by the fineffe of the courts of law in 12 Edward IV. in order to put an end to all fettered inheritances, and bar not only eftates-tail, but alfo all remainders and re- verfions expeftant thereon. We have here, therefore, only to confider, firft, the nature of a common recovery: and, fecondly, its force and effeB. 1. A common recovery is a fuit or a&ion, either ac¬ tual or fiftitious: and in it the lands are recovered aCTainll the tenant of the freehold ; wdiich recovery, being a fup- pofed abjudication of the'right, binds all perfons, and veils a free and abfolute fee-fimple in the recoverer. To ex- plam this as clearly and concifely as poflible, let us, in the nrll place, fuppofe David Edw-ards to be tenant of the freehold, and defirous to fuffer a common recovery, in order bar all entails, remainders, and reverfions, and to convey the fame, in fee-fimple, to Francis Golding. o f-fteot this, Golding is to bring an adlion againft him tor the lands 5 and he accordingly fues out a writ called a preccipe quod reddat, becaufe thefe were its initial or moll operative words when the law- proceedings were in Latin. In this writ the demandant Golding alleges lhat the defendant Edwards (here called the tenant) has 4 county. So that this collufive recovery operates merely m the nature of a conveyance in fee-fimple, from Ed¬ wards the tenant in tail to Golding the purchafer. The recovery here defcribed, is with a fingle voucher only j but fometimes it is with a double, treble, or far¬ ther voucher, as the exigency of the cafe may require. And indeed it is now' ufual always to have a recovery with double voucher at the leaft : by firft conveying an eftate of freehold to any indifferent perfon, againft whom the pracipe is brought j and then he vouches the tenant in tail, who vouches over the common vouchee. For, 1 a recovery be had immediately againft tenant in tail it bars only fuch eftate in the premifes of wEich he is t icn adlually feifed j whereas if the recovery be had againft another perfon, and the tenant in tail be vouch¬ ed, it bars every latent right and intereft which he may have in the lands recovered. If Edwards therefore be tenant of the freehold in poffeflion, and John Barker be tenant in tail in remainder, here Edwards doth firft vouch Barker, and then Barker vouches Jacob Morland the common vouchee ; who is alw-ays the laft perfon vouched, and always makes default j whereby the de¬ mandant Golding recovers the land againft the tenant Edwards, and Edwards recovers a recompenfe of equal value againft Barker the firft vouchee ; ‘who recovers the like againft Morland the common vouchee, againft whom fuch ideal recovery in value is always ultimately awarded. J T his fuppofed recompenfe in value is the reafon why the iffue m tail is held to be barred by a common re¬ covery. For, if the recoveree fliould obtain a recon> penfe REG [ 665 ] R E C Recovery, penfe in lands from tire common vouchee (which there is a pcffibilhy in contemplation of law, though a very- improbable one, of his doing), thefe lands would fup- ply the place of thofe fo recovered from him by collu- lion, and would defcend to the iflue in tail. The reafon will alio hold with equal force as to moil remainder¬ men and reverfioners, to whom the poffibility will re¬ main and revert, as a full recompenfe for the reality which they were otherwife entitled to : but it will not always hold 5 and therefore, as Pigott fays, the judges have been even ajiuti, in inventing other reafons to maintain the authority of recoveries. And, in par¬ ticular, it hath been faid, that though the eftate-tail is gone from the recoveree j yet it is not deftroyed, but only transferred, and ftill fubfitb; and will ever con¬ tinue to fubfift (by conftruftion of lawr) in the reco- verer, his heirs and afligns : and as the eftate-tail fo continues to fubfiit for ever, the remainders or reverfions expedant on the determination of fuch eftate-tail can never take place. To fuch aukward fliifts, fuch fubtile refinements, and fuch ftrange reafoning, wrere our anceftors obliged to have recourfe, in order to get the better of that itub- born ftatute de donis. The defign for which thefe con¬ trivances were fet on foot, was certainly laudable j the unrivetting the fetters of eftates tail, w'hich were at¬ tended with a legion of mifchiefs to the commonwealth : but, while wTe applaud the end, we cannot but admire the means. Our modern courts of juftice have indeed adopted a more manly wray of treating the fubjed ; by confidering common recoveries in no other light than as the formal mode of conveyance by which tenant in tail is enabled to aliene his lands. But, fince the ill confequences of fettered inheritances are now generally feen and allowed, and of courfe the utility and expe¬ dience of fetting them at liberty are apparent, it hath often been wfilhed that the procefs of this conveyance was ftiortened, and rendered lefs fubjed to niceties, by either totally repealing the ftatute de donis ; which per¬ haps, by reviving the old dodrine of conditional fees, might give birth to many litigations : or by veiling in every tenant in tail, of full age, the lame abfolute fee-fimple at once, wdiich now he may obtain whenever he pleafes, by the collufive fidion of a common reco¬ very •, though this might polftbly bear hard upon thofe in remainder or reverfion, by abridging the chances they would otherwifg frequently have, as no recovery can be fullered in the intervals between term and term, which fometimes continue for near five months toge¬ ther: or, laftly, by empowering the tenant in tail, to bar the eftate-taii by a folemn deed, to be made in term-time, and enrolled in fome court of record ; which is liable to neither of the other objedions, and is war¬ ranted not only by the ufage of our American colo¬ nies, but by the precedent of the ftatute 21 Jac. I. c. 19. which, in the cafe of a bankrupt tenant, in tail, em- powTers his ccmmiftioners to fell the eftate at any time, by deed indented and enrolled. And if, in fo national a concern, the emoluments of the officers concerned in palling recoveries are thought to be worthy attention, thofe might be provided for in the fees to be paid upon each enrollment. 2. The force and eft tel of common recoveries may appear, from wdrat has been faid, to be an abfolute bar •not only of all eftates tail, but of remainders and re- Vol. XVII, Part II. verfions expedant on the determination of fuch eftates. Recovery So that a tenant in tail may, by this method of affu- II . ranee, convey the lands held* in tail to the recoverer, ^cc‘u,t-' his heirs and afligns, abfolutely free and difeharged of ail conditions and limitations in tail, and of all remain¬ ders and reverfions, But, by ftatute 34 and 35 H. VH. c. 20. no recovery had againlt tenant in tail of the king’s gift, whereof the remainder or xeverlion is in the king, lhall bar fuch eftate-tail, or the remainder or re- verfion of the crown. And by the llalute 11 H. VII. c. 20. no woman, after her hufband’s death, lhall fuller a recovery of lands fettled on her by her hut band, or fettled on her huiband and her by any of his anceftors. And by ftatute 14 Eliz. c. 8. no tenant for life, of any fort, can fuller a recovery fo as to bind them in remainder or reverfion. For which reafon, if there be tenant for life, with remainder in tail, and other re¬ mainders over, and the tenant for life is defirous to fuf- fer a valid recovery, either he, or the tenant to the prev- cipe by him made, mull vouch the remainder man in tail, otherwife the recovery is void : but if he does vouch fuch remainder-man, and he appears and vouches the common vouchee, it is then good ; for if a man be vouched and appears, and fuffers the recovery to be had, it is as effedlual to bar the eftate-tail as if he himfelf were the recoveree. In all i-ecoveries, it is neceflary that the recoveree, or tenant to the preecipe, as he is ufually called, be atluallv feifed of the freehold, elfe the recovery is void. For all actions to recover the feifin of lands mull be brought a- gainll the aflual tenant of the freehold, elfe the fuit will lofe its effedl j fince the freehold cannot be recovered of him wdro has it not. And, though thefe recoveries are in themfelves fabulous and fiflitious, yet it is neceffary that there be adores fabulce^ properly qualified. But the nicety thought by fome modern pradlitioners to be requi- fite in conveying the legal freehold, in order to make a good tenant to the prtecipe, is removed by the provifions of the ftatuLe 14 Geo. II. c. 20. which qna£ls, with a retrofpeft and conformity to the ancient rule of law, that, though the legal freehold be veiled in lefiees, yet thole who are entitled to the next freehold eftate in re¬ mainder, or reverlion, may make a good tenant to the preecipe; and that, though the deed or fine which creates fuch tenant be fubfequent to the judgement of recovery, yet if it be in the fame term, the recovery ftiall be valid in law7: and that though the recovery it- felf do not appear to be entered, or be not regularly en¬ tered on record, yet the deed to make a tenant to the preecipe, and declare the ufes of the recovery, lhall after a poflellion of 20 years be fufficient evidence on behalf of a purchafer for valuable conlideration, that fuch re¬ covery was duly fullered. Recovery ol perfons drowned, or apparently dead. See Re-animation, and the articles there referred to. RECREANT, Cowardly, Faint-hearted; formerly a word very reproachful. See Battel. RECREMENT, in Chevtijlry, fome fuperfluous mat¬ ter feparated from fome other that is ufeful j in which fenle it is the fame with fcor ice ^ feeces, and excre¬ ments. RECRIMINATION, in Law, an accufation brought by the accufed againft the accufer upon the lame fadl. RECRUITS, in military affairs, new-raifed foldiers defigned to fupply the place of thofe who have loft 4 P their P, £ C [ Re Eefides, fince all feas are m faft but one, what is it that hinders the Indian ocean to now to its level r What is it that keeps the In¬ dian ocean up ? Till this laft branch of the queftion is 668 ] RED refolved, I fhall take it for granted that no fuch differ- Red Sea ence of level exifts, whatever Ptolemy’s engineers might have pretended to him ; becaufe, to fuppofe it fa6t, is to fuppofe the violation of one very material law of na¬ ture.” The next thing confidered by our author is the paf- fage of the Ifraelites through the Red fea. At the . place where he luppofes the paffage to have been, the lea is not quite four leagues broad, fo that it might ea- fily have been croffed in one night without any miracle. There is about 14 fathom water in the channel, and nine at the fides, with good anchorage every where j the fartheft fide is a low' fandy coaft, and a very eafy land¬ ing place. “ The draught of the bottom of the gulf (fays he) given by Br Pococke, is very erroneous in every part of it. It was propofed to Mr Niebuhr, when in Egypt, to inquire upon the fpot, whether there were not fome ridges of rocks where the water was fnallow, fo that an army at particular times might pafs over ? Secondly, whether the Etefian winds, which blow ftrongly all fummer from the north-weft, could not blow' fo violently againft the fea, as to keep it back on a heap, fo that the liraelites might have pafl'ed with¬ out a miracle ? And a copy of thefe queries was left for me to join my inquiries likewife. But I muft con- fefs, however learned the gentlemen were who propofed thefe doubts, I did not think they merited any atten¬ tion to folve them. lithe Etefian winds, blowdng from the north-weft in fummer, could heap up the fea as a wall on the right or to the fouth, of fifty feet high, ftill the difficulty would remain of building the wall on the left hand or to the north. Befides, water ftanding in that pofition for a day, muft have loft the nature of a. fluid. Whence came that cohefion of particles that hindered that wall to efcape at the fides ? This is as great a miracle as that of Mofes. If the Etefian winds had done this once, they muft have repeated it many a time before and flnee, from the fame caufes. Yet Dio¬ dorus Siculus fays, the Troglodytes, the indigenous in¬ habitants of that very fpot, had a tradition from father to fon, from their very earlieft and remoteft ages, that once this divifion of the fea did happen there ; and that, after leaving the bottom fome time dry, the fea again came back and covered it with great fury. The words of this author are of the moft remarkable kind. We cannot think this heathen is writing in favour of reve¬ lation. He knew' not Mofes, nor fays a word about Pharaoh and his hoft ; but records the miracle of the divifion of the fea in W'ords nearly as ftrong as thofe of Mofes, from the mouths of unbiaffed undefigning pa¬ gans.” RED-Shank. See ScOLOPAX,! Red Start. SeeMoTACiLLA, V Ornithology Index. RED-Wing. See TURDUS, _) REDANS, in Field Fortification. See the article Redans. REDDENDUM, in Law, is ufed fubftantively for the claufe in a leafe wherein the rent is referved to the leffor. The proper place for it is next after the limita¬ tion of eftate. REDDITIO, was the third part of the facrifice of the heathens, and confifted of the folemn aft of putting in again the entrails of the viftims, after they had been religioufty infpefted. See Sacrifice. REDDLE, a foft, heavy, red, ferruginous earth, of great Reddle. Redemp¬ tion I! . Reduction. RED great ufe in colouring ; and being waflred from fand, is often fold by our druggifts under the name of bole armeniac. REDEMPTION, in Law, a faculty or right of re¬ entering upon lands, &c. that have been fold and af- ligned, upon reimburfing the purchafe-money with legal colls. Redemption, in Theology, denotes the recovery of mankind from fin and death, by the obedience and fa- crifice of Chrift, who on this account is called the Re¬ deemer of the world. See Theology. REDENS, Redans, or Redant, in Fortification, a kind of indented work in form of the teeth of a law, with faliant and re-entering angles 5 to the end that one part may flank or defend another. It is likewife called faw-work and indented work. The lines or faces in this flank one another. Redens are ufed in fortifying walls, where it is not neceffary to be at the expence of building bafiions ; as when they Hand on the fide of a river running through a garrifon town, a marfh, the fea, &c. But the fault of fuch fortification is, that the befiegers from one battery may ruin both the fides of the tenailie or front of a place, and make an afihult without fear of being enfiladed, fince the defences are mined. The pa¬ rapet of the corridor is likewife often redented or car¬ ried on by the way of redens. The redens was ufed be¬ fore baftions were invented, and fome people think them preferable. REDI, Francis, an Italian phyfician and polite fcholar, was born at Arezzo in Tufcany in 1626. His ingenuity and learning recommended him to the office of firft phyfician to Ferdinand II. duke of Tufcany ; and he contributed not a little toward the compiling of the Dictionary of La Crufca. He wrote upon vipers, upon the generation of infefts, and compofed a good deal of poetry. All his writings are in Italian ; and his language is fo fine and pure, that the authors of the Dictionary of La Crufca have often cited it as a ftan- dard of perfection. He died in 1697. REDINTEGRATION, is the finding the integral or fluent again from the fluxion. See Fluxions. REDOUBT, in Fortification, a fmall fquare fort, without any defence but in front •, ufed in trenches, lines of circumvallation, contravallation, and approach ; as alfo for the lodgings of corps de-gard, and to defend paffages. REDUCTION, in the fchools, a manner of bringing a term or propofifion, which w^as before oppofite to fome other, to be equivalent to it. Reduction, in Arithmetic, that rule whereby num¬ bers of different denominations are brought into one de¬ nomination. See Arithmetic. REDUCTION cf Equations, in Algebra, is the clearing them from all fupenluous-quantities, bringing them to their loweft terms, and leparating the known from the unknown, till at length only the unknown quantity is found on one fide, and known ones on the other. 1 he reduCHon of an equation is the laft part of tne refolution of the problem. See Algebra. REDUCTION of a figure, defign, or draught, is the making a copy thereof, either larger or {mailer than the original ; ftill preferving the form and proportion. 1 he great ufe of the proportional compares is. the reduction F 669 ] RED and freed of figures, &c. whence they are called compafies of re-Reduction Redundant. dudlion. See the article Compass. There are various methods of reducing figures, &c. the molt ealy is by means of the pentagraph, or paralle¬ logram •, but this hath its defeCts. See the article Pen¬ tagraph. The belt and molt ufual methods of reduction are as follow : I. To reduce a figure, as ABCDE (fig. I.), Plate into a lefs compafs. About the middle of the figure, ccccxlviii as %, pitch on a point, and from this point draw lines to 1“' I’ its feveral angles A, B, C, &c. then drawing the line a b parallel to AB, b c parallel to BC, &c. you will have the figure a b cd e fimilar to ABCDE. If the figure a b c d e had been required to be enlar¬ ged, there needed nothing but to produce the lines from the point beyond the angles, as ss D, z C, &c. and to draw lines, viz. DC, CB, &c. parallel to the fides dc, c b, See. 2. To reduce a figure by the angle of proportion, fuppofe the figure ABCDE (fig. 2.) required to be di-Fig. 2. rninifhed in the proportion of the line AB to a b (fig. 3.) draw the indefinite line GH (fig. 4.), and from Fig. 3. G to H fet off the line AB. On G defciibe the arch and 4- HI. Set off the line a b as a chord on HI, and draw GI. Then with the angle IGIi you have all the mea- fures of the figure to be drawn. Thus to lay down the point c, take the interval BC, and upon the point G deferibe the arch KL. Alfo on the point G deferibe MN ; and upon A, with the diftance MN, defevibe an arch cutting the preceding one in c, which will deter¬ mine the fide b c. And after the fame manner are the other fides and angles to be deferibed. The fame pro- cefs will alfo ferve to enlarge the figure. 3. To reduce a figure by a feale. Meafure all the fides of the figure, as ABCDE (fig. 2.) by a fcale, and- lay down the fame meafures refpeCbively from a fmaller fcale in the proportion required. 4. To reduce a map, defign, or figure, by fquares. Divide the original into little fquares, and divide a frefli paper of the dimenfions required into the fame number of fquares, which are to be larger or lefs than the former, as the map is to be enlarged or diminithed. This done in every fquare of the fecond figure, draw what you find in its correfpondent one in the firft. Reduction, in Metallurgy, is the bringing back me¬ talline fubftances which have been changed into fcoriar or affies, or otherwife divefted of their metallic form, into their natural and original ftate of metals again. See Obes, reduction of. Reduction, in Surgery, denotes an operation whereby a diflocated, luxated, or fra&ured bone, is reflored to its former fiate or place. REDUNDANCY, a fault in difeourfe, confiding in the ufe of a fuperfluity of words. Words perfe&ly fynonymous are redundant, and ought to be retrenched. REDUNDANT, in Mufic. What the French call une accord fupcrjlue, which we have tranflated a redun¬ dant chord in the article Music (from D’Alembert), has by others been rendered a chord extremely Jharp, as in the tranfiation of Rameau’s Principlesof Compofition. Their nature will be bed underftood by a few examples, and an account of the number of tones, femitones, or leffer intervals, contained in each. The fecond redundant is compofed of a major tone, and REE [ 670 ] RE F and a minor femitone : as from fa to fol fliaip. Its pro¬ portion is as 64 to 75. The third redundant confifts of two tones and a femi¬ tone, as fa la, fharp. Its proportion is as 96 to 125. The fourth redundant is the fame with the tritone. I’ rom thefe examples compared with the fame inter¬ vals in their natural Hate, the reader may form a general idea of what is meant by redundant. REE, Reis, or Res, a little Portuguefe coin. See MONE T- Table. REED, in Botany. See Arundo and Bamboo. There are two forts of reeds, fays HalTelquilt, grow¬ ing near the Nile. One of them has fcarce any branch¬ es ; but is furniihed with numerous leaves, which are narrow, fmooth, channeled on the upper lurface ; and the plant is about 11 feet high. The Egyptians make ropes of the leaves. They lay them in water like hemp, and then make them into good ftrong cables. Thefe, with the bark of the date tree, form a'lmolt the only ca¬ ble ufed in the Nile. The other fort is of great confe- quence. It is a fmali reed, about two or three feet high, full branched, with thort, (harp, lancet-ihaped leaves, lire roots, which are thick as the Hem, creep and mat themfelves together to a confiderable diilance. This plant feems uielefs in common life ; but to it, continues the learned author, is the very foil of Egypt owing : for the matted roofs have Hopped the earth which floated in the waters, and thus formed, out of the fea, a country that is habitable. Fire-REEDS. See FlRE-Shtp. Reed, a term in the weft of England for the ftraw ufed by thatchers, which is wheat ftraw finely combed, confifting of ftiff, unbruifed, and unbroken ftalks of great length, carefully feparated from the ftraw ufed for fodder by the ihrefher, and bound in fheaves or nitches, each of which weighs 28 lb. and are fold from 2is. to 3is. per hundred nitches, according to the fea- fon. This is a great improvement in the art of thatch¬ ing, as it gives a finilh to the work which cannot be at¬ tained by draw, rough and tumbled together, without any feparation of the long and ftrort : it is alto a readier mode of working. REEF, a term in navigation. When there is a great gale of wind, they commonly roll up part of the fail be¬ low, that by this means it may become the narrower, and not draw fo much wind \ which contrafling or ta- king up the fail they call a reef or reefng the fail: fo alfo when a top-maft is fprung, as they call it, that is when it is cracked, or almoil broken in the cap, they cut off the lower piece that was near broken off, and fetting the other- part, now much fhorter, in the ftep again, they call it a reefed top-maf. REEL, in the manufactories, a machine ferving for the office of reeling. There are various kinds of reels ; forne very fimple, others very complex. REELING, in the manufaflories, the winding of filk, cotton, or the like, into a fkain, or upon a button, to prevent its entangling. It is alfo ufed for the char¬ ging or difch'arging of bobbins, or quills, to ufe t hem in the manufacture of different fluffs, as thread, filk, cot¬ ton, Sec. Reeling is performed in different ways, and on different engines. REEVING, in the fea-language, the putting a rope through a block: hence to pull a rope out (ft a block is called unrcdiing. RE-EXCHANGE, in commerce, a fecond pay- Rc-Ek- ment of the price of exchange, or rather the price of a thanae new exchange due upon a bill of exchange that comes to ;0lT be protelled, and to be refunded the bearer by the ,r - drawer or indorfer. RE I EC LION, among ecclefiaftics, a fpare meal or repaft, juft fufficient for the fupport of life : hence the hall in convents, and other communities, where the monks, nuns, &c. take their refeCtions or meals in com mon, is called the refeBory. REFERENCE, in writing, &c. a mark relative to another fimilar one in the margin, or at the bottom of the page, where fomething omitted in the text is added, and which is to be inlerted either in reading or copy¬ ing- ^ REFINING, in general, the art of purifying a thing 3 including not only the effaying or refining of metals, but likew-ife the depuration or clarification of li¬ quors. See Clarification 3 and Pharmacy, under Materia Medica ; and Ores, ReduBmn of Gold and filver may be refined by feveral methods, which are ail founded on the effential properties of thefe metals, and acquire different names according to their kinds. Thus, tor iniiance, gold having the property which no other metal, not even filver, has of refilling the aftion of fulphur, of antimony, of nitrous acid, or marine acid, may be purified by thefe agents from all other metallic fubftances, and confequently may be refi¬ ned. Thefe operations are diftinguithed by proper names, as purification of gold by antimony, parting, concentrated parting, dry parting. The term refining is chiefly ap¬ plied to the purification of gold and filver by lead in the cupel. See Ores, RcduBion of REFLECTION, the return or progreflive motion of a moving body, occafioned by tome cbftacle which hindered it from purfuing its former direction. Circular Infrument of REFLECTION, an inftrument for meafuring angles to a very great degree of accuracy. It was invented by the celebrated affronomer Mr To¬ bias Mayer of Gottingen, principally with a view Pto do away the errors of the divifions of the limb 3 and has fince been much improved by the Chevalier de Bordjt, and M. .1. H. de Magellan. This inllrument is particu¬ larly applicable to the meafuring of the diftances of the heavenly bodies, and was uled by the French in their part of the operation for determining the difference of meridians of Paris and Greenwich. For the deferip- tion, rectification, and ufe of this inftrument, lee Navi¬ gation. REFLECTION of the Rays of Light, in Catoptrics, is their return, after approaching fo near the furface of bodies as to be thereby repelled or driven backwards. For the caufes of refledion, fee Optics Index, at Rays of Light, and RefeBion of Light, &c. For the appli¬ cation of the doftrine of reflection to minors, fee Op¬ tics. See alfo Mirror, BuRNING-Glafs, and Glafs- G RINDING ; and for the coating or foliating of mirrors, fee the article FOLIATING of Looking-glajfes, &c. See alfo Telescope. Reflection of Heat, fee Chemistry, N° 170. REFLECTION of Cold. For an account of this cu¬ rious phenomenon, fee alfo Chemistry, N° 272. It has been generally fuppofed that this fact w-as firft noticed by Profeffor Pictet of Geneva 3 but we have been informed from good authority (for w-e have not yet 3 REF [6 Redeclion yet liad an opportunity of feeing the book), that the !!' fame fact is diitinbtly mentioned by Bap lilt a de Porta Reflectors, pj|s J\,Jagia JSctluraHs. Reflection is alfo ufed, figuratively, for an opera¬ tion of the mind, whereby it turns its view backwards as it were upon itfelf, and makes itfelf and its own ope¬ rations the object of its difquifition 5 and by contem¬ plating the manner, order, and laws, wdrich it obferves in perceiving ideas, comparing them together, reafon- ing, &c. it tiames new ideas of the relations difcovered therein. See METAPHYSICS. Reflectors for Light-Houfes, have of late years been very fuccefsfuily adopted in-dead of coal fires. They are compofed of a number of fquare pane glafs mirrors, fimilar to thofe which, it is laid, were em¬ ployed by Archimedes in fetting fire to the Roman fleet at the fiege of Syracufe. The mirrors are an inch fquare, and are dilpofed clofe to each other in the con¬ cave of a parabolic fegment, formed of itucco, or any other fubftance wfliich retains them in their place. Stucco, however, is found to anfwer fufficiently well, and is employed in the reflectors of all the light-houfes which have been erefted round the coaft of Scot- V.nd. Tne parabolic moulds are from three to five or fix feet in diameter, and in the centre of each there is a long {hallow lamp of tin plate, filled with whale oil. There are fix cotton wicks in each lamp, nearly contigu¬ ous to each other, and lo difpofed as to Hand in no need of trimming for the fpace of fix hours. The light is re¬ flected from each mirror ipread over the concave fur- face, and is as it were multiplied by the number of mir¬ rors. Tin plate covers the back of the itucco mould¬ ing, from which a tube, immediately over the lamp, proceeds to the roof ot the light room, and anfwers the purpofe of a funnel, through which the imoke paiTes without fullying the face of the mirrors. The light- room is a lantern of from eight to twelve fides, entirely made of glais, fixed in frames of cait-irdn, and roofed with copper. The relief!ors with their lamps are placed on circular benches palling round the infide of this lantern, at about 18 inches from the glafs frames, fj that the concave furfaces of two or three of the re- ilecfors front every point of the compcfs, and throw a blare of light in ail directions. There is a hole in the roof, direftiy over the centre of the room, through which all the funnels pafs, and by which frefh air is alfo conveyed to the lamps. This light-room is fixed in fuch a manner on the top of a round tower, that no weather can move i.t ; and the number of the refieffors, and the height of the tower, are greater or lefs, according as the light is intended to be feen at a greater or lefs difiar.ee. It has been propofed to make the concave furface of the parabola one fpeculum of metal, infiead of covering it over with a number of plain glafs mirrors, or to di¬ minish the fize of each mirror, if they are preferred to the metallic fpeculum. It muft be obvious to every man who knows any thing of optics, that either of thefe alterations would be improper. The bright eft metal does not relief! fo much light as plain clear glafs, and if the fize of the mirrors was diminiihed, the num¬ ber of joinings would be increafed’, in each of which fome light is loft. 1 3 REF A man wholly guided by theory, would be ready to Reflectors condemn light-houfes of this defeription } becaule a ji violent ftorm will (hake the firmed building, which, in Rei°rm‘ , his opinion, would throw the whole rays of light into the air, and thus mifiead the bewildered mariner. Ex¬ perience, however (hows, that fuch apprehenfions are groundlefs, and that light-houfes with lamps and reflec¬ tors, are in all refpects preferable to thofe with fires burning in the open air. They are lefs expenfive; they give a more brilliant light, and are feen at a greater di- itance, and cannot be obfeured by firroke, or driven down on the lee-fide by the moft violent wind. If to- this we add, that the lamps do not ftand in need or trimming fo often as fires require fuel, and that the light-man is never expofed to the weather, we mull al¬ low that light-houfes with refledlors are not fo liable to be neglecled in ftormy weather as thofe with open fires, which alone muft give the former a preference over the latter. It has been affected, and particularly ffated, in the fupplement to the third edition ot this work, that Mr Smith of Edinburgh, the principal, and we believe now the foie contractor for managing and keeping in repair the light houfes round the coaft of Scotland, is the lint who conceived the idea of illuminating light- houfes by means of lamps and reflectors. We do not underftand that Mr Smith himftlf ever claimed the merit of this invention ; but it appears that reffedtors, fuch as are deferibed above, were invented by Mr Ezekiel Walker of Lynn Regis, who fays, in a letter dated Oc¬ tober 1801, and addreffed to the editor of the Monthly Magazine that fuch refledtors were made and fixed up under his direction, in a light-houfe on the coaft of Nor- * Vol. xiL folk, in the year 1779 ; and adds farther, that in the year?- 402* 17S7, at the requeit of the truftees appointed by adt of' parliament for eredting four light-houfes on the northern coaft of Great Britain, he inftrudled Mr Smith in this method of conftrudting light-houfes. Mr Walker’s ftatement of the fadt is confirmed by a letter from Mr Grieve, then lord prevoft ot Edinburgh, who informs Mr Walker that the truftees had agreed to pay the premium required for communicating the invention, and that Mr Smith was engaged to go to Lynn Regis to re¬ ceive inftrudtions from Mr Walker in the method of conftrudting the new reflectors. REFLEX, in Painting, means thofe places in a pic¬ ture which are fuppofed to be illuminated by light re- fledted from fome other body in the fame piece. See Painting, Part I. fedt. 2. and 5. REFLUX, the backward courfe of water, has the fame meaning as the ebbing of the fea, and is op- pofed to flood, flux, or the flowing of the fea. See Tides. REFORM means a change from worfe to better, a re-eftablifhment or revival of foimer negledted difciplir.e, or a corredtion of abufes therein. The term is much ufed in a monaftic fenfe for the reducing an order or congregation of religious to the ancient {’evenly of the rule from which it had gradually fwerved, or even for improving on the ancient rule and inflitution itfelf, and voluntarily making it more fevere. In this fenfe the order of St Bernard is faid to be only a reform of that of St Benedidt. In this country it is applied botk to politics and religion, and may innocently be applied tQ> Pi E F [ 072 ] REF to any endeavours to change an eftablithment from worfe to better. But it appears at prefent to have been chiefly made a pretence for deiigns which could not fairly or fafely be avowed. A reform in religion and in parliament (fee Parlia¬ ment), has, we know, been molt loudly called for by men whole religious notions are immenfely different from what has been generally reckoned chriffianity, and whofe defigns, as has been legally proved, went to the overthrow of all civil order. For infidious purpofes like thefe, the word reform is a good cloak, efpecially if any thing can be fixed upon, cither in the religion or government of the ftate, which, with the help oi exag¬ geration and diftortion, can be reprefented to the w’eak and unthinking as extremely defective and erroneous. The general error of thefe men feems to be, that having picked up a fet of fpeculative notions which flatter their own pride and the pride of thofe who liften to them, they will allow nothing to the arguments of their opponents or the experience of mankind. They think fo often and fo much upon their ideal reforms, that while they imagine their notions are liberal and ex- tenfive, they become contracted beyond imagination ; ■while their judgements, of courfe, are warped with the moft inveterate prejudices (fee Prejudice). They fee, or think they fee, the propriety of their fchemes ; but they feldom, perhaps never, refleft, that that may be true in fpeculation or in theory which cannot poflibly be reduced to practice. They will not take the world as it is, and allow it to profit by the wifdom and expe¬ rience of ages ; but they will reform it according to thofe ideas of right which they have learned from their own fpeculations and airy theories ; feldom confidering what may be done, they are determined to do what they think ought to be done. Liberty of confcience, and liberty of aftion, have been claimed by them as the unalienable rights of man j and fo we ourfelves are difpofed to think them : nor have w7e heard that in this country they have been denied to any man, or fet of men, fo far as has been thought confiftent with the fafe- ty of the ftate, and that of the other individuals who compofe it. At the fame time, the very fame men hefi- tate not to blame, with acrimony the moft violent, and to the utmoft of their power to reftrain, the aflions and opinions of thofe who, with equal convi&ion, often on better grounds, and generally with more modefty, differ from them. Amidft that exceflive ardour, too, with w-hich they propagate their opinions, they forget the extreme dan¬ ger of withdrawing the attention of that part of the community, who muft earn their bread by the fweat of their brow, from their proper occupations, to the tempeftuous fea of political debate, for which their education and mode of life cannot poflibly have quali¬ fied them. It requires but very little penetration, however, to be able to fee, that it can be of no real lervice either to the individuals themfelves, or to the community at large, in whatever light we look upon it. Indeed, to make thofe the judges of the law, and the reformers of the legillature, wdio have ail their lives been employed in manual labour, is the extreme of fol¬ ly ; and yet it is what Ibme men of confiderable abili¬ ties, and from whom we had. reafon to expeft better things, have more than once attempted. The cffetft of fuch a mode of feduclion, (and it deferves no better Reform, name), when it fhall become general, inftead of ferving the purpoles of a real reform, muft be to annihilate all civil order. Diffatisfaclion is the molt powerful check to honeft induftry j and diffatisfaftion and idlenefs muft be the effedl of the wandei ings of fuch men in the laby¬ rinths of politics 5 which, for uncultivated minds efpe¬ cially, paves the wTay for every fpecies of vice, and gradually ripens them for any wickednefs, however atrocious. For the-truth of thefe remarks, we appeal to the hiftory of mankind from the creation to the pre¬ fent time : and we would .ferioufly requeft the Joker friends of reform, and many fuch, we doubt not, there are, to refieel, that in the prefent day we have more to fear from licentiouinefs than from defpotifm ; from re¬ form carried to an extreme than from the pretended at¬ tempts either of kings or minifters to annihilate our real liberty. It may alfo be worth their while to confider, that times of public danger are not generally the belt adapt¬ ed to attempt changes of government ; becaufe what might fatisfy one party would probably be thought too little by another, and divifions at fuch a period are moft dangerous. When, therefore, attempts are made for re-' form which appear to be inconfiftent with the fafety of the ftate, reilriftions muft be ufed, which may by fpecu¬ lative men be thought fevere and unneceffary, but of which they themfelves are the caufes. Thefe re- ftridtions too will be patiently fubmitted to by the wifer part of the community, when in more peaceable times they would neither have been thought of nor al¬ lowed. Speculative reafoners may fpeak as much as they will of enlightening the minds of men, and of reform- ing government by the difiates of a refined and dlff paflionate philofophy ; but when they ccme to apply their notions to prablice, they will either find their re- prefentations little better than empty founds, and there¬ fore ineffectual ; or, as is more generally found to be the cafe, thefe fchemes which in theory appeared to be perfedl, will in praftice, when combined with the ma¬ lignant and ambitious paflions of men, lead to ruin and diforder. The firrt inftitulion of government, except among the Jews, was unqueftionably the effeCi of paf- fion and inlereft combined ; and this paffion and tin’s intereft, reftrained within due bounds, is productive of much happinefs. That government, we believe, too, will be belt fupported, and moft productive of happi¬ nefs, in which the mutual paflions and interefts of the individuals who compofe it are fo equally poifed as to fupport one another, and to promote each the ends and fuccefs of the other : and this by the ablcft reafoners and the belt men has been thought to be the cafe with the Britifh conftitution. If the modern favourers of reform fhould think this an unftable fupport, if they will confider the world as it ever has been, and as it is, they will find it the only one we have, except religion ; and they will thence be inclined to make the belt of it. If, after all, however, they fhould be difpofed to doubt the pofition, we have only further to requeft them, with the fincerity of men and of Chriftians, to confult their own breads, and ferioufly to confider the probable mo¬ tives of thofe who aft with them. They will then per- liaps fee, and they furely ought to acknowledge, that REF the whole world. Reforma- few men have a fled more according to the impulfe of , tlor1, paflion, intereft, and ambition, than thofe who have for * fome time paft founded the toczin of reform. REFORMATION, in general, an a