I 1 I, (5. ^ntXtxmn. 1X IXidvv ^nttrrsnn iWm-U, Hartford, Conn. ^ ( /'SfT ^^^ ^ ^ "^ ) Digitized by tine Internet Arciiive in 2010 witii funding from Research Library, Tine Getty Researcii Institute http://www.archive.org/details/buildersdictiona01toms I' Tr Farr' ////- TuK'^. ^o Sn^e// t/t^ Tarraj <^r to S/mJ: y ^rx^ T^'//ij J.^u^i/ .-('-C THE Builder's Di6lionary: ; O R, I Gentleman and Archited's COMPANION. Explaining not only the TERMS of ART In all the feveral PAkTs ofARCHITECTURE^ But alfo coiitaining the THEORY and PRACTICE Of the Various Branch 1-5 thereof, requifue to be known by " " PlaistererS, Painters, Glaziers, Smiths, | Alfo Neceflary Problems in Arithmetic,Geometry, Mechanics, Perspective' Mydrauucs, and other Mathematical Sciences. Together with TheQuantmes, Proportions, and Prices of all Kinds of Materials ufed in Building ; with Directions for Chafing, Preparing and U!ing th^m: The feveral Proportions of the Five Orders of Architecture, and all their Members, according to Vitruvius Falladio, Scamozzi, Vignola, M. Le Clerc, ^c. ' With Rules for the Valuation of Houses, and the Expence calculated o^ Ereaing any Fab rick. Great or Small. The Whole Illuftrated with more than Two Hundred Figures, many of them cunoufly Engraven on Copper-Plates : Being a Work of Xat Ufe, "°^ o"ly f° Artifxcers, but likewife to Gentlemen, and others concerned m BUILDING, i^c. 'juicrs, Pa khfully Digeftedfrom the mofl Approved Writers on thefe Su bjeBs. In TWO VOLUMr'^ "^ Masons, Carpenters, joiners, Bricklayers, Turners, Carvers, Statuaries, Plumbers, ^r; c.,, LONDON- Rer^: and S- Austen, at the ^.^./ and ^£/, in St.Paur^S^J'hrJl January ii. 173I0 WE have pernfid thefe Two Volumes of the Builder's Didionary, and do think they con" tain a. great deal of ufeful Knowledge in the Uuild'^ ing Buftnefs, Nicholas Hawkfmoor, John James, James Gibbs. / THE PREFACE. A RCHITECTVRE is one of thofe y% Arts which Neceflity has made univer- / ■ % fal : From the Time that Men firft felt / ^^ the Inclemencies of the Seafons, it had its ^^ ^ beginning ; and accordingly it has f pread wherefoever the Severities of the Climate demanded Shelter or Shade : It is to be traced in the Indian'^ Hut and the Icelander^ Cave; and ftill Ihews, in thofe barbarous Parts of the Globe, from what mean Original it rofe to its prefent Glory. As Diftrefs was the Parent of it, fb Convenience was the firft Objed it regarded : Magnificence and Decoration were the Refult of long Refinement, and de- ligned to flatter the Often cation of the Owners : Po- litenefs is but a more delicate Term for Luxury ; and was it not natural for Men to grow wanton with Eafe and Affluence, all the Sciences in general had laid in- active, nor ever ftarted into Being. "Tis eafy" to conclude from hence. That Convenience ftiould ftill be the Builder's firft View : Every Struc- ture is raifed to anfwer fome particular End ; and the moft obvious and fimple Means are always the bcft to obtain it. When fuch a Plan as this is uniformly and confiftently laid ; when all its Ufes may be compre- hended at a fingle Glance, and all appear undeniably realbnable and perfect ; then the Artift is at Liberty to add Grandeur and Elegancy to Strength and Pro- * priety, The PREFACE.. piicty, and finlfh the Whole with the full Splendor of Beauty and Grace. !By this Divifion of Archite6ittre into Beauty and tXlej. 4t will be demonftrable to every Reader, that 'tis partly an Art, and partly a Science ; that the firft is mechanical, and the laft the Refult of Genius and fu- perior Underftanding : One calls in all the Aid of Fancy and Imagination, grows poetical in Defign, and pitturefque in Decoration ^ the other lays down fix'd and ftated Rules, proceeds in the fame invariable Track of Reafoning, and comes always to the fame Conclufions. Hence it happens, that many an excel- lent Workman has proved himfelf a mere Mechanick, and many a furprizing Genius, that he was ignorant of the very Principles of the Art he made it his Pro- feflion to underftand. To make a thorough Malter, both muft be united ^ for the Propriety of a Plan is feldom attended to, and feldomer underftood ; and a glaring Pile of Beauty, without Ufe, but mocks the PolfelTor with a Dream of Grandeur he can never en- joy. The Defign of this DICTIONARY is chiefly for the AfTiftance of fuch, who ftudy the Mechanical Part of Building, and will be of the greateft Service to all Profeflions that have any Relation to it : The Elernents of the Art will be fully explained, and in fo regular a Method too, that it can hardly be in the Power even of a Novice to miftake. Neither is it impolTible that the moft linifh'd Artift, or moft per- fe^ Critick, (hould iland in need of its Help ; It will ferve, at leaft, as a kind of Remembrancer, or Com- mon Pi ace-Book, where all their Knowledge lies re- gularly digefted, and may be referred to with Kafe and Pleafurc. "^l^j^f '^ ''' To do this niore 'cnc£lually, all the valuable Au- thors, which iiaye wrote on the Subjed have been The P R E F A C E. examined, confultedj and reduced rnt6'W"ethod aiicl Coh- fiflency with each other : We may quote a great Va- riety of emiaent Names ; but as Le Qlcrc has been re- ferred to the mod, we fhall content ourfelves with his Authority only, and recommend the Steps he, in pkr- ticular, has pointed out, as the fureft Methods to attain to any Degree of Perfedion in this Art. Arithmetick is the firft, as being the Ground- Work of Menfuration, either as to Extent or Solidity, as being the Medium of all Calculations, and the only Road to any Degree of pradical Knowledge in the Mathematicks : For thefe Reaibns, we have made no Scruple to add all the neceffary common Rules, and fome brief Examples for the Extraction of the Square and Cube Roots; as likewife the Ufe of feve- ral InRruments; fuch as Meafuring by Scale and Com- pafs, the Ufe of Gunters Line, Sliding Rule, ^c. Under this Head too we have added various Tables for calculating the Value of various Kinds of Work belonging to Building, according to their Dimeniions, and at feveral different Prices: Which, though no Way of a Piece with the Theory of this Art, are of no fmall Ufe in the Pradice. Geometry follows in the next Place, and is in- deed the Foundation that all Students muft build up- on, fince 'tis impoflible to attain to any PeifeClion in ArchiteBure without it : -"Tis Geometry that lays down all the firft Principles of Building, that adjufts all Bearings and Proport'ons, and meafures Points, An- gles, and Solidities. In ihort, there is no being a Ma- fter of Architefture, wit^hout being perfed in all the Parts of Geometry \ and he that is fo, though he may err in' Decoration, can never do the fame, cithei in Strength or Proportion. To anfwer this important Purpofe, we have not only inferted all fuch Articles of Geometry a« are neceflary to be known by the Archi- The FK E F A C E te^, but even fach as may be of Ufe to CarpenterSj Joiners, Maibns, &c. containing, at once, the Defini- tions, TheoremSj Problem.^, and their Denionftrations ^ ana likewife the^'engrav'd In eprefentations of the Fi- gures To defined. And htnce, we flatter ourfelves, the yoiiiig Practitioner v,'iil be much better able to form his Models, by making himfelf Mailer of thcie Rules, than by the jtiiolt reafonabte Notions which may refulc from his own uncertain fancies and Conjectures. Masonry, or the Mechanical Mcjns ot railing Perpendiculars, turning Arches, ercctin;-!, Bridges, and forming Stair-Cafes, is -""nother Branch of this Art, and niufl be underiLOod with great Accuracy and Readi- nefs J as being the Execution of the Whole which th^ Student dcfues to learn. On this Head, therefore, we have colleded the belt Ihftrudliions to be found, from heaving the Stones out of the Quarry, to their Ar- janeement in the Structure ; and in rcf2,ard little is to be found on Bridges in Vitruvms^ or, befide VaUad'to^ in almoft any of the modern Architeds, we have gi- ven an Extraft from a French Treat t/e of Br'tdigesj publillied by M- Qautier^ Architect and Ingineer to Lewis the Fourteenth, LEyit-LiNG^ and HydRaulicks, are likewife of great Importance to the Builder: The firft at once enabling him, to underftand good Situations, or amend them if ihey are otherwife: And the laft^ of courfe, direding the Conveyance of Water, the Draining of low Grounds, and teaching the whole Secrets of colledling Refervoirs, or afterwards employing them to the beft Advantage. In fhort, on tfcefe depend both the ne- ccfTary Ufe of Water for Family- Supply, and alfo all the beautiful Effecls that can refult from it in Gardens, by Bafbns, Fountains, Cafcades, ^c. On this Head, we have added a Delcription of the moil ufeful Inftruments for thefe Purpofes, as iikewife The PREFACE. likcwife the moR appioved Methods of empjQving them to Advantage. ^ i/ .Ssx Mechanicks is another Eflcntial in this noole Art?> 'Tis by undevftanding their Power and Ejffed, that ^ fuch Machines are contrived, as alone are able to raife up the heavy Materials to Buildings of any confidefa- ble Height, or empty Waters from a Bottom, or drain a Level, or force them upwards, as Art would diredl:, or Necellity require. And to anfwer thefe Purpoles the better, we have not only annexed Definitions, Theorems, and Problems, which are the Fundamen- tals of this Study, but have likewife added Plates, with explanatory Figures, for the greater Eafe and Facili- ty of learning the Mechanical Powers, the Balance, Lever, Pully, Screw, Wheel, and Wedge. Thefe, with the Art of Sketching and Drawing, are all the diiferent Branches of Study which are ne- ceffary to form a Compleat Mechanical Architects But when he is thoroughly initiated in them all, fo as not to err, even in Principles or Pradice, if he canngt add as much Knowledge rnore of his own, in their Uic and Application, he will be fit for nothing more than the Overfeer of a Work, or a Judge of the mere Methods to carry on and finilh the Whole. The Science of Designing isflill wanting to form a Great Mailer, or produce luch Plans as would vie with the antient Beauties oi Greece and Rome. But if this is not in the Genius, it is never to be learned ;, To be able to enter into this Secret, the Student muftv have great natural Parts ; a noble and fruitful Imagina^^, tion, a thorough Infightand Acquaintance with Beauty,' and Judgment fedate and cool enough to form ajult arid delicate Tafte. V¥ithout Tafte, even Genius itfelf wahi^ ders blindfold, and fpends itfelf in vain. Genius is^; indeed, the firlt Quality of the Soul ; but Tafte muil beaddedj or we ihall cenfurc the Wildneis, inftead of The PREFACE. | admiring the Beauty; we fiiall be difTatisf/'d with 1 the Irregiilaricy, inftcad of being pleafcd with the Magniticcnce. \ '■■ But though Genius cannot be learn *d, it may be ' improved : And though theGIfc of T^efign'ing is born with a Man, it may be methodized by Study and Obfervation. The principal Points, therefore, that the ^ejigner Ciould have in view, are iirft Convenience, as has been hinted already, and then Beauty and Magnificence. With regard to Convenience, few Diredions can be gi- ven, fince it means no more than contriving all the Re- quifites belonging to your Plan, in the nioft clear and elegant Manner, and then laying out the Space they are to be ranged in with the moft perfed Order and Oeconomy. As to Beauty and Magnificence, they are Themes never to be exhauftcd \ and though many . Volumes have been written on them already, as many more might ftill be added. Simplicity is generally underftood to be the Groundwork of Beauty, and Decoration of Magnifi- cence. 'Tis certain, the fewer Parts a Building is compofed of, if they are harmoniz'd with Elegance and Proportion, the more beautiful it appears : The Eye is beft fatisfyM with feeing the V\ hole at once, not in travelling from Objed to Object; for then the Whole is comprehended with Pain and Difficulty, the Attention is broken, and we forget one Moment what we had obferved another. - ,/,But a Contraft of F'tgttre muft be preferved even in the Midft of this Simplicity. ■'Tis in Build- ing, as m Mufick ; the Parts are various and difagreeing in thcmfelvcs, 'till reconcil'd by the Skill and Judg- ' mcut of the Mafter. A Samenels of Form betrays. ^ A Poverty of Imagination ; and is the fime in Archi-'; tedure^ as Dulnefs is in Writing : The Mind is glutted r:<; J with Thf ,,P R ,E. F ACE. with it inftantly, and turns away diflatisfy'd. ■ Itis therefore a principal Thing to be regarded by the Stu- dent, to delign limply and varioully at the ikmt Tyne, and Beauty , will infaliibiy be the Refult of the Whole. ;^-i P.sRSPECTivE is another grand Ptirt of Defignlng^^' which demands the Matter's moft critical Regard, in as much as nothing contributes more to Grandeur and Beauty, if well underftood ^ and nothing is underftood with more Difficulty or Study. By Perfpedive, is commonly meant the thorough Infide Profpect of a Building : But if it cannot be applied with Propriety to the Art, we would take the Liberty of fubftituting the Painters Word Keeping in the Stead of it. For in all Buildings, as in Pictures, there muft be one principal Figure, to which all the others muftbefub- ordinace ; and from whence you muft fet out to examine the Parts, and to which you mult return to determine of the Whole. Decoration, or Choice and Difpofition of Orna- ments, is the laft grand Rcquifite to make a compleat Architect: And this depends partly on Genius, and partly on Fancy ; but both muft be under the Con- dud of the fevereft Judgment and exactcft Tafte. In Ihort, all Ornaments are ill-placed, that may bcfpar'd without being miffed j as all empty Spaces are abfurd," where Nakednefs hurts the Eye, and Propriety would admit of Decoration. ' a We can't fufficiently recompiend to all Perfons,/* who build fumptuoufly, to calculate their Buildings according to the Point of Light from whence they are to be viewM : If they may, or ftiould befeen from tar, their Parts ftiould be fimple, great, and noble ; if the Prolpect is near, the Workmanfhip ftiould be neat and little, that it may be fecn and underftood, as the Na* ^ ture_jQf.^s,S{ii;^ia;ioihwin ^i;yj?.Lcav;e^. ;i ■ - , Upon The PREFACE. Upon the Whole, nothing but Nature, and a long Study of the antient and modern Strudures, will en- rich the AJind lufficiently to excel in this noble Art ; and this T>i5iionary will be found a proper Ke)^ to explain their Beauties, as well as a needful Caution to avoid their Defeds. To conclude; We have nothing more to add, but our grateful Acknowledgments to thofe Gentlemen! and Artifts, who have favoured us with their Affif- tance in this ufeful Undertaking ; and that we hope our Labours will lie fecure from Cenfure at leaft^ if they may not be judg'd altogether worthy of Ap- plaufe. ^'ireBions to the Binder, Vol. I. Pinte I. II. at the End of Sheet K, facing it. III. in Sheet P, facing Chissel,: IV. in Sheet V, facing Doors. V. in Sheet Z, facing E A. VI. In Sheet A a, facing Fluids. VII. ill Sheet Bb, i\c\xs%Vttlgar Fractions, VIII. in Sheet Ee,facingGRATi- CULATION. IX. in Sheet Ee/acingGRAViTY X. \w Sheet Ff, facing Groin. XI. inShcet G g,tacing Hip-Rcof yA\. in Sheet G c, following Plate XI. XIII. in ^\\Qti li, at the End. XIV. in Sheet I i, at the End. XV. in Sheet I i, at the End. for placing /^^ Plates. Vol. II. XVI. in Sheet H, facing Orle. XVII. in Sheet I, facing Para- BOLICK. XVIII. inSheetK, facing Per- sian Order. XIX. inSheeiM, facing Point. XX. in Sheet N, facing Pump. XXI. inSheetN,fac. Quadrant. XXII. inSheetO, facing Rides. xxni. XXIV. XXV. XXVI. in Sheet P,facingRuDENTURE. XXVII. in Sheet S,facingSTEPS. XXVIII. in Sheet Y,' facing Triglyphs. XXIX. in Sheet Bb, facing Va^ GIN A. XXX.inSh.Cc/ac.WAiNSCOt XXXI. in Sheet Dd,fac.WATfcR XXXlI.inSheeiGg,fic. Wedge XXXIlI.inSheet Gg,f.WiNDMiL * Place facing Triangle. THE I THE NEW B u I L D E r' s Dmiomry : O R, Gentleman's «/?^ Ar chited's COMPANION. A B ABACUS [h Latifi of 'A3a5, Gr. which h'gni- fies feveral Things; as a fqu.ire Trencher, and fometimes a Cup-board, b'f.] But in Architedture,/^^'^^ z^3t ot axa'a, Gr. to hear] the DoClrine or Theory of Sounds. Dr. Hook fays, it is not impof- fible to hear the lowelt Whifper that can be made to the Dilbnce of a Furlong ; and that heknows a Method to hear any Perfon fpeak through a Brick Wall of three Foot thick. See l^'hifper- im-Plice. ACROTERIA 7 [AKpoT>ip/«of ACROTERESS ^npo?, Gr. the Extremity of any Thing] fmall Pedellals, ufually without Bafes, placed on Pediments, and ferving to fupport Statues. Thofe at the Extremes ought to be half the Pleight of the73'»2- panum^ and that in the Middle, according to f^itruvius^ one eighth Part, or more. ACROTERIA aHb are fome- times ufed to fignify Figures, ei • iher of Scone or Metal, placed as Ornaments or Crownings on the Tops of Temples, or other Build- ings. Someiimes the Name is ufed to (ignify thofe fliarp Pinacles or fpiry Battlements, which Itand in Ranges about flat Buildings, with Rails and BalluAcrs. A D ACUTE Angled Triangle, is one whofe three Angles are all alike ; and is alfo called an Oxi- gonoub Angle, as in the Fi- gure. ACUTE Angular Seftion of a Cone, a Name by which An- tient Geometricians called the Ellipjis. ADJACENT Angles are made by continuing out one Side of an Angle ; whence ad)acent Angles are contiguous, but not on the contrary. ADIT, the Shaft or Entrance into a Mine. ADYTUM f'ASJlopofaPriv. and Sua), Gr. to enter] a fe- cret or retir'd Place in the Pagan Temples, where Oracles were given ; and into which, none but the Prielts were permitted to en- ter; in Imitation of the SanBum Sancl'jrum of the JeUi'tp Tem- ple, AERIAL, confifting of the Air, or fomcthing that has a Re- femblance to it. AERIAL "PerfpeSi'tve, is that which is reprefented both weak and diminim'd, in Proportion to theDiliance from the Eye. It is founded on this. That the longer a Column of Air an Ob- jcdl A G A L j.e£t is feen through, the weaker do the vifual Ra) s emitted from it afteft the Eye. The Objed of Aerial Perfpec- tive is chiefly Colours of Objeds, whole Force and Luftre it takes off more or lefs, to make them appear as if more or lefs remote. AGEOMETRICAL, Un- geometrical, or defeSive in Point of Geometry. AJUTAGE [inHydraulicks] Part of the Apparatus of an ar- tiiicial Fountain; being a fort of Jet cVeau^ or kind of Tube fit- ted to the Mouth or Aperture of a VelFel, through which the Wa- ter is to be play'd, and by it de- termin'd into this or that Form or Figure, ALABASTER, a Kind of Stone Ibfter than Marble ; but harder than Plailter o? 'Paris-, if it be fofoft, as that it can be cut, it is called Gypfurn. It is found or digged in the/z?- dies^ JE^ypt^ Syria, &c. There is aUo ibme found in Lincoln- (bire and Staff or djhire. It is found of feveral Colours; fome extreamly white and fhi- ning, which is the moft com- mon ; fome red, like Coral ; and fome of the Colour of the O- nyx ; which thence is called Onyx-, though it differs very much from it in Nature or Qua- lity. Its Ufe Is chiefly in making Monuments in Churches, ^r. where there are many Figures in Relief, or Bafs-Relief, ^c. car- ved : It is alfo ufed for carving Coats of Arms cut in Relief, to be fet in Brick or Stone in the ,Fronts of Houfes. Alabaftercuts veryfrnooth and «ft{y, and is much ufed by Scul- ptors fn making Jittle Statues Vafcs, Columns, ^c. It is alfo ufed like Plainer of Paris, being firit burnt and cal- cin'd; then mix'd up with Wa- ter to a thin conlillence ; which being afterwards cad into a Mould, it very readily coagu- lates into a folid Body. ALCOVE loiAkoba, Spani/ky of Elkans, Arabick, a Cabinet ;or of Elcobat, a Tent, pr Place to lleep in] is a Recefs or Part of a Chamber, fcparated by an Ef- trade or Partition of a Column and other correfpondent Orna- ments ; in which is placed a Bed of State, and fometimes Seats to entertain Company. The Bed is frequently raifed up two or three Afcents, with a Rail at the Feet. Thefe Alcoves are fre- quent in noble Houfes in Spain^ and other Places. ALDER is an AquatickTree, too well known to need any Defcription. In former Times, large /f/- ^/c-rj- were ufed for building Boats; and now they are very much eflcem'd for fuch Parts of Works which lie continually under Water ; where it will be- come as hard as Stone; but if fui^er'd to lie fome Times ex- pos'd to the Weather, and at others to lie under theGroundirn watry Places, it will decay in a little Time. We are informed hy Fitruviur, that the AhraJJes about Ravenna in Italy^ were piled with Alder Timber, in order to biiild upon; for which Ufe he highly com- mends it. And the Riaho, that famous Bridge at Venice, which pafies over the Grand Canal, and bears B 3 a vaft A L a vaft Weight, is built upon Piles of this Wood. Trunks of Trees or Poles of this Wood, are exrranrdinary utefal in making i-'umps, VVutcr- Pipes, cj^f. They are ufed (in the Coun- try) for Waier-Pipes for the Conveyance of Water through Bays and Dams; and a'fo tor Water-Pipes for conveyii,g Wa- ter from any Spring, to fupply a Honfe with it; and large Poles or Trees of this Wood are ufed for Ground Guts, for conveying Water out of Stews. Thefe Poles are about eight or ten In- ches diameter, and the Cavity in them about four, or four .and a half; for boring and fitting up of which Size, they give about 3 J. 6d. f:r Rod for Workman lliip. But for Water-Pipes , the Poles need not be above four or five Inches diameter, and the Cavity about an Inchand quarter, or an Inch ancl half diameter. jis to the Method of boring Alder Poles, Thefe Poles being laid on Horfes or TrefTels of a fit Heighth, to relhhe Augur up- on while they are boring, they fet up a Lath, to turn the lealt End of the Poles, to fit them to the Cavities of the great End of the others : The Lath being fct up, and the Poles cut to the Lengths, they will conveniently hold, Tiz.. eight, ten, or twelve Foot. They turn the Imall Ends of the Poles about five or fix In- ches in Length, to the Size they intend to bore the bigger Ends, about the fame Depths, viz. five or fix Inches (this is defigned to make the Joint to fliut each Pair A L of Poles together, the concave Part being the Female Part, and the other Part, the Male of the Joint.) In turning of »he Male Part, they turn a Channel in it, or afmallGroove at acertain Dif- tancc from the End ; and in the Female Part, they bore a fmall Hole to fit over this Channel. I'his being done, they bore the Poles through ; and to prevent tnem from boring out at the Sides, they fiick great Nails at each End, to be a Guide to them in boring Itrait through; though they ufually bore them at both Ends ; lb that if a Pole be crooked one Way, they can bore it through, and not fpoil it. The Poles being bored, they form them into Pipes in the Grcmnd ; in order to which, they dig a Trench, and prepare it with Clay, to ram them in the Female Part, which is firft bound with an Iron Ring round it, to prevent its Splitting, afterwards !] they drive in the Male Part till the i GrooveinitisjullundertheHole; i' and pour melted Pitch hot into the j Hole, in the Female Part, which ! will flow round in the Groove i which was turned in the Male i Part : By this Means, the June- ! tures are render'd very (launch and clofe ; and in this Manner they proceed till they have laid all the Poles or Pipes in their Order. As to the Charge of prepa- ring thefe Pipes : For the Woik- manfhip only, they ufually re- quire about 2X. 6d. or -^s.per Rod, IS. for boring and fitting then\; but the Charge of all the Worlt. and Materials, Boringy Digging the Trench, L(2v/»j^ and Ramming in the Clay, k^c and alfo A L A L alfo the Charge of the 'Pohs^ Clay., Pitchy and Iron Ri»^s^ will amount from ds. to 6s. per Rod, according as the Materials can be procur'd. ALGEBRA is a Method of refolviug Problems by Means of Equations. ALIQUANT P^r^ [iitJnd- metick] is that which cannot meafure or divide any Number exaftly; but that there will be at laft fome Remainder ; as 5- is an Aliquant Part of 12; for being taken twice, it falls fhort, and if taken three Times, it exceeds 12. MjlQlJOTPart [i-a Artthrne- iick'\ is fuch a Part of a Number as will meafure it exa6fly without any Remainder, as 3 is an Ali- quot Fart of 9, and 4 of 12. ALLEY [in Perfpeaive~\ is that which is larger at the En- trance, than at the IfTue ; to give it a greater Appearance of Length. ALTERNATE jln^rUs are the internal Angles made by a Line cutting two Parallels, and lying on the oppofite Sides of the Cutting Line ; the one below the firft Parallel, and the other above the fecond, as the Angles E and D and F and C. ALTERNATE Proportion, or Ratio.^ [in A7jthm$U(k^'\ is the aflTuming an Antecedent to an Antecedent, as the Confe- quent to the Confcquent ; as if A B, CD, then by alternate Proportion, will AC, BD. ALTERNATION is ufed by fome for the ditferent Chan- ges or Alterations of Order in any Number of Things pro- pofed. This Alternation is eaiily found by only multiplying continually all the Numbers, begining at U- nity : As fuppofeitbe required to know how many Changes can be rung upon five Bells; you need only writedown 12345', and then multiply all thofe Numbers continually one into another, ond the laft Produdt will be 120, the Number of Changes. ALllMETRY [of ^//^ high Things, and metiri to meafure"] the Art of taking or meafuring of Altitudes or Heights, whe- ther acceffible, or inacceffible. ALTITUDE, the third Di- menlion of Body ; called alfo Heighth, or Depth. The A L T I T U D E, or HEIGHTH of Figures, is the parallel Diflance between the Top of a Figure and the Bafe, So the Heighth of the Trapezium C E FH IS the Perpendicular CD ; B 4 ' becaufc A M becaufe it is in the ncareil Dif- tance between the parallel Lines AH, the Top, and F D H, -:,? BaG.-. And it is the fame ot orhcr Figures ; as a Triangle, }-Iexa^on, ^c AMBLYGONIAL [in GeoMciry^ Obtufe- Angular. AMBLYGONOUS A»gU, h an Obtufe Angle, or Angle confifting of more than 90 De- grees. AMPHIPROSTYLE[in ArJtie-tit ^rch'ttedure~\ a Kind of Temple which had four Co- lumns in the Front, and the fame Number in the Face be- hind. AMPHITHEATRE [of Ajx^jfiearponof 'afjttpi'. on both Sides, and 8£aoM.««- 1 i)chold. Gr.] and ts a fpacious Edifice or Build- ing Ml cither a circular or oval Form, having its Area encom- pafled with Rows of Seats ari- fiii'j; gradually one above another; where Spcdators might fit to behold Spcftacles, as Stage-Plays, C .nihats of Gladiators, and thofe of wild Beafts, z^c. The Theatres of the Antients were built in the Form of a Semi- circle, only exceeding ijuft Se- micircle bv one fourth Pirt of the Diameter; and the .'imphltbeatre is nothing elfe but a double Theatre, or two Theatres join'd together ; fothat the longeft Dia- meter of the Amphitheatre^ was ' TO the fhortell, as One and a half to One. The Amphitheatre of yefpa- fittf, caird the Colifccum^ that at Verona in Itals^ and that at Nlf- r/fes in Lafiguedoc^ are the moft celebrated that we have now re- maining of Antiquity. A N Plinv makes mention of an Amphitheatre built by Curio^ which turned on large Irni Pi- vots ; fo that of the fame Am- pnitheatre, two I'cvcral The.ures were made occnfionally, on which ditKrent Entertainments were exiiibited at one and the fame Time. ANABATHRUM ['Avr.Ca- fipsn of civxSulvw to afcend, G>.] a Place that is afcend -d to by Steps. ANALOGY [in Geoynetry, C5f f .3 is the Comparifon of feve- ral Rations together; and is the fame as Proportion. ANAMORPHOSIS, or Mm^ JlroHS Projeilion of an Image ^ [in 'Perfpedive^'] is the Deiorimnon of un Image on a Plane, or the Superficies of fome Body, which feen at a certain Diftance, wiil appear formous. If it be required to delineate a monjlrous Prsje^ion on a Plane, proceed thus ; B Firji^ Make a Square A B C D, (called' the cratkular Proiolype,) of a Bigncfs at Pleafure, and di' vide the Side AB into a Num- ber of equal Parts, that fo the faid Square may be divided irto a Number of Areola's, or klTer Squares* Secondly^ A N A N Secondly^ In this Square let the Image, to be reprcfcnted de- form'd, be drawn. i\\\ i- f Thirdly^ Draw the Line <7^=: AB, anii divide ir inio the laiiie Num.>er of eanal Parts as rhe Side, (if the Protolyjje A B is di- vided. Fourthly^ In E, the Middle thereo., cre(ft the Perpendicular E V, fo much the longer, as the Deformation of the Image is to be greater. Fifthly^ Draw VS perpendi- cular to E V, fo much lels in i/eng.th. Sixthly^ From each Point of Divilion, draw (Irait Lines to V, and join the Points a and S, as alfo the Right Line aS. Seventhly^ Through the Points ^i^ift^-t ^raw Right Lines pa- rallel 10 ab\ then will lof /IkkuIus ANNULETS^ aRinK,L.] are fniall Iquare Members in the Doric Capital, under the Quarter- Round, ^c. Annulets are ufed in Archi- tecture to fignify a narrow, flat Moulding, (of which Ice Capi- tal \) which is common to divers Places of the Columns, as in the Bafes, Capitals, ^c. It is the fame Member which M. Mauclerc^ from yitruvim^ calls a Fillet ; and Palladia, a Lifiel, or C injure ; and M. Brown, from Scamozzi, a Super- (ilium, a Liji, Tinea, Eye-brow^ Square, and Rabit, ANTA [in Architedure'] is ufed by M. Le Clerc for a kind of Shaft of a Pilafter, without Bafe or Capital, and even with- out any Moulding. ANTjE, Pillars adjoining to a Wall. Vide TaraC^atce. ANTE-CHAMBER 7 An ANTI-CHAMBER 5 outer Chamber, before the principal Chamber of an Apartment, where the Servants wait, and Strangers flay till the Perfon to be fpoken wichal is at Leifure, efr, 2. As to its Proportions.^ A well-proportionM A'/zte-Chamber ought to be in Length the Dia- gonal Line of the Square of the Breadth, and not to exceed the 13read and half at moft. 3. As to their Height. "^ They are made either arched or flac ; if they are flat, their Height ought to be, from the Floor to thejoilts, two third Parts of their Breadth. Bat if you have a mind to have it higher, divide the Breadth into icvca Parts, and take five of them for the Height. Or eife divide the Breadth into four Parts, and take three of them for the Height. In large Buildings, the Ante- Chamber, Hall, and other Rooms of the firft Story, may be arched, which will render them hand- fome, and lefs fubjcft to Fire : And in fuch Buildings, the Height may be five Sixths of the Breadth, from the Floor to the Bottom of the Key of the Arch. But if this Height fliall be thought too low, you may make the Height feven Eighths of the Breadth. Or it may be elevea Twelfths, which will render it yet more lately. 4. Of their Situation. ~\ Ante- Chambers, &c. ought to be fo fi- tuated, that they may be on each Side of the Entry, and of the Hall: And this likewife ought to be obferved, that thofe on the Right Hand may anfwer, and be equal (or nearly fo) to thofe on the Left ; to the End, that the Buildings may, on all Sides, bear equally on the Roof. Sec Halls. ANTERIOR, before another, in refped to Place; in which Senfe the Term Hands oppolite to Pofterior. ANTiCK [in Sailpture and Painting'] is ufed to tignify a confufed Compofure of Figures, of different Natures and Sexes, ^c. as of Men, Beafis, Birds, Flowers, Fifhes, zsfc. And alfo lach-like Fancies as are not to be found in Nature. It would be tedious to enume- rate all the/^»;?V^ Forms and Fan- cies by which the Heathens re- prefented their feveralGods, and their Poets, Painters, and Scuip^ tor* defcribcd them. They A N A P They had alfb ftrange and monftrous Figures of human Creatures, (and lo reprefented them in Sculpture, ^c.) as of Centaurs, half Men and half Horfes; Sagitaurs, half Men and half Bulls ; Syrrns, or Mermaids, half Women and half Fifl-i; Har- pies, half Women and half Birds; Griffins, half Beads and half Birds; Dragons, Fart Serpents and Part Birds; theSpread-Eigle with two Heads; and many other of the like Nature. Thev alfo reprefented divers forts of Flow- ers and Fruits growing on the fame Plant, ^c. and many fuch like Fiftions, which we have rca- fon to believe are not to be found in Nature; though the Belief of their Exigences hath been propa- gated by Poets, ^c. upon ac- count of their Fitnefs to be made ufe of in the Wav of Similitude. Thefe Sorts ofReprefentations the Italians call Grotefca^ and the French Grotefque ; which ilgni- fies comical, pleafanr, apt to make one laugh; alfo ridiculous; and their Word Grotesques l]g- iiifies idle, fooliili Fancies. ANTICUM, a Porch before a Door, a Fore-door, a Hatcb^ "ANTIPAGMENTS, Orna- ments or Garnilliings in Curv'd Work, fet on the Architrave, (Jaumbs, Ports, or Puncheons of Doors,) whether of Wood or Stone, after the Lati-a antique Word Antipazmcitta. ANTK^UE, Fimething that is ancient. 'Fhe Term is chiefly ufed by Architects, Sculptors, Painters, l^c. who apply it to fuch Pieces of Architedure, Sculpture,P.iint- JiiS? ^^'- *s were made at the Time when their Arts were in their greateft Perftdion among the antient Greeks and Romans^ Tiz. between the Time ot /Alex- ander the Great^ and that of the Emperor Pbjcas^ when Italy be- came over-run by the Goths and Vand.ils^ about the Year 6co, a- boui which Time the noble Arts were extinguilli'd. Fhus we fiyan Antique Build- ings or a Building after the An- tique ; an Antique BuJ}^ or BafsRc lievo^ Antique Manner^ T^ft^-, ^'-C. ANTIQUE, is fometimes e- ven contradiflinguifhed from An- tient^ which denotes a lefTer De- gree of Antiquity, when theArt was not i:i its urmoft Purity. Fhus Antique Architedurc is frequently dillinguilhed {xom An- tient Architeiture. Alfo fome Writers ufe the compound Word ANTIQUO iVlODERN, in fpeakir.g of old G'o//?»;V Churches, to diflinguiOi them from thofe of the Greeks and Romans. APHRTIONS 1 [from the APERTURES.S Latin a- perio^ to open, lignitiesOpenings.] In Architecture the Words are ui ; or of the third and fourth Point, A R A R Point, as fome Workmen call them ; thoiif^h the hultans call thcin Di 'Terz'j and Jh-iarto /huto^ bccaufo they ;ilvvays meet iu an Acute Angle at the Top. Scmcircular Arches^ are thofe Arches which are an exaft Se- micircle; and have their Center in the Middle of the Diameter, (or Chord of the Jrch^') or the Ri.^ht Line that may be drawn betwixt the Feet of the Arch, Of this Form the Arches of Bridgc:s, Windows of Churches, and i;reat Gates, arc fometimes nude in modern Buildings. Scheme or Skeen Arches^ are thofe which arc lefs than a Jjemicircie, and confcquently are flatter Arches^ ct>ncaiuing fome 90, fome 70, and others 6q De- gnes. Semic'.rctilar^ are eafily difiin- giillicd from Scheme Arches by this ; That the Chord ("or Right Line) drawn between the Feet of a Semicircular Arch, is juft double to ics Height, (bLingmea- fured from the Midale of the Chord to the Key-Piece or Top of the Arch;) vVhereas the C/:;or^ of a Scheme Arch of 96 Degrees will be more than four Times its Height, and thi.- Chord of a Scheme Arch oi 6d Degrees will be more than fix Times its Height. The I'lmons Albcni, in his Ar- ch'itedtira^ fays as follows : III all Openings \i\ which we make , Arches, we ought to contrive to have tiie Arch never lefs than a Semicircle, with an Addition of . the fevcnth Part of half its Dia- r merer ; the moll: experienced Workmen having found that//rf/:> to be by much die b.lf adapted • f >r enduring, in a manner toPer- pef^ury; all oihec Arches being Vol. L thought lefs ftrong for fupport' ing the Weight, and more liable to Ruin. It is alfo thought that the half Circle is the t)nly Arch that has no Occalion either for Cnain, or any other Fortification; whereas all others arcfound either toburll out, or fall to ruin by their own Weight, it they are not either chain'd, or fome Weight be placed againft them for a Coun- terpoife. I will not here omit ((ays he) what I have obferv'd among the Antients, a Contrivance certainly very excellent and praifc-worthy : Their befi; Architeds plac'd thefe Apertures, and the Arches of the Roofs of Temples, in fuch a Manner, that even though you took away every Column from under them, yet they would ftill ftand firm, and not fall down, the Arches on which the Roof was placed being drawn quite down to the Foundation with wonderful Art, known bat to a few : So that the Work upheld itfelf by being only fet upon Arches \ for thofe Arihes having the folid Earth for their Chain, no wonder they Hood firm with- out any Support. Arches of the third and fourth Point. Thefe confift of two Arches of a Circle meeting in an Angle at the Top, and are drawn from the Divifioii of a Chord ni- to three, or four^ or more Parts, at Pleafure. Of this Kind are many of the Arches in old Gothick Buildings; but on account both of their Weaknels, and IJnfightlinefs, they ought, in the Opinion of Sir Henry i^^otton, to be tor ever ex- cluded out of all Biii'dings. C Elliptical A R A R Elliptical Arches. Thefe Ar- ches Coll lilt of a Semi- Ell ip- fis, and were formerly inucli iis'd iiilicad of Mantle-Trees in Chimneys. They are, com- ifionlydi-fcribedonthree Centers ; botth-y may be drawn otherwife : Thefv.- conlill of three Parts, 'oiz. two blanches^ and w 'Scheme. E.ich End of thefe Arches are called i/d»f/j;eibyVVorkmen ; and ihefe Hanches are always theArches of Circles, fmall.r than the Scheme.^ which is themiadle Fart of th^^fe N. B. That each other Courfe in thefe Arches, confuts of two Stretchers^ which arc feven In- ches long each, (when the Arch is fourteen Inches deep,) and the other Courfes betwixt thefe of three Headers^ and two Clofers ; the Length ot the Headers ought to be three Inches and a half, and i\\iiClofers one Inch and three quarters : Tnus one Courfe of the Arch will be divided into two Stretchers ; and the other aUernutely into three Headers^ Arches, and conlllls of a Part of and two Clofers throughout the a larger Circle, which is drawn whole Arch betwixt the two Haaches.io con- join them all together, in order to make, as it were, one Ihliacal Llne^ and confequently, an El- liptical Arch. To thefe Arches there arc commonly aiL^^'-iVo»£' and C^^/*- trels : The Key- Stone is that ■which is the very Summity or Top of the Arch, and is equal- ly ditfant from both Ends ; and the Breadth of this Key-Stone at the Top, ought to be equal to the Height of the Arch (which is ufually about fourteen Inches, "when made of Brick ;) and J//«z- tncr^ (or Point with tw^o Edges, to the Center of the Scheme.) How to defcribe an Elliptical Arch to any Rife or Width, by the Interfedion of Righr L'nes. Firlt draw tne Line AB, then draw BC perpendicular to AB, and as high as you defign the Arch fhall rife, and draw the The Key-Stone ought to be fo Line CD parallel to AB, which much without the Arch, as the Chaptrels projciSl over the "Juumhs. The Chaptrels.^ I fuppofe to be the fame that moft Architects call Impolls ; and 'tis thofe on which the Feet of the Arches divide into two equal Parts at E ; then divide AC and BD into any Number of equal Parts ; al- fo CE and ED into the fame Number of equal Parts, and draw Right Lines to each cor- refpondcnt Divilion, as from i (land, the Height or Thicknefs of to i, from 2 to 2, and fo on; which, ought to be equal to the and then will the Interfedions Breadth of the lower Part of the of thofe Lines create the Arch Key-Stone. AEB. How A R A R How to draw and Ellipiical /Irch reverie. Firft draw the Eafe Line AB then draw the Line CD parallel and equal to the Line A B, and lo far diitaiit as you delign the jlrch iliall rife, and draw the Lines CA and DB; then divide CA'and DB into any Number ot equal Parts, alio C E and ED into the fame Number of equal Parts, and draw Ri^ht Lines to each correfpondent Divifion, as from X to I, from 2 to 2, and fo on, till you have delcribcd the /Ircb AEB. Which was 10 be done. To ftrike and find the Moulds of an Ellipiical Arch^ cither in Bricii or Stone. DO Firrt place the Trammel ABCD, (on which is a Groove, as ABaiid CD;) then propofe the Widths OQ, OL, and QN, prepare allraight LachEF, fome- what Ioniser than half the Bafe Ci CL A R A R CL or CN; then put in a Pen- cil or Marker at K; alio at I, lb that IK is equal to QN, or O L, or P M ; then put in a wooden Pin at H and G, let'tini? IH be equal to CP, alio GK to GN ; then fix one Hand atK, and the other at G, and keep the twoPinsG andH in theGrooves AB and CD, and turn about the Lath FE ; then will the Matfiers marked I and K, create ihe two Grebes LMN andOPQ. To gi\e the Bncks or S:a/,cs the true Sumir.erinj:^, divide the Arch LMN into lb many equal Parts as the Thicknefs of the Brick will allow, as 1,2,3,4,^^^. Bring down the SliJing-Lath to I, and on its Edge draw the Summering or Joint of the firlt Brick, then move it to 2; in the fame manner draw the Summer- ing of ihe next Brick, and fo on. The Crois-Joinrs are drawn by the lame Rule, as the Arches LMN or OPQ^ To draw the i^Wpilcal Arch ramping. Eiill draw the Level Line AP", and divide it in the Middle at G; then ere£t a Perpendicular at Pleafure from V to E, :;Mo from G towards D, and from A towards C ; then draw the Ral.iiig Line AB, and let up the iIeii;ht,of the Arch from A toC, and from B to E, and draw the Line C E; then divide the Luks AC and CD into any Number of equal Parts ; alfo the Lines ]3E and ED, and draw the Right Lines, as in the foregoing Exa'.npies, which will create the Atch hl>B. Strar^bt ARCHES are thofe whofe upper and under Edges are (Iraight ; whereas in the others, they are carved ; and thofe two Edges alfo p.irallel, and the Ends and Joints all pointing towards one certain Centre. Thefe arc principally ufed over Windows, Doors, cj^-. And it isa general Riileamong Workmen, that according to the Breadth of the Peers between the Windows, fo ouglii the Skew-back, or Summering of the Arch, to be ; for if' the Peers be of a good Breadth, as fuppofe three or four Bricks in Length, then the Straight Arch may be defcribcd from the Ox':^ (as it is vulgarly called by Workmen,) being a Contraction of the Word Oxsgomum^ which is the Name of an Equilateral Triangle : But if the Peers are fmall, as they are fometimes, being but of the Length of two liricks, and fometimes, again, but of one Brick and a Half, then the Breadth of the Window, or more, may be the Perpendicular (to the Middle of the Undcr-lide of the Arch,) at the End of which, below, fliall be the Centre, for the Skew-hack or Summering to point to. Thefe Straight Arches arc ufu- ally about a Brick and half, which wfren rubb'd, makes a- bout twelve Inches high, al- though fometimes they are but cleveu A R A R e'evcn I'lchcf;, or thereab'int':, which arifwcrs to four Cour- fcs ot Bricks ; bu: iiotv.ith(tand- ing, they m.iy be made cither more or Ids in Height, accord- ing as Occalion requires. A^ B. By the Term Skew- hack^ is to be underftood the Levclling-Endof the Arch ; and by Siimmcrin^^ the Ll-vc1- Joints betwixt the (Jourfes of Bricks in an Arch. Thcfe Arches ufualiy coiitift of a^^rr/f/^^rand a Header ill Height ; the Stretchers being a \vhoie Brick's Length, and the Headers^ a Brick's Breadth. The Doctrine and Ufe of Ar- ches is well deliver'd hyS'w Hen- ry IVotion^ \^ the five following Theorems. %keorer/il. All Mn!:ter,unlefs impcded^teiids to the Centre of the Earth in a perpendicular Line, or dcfcends perpendicularly down- wards ; becaufe Ponderofity Is a natural Inclination to the Cen- tre of the Earth, and Nature per- forms her Motions by thefhortcft Lines. Thencrn 11. All folfd Ma- terials, as Bricks, Stones, c^.:. moulded in their ordinary Re6t- angular Form, if laid in Num- bers, one by the Side of another, in a level Row, and their Ex- tteam Ends fuftain'd between two Supporters, all the Pieces between wi!l ncceffirily fink even by their own natural Gra- vity ; and muft much more, if they are prelled down, or fnffer any Preffure by a fupcr-incum- bent Weight ; becaufe their Sides being parallel, they have Room to defcend perpendicularly, with- out Impediment, according to the former Theorem ; therefore, to make them ftand, either their Figure or their Pofition mufibe altered. The-jrera III. Stones, Bricks, or other Materials, being figur'd crineat'im^ i. e, wedge- wife, Ibmewhat broader above than below, and laid in a level Row, with their two Extreams fup- ported, as in the preceding Theo- rem, and pointing all to the fame Centre ; none of the Pieces be- tween can fink, till the Suppor- ters or Hutments give way ; becaufe they want Room in that Situation, to defcend perpendicu- larly. But this is but a weak Struc- ture ; becaufe the Supporters are fubject to too much Impulfion, efpecially where the Line is long; P^or which Reafon, this Form of Straight Arches is feldom ufed, but over Doors and Windows, where the Line is fliort. ■ ^ Therefore, in order to fortify the Work, the Figure of the Mate- rials mufi not only be chang'd, bur the Pofition of them too ; as wiil appear in the following Theorem. Theorem IV. If the Materials he fhap'd w-edge-wife, and dif^ pofed in Form of a Circular Arch., and pointing to fomsCen^ tre : In this Cafe, neither the Pie- ces of the Paid Arch can fink downwards for want of Rooni to defcend perpendicularly, nor can the Supporters or Butments of this Arch Patferfo much Vio- lence, as in the preceding flat Form; for the Roundnefs or ra- ther Convexity, will always maJce the incumbent Weight rather reft upon the Supporters, than heave or fiiove them outwards; whence this Corollary may be ^irly de- duced, Th»t tlielafeft or moft fe- C 3 curg A R A R cure of all the Arches above mention'd, is the Semicircular ; and (if a!! Vaults, the Hcmi- fphcricai, ilthough not ablblutc- ly e.\empted from fome natural Imbecility, (which is the fole Prerogative of Perpendicular Lines and Right Angles,) as has been obfLrv'd byBcrnardi}joBaldi^ Abbot of Guajlalla^ ill his Co.n- nientary upon /Injlytle's Mccha- n'icks ; where, by the way, it is to be noted, that when any Thing is demonflrarcd mathematically to be weak, it is much more fo me- chanically ; Errors always occur- ring more eaiily in the Manage- ment of grofs Materials, than in Lineal Dcfigns. Theorem V. As Semicircular Arches, orHemifphericsl Vaults, rais'd on the whole Diameter, are the llrongeft and fecureft by the precedent Theorem, fo they are alCo the mod beautiful ; which keeping precifely to the fame Height, are yet diflended one Fourteenth Part longer than the faid Diameter ; which Addi- tion of Width will contribute greatly to their Beauty, without dimiin'fhing any Thing conlide- rable of their Strength. Hov/ever, it is to be obfcrv'd, that according to Geometrical Stridnefs, in order to have the Itrongcft Arches^ they mull not be Pc»rtions of Circles, but of anotlier Curve, called the Cate- 9iaria\ the Nature of which is fuch, that a Number of Spheres difpoled in this Form, will fuf- tain each other, and form an Arch. See Catatarla. Dr. Grej^ory^ ^hilo/hph. T'ranf- tfi^/W/, N°23r. has fhewn, that Arches conllruc'ied in other Carves, only (land or fullain themfjlvcs by Virtue of the Ca- ienarta cojitain'd in their Thick- iiefs ; fo that if they were made infinitely llender or thin, they mult of courfe tumble ; where- as the Catenar'ta^ though infinite- ly llender, mull ftand,' by realon that no one Point of it tends downwards mc-re thanany other. Of , '\"icaft4r:ng Arches. Whe- ther the Arches b«i llralght or circular, they mull be meafured in the Middle, i.e. if a jhaight Arch be ten Inches in Height or Depth, the Length mull be mea- fured in the Middle of the ten Inches; which Length will not be any longer, than if it were mealured at the Under- fide next to the Head of the Window, by fo mucli as one Side of the Springing Arch is skevv'd-back from the Upright of the Jaumbs, Peers, or Coins of the Win- dows. A;id alfo in CWculir Arches., it is to be obferved, that the up- per Part of the Arch is longer (if girt about) than the under Part, by realon that it is the Seg- ment or a greater Circle, cut off by the fame Right Lhie that the Idler is, and for thatReafon muft be girt in the Middle. As to the Price. As for the Workmanfliip of Straight Ar- ches^ (of Brick,) handr(;me!y fet, and well rubb'd, in Lond)rt., a- bout eight Pence or nine Pence a Foot; but if the Workman finds Materials, he will have ten Pence, or one Shilling fer Foot. But in fome Parts of SKJ]ex and Ke:^:^ they will require oneShil- ling/'frFoot; nor will they do it under running Meafure. Scheme A R A R Scheme or Sheen Arches^ and Elliptical ones of ruhlj'd Brick^ are usually much nbout the fame Price as Straight Arches. But if the Scheme Arches are of un- rubyd Bri'h^ I'ney are ufually included in the Piaiii Work, un- lefs the Plain Work be done at a low Pi ice: But yoa mult take notice, that tlie Owner or Ma- ftcr of the Bui'Jing muft be at thv Charge of the Centres to turn the Arches on., and not theWork- inan, unlefs an Allowance be made him for it in the Price of the Work. How to dcfcribe a Scheme Arch., when the Bafe and Per- pendicular are give/ii. FirH: draw the Line A B, then draw a Line at Right Angles with it, through the Middle D, at Plcafure, -xno let up theHcigiit you defire to rif.- from D to C, and draw the Line CA; then open \ourCompalKS to any con- venient Dirtnnce, fet one Foot in C, and ftrike the Arch FE ; with the fame Opening of the Cumpalles, fet oi;e Foot in A, and ftrike t!ie Arch from GtoH, at Pieafure; then take the Radius EF in your CompalTes, and fet ft on the Arch G H, as at I, and draw a Right Line from A through I, to cut the Perpendi- cular, as at K ; then is K he Centre to Ihike the Arch ACB, Wiiich was to be done. 7'he Bafo and Perpendicular of a Scheme Arch being given, how to dcfcribe it by an inter- fedh'on of Lines. Firlt draw the Bafe AB, and Middle at E, from whence fee up perpendicularly to C, twice as much as you would have the Arch to riie, and draw the Lines CB and CA, and divide each Line into any Number of equal Parts, and draw Right Lines to every correfpondent Diviiii)n, as from I to I, from 2 to 2, from 3 to 3, and fo on ; and then will the Interfedions of thofe Lines create the Arch ADB. Which was to be done. It is the ordinary Proportion of Arches., that the Height be made double the Width ; but this may be varied, and made a little more or a little le!s, as Oc- cali'.>n requires. Le Clerc. Wlien Arches are to bo at fome Diftance from each other, for the Conveniency of any Appart- ments, either above or under- neath, the Columns which fcpa- rate them (;ught to be in Couples ; but when they are in Couples, they fhould h^ive but one Pedc- flal, if they have any Pedella! at all. C ^ ARCH A K J\ iX 'Arch is particularly ufed for the Space between the two Peers of a Bridge. The Chief or Vi-x- a^xArch^ is that in the Middle, which is the wideft, and com- monlv higheft, aiid the Water that runs under it the dccpert, being dctign'd for the Paflage of B'arsi or other VefTels. Some Relations mention Bridges in the Eafl. having 300 Arches. See Bruige. A Triuynphal Arch is a Gate or FilTage into a City, magiu'fi- cently adorn d with Architec- ture, Sculpture, Infcriptions, cTf. Avhich, being ereded either of Stone or Marble, are u 3, the Quotient w ill be the Arch-Liyie ACB fought. 19. 8 AC. 1^8. 4 34- 4 AB. 124 Arch-Line 41. 333 Another Way. From the double Chord of thjrd Part of the Difference add- half the Segment's ^Vrch fubtraft ed to the double Chord o h a t the Chord of the Segment, one the Segments Arch, the Sum ts A R A R the Arch Line of the whole Seg- ment. Thus, if AG 19. 8 be ': doubled, it makes 39. 6 ; from "Which, if yoa fubtn-ct 34. 4, the I Rem^mer is fi; which divided ; by 3, theQuoiicntis ». 733 : This j being added to 39. 6, (the doable \ (^hord of the Half Segment) the ■ Sum will be 41. 333. So if the Arch-Llnc ACB were ftretch'd out llrait, it v/ouM then contain 41. 333 fuch Parts as the Chord AB contains, 34. 4 of the liive Parts. ARCHITECT [■Apx'TEKTo;., of cc^xoc. Chief, and Tiy.ruiv an Ar- tificer or Builder, Gr.'] a iVlaller Workman in a Building, he who defigns the Model, or draws the Plot, Plan, or Draught of the whole Fabrick ; whole Bulincls it is to conlider the who'e Man- ner and Method of the Build- ing ; and alfo to compu'ic the Charge and Expence. In the managing of wnich, he ought to have ieg:trd to its cue Sitmu'ion^ Contrivance^ Rece'pt^ Strength^ Beauty^ Form^ and Alatertals. The Name ArchiteSi is alfo ufed for the Surveyor^ or Srtper- intendant of an Edifice, the Ma- nagement being wholely com- mitted to fiis Circumfpeftioii ; wherefore he ought to manage the whole Aff\ir prudently and advifedly, with the utmofl Cau- tion, that all Matters may be or- dered and difpofed, (in all Cir- cumflances,) fo as to anfwer the Owner's Defign, and be confen- taneous to Reafon. But notwithdanding the Care of the whole Fabrick be incum- bent on this Surveyor^ oxSuper- intevidant^ yet Sir Henry Wotton advifes the having a fecond Super- rntcndant^ {oxOjficimtor^ as he is ■CT called by Vltrnvtus^ whofeBufi- nefs is to chufc, ( or examine, ) and fort all the Materials for every particular Part of iheBuild- ing- l/^itruv'tus enumerates 1 2 Qua- lifications roqoilire for a com- plete Archhett ; that he be docile and ingenious, literate, skili'd in Defign ing, in Geometry, Op- ticks, Arithmetick, Hidory, Phi- lofophy,Mufick, Medicine, Law, and Aftrology, The molt celebrated ancient Architeds are Vitrwvius^ ^Pah'a- d'O^ Sccifnozzi^ Serito^ V'tgnola^ Barharo^ Cataneo^ Alberti^ Vida^ BuUant^ 1)e Lorme^ and many others, ARCHITECTONICK, that which builds a T hing up regu- larly, according to the Nature and IntentioTis of ir. The Term is ufually appiy'd. to th.it plallick Power, Spirit^ or whatever elle it b(\ which hatches the Ova of Females into living Creatures, which is called the Arcbitedonick Spirit; yet it is alfo appiy'd to the chief Overfeer of Buildings, or an Archireft, ARCHITECTURE, the Art of Building, or a Mathematical Science, which teaches the Art of erefting Edifices proper either for Habitations or Defence; being a Skill obtain'd by the Precepts of Geometry; by which it gives the Rules for defigning and rai- fing all forts of Scrudures, ac- cording to the Rules of Geome- try and Proportion^ and contains under it all thofeArts which con- duce any Thing to the framing Houfes, Temples, 'Sc The Scheme or Projection of a Building is ufually laid down in three feveral Deiigns or Draughts. '^The A R A R The fir/l is a P/aft, which ex- hibits the Extent, Divilioii, and Dillribution of the Ground into i^pariiiienis and oaicr Conve- niences. The fi'cond fhews the Stories, their Heights, and the outward Appearances of the whole liin'ld- iiig : And this is ufually called the Deji^u or ElevaUon, Fhe chird is cwmmnnly called the Settfin. and itievvs the lulidc oh the Kibrick. From tiieie three D.figns, the Undertaker frames a Co!iipi:ra- tion of the Charges of the whole Bui!dii:g, rsnd the Time reqaiiice to complete ir. As to the Antiquity of Archi- ieiiure : Architedure is fcarce inferior, in Point of Antiquity, to any oihcr Arts. N.uure and Neccffity taught the firit Inhabi- tants of the Earth to build or fet up Huts, T^ents, and Cottages ; from which, in Procefs of 1 ime, they gradually advanced to rai- ding more regular and (lately Dwellings, fet off with Variety of Ornaments, Proportions, 'i^c. Antient Writers afcribe the carrying of Architedure to a to- lerable Height to the Tyrlans^ ■who were therefore fenr for by Solomon for the Building of his Temple. But V'lllnyandus will not al- low thofe- who were fent for from Tyre to be any more than under Workmen, fuch as Artifi- cers in Gold, Silver, Brafs, ^r. and fuppofes that the Rules of Architedure were delivered by God him.felf to Solomon. So that the Tyrians rather learnt Architedure from Solomon^ than he from them; which they after- wards communicated to the £- gyptians., and thefe to the Greeks^ and the Greeks to the Romans, He undertakes to prove, that all the Beauty and Advan- tages of the Creek and Roman fabricks were borrowed from Solomon'^ Temple. Sturmius produces feveral Paf- fages in l^itruvius in Confirma- tion of this, where the Rules laid down in h'xs Lib. VI. cap. ii. andL/Z'.V. r^/?. i. Iquare exadly with whaijofephus relates of the Jewijh Temple, in his Sixth Book. But the 23d Chapter of Ifaiah, Ver. 8, informs us to what a Pitch of Magnificence the Tyri^ ans and E^yptans had carried Ar~ chitedure., before it csme to the Greeks-, and ^/Vrz/zi/aj alto gives an Account of the Eg)ptian Oe~ cus, their Pyramids., Obelisks., &c. Yet, in the commow Account, Architedure feem.s to be whol- ly of Greek Original. Three of the regular Orders or Manners ta'ce their Names from the Greeks., a-^ Corinthian., Ionic, and Doric ; and we have fcarce a Parr, a lingle Member, or Moulding, but what comes to us with a Greek Name. And it is certain the Romar-^., from whom w^e take ir, borrow- ed all they had eiuirely from the Greeks \ nor do they feem to have had before any other Notion of the Grandeur and Beamy of lar'^c Buildings, but what arifes from Magnitude, Strength, C5^,f. Architedure is accounted to have arrived at its Glory in the Time of Augujhis Ca-fur ; but both that, and other polite Arts, were negle6ted under Tiberius. Nero, indeed, notwithftanding his many Vices, retain'd an un- common I A R A R commnn P^lTion for Archheclure ; bin Luxury and DKVolurencfs had , a grc:!ttr Share in ir, than true |< M.igniticence. In mc I ime of i Yrajayt^ Apollodorus excell'd in the I Art; by which he merited the [ Favour of that Prince, and cred- .' ed that famous Column called , Traja-r/s^ which ii remaining to • this Day. [ But after his Time Arch'itec- ; trire began lO decline; though it v/as for fome Time foppc rted by the Care and Magniticence of Alexander Sever us ^ yet it fell ■with the Welt rn Empire, juid Hmk into Corruption ; from whence it was not recovered for the Space of 1200 Years. Ali the molt- beautiiul Monu- ments of Antiquity were de- Itroyed by the Ravages of the ^ifiooths ; and from that Time Archite£lure became fo coarfe and artlefs, that their profc'lTed Archictds knew nothing at all ol jult Deligning, whereiii the \\ hole Beauty of Architcdtire conlills : Hence a new Manner of Arch'itcdure^ called Gothic^ took its Rile. Charlemagne fet himfelf indu- Hrioufly about the Rcftoration of Arcl:i',edure\ and the French ^p- p'icd themlelves to it with Suc- ccventh of the Archi- tx^Yia:. A Fourth of this Seventh h the F-L't^ lo which the jOrops han^.; ti,, three iv/tAz'j, aiid a C\mat'ui/n\ whicn is divided, as follows : He divides the whole Altiiude into feven Parts, the uppcrmoft of which, he allots to iW^Cymatmrn^ which he llibdivides into three Parts ; the r.ppermoll of which, is for the L//'j, and the two reman- ing lor the Ogee. The other fix remaining Parts are divided inio twelve; live of which he makes the upp.r Fa- fcia^ four the middle one, and three the lowcft. The A R A R The other for the loftick Co- lumn wich a Pedeftal, he propor- tions, as follows, viz. he reckons the whole Altitude of iht Archi- trave, Freeze^ and Cornijh.^ to be two Mod. which are divided in- to ten Parts ; three of which, are for the Architrave^ (which is thirty-fix M.) which he dii- tinguifhes into iix minuter Parts, or Members ; which he names as follows, (beginning at the Top, and fo defcending,) viz. a Ftllet^ a Cima^ a T'horus^ and three Fafciaf; all which fmaller Members he thus finds, viz. Firft, he divides the whole Al- titude into Iix equal Parts; the uppermod of which Parts, he fub- divides into four Parts : The higheft of thefe four is for the Fil/et^ the two next of the four are allotted to the Ci-ma., and the Fourth, that remains, is for the Thorus. Thefivegrand Divifions,which remainjarefubdivided into twelve, which are diilributed as follows, viz. five for the uppcr^ four for the middle, and three for the lower Fafcia. Palladia affigns thirty-four M. for the Height of this Ar- chitrave. According to his Scheme of this Member, it is compofcd of feven Parts, viz. a L//2, a Cima^ three Fafcias^ and two AJiragah ; which are proportion'd as fol- lows : To the Lift ( which is above the Cima^) he allots two three Tenths M. to the Cima^fom three Fifths M. to the up- per Fafcia he allows ten one Eighth M. to the Aftragal, at its Foot, one Third M. the middle Fafcia is to contain feven fifty-twoSjitieibs; and theAllra- gal at its Foot one Third M. to the lower Fafcia he alligns (ir nine Tenths M. All which being added together, amount to thir- ty-four one halt M. Scamozzi makes the lonick Ar- chitrave thirty-five M. high, and of the fame Form with that of the Second oiVitrKvius., confid- ing of fix Parts, viz. a Lift., Ci- ma^ Aftragal^ (or T'horus^) and three Fafcia's ; which he propor- tions, as follows : He allots two one half M. to the Lift^ to the Cima four, to the 'thorus twoi to the upper Fajcia eleven one half, to the middle one eight one half, and to the lower one fix one half. Figmla allows thirty-feven one half to the Ionic Architrave in Altitude; and as to theForm^ it is much the fame with that of Fitruvius\ firft Order. The Corinthian Architrave ^ic^ cording to l^itruvius^ ought to be half a Mod. in Height; but it is to be obferv'd, that this is for the Corinthian Column without a Pedeftal. This Member he di- vides into feven Parts, of which the uppermoft is the Cymatium ; thefix remaining Parts hedivides into twelve, of which he allots five to the upper F^/c/^; alfo al- lowing one Eighth of this Fafcia for 2iBead2i\. its Foot, he allows four of the twelve Parts to the middle Fafcia^ and one Eighth of this Fafia for the Be-;d at its Foot, and makes the loWer Fa- fcia of the three remaining Parts. The Architrave for the Corin- thian Order with a Pedeftal, ac- cording to Vitruvius^ is allow'd a greater Altitude than that without, confiding of tht- fimie D M?.u- A R A R Members, both as to Number and Form with the former Ar- chitrave, but differing in Dimen- fions. The whole Altitude of the Architrave ought to be one Quar- ter of the Altitude of the Co- lumn, nearly to two Eighths of the Body of the Column below, which is — — to forty one half M. This Altitude he divides into feven equal Parts, and makes a Cymatiur:^ at the uppermoft of thete feven, and divides the lix that remain into twelve equal Diviiions ; of which, five he al- lots to the upper fafcia^ four to the middle, and three to the lower one. He fubdivides the upper and middle Rifcia^ each into eight Parts, and allows one of thefe Eighths for a Bead at the Foot of each of thefe Fa- fc'tas. (Palladio makes this Architrave to contain eight Parts, viz. one Ltjl^ one Cima^ three Beads ^ and three Fafcias ; the Height of all which, he allows to be thirty- fix M. Whi-ch are thus fubdivided, viz. to the Liji (or upper Mem- ber) he allows two three quar- ters M. the next in Order is a Cima^ and the next in Order is of two M. high, at the Foot of which is a Bead ; after this is the upper Fafcia, its Bead at its Foot, both which contain about thirteen one half M. After this is the middle Fafcia, and its Bead at its Foot, which contain eight oncEighthM. andlaflof all, the lower Fdjl-ia^ which is lix one quarter IVl. in Heighr. Scamozzi makes the whole Al- titude of this Architrave to be forty M. Which he fubdivides in- to nine fmall Members, (begin- ning at the Top, and defcending) a LiJl of two M. a Cafement three one quarter M and an O^ee of two three quarters, a Bead of one one half M. a Fafcia of twelve M. and its Bead of two M. the middle Fafcia eight one half M. and its Bead one three Fifths M. and the lower Fiifcia fix one half M. which being all added together, make forty M. Vignola makes the Corinthian y/rr/j/Vr^^t'if forty-fiveM.inHeight, and fubdivides it into eight fmal- ler Members, as Palladia doth, viz- a L//?, zCtma^ three Beads ^ and three Fafcia's. The Cofnpqfite Architrave, f^i- triivius makes the Architrave of tJMS Column, and the Frieze and Cornitli, all of an equal Height, viz. each of which is equal iii Height to the Diameter of the Colnmn above, jult under the Ca- pital^ which is ten Twelfths of a Mod. fifty M. This Archi- trave he divides into fix Parts, one of which, is for the Cyma- tiurn^ and its Boultin under it : This upper fixth Part he divides into four, and allows one of thefe four for the Fillet above the Cima^ and the two next for the Ciyna itfelf ; and appoints the Fourth, that remains, for the finall Boultin under the Cima; and fubdivides the other five grand Divifions into twelve mi- nuter Parts, affiguin^ five of them for the upper tafcia^ four for the middle one, and three for lower ; and alfo fubdivides the middle Fafcia^s^ each into eight Parts, allowing one of thefe Eighths for a Bead at the Foot of each of thefe Fafcia's. "Palladia A R A R Palladto makes this Architrave forty-rive M. in Height, and di- ilribuces thc:r. iiuo Icven particu- Jar miiuiter Members (beginning at the Top, and lb delcending:) Firll, he allows two one Eigluh M. to the Lijl^ four one Eighth to the Ca[ement^ to the Ogee nine one quarter, to the ^c^^ one one quarter, to the upper Fa[cia fifteen M. two one quarter to the Ogee at its Foot, and eleven M. to the lower Fascia. Scamo-czt makes \\\\% Archkraz^e forty M. in Height, which he dillribates among tiiefe eight fol- lowing Members, -yy^. (defcend- ing :) Firft, a Lifi of two M. Se- condly, au Ogee of four one half A'l. Thirdly, an Ajhagal of two M, Fourthly, the upper Fdjcicoi eleven three quarters M. Fiithly,a Beati at its Foot of two one quarter M. Sixthly, the middle FafcU of eight one half M. Se- veiuhly, at its Foot, one one half M. Eighthly, the lower F^yW^ of lix one half. yigmla makes this Architrave forty-tive M. in Height, which he divides into leven Pvlembcrs, Z Liji^ % Cafement^ a Boiiltra^ a FilUt^ a Fujcia^ a Bead^ and a Fafcia. Meafur'ing tf Architraves. Ar- chitraves in Buildings (either of Brick or Stone) are ufually done by the Foot lineal ; and therefore , having -taken the Length in Feet, you have alfj the Content at the fame Time. 'The Price of Architraves, T^hat is different, according to the Breadth or Width of them. Stouc Architraves^ about Doors or Windows (according to Mr. IVing) are ufually reckon'd at a Fenny an Inch iu Breadth at one Foot c g^ if k be nine Inches broad, it's worth nine Pence a Foot, ten Inches ten Pence a Foot, i^c. The Faces of an Architrave^ fays M. Z. Clerc^ ought not to have Ornaments, but to be left plain; and particularly when the Frieze is inrich'd. '^i'he Proportion of Architraves by equal Parts. The Ionic Architrave is divided into nine, giving one and three Fourths to the firft Face, two and a half to the fecond, and three to the third; one and one Fourth to the Ogee, and one half apart to the Fillet: The PiojcSion of the fecond and third Faces have a quarter of a Part each, and the Whole two of thcfe Parts. The Corinthian Architrave is di- vided into nine, giving one and a half to the firft Face, on« Fourth to the fmall Bead, two to the fecond Face, three Fourths to the fmall Ogee, two and a half to the third Face, half apart to the Bead, one ro the Ogee, and half rpart to the Fillet : The Projection of the fecond Face hath i;ne Fourth ot a Part, the third Face one of thefe Parts, and the Whole two. The Height ot the Cumpojits Architrave into nine, giving two and a half to the liift Face, one half apart to the Ogee, three and one half to the fecond Face; one Fourth to the .Ajfrrigal, three Fourths to the Ovolo, one torhe Hollow, and half apart to the Fillet: -The Projection of the fe- cond Face hath one half apart, the Ovolo one ^nd one Fourin, and the Whole t\vo, D 2 ARFA A R A R AREA, properly denotes any plain Surface whereon we walk. The Word is Latin. Area^ in Architcdurc, fignifies the Extent of a Floor, l^c. Area., in Geometry, denotes the Compafs, or iuperficial Con- tent of any Figure; thus, exempli gratia.^ if a Plot of Ground be exa611y fquare, and its Side be 30 P'eet, the Area will be 50 multiply'd by 30, i.e. 900 Feet. ARlTHiMETlCK ['Ap.6fxer<«J| of ipin Numbers given, to find others whofe Relation to the for- mer is not known. Political Arithmetick is the Ap- plication of Arithmetick to Po- litical Subjects, as the Revenues of Princes, Number of Subjects, Births, Burials, i^c. Arithmetick of Infinites., is the Method of famming up a Se- ries of Numbers, confiding of infinite Terms, or of finding the Ratio's of them. ARRANGEMENT, theDif- poficion of the Parts of a Whole in a certain Order. ARSENAL, a Royal or Pub- lick Building, or Magazine, for the making and keeping of Arms neceflary A R A R neceflary either for Defence, or AfTault. ARTICLE [in Arithmetick] fignifies the Number lo, or any Number juftly divifible into ten Parts, as 20, 30, 40, ^c. which are fometiines called round Numbers yir\ 3 J' A? A R A S 3. As to the Goodnefs of the Stunes, either for their Durable- ncfs, or Largenefs. As for their Durahlcnefs, that only is to be known by Experience : For at the lird opening (-f anew Quarry, no body can rcli how the Stones may prove. For lome Stones, when ^rlt taken out of the Quarry, are very foft and friable, and will moulder to Sand, by being ex- posed to the Weather but a few Years : Whereas others of thofe Ibfr Stones will be indurated, or Iiardened, by being expofed to the open Air. Firif, Tiiofe Stones that come hard our of the Quarry, arc generally durable, being of a more iirm and Dlid Confiltence. Secondly, as to their Largc- nefs, I need not fay much, all knowing that large Stones mull needs be better, and make firmer Work than fmall ones ; which are onlv fit for filling \Vork in tluck Walls; or to be ufed in fuch Places where the Country affords no better. There is a great Difierence in Quarries, in Reipcti: to thePofi- tion o[ the Sso}2es in the Ground ; ■^vhich may be confider'd undt-r two Heads, viz- Firlt, as to their Depth in the Ground : For when they l:e a conliderable Dcprh in the Ground, it requires a great de/il of Labour to uncopc them, (as they term it) i. e. to remove the Earth. Secondly, if ihcy do lie alraoft even with the Surface of the Ground, then it will re- quire thclcfs Labour to uncover them. And be/Tdcs, an Allowance is to be made, as to the Manner of «f their lying in the Ground : For of the Quarry is a Rock. In this Cafe, it requires the more Labour to raifethe Stones, and break them fit for Ufe, than if they lay feparate anddifunited : So that thcfe Circumftances i'o vary the Price, that fome have been drawn /or gJ. the Load, when others have coft 3 j. ASHLERING [with Buil- dcrs'] Quartering to tack to in Garrets, about two Foot and a half or three Foot high, perpen- dicular to the Floor, up to the Underlide of the Ratters. The Vv orkmanOiip is from 4^. to 61^. a Square. ASSEMBLAGE, the Join- ing or Uniting of feveral Things together; alfo the Things them- felves fo joined or united : Of which Allcmblages, there are di- vers Kinds and I'^orms ufed by Joiners, as with Mortoifes, Te- nons, Dove- tails, l^c. Ajfcmblage of Orders. M. Le CUrc fays, wii n two Columns arc placed oi^e over another, they muft be of different Orders, the Stronger alwa}S- to fupport the Weaker. For Inffance, i.The Doric may be placed over the Tufcan^ the Ionic over the Done, the Roman over the Ionic ^ the Spafii/h over the Ro;7!a'/}, and the Corimhian over the Spanip. 2. That the upper Order mufl always be lefs mnfllve than the Under, agreeable to the Maxim, 1 hat the Strong ought to fulfort the ireak. 3. Tli3t the Columns ought to ffand cxadlyover each other; io that their two Axis's may be both found in the fame Perpen- dicular. 4. The A S A S 4. The Diftances between the lower Columns, mult be deter- min'd by the Intcrcolumniations of the Order, that is, without Pe- deflals ; and the Diftances of the upper Columns, by the Intcr- columniations of the Order, with Pededals, taking Caie, by the Way, that the firfl: Order be mounted on a pretty high Zocle, or an Afcent of feveral Steps, to ferve inftead of a continu'd Pe- deftal, or Foot. He gives a Pedeftal to the Up- per Order ; becaufc being con- fin'd to the Breadth of the Inter- columniation of the Lower Or- der, its Columns, by this Means, are render'd fmaller, infonnuch, that the Diameter of their B.^fc does not exceed that of the Top of the Under Column; which is a Rule (in his Opinion) not to be difpenfed withal. He Remarks that Fitrwvlus will not allow the Upper Or- der more than three quarters of the Height of the Under, But if this Redudion were follow'd, the Columns would be too fmall, and confequently too far afunder, with Refped to their Height, if placed one over another. In order tofind theMod.of an Order that is to be placed over another, he propofcs, for Inftance, to place iht Ionic over the Doric ; and advifes, Toconfidcr, firft, that in the Doric Order, without a Pcdelial, which is to give the Meafures of that firft Order, that the Columns are placed at the Diftance of eleven M. from each other, in Portico's. That in the Ionic Order with a Pcdeftal, the Columns are fifteen M. a-part; and that to place this Order upon the 'Doric^ you muft divide the In- tercolumn, or its Equal, into fif- teen equal Parts ^ one of which Fifteen will be the M. for rai- ding the/o»/V Order, with its Pe- deftal. He like wife obferves, that when two Portico's are placed over each other, the Higher ought to be tegulated by the Lower : He means, that the Width of the Upper Arch fhould be made equal to that of the Under; it being but juft, that the two Arches fliould have the fame Width. On fuch an Occafion, the lower Arch may be made ten or twelve Minutes narrower than ufual, that the Width of the Upper Arch may be better pro- port ion'd. When Columns are to be without Portico's, he fays, there needs only be four Triglyphs made between the Doric Co- lumns, that is, an Interval of eight Mod. Tour Minutes, which are equivalent to twelve M. in the Ionic ^ as appears by the Rule of Proportion ; and that the fame Thing may be obferv'd of coupled Columns, The Roman Order, he fays, does not match perfettiy well with the Ionic ; becaufe its Capi- tal is higher, with refped to its Column, than the Ionic Capital, with refpecl to the Ionic Co- lumn; and becaufe the Denticles of the Ionic appear fomewhat weak underneath the Modillions of the Roman. However, the Roman Order being in this Place Icfs than rhe the/o»?/V, the Difproportion be- D 4 tween A S AS tween their Capitals, becomes lefs ffnhble, as well as that be- tween the Denticles of the one, jind the Modillions of the other. To find the M, for raijing a Corinthian Column over a Spa- pi (h Order^ he fays, It is evident, that the Modil- lions of the Upper Order mufl be the fame in Number with thofe of the Under, in order to have them exactly one over ano- ther, Novtr the Inter-Modillionsof of the CorwthiaK Ordet contain- iDc juft 40 Minutes, where the Column has no Pedeftal, thefe 40 Minutes muft be mul- tiplied by the Number of Mo- dillions ; which being ii,thcPro- fduawill be 440; which being divided by 30, the Mod. the Quo- tient will be 14M.20 Minutes; which istheDivifionof the Scale for raifiug the Corinthian Or- der. He obferves, that there is a Difficulty in placing three Or- ders over each other ; which con- fifts in this. That the Second Order having a Pedeftal, the Columns of the Third become a little to big at the Bottom ; though 'tis fo very little, that the Eye can hardly perceive it. But this Inconveniency , however, may be remedied, by taking the Excefs away imperceptibly , ■wholly from the Bafe of the Co- lumn. It is true, this will oc- calion a little Swelling ; but that won't do any Harm. Again, he is of Opinion, it would not be proper to under- take the placing of more than three Orders of Columns over one another; For, befides that In the fourth Order, the Columns would be too far afunder, in refped to their Height, it ought likewifc to be confider'd, that four Co- lumns raifed over one another, can't well be very ftrong : In- deed, the tirft may have a Ruf- tick Order, whereon it is raifed, and which may ferve it as a Foot. Ajfemhlage of P:!aJIers. See Pilaster. ASTR AG AL [' A^pav^Ao,-, Gr. which figuifies the Ankle, or Ankle-Bone] is, in Architedure, a little round Member, in the Form of a Ring, or Bracelet, ferving as an Ornament at the Tops and Bottoms of Co- lumns. The 4/^ ragal \s alfofometimes us'd to feparate the Fafcia of of the Architrave. In which Cafe, it is wrought in Chaplets, or Beads and Berries. It is alfo ufcd both above and below the Lifts adjoining im- mediately to the Dye or Square of the Pedeftal. The Ajiragd of a Column, M. Le Clerc fays, ought always to be plain, excepting in the Ionic Order, where the Allragal of the Shaft is converted into a Chap- let of Pearls and Olives, for the Capital, /ifiragal^ or Baguette^ has the Figure of a Staff, when it is join'd to a Fillet ; the Height of which Fillet, M.Le CArr divides into three Parts ; two of which, he gives to the Aftragal. And this Rule, he fays, he obferves on all Occafions. This A S A T This Aftragal is frequently carv'd with Pearls and Olives, •which the French call 'Pater- Kofters. ASYMMETRY, a Want of Symmetry, or Proportion. ASYMPTOTES, are proper- ly Straight Lines, which ap- proach nearer and nearer to the Curve they are faid to be A- fymptotes of; but if they, and their Curve, are indefinitely con- tinu'd, they will never meet. Or ylfymptotes^ -kxe. Tangents to their Curves, at au infinite Diftance. And two Curves are faid to be afymptotica! , when they continually approach to one another; and if indefinitely con- tinu'd, do not meet. As two Parabola's, which have their Axis placed in the fame Straight Line, are afymptotica! to one another. Of Carves of thefecond Kind, that is the Conic Se6lions only the Hyperbola has Afymptotcs, beii^g two in Number. All Curves of the third Kind, have at leali, one Afymptote ; but they may i.ave three. And all Curves of rhe fourth Kind, may havcfuur Afymprotes. The '"vf/choid^CiJjoid^ and Lo- garithmick Curve, have each one Afymptote. The Nature of an Afvmptote will be very eafily concciv 'd from that of the Conchoid: For if CDE be a Part of the Curve of the Conchoid, and A its Pole, and the Right Line M N be fo drawn, that the Parts BCGD F E, csV. of Right Lines drawn from the Pole A, be equal to each other, "then the Line M N will be the Afymptote of the Curve^ becaufe the Perpendicular Dp is fhorter than B C, and E/> than D/*, and fo on ; and the Points E, (d'c. and />, can never coin- cide. ATL ASSES [in Archlteaurel a Name given to thofe Figures, or half Figures of Men, fo com- monly ufed inftead of Columns or Pilafters, to fupport any Member in Architedture, as a Balcony, or the like. Thefe are ocherwifc called Telawones. ATTIC, fignifies fomething relating to Attica^ or the City of Athens. Attic is alfo ufed in Architec- ture for a kind of Building, wherein there is no Roof or Co- Ytring to be feen ; tlius called, becauic ufual at Athene. Attic^ or Attic Order .^ 15 a fort of little Order raifed upon a lar- ger one, by Way of crowning, or to finifli the Building. It is alfo fometimes ufed for the Conveniency of having s^ Wardrobe, or the like, and in^ {lead of regular Columns, hason- ly Pilafters of a particular Form. Attic Order., according to M. Le Clerc, is a kind of rich Pedc- ital. A T A V ftal. Some Architects give it the fcvcral Capicals of all the Orders of Columns; bat heliys, the lonic^ Romcin^ and Cor'iKthian^ do not nt a!! b.come if. The bed Way., in his Opinion, is only to diftinguifli the Capitals by a Dif- ference in their Mouldings ; ■which may be m-^de more or Jefs fimple, and more or lefs de- licate, according to the Relation they arc to bear to the Archi- tefture ut;dcrneath. The Name-^/^/V, is alfo given to a whole Story, into vrhich, this Order enters; this HttleOi-- der being always found over another that is greater. This Pedelhl, or P'alfc Pilaf- ter, he fays, ought always to have the fame Breadth with the Column, or Pilaller underneath; and its Height may be equal to a Third, or even rJ Half of the lamcColumn or Pila(kr,by which it is fupported. yittic of a Roof, is a kind of a Parapet to a Terras, Platform, and the like. /Ittic Co:2tinu'dy is that which encompaffes the whole Pourtour of a Building, without any Inter- ruption, following all the Jets, the Returns of the Pavilions, ^tt'ic ^Interpoi'd is one fituate bet wee ;i two tall Stones, fome- timey adorn'd with Columns or Pil^'lters. /iftic Bafe^is apeculiar Kind of I'^afe ufed in the Iokic Order by ^thc ancient Architcds ; and alfo by h^nllidio^ and other xModerns, in iht Doric. It is the molt beauti- ful of all Bafes. ATTITDDE [in Sculpture and Pai'/itlng] is the Pofture of a Statue or Figure, or the Di(- pofition of its Parts; by which, we difcover the A6tion it is en- gaged in, and the very Senti- ments fuppofed to be in its Mind. The reprefenting thefe in a ftrong and lively Manner, makes what they call agoodExpreflion.- The Word comes from the Italian Attitudo ^ which fignifies the fame Thing. ATTRIBUFES [in Sculp- ture^ ^c.\ are Symbols added to feveral Figures, to 'fdenote their particular Office and Cha- ra£ler ; as a Club is the Attribute of Hercules ; a Trident, of Nep- tune ; a Palm, of Victory^ the Eagle, oi Jupiter ; a Peacock, of AVIARY, a Houfeor Apart- ment for the keeping, feeding, and breeding of Birds. AU REOL A, a kind of Crown of Glorv, given by Statuaries, ^c. to S;tints, Martyrs, ij'c. as a Mark of the ViSory they have obtai n'd. AXIS properly fignifies a Line or long Piece of Iron, or Wood, pafTmg through the Centre of a Sphere, which is moveable upon the fame. Spiral Axis, in ArchiteQure, is the Axis of a twilled Column drawn fpirally, in order to trace the Circumvolutions without. Axis of the Ionic Capital, is a Line pafTmg perpendicularly through the Middle of the Eye of the Volute. Axit in Mechanicks, as the Axls^ of a Balance, is the Line upon which is moves or turns. Axis A X A X ylxis of Rotation^ or Clrcum- "joltit'ton in Geometry^ is an ima- ginary Ri^ht Liuc, about which any plain Figure is conceived to revolve, in order to generate a Solid. Thus a Sphere is conceived to be form'd by the Rotation of a Semicircle about its Diameter, or Axis, and a Right Cone by that of Right-angled Triangle about its perpendicular Leg ; which is here, its Axis. Jx'is of a Circle or Sphere^ is a Right Line paffuig through the Circle, or Sphere, aud termina- ting at each End in the Circum- ference of it. jixis is yet more generally ufed for a Right Line proceeding from the Vertex of a Figure, to the Bafe of it. Jxis of a Cylinder^ is properly that quielcent'Right Line about which the Parallelogram turns, by the Revolution of which the Cylinder is form'd. Though both in Right and Ob- lique Cylinders, the Right Line joining the Centres of the op- pofite Bafes, is alfj call'd the Axis of the Cylinder. Jxis of a Cone^ is a R.ight Line or Side upon which the Right- angled Triangle forming the Cfiie^ makes its Motion. Jxis of a Vcjfel^ is that quief- cent Right Line paffing through the Middle of it perpendicular- ly to its Bafe, and equally diftant from its Sides. Axis of a Conick Se^i'jK^ Is a Quiefcent Right Line pafling through the Middle of the Fi» gure, and cutting all theOrdi- iiates at Right Angles. Jixts in Opticks^ is a Ray paf- fing through the Centre of the Eye ; or it is that Ray, which proceeding out of the Middle of the luminous Cone, falls per- pendicularly on the Chryftalline Humour, and confequently paf- fes through the Centre of the Eye. /ixis of Ofcillatio>j^ is a Right Line parallel to the Horizoa palling through the Centre, about which a Pendulum vibrates. Common or Mean Axis^ is a Right Line drawn from the Point of Concourfe of the two Optick Nerves, through -^, which joins the Extremity of the fame Op- tick Nerves. Axii of a Len;^ or Glafs^ is a Right Line palling along the Axis of that Solid, of which that Lens is a Segment, Thus a Spherical Convei Lens being a Segment of fome Sphere, the Axis of the Lens is the Axis of the Sphere ; or it is a Right Line paffing through the Centre of it. Axis of Incidince^ mDiopirickSy is a Right Line drawn through the Point of Incidence perpen- dicularly to the Refrading Sur- face. Axis of Refra£iion^ is a Right Line, continu'd from the Point of Incidence , or Refraftion, perpendicularly to theRefrafting Surface along the further Me- dium. Spiral Axis^ in Architecture ^ is the Axis of a twilled Column drawn fpirally , in order to trace the Circumvolutions with- out. Axis of the Ionic Capital^ is a Line pafling perpendicularly through the Middle of the Vo- lute. The A X A X The y^xis in Vcrlirochio^ confifts of a Circle concehtrtck with the Bafe of the Cylinder, and is moveable together with it about it^ Axis. . The Cylinder is called ihtAxi^ ; theCircle the Perkrochium\ and the Rad'i't^ or Spokes, which are fometimes fitted immediately in- to the Cylinder, without any Circle, the Scytala. Round the Axis winds a Rope, whereby the Weight, ^c. is to be rais'd. The /ix'is in Peritrochio takes Place in the Motion of every Machine, where a Circle mny be conceiv'd, defcrib'd about a fix'd Axis, concentrick to the Plane of a Cylinder, about which it is placed ; as in Crane-Wheels, Mill-Wheels, Capftans,es?'f. See Wheel. The Dodrine of the Axis iu Periirochioy is as follows : I. If the Power apply'd to an Axis iK Peritrochio^ in the Di- redionAL perpendicular to the Periphery of the Wheel, or to &^G the Spoke, be a Weight G, as the Radius of the Axis GCis to the Radius of the Wheel C A, or the Length of the Spoke, the Power will juft fuftain the Weight, i. e. theWeight and the Power will htin aqtiilibrio. 1. If a Power be apply'd to the Wheel in F, according to the Line of the Diredion F D, which is oblique to the Radius of the Wheel, though paral'd to the Perpendicular Diredic^n, it will have the fame Proportion to a Power; which acts according to the perpendicular Diredion A L, which the whole Sine has to the Sine of the Angle of the Direftion D F C. Hence, Since the Diftance of the Power in A, is the Radius CA the Angle of Diredion being given, the Diftance DE C, is eafiiy found, 3. Powers A X B A 3. Powers apply'd totheWheel, in leveral Points F and K, ac- cording to the Diredions F D, and K 1, and I parallel to the Perpendicular on AL, are to each other, as the Diftancesfrom the Centre of Motion C D, and D I reciprocally. Hence, as theDiflancefromthe Centre of Motion increafes, the Power decreafes, and -vice verfd. Hence alfo, fince the Radius A C is the greatcft Diftance, and £grecs to the Power, afting ac- cording to the Line of Direc- tion, the perpendicular Power will be the fmallelt of all thofe able to fuftain the Weight G, according to the feveral Lines of Direction. 4. If a Power, a6ling according to the Perpendicular AL, lift the Weight G, the Space of the Power will be to the Space of the Weight, as the Weight to the Power; for in each Revolu- tion of the Wheel, the Power paiTes through its whole Periphe- ry ; and in the fame Time, the Weight is rais'd equal to the Pe- riphery of the Jxis : The Space of the Power therefore, is to the Space of the Weight, as the Periphery of the Wheel to that of the/^A-zj; But the Power is to the Weights, as the Radius of iheAxis is to that of the Wheel ; therefore, ^c. f. A Poiver and Weight being givea to conjiru6i «« Axis in Peri- ixochxo ^whereby it J]jaH be fujlamd _ Let the Radius of i\\c/Jxts be big enough to fupport the Weight without breaking. Then, as the Power is to the Weight, fomake the Radius of the Wheel, or the Length of the Spoke, to the Pla- dius of the ^xis> Hence if the Power be but a fmall Part of the Weight, the Radius of the Wheel muft be vaftly great, ex. gr. fuppofe the Weight 3000, and the Power 5-0, the Radius of the Wheel will be to that of the X.v;j,as6o to i. This Inconvenience is provi- ded againft by increafing the Number of Wheels, and jixes., and making one turn round ano- ther, by Means of Teeth, or Pinions. See Wheel, and Pe- RITROCHIO. B A TJACK, See Baguette. ^ BACK-NAILS, a Sort of Nails made with flat Shanks, foasto hold faft,andnot to open the Grain of the Wood, ufed in nailing Guts together, for fav- ing Water under the Laves of a Houfe; or by Back- Makers, in nailing of Boards together for Coolers, or any Veffels made of Planks or Boards for containing Liquors. BACULOMETRY, the Art of mealTning acceflible or \n- acefllbic Lines, by the Plelp cf one or more Staves. ^ BAGNIO, an ItrMan Term, iignifying a Bath. Thence Ba- gnio is become a general Name in Ttirky.^ for thePrilbns in viiiich the Slaves areconfin'd, it being u- fual to haveBaths in thofePrifons. BAKE-HOUSE, is aR-ooni of Office, or an Appartment be- longing to noble Buildings, atid other private Buildings, in which an Oven is built. A<: to the Pojltion^ it ought (ac- cording to the Rules laid down by Sir Henry Wot ton') to bt' pla- ced B A B A ced on the South-Side of any Building. BAGUETTE [hi Jrchhec- ture^z little round Moulding, lefs than an Jftm^al ; fometinies carv'd and enrich'd with FohV ges, Pearls, Ribands, Lawrels, XsC Though, according to M. Le Clerc^ when ^Baguette is in- rich'd with Ornaments, its Name is ch3ng'd,ftnd it is called :i Chap- lei. OiBugtiette^'is aTermufed by Carpenters, for a kind oiJf- tra^al^ Or Hip-Moulding ; by which is meant the outward An- gle, or the Hips or Corners of aRoof; which in fquarc Frames, where the Roof is three quarters pitch, contains an Angle of one hundred and lixtcen Degrees and twelve Minutes. BALANCE, in Mechanlch, IS one of the fix limpJe Powers principally ufed for determining the Equality or Difference of Weights in heavy Bodies, and confeqL^.ent!y other Maffcs and Quantities of Matter. The Balance is of two Kinds, "VIZ. the Anticnt and Modern. The AMicnt^ or Ro.nan^ called the Statera Kuinana.^ or Stcel- Tard., conijfts of a Lover, or Beam, moveable on a Centre^ and fufpendcd near one of its Extremes : On one Side the Cen- tre are applied the Bodies to be weigh'd, and their Weight mea- fured by theDivilions mark'd on the Beam, in a Place where a Weight moveable along the Beam, being fix'd, keeps \.\\cBa- iiKcc in (cqitii'ibfio. This is Hill in ufe in Markets, l^c. where large Bodies are to be weigh'd. The modern Balance now or- dinarily in ufe, confills of a Le- ver, or Beam, fafpeudcd exactly by the Middle, to the Extremes whereof are hung Scales. In each Cafe the Beam is cal- led the Brachia ; the Line on wiiich the Beam turns, or which divides its Brachia, is called the Jxis ; and when confidered with refpcdt to tl.e Length of the Brachia, is efteem'd but a Point, and called the Centre of the Ba- lance ; and the Places where the Weights arc applied, the Joints of Siifpcnjion, or Application. In the Roman Balance, there- fore, the Weight ufed for a Coun- ter Balance is the fame ; but the Points of Application various : In the common Balance, the Counter- Poife is various, and the Points of Application the fame. The Principle on which each is found is the fame, and may be conceiv'd from what follows. The^o6irine of the Balance. The Ecam AB, the principal Part of the Balance, is a Lever of the firft Kind, which ( in- (fead of reding on a Fulcrum at C, the Centre of its Mo- tion,) is fufpended by fome- thing falkned to C its Cen- tre J5 A 15 J\ trc of Motion. Hence the Me- chanifm of the Balance depends on the fame Theorem as that of the Lever. See the Figure. Wherefore as the known Weight is to the unknown, fu is the Dif- tance of the unknown Weight from the Centre of Motion to the Dillance of that of the known, where the two Weights will coun- terpoife each other ; confequent- ly the known Weight ihews the Quantity of the unknown Weight : Or thus, the Adion of a Weight to move a Balance is by fo much greater, as the Point prefs'd by the Weight is more prefs'd diftant from the Centre of the Balance^ and that Aftion follows the Proportion of the Diftance of the faid Point from that Centre. When the Balance moves a- bout its Centre, the Point B de- fcribes the Arch B^, whilft the Point A defcribes the Arch A om thele Computations, we may- compute the whole Value of a Square of fuch Timber-Work to be worth from 3/. 6i. to 16/. €d. per Square. BARS of Iron, upright ones for Windows; their ufual Price is three Pence Halfpenny, or four Pence a Pound in London. BAR' POSTS, a Sort of Ports, two of which, and five Rails or Bars, ferve inliead of a Gate,for an Inlet into Fields and other Inclofures : Thefe Ports conljfi E 4 ^ eac£> B A B A each of five Mortoifes ; and the Polls are vifually fix Foot, or {ix Foot and a half long, four of "vvhich (land above the Ground. Thefe Pofts are, in fome P!a- ces, made by the Piece, wz. o. Penny or three Halfpence per Poft hewing, and a Halfpenny per Hole, for mortifing. BASE [of BcUa, Gr. Reft, Support, or Foundation] is ufed to {ignify any Body which bears another ; but particularly, for the lower Parts of a Column, and a Pedeftal. The Bafe is alfo fometimes cal- led Sp'ira^ixow.Sp'ira, the Folds of a Serpent laid at Reft, which forma Figure notmuch unlike it. The Bafe of a Column, is that Part between the Shaft and the Pedeftal, if there be any Pede- llal ; or if there be none, be- tween the Shaft and the Plinth, or Zocle. The Bafe is fuppofed to be the Foot of the Column ;or,as fome define it, it is that to a Column, that a Shoe is to a Man. The Members or Ornaments whereof a Bafe is con^spos'd, are fuppofed by others, to have been originally defign'd to reprcfent the Iron Circles with vvhich the Feet of Trees and Pofts wore girded, which fupportcd the Houfes of the Antients, in order to ftrengthen them. The Bafe is different in the different Orders. The Tufcan Bafe is the mo ft fimplc of all Orders; confift- ing, according to fome, only of a fingle Tore^ befides the 'Plinth, The Doric Bufc has an JJira- ^al more than the Tufcan,, al- though that was introduced by r.Vo \loderiis. Tr-iC Ionic Bafe h^s zVjLT^eTore over two flender Scotia, fepara- tcd by two Jjira^ah : But there are no Bafes at all in the moft antient Monuments of this Or- der ; which Architeds are at a Lofs to account for. Fhe Corinthian Bafe has two 'Tores ^ two Scotia's^ and two /If tra^als. The Compofte Bafe has an Af- tra^al lefs than the Corinthian. The Attic Baje^ is fo deaomi- nated, becaufe it was. fir ft ufed by the Atheniant. It has two Tores^ and a Scotia^ and is very proper for Ionic and Compojite Columns. The Parts or Members ex- ceed the Number of theiCinds; becaufe fome Authors diff'erfroni others in their Form, according to the Account following : The Tufcan P^/^, according to Vitrwuius^ is to be one half Mod, in Height. This crofs Member confifts of three fmallerMembers, or Parts, viz. a Plinth^ a 7or«.r,and a Fillet ; and is divided, and fub- divided as follows : The whole Height being 30, is divided into two equal Parts ; the lower of which Parts is for the Plinth ; and the upper Part of the two is to be fubdivided into three equal Parts ; the upper of which is for the Ftllet., and the lower, for the Torus. 'Palladio alfo allows the Alti- tude of this Bafe to be thirty Minutes; which he diltributes among three fmaller Members, viz. a Plinth^ or Cr/o, a Torus., and a Lijlella., or Cindure; the 'Plinth is fifteen Minutes the Torus twelve and a half, and the Liflclla.,two and a half high, Scarnmozzi alfo allows thirty Minutes to the Altitude of this Bafe ; bul then he allows it but two B A two Members, or Parts ; which are, a Plinth ot eighteen Mi- nutes, and a Thorus of twelve Minutes ; altho' at the fame Time he places a Lift oi three Minutes above the Thorus. yigmla alfo makes thisBafe to conlilt of three Parts, a Plinth, Thorus^ and billet : All which he reckons thirty Minutes — half a Module. The Doric Bafe. This Bafe Fitruvius makes to coniilt of l-ix Parts, viz. zPlifith^iwoThorus's, one Scotia^ and two Lf/ls : To the whole Height of all thefe, he allows thirty Minutes, which he thus divides, viz. Firft, into three Parts; the lower one of •which is for i\\Q Plinth, and iub- divides the two remaining Parts "' into four ; the upper one of -which he allots to the upper Zio- rus, and the three lower Parts of thele four he divides into two; the lower of which two is for the lower Thorns : After which he fubdivides the upper Part of thefe two into ieven equal Parts; the upper and lower of thefe fe- ven Parts, are for the two Lifts, and the iiv^ which are betwixt them, are for the Scotia. But among all thefe fix Mem- bers, or Parts of the Bafe, there is one large Tiller, which is one twelfth Part of the Mod. but he does not reckon this Fillet to be any Part of the Bal>, but a Part of the Body of the Column. 'PalLzdio alfigns thirty Minutes to the Height of this Bafe ; Ac- cording to his Scheme of this Member, it is compofed of fe- ven Parts, viz. a T^limh, i\\-o Thorus' s, three Annulets, and a Scotia, or Cavetto, which he pro- portions as follows : To the Plinth^ which is wrought hoi- P A low, (and might perhaps be more properly called a Scotia, or Caff- rnent,) he allows ten Minutes; to the lower Thrrus feven one Third Minutes, a.id to the lower /imisilet. One one Fourth Minute, and to tlie Cuvettu Four two Thirds Minutes ; to the middle Anmilct One one Fourth Minute, to the upper Thorus four one Fourth, and to the upper Anmi- let One one Fourth Minute. Scamozzi makes the Doric Bafe thirty Minutes in Altitude, which are fubdivided among fix fmaller Members, viz. ift, a Plinth, (be- ginning below, and fo afcend- ing,) allowing to it ten Minutes one Sixth, idly, A Thorns of eight Minutes. '' "i^dly, A Lift of one Minute, ^thiy', A Scotia of four Minutes. 5-?^', A Lift of one Minute. And 6thly, A Tho- rns of live Minutes and a half. Above all thefe he places a Lill of two Minutes, which he does not reckon into the Eafe, but to the Part of the Body of the Co- Inmn, Vignola, inlikemanner, allows the Altitude of the B.ilc to be one half of the Diamerer of the Column below ; but he makes it to conlill of but four Parts, viz. a Plinth, a large and a fmallT/ja- rns, and a Lift. The Unic Bafe, according to Vi' trmnns, is half a Mod. fn Height, and in this Order defcribes two forts of Bafcs; the one for the Ionic Column, without a Pedeftal, andthe other for tijat with. Each of which Bafes confifts of fmal- ler Members ; But the Bafes are different in the Dimenfions of their Parts. The Members of which they con lift are thefe that follow, viz, a 'Flint h.^ lour Fillet s.^ two Sco- tia's, B A ila's^ two Jiftragals^ and a Tho- rns. Firft, as to the Ionic Bafe with- our a Pedelial. He divides and fuodivides this Bife as follows : He divides the whole Altitude of the Bale into three equal Parts ; ihc lower one of which is the Height of the Plinth^ the two upper and remaining Parts he lubdivides into feven equal Parts, the upper three of which make the Thorns ; and the four Se- venths remaining^, he fubdivides into eight equal Parts ; Half of the lower Eighth mrJics the low- er Fillet^ the other Half, and the fccond Eighth, and half the third Eighth, make the firll Scotia^ and the upper half oT the tlurd Eighth makes the fccond Fillet ; the fohirth and fifth makes the two JJlra^ab^ half the lixth Eighth makes the third Ftllct^ the upper half of the lixrh Eighth, and all the fcventh, and one Third of the lafl, or uppcrmoft Eighth, makes the fccond Scotia ; the t\i^o Thirds of the lafh Eighth which remains, makes the upper Fillet which flibjoins to the Thorns. He alfo places another Fillet a- bovc the Thorns^ which he does not account any Part of the Rife, but a Part of the Body of the Column'^ which Fillet is one Twelfth of the Body of the Co- lumn, =:five M. TUcIoaic Baf-, with aPedeftal, according to l^'^itriivias., is di- vided into Parts, as follows : Firfl, into three equal Parts, the lower of which is the Altitude of the Pliiiih ; the two Thirds remaining, he divides into three equal Parts, th.e uppermofl of which he afllgns for the Thorns; and the tv/o Thirds remaining, B A he fubdivides into twelve equal Parts ; half the lower one Twelfth he afligns for the fillcf above the 'Plinth ; the remaining Half of one Twelfth, and the three next Twelfths, make the fir(t Scotia ; the firth Twelfth makes the fecond Fillet^ the lixth and fevcnth make the two Jftra- ^als^ and Half the eighth makes the next Fillet; the other Half of the eighth and ninth, tenth and eleventh, make the fecond Scotia ; and the twelfth and laft Part makes the upper Fillet which is under the Thorus. There is alfo a Fillet above. thtThorus., which is of the fame Height with that without thePe- deftal. 'Palladia ailigns thirty Minutes for the Height of this Bafe ; and according to his Scheme of this Member, he divides it Into fix fmaller Members, viz. i/?, A ^Pliathj or rather, as be deli- neates it, a Ca/emeiit of ten Mi- nutes. 2 Vv, A Thorus of feven Minutes aiid a half. 3jiti or Rowan Bafc^ B A according to Vitruvius^ contain thirty Minutes in Height. This grand Member he divides into ten fmaller, viz. a Pluith. two Thorus^s^ (one of which is in [he Middle, where the two y^.firagals are in the Corintblart Order,) four Fillets^ and two Scotuis. He firft divides this Member into four Parts, the lower of which is for the Altitude of the Plinth; and then he fubdivides the other three Parts into five. Of the uppermoft cf the five, he makes the upper Thorus ; of the lower Fifth, and one Fourth of the fecond, he makes the lower Th:.rus\ (fo that the lower TT^o- rus is four Fifths high : ) The fe- cond fifth Part and three Fourths that remain, he fubdivides into twelve equal Parts ; of half the lower twelfth, he makes the firft Fillet \ of the other Halt, and all the Id', 3^, 42*/% and half the ^th^ he m.akes the firft Scotia ; of the remriiiiing Half of the -^th, he makes the ftcond Fillet ; of the 6th and -jth^ he makes the middle Thorus; of half the 8/^, heinakes the third Filtet; of the remaining Half of the S//', and all the ^th^ loth^ and iith^ and half the iith^ he makes the fecond Scotia; of the remaining Half of the 122'^, he makes the lart Fillet^ which is juil under the upper Thorus. Above the L'a/c*, on the Foot of the Cohtmn., he m.ikes a Fillet^ which is one twenty-fourth of the Diameter of the Column below. 'Tdlladio makes this Bafe thirty Minutes in /\ltitude, and dividci it into eleven fmall Members, viz. an Orlo., two Th<>rus''s^ four" Lifts., two Scotia s^ and tvio A- ftragals. To B A To the firft Member, being an hlo^ (which is concave) he al- Dws nine Minutes; next to that i^g re the two Thorus^s^ which are ;ven Minutes; then a Lift of a!f a Minute ; after that a Scotia f three Minutes ; then another /tft of one half of a Minute; ftcr that the two Aftragals^ of nc Minute each ; then a Fillet^ T Lijl^ of half a Minute ; and ext the upper Thorns of four Minutes. Above this, on the Foot of ie Column^ he places another 'ijiragal of three Minutes ; and llfo a Lift, of one Minute above nat. Scamozzi allows thirty Minutes :ir the Altitude of the Roman iafe, and divides thefe into fe- en fmatkr Members, allowing °n Minutes to a concave ^//W/5>, nd fcven Minutes to the firfl: '^horus; two Minutes to an J- ^raj^al; and to the firft Lift one "/linute ; to the Scotia four Mi- lutcs ; and the fecond Lift one vlinute, and to the upper Thorns ive Minutes, which is the high- ft Member of the Bafe. But he places two Members bove the Bafe^ viz. an Aftragal f two Minutes and a half, and Lift of one Minute one Fourth. Fignola mzkQS his Roman Bafe [cry much like that oiVitruvtns; ept, that he places two J(}ragels 1 the Middle between the two ^cotia's^ where yitruuins places Thorns. M. Le Ckrc fays, all the Parts f the Bafe of a Column ought 5 be plain, in order to ferve as Reft to the Flutings of the haft. However, he fays, there are 3me Occafions wherein the Th'- B A rns may be inrich'd ; of which w© have an Inftance in the new Cha- pel ail/erfaiiles^ where "tis done with a great deal of Prudence, For as nothing fliould be ex- pofed to the Eyes of a great Prince, but what fs fom( W:iys diftinguifh'd by its Richnefs ; and as the King here has in fight the Bafes of the Columns of his beat, 'tis but juft they fliouId be in- rich'd like the reft of the ( .hapel, which is extremely ponpous : But, fetting afide fuchOccafions^ it would be a Fault to adorn the Bafes of Columns; though Sca- mozzi is of another Opinion. ^Bafe of any ft)lid Fignre^ \S its lowermoft plain Side, or that on which it ftands ; and if the Solid has two opposite parallel plain Sides, one of them is the Bafe; and then the other is alfo called its Bafe. BASIL, with ^'o/W^rj, &c. the Angle to which the Edge of an iron Tool is ground. To work onfoftWood, they ufuallymake their Bqfil twelve Degrees ; for hard eighteen Degrees ; it being obferv'd, that the more acute or thin the Baftl is, the better and fmoother it cuts; and the more obtufc, the ftronger and fitter tor Service. BASILIC ?[ofB«m.««, Gr. BASILICAS aRoyalHoufe or Palace] aTcrm antiently ufed for a large Hall, or publick Place, with Iftes, Portico's, Galleries, Tribunals, ^c. where Princes fat and adminiftred Juftice in Perfon. But the Name has fince been transferred, and is now applied to fuch Churches, Temples, cjf Extend them trom one hun- dred forty-four to one hutidred fiftv-lix, (the Length HI Inches;) and the fame Extent will reach from fixteen to feventcen Feet one Third, the Content. ^ Exarr^plciX. Ifa Board be nine- teen ln?hes broad, how many Inches in Length will make a Foot ^ Divide one hundred and forty- four by nineteen, and tne QucA- tientwillbefevenvery near; and fo many in Length u^ a Board be nineteen Inches broad, will make a Foot. Inc. Inc. Inc. Inch. 19 : 144 •■: I : 7- 1 1 or 5 8 fere. II 13 U Again ; Extend the CompnfTes froin nineteen to one hundred fortv-Iour; that Extent will reach fromtnie to leven, fifty-eight,;.^. feven Inch-s and fomewha'- more than a half; fo that if a Board be nineteen Inches broad, if yt'U take feven Inches, and a little more than a hnlf in your Com- paffes, from a Scale of Inches, and run that E>tent along the Board ffom End to Er.d, you may find hov/ many Feet that Bonrd contains, or you may cut oft from that Board any Number ot Feetdefired. For this Purpofe there is a Line upon mort ordinary Jomt- Rules, with a little Table placed upon the End, of all fach Num- bers as exceed the Length of the Rule, as in this little Table an- nexed. Here you fee if the Breadth be one Inch, the Length mull be twelve Feet; if two Inches, the Length is lix Feet; it fiye In- ches broad, the Length IS two Feet five Inches, c/^ • The relt of the Lengths are exprefs'd in the Line thus : It the Breadth be nine Inches, you will find it againft fifteen Inches, counted from the other End ot theRulc;iftheBreadth be eleven Inches, then a little above thir- teen Inches will be the Length ot a Foot, {^c. , ^ BOARDING of Walls. See IVcather Boarding. ^ BOAT NAILS, a certain Sort of Nails. ^ , , • BODY [in Geometry^^ is that which has three Dimenfions, Length, Breadth, andThickneis. As a Line is form'd by the Mo- tion of a Point, and a Superfi- cies by the Motion ot a Line, lo a Body is general by the Motion of a Superficies. ^^^ r- -u To BEAR A BODY [with Painters.-] A Colour is faid to bear a Body, when it is ot iucU a Naiure, as is capable ot being eround fo fine, and mixing wita the Oil fo intirely, as to f:era onlv a very thick Oil of the fame Colour; and of this Nature are White-Lead and Cerufe, Lamp; Vermillion. Lake., 'Pmk., fellow Oker, Vcrdegreafe, IndJgo, 'Jmhcr and Spanifo Brovjn; Bim D- . ^.-.^ Ti^A.].o^I are not lo BluL Ye. Bke and Red- Lead are not fine ; but yet fo fine, that they may be faid to hear a very good Body. All thefe may be ground fo fine, as to be even like Oil it- 'F4 ^-^^ B O Vi-*'f ; and then they alfo may be ^aid to work well, Ipreading fo fmooth, and covering the Body or' what yoa lay upon it lb in- tirelv, as that no Part will re- main viliblc where the Pencil hath gone, if the Colour be work'd (litf enough. Whereas, on the contrary, Verdiccrs and Smalts, with all the grinding imaginable, will never be well imbodied with the Oil, nor work well : Indeed Bice and Red-Lead will hardly grind to an oily Firmnefs, nor lie intirely fmooth in the work- ing ; yet may be i;ud to bear an i-ddifferent Body, becaufe they will cover luchVVork very vvell, that they are laid upon; butfuch Colours as are faid not to hear a Bodv^ will readily part with the Oil, when laid on the Work ; fo that when the Colour fhall be laid on a Pit^ce of Work, there will be a Separation, the Colour in fomc Parts, and the clear Oil in others, except they are tcm- per'd extreme thick. BOLTS of Iron, for Houfc- B'aiiding,aredi(linguifi"!'dbyIron- Mongers into three Kinds, viz. Plate ^ Rounds and Spring Bolts : 'Plate and Sprin'T Bolts are ufed ior the hifleuing Doors and Win- dows, and thcCe are of ditrc;renr Sizes and Prices: S\t\^\\ Spring Bi)its have been fold lor three Pence Plxlf- penny per Piece, others at tn'ne Pence, others at fourteen Pence-; and fo like wife .'^late Bolts fome nine Pence, and fjme ten Pence a Piece. Tliere are alfo Brap-knoFd Bolts^ fliort and long; the iliort pre fold for aiiout ten Pence per i'iece ; and long for Folding- ^.*iHM'-. at e;;:r,tec:i Pence per B O Piece; and Iron Balcony Bolts at-- about ten Pence per Piece; and Round Bolts^ (or long Iron Pins,) with a Head at one End, and a Key-Hole at the other, which are ufually fold by the Pound, VIZ. three Pence Halfpenny or four Pence per Pound. BOND, a Term among Workmen, as make good Bond., means that they fliould fallen the two or more Pieces together, either by tenaniing, mortiiing or dovetailing, ^c. BOSSAGE 1 'w\ Arc kite dure ^ BOSCAGE 5 is aTermufed for any Stone tn.it has a Projec- ture, and is laid in a Place in a Building Lineal, to be after- wards carved into Mouldings, Capitals, Coats of Arms, C5^- ■ BoJ/a'^e is alfo that which is otherwifc called Ruflick l^'ork; which confills of Stones whxh feem to advance beyond the Na- ked of a Building, by reafon of Indentures (ir Channels \ef' in the Joinings : Tnefe are chiefly u{^A in the Corners of Edifices, and thence called Ra flick Quoins. The C-u iiies or Indentures are fnm.uimes round, and f imetimes chain-fram'd, or bevell'd ; fome- times in a Diamond Eorm, and fomctimcs it is inclos'd with a Cai-etto, and fomctimes with a Lidel. BUVHAM NAILS, a fort of Nails ih called by Ironmongers. BOULDER WALLS, a kind of IJ'^alls built of round IHints or Pebbles, laid in a ftrong Mort.ir; ufccl where the fea has a Beacn cad up, or where there arc plenty of Flints. As to the Manner of building thefc- ;rrt//x, a Bricklayer which has been ufed to diis kind of Wo-'^-. B R ■VVoik, Tiys, that in this Work they always ul'e a very ftrongl^ft' Mortar; and that it" they can fo order ir, they always worK two :r it at a time, one at one Side c ;■ the // rf//, and the other at the other ;,and one to the Right Hand :rad the other to the Lcrt; and t lat therefore it is beft if one of tiie Workmen be left handed : That they have a Hod of Mor- tar poured down on their Work^ band fo they fprcad jt betwixt them, each Iprcadhig it to'.vards 'ihis ov\n 5ide, and then lay their 'Boulders or Flints. He adds, that they had need have a good Length of Work before them, for chey work but one >. ourfe in height at a time ; for if they fhould do more, it would be apt to fwell out at the Sides, and run down; and for that Reafon are obliged to work continually lengthways. And that \^ this Work be done in miily Weather, it is very ditticult to make it ftand. Jls to the Price of this Work : It is commonly done by the Square, or hundred Foot, for ■which their ufual Price is twelve Shillings for Workmanfhip only. BOULTINE, a Term which 'Workmen ufe for a Moulding, tvhofe Conve.xity is juft one Fourth of a Circle ; being the Member next below the Plinth in the TufcaTi and Doric Capital. See Quarter Rou.\d. BRACE, in a ikilding, a Piece of Timber fram'd with bevel Joints. Its Ufe is to keep the Building from fvverving ei- ther Way. When Braces are fram'd into King-Pieces, or prin- cipal Raftei's, they are called \$trHts» B R BRADS, a kind of Nails ufcd in Buildmg, which have no Ipread- ing Heads, as other Nails have. Thefe are diliiiiguifhed by Iron- mongers by fix Names, i^Joincrs Brads y Flooring Brads ^ Batten Brads^ Bill Brads^ or Quarter Heads ^ &c. Juiyiers Brads ^ for hard Wood- Wainfcor, from one Inch to two and a quarter in Length. Batten Brads^ for foft Wood- Wainfcot the forts are O.ne-pen- ny. Two-penny, Three-penny ; dttto^ large ^^our-penny ; ditto^ large Five- penny, Six-penny. For Fhoring^ plain or foft Wood joilts, the forts are four- teen, fifteen, eighteen, nineteen, twenty, twenty-one, tw^enty-two, twenty-three, twenty-eight, thir- ty-two, and thirty-fix Pound per M. Ditto ftrong^ fit for hard Joifts, the forts are fifteen, eighteen, nine- teen, twenty-four, and thirty-two Pound /jfr M. Quarter Heads ^iox foft Wood, the Sorts arc ten, thirteen, fifteen, eighteen, nineteen, twenty, twen- ty-two, twenty -three, twenty- eight, and thirty-two Pound per M. ^itto ftror.g^ for hard Wood Joilts, the Sorts are fourteen, twenty, thirty-tour, forty-four, and fifty-four Pound fer M. N. B. All />'/// Brads, alias Quarter Heads, are very fit for fhallow Joints that are fubjed to vvnrp; or for Floors which are laid in hafte, or by unskilful Pcr- fons, becaufe the Bill with the Head will hinder the Boards from ftarting from the Joifts ; but do not makefo fmooih Work as the plain Brads. As B R As to the Prices of Brads^ of which I fhall fet down a (tv7^ as follows : As Joiners Brads^ the ufual Price d. OfaM. of ■4Ii>'Ii.chis-JI5' Quarter H. vds, or Pill-Brads, for foft Wood Floors, the ulual Price II;. s. d. 4 9 .5- 6 OfaM. of^^j^^is BRANCHES [in Architcc- turej are the Arches of Gothk Vaults. ThefeAicbes traverfing from one Angle to another Dia- gonal-wife, form a Crofs be- tween the other Arches, which make the Sides of the Square of which the Arches are Diago- nals. BRAZING, the Soldering or Joining two Pieces of Iron, by Means of thin Plates of Brafs melted between the two Pieces to be join'd. If the Work be very fine, as when the two Leaves of broken Saws are to he join'd, it is co- ver 'd vviih beaten Borax, moif- tcned with Water, that it may be incorporated with the Brafs Dall, which is here added ; and the Piece is expofed to the Pire with- out touching the Ccals, 'till the Brafs be oblerv'd to run. Laft'y.to:-)rze with a Hill greater Degree uf Delicacy, they ufe a Sol- der made ot Brafs, wich atenth Part of Tin ; or another, one Third Brafs, and two Thirds Silver; or Borax and Rolin ; ob- lerving, in all thtfe Manners of B R Brnz:ng^x\i2X the Pieces be join'd clofe throughout ; the Solder only holding in thofe Places that touch. To BREAK IN [in Archi- tedure] is a Term ufed by Car- penters, when they cut, or rather break a Hole in Brick-Walls, with a ripping Chizxel. BREST, a Term in Archi- tefture, ufed, by;fome, to fignify the flimc Member in a Column, that others call a Thorns. BREST -SUMMERS, in Timber Buildings, are Pieces in the outward Parts of a Building, into which the Girders are fra- med ill all the Floors but the Ground- Floor, then they call it a Cell ; and Garret-Floor, then ic^ is call'd a Beam. As to their Size and Square, it is the fime according to the Acl of Parliiunent, with that of Girders; which fee. It is here to be obferved, that it is not here meant, all the Pie- ces which have Girders in them,; (and are rot in the Garret, or Ground Floor:) but all fuch as are in the exterior Part of the; Building; v,hethcr in the Front, Flanks, or exterior P.rt of thd Building ; for the Pieces in the. Internal Part of the Building,; into which the Girders arc iram'd ( are call'd Snynmers. Mr. Leybourn favs that th( Brejl-Summers^ in London^ ar( meafur'd by the Foot, running Meafurc; but it is uncertain whether he means only for ih< Work or Timber, or both. Com. Comer fays, that Brcflk Summcr^^ \\\ London., arevalue^/. The firft werecall'dDidoron, AfSx'pov, i. e. of two Palms, The fecond, Tc- tradoron, TsTpa^topov, i. e. of four Palms. And the third, Penta- doron, nevrxlupou, i, e. of five Palms. They had alfo other Bricks juft half of thefe, to ren- der their Works more folid, and alfo more agreeable to the Sight, by the Diverfities of the Figures and Sizes of the Bricks. Of the Matter whereof Bricks are made. Plin^ fays, if yon would have good Bricks^ they muft not be made of any Earth that is full of Sand or Gravel, nor of fuch as is gritty or ftony, but of a greyilh Marl, or whiiifli C^^alky Clay, or at leaft, of a reddifh Earth : But in cale there is a NecelTitv to ufe that which is fandy, that is to be made choice of, which is tougn and Itrong. He alfo adds that the bell Sea- fon for making Bricks^ is in the Spring; becauie they will befab- je6t to crack and be full of Chinks, if made in the Summer. Hedi- reds, that the Loam of which the Bricks are made, be well fteep'd or foak'd, and wrought with Water - Mr, B R Mr. Inco mAIech. Excr. fays, that the Bricks made of the whi- tifh Chalky Sort of Earth, and the rcddifli are the bcfl:. hlLunenhurgh m Saxony ^x.\\Q.\t Bricks are made of a fat £arth, full of Allum. At Patana^ in AJia^ they make good Bricks of a Pumice Sort of Earth, which being dry'd, will fwim in Water, and not link. But here in England^ they are for the moft part made of a yellowifh-colour'd fat Earth, fomewhat rcddifh, vulgarly cal- led Loam. As for thofe Bricks made in England^ they fliould not be of fandy Earth, which will make them both heavy and brittle ; nor muft the Loam be too fat, which will make them crack in drying; they ihould alfo be m.ade either in the Spring or Autumin. Mr. Leyburn fiiys, that the Earth for Bricks ought to be dig- ged before Winter ; but not made into Bricks 'till the Spring Sca- Ibn. When Brickt have been made, they fhould be fhelrered from the Sun, if h be too hot, but yet muii be expcfed to the Air to dry. If they be made in frofty Weather, they muli be covered with Sand, and in hot Weather, with wet Straw. Of their Kinds andAppcUatiojjs. ^ricks^ among us, arevarious, ac- quiring various Forms, Dimen- lions, Ufes, Method of making, Place where, ^c. Thofe from their Foim, mxc Compafs- Bricks, of a circular Form, ufed in ftevning of Walls. 2. Concave^ or H'^'iovj Bricks^ on one Side ^ar, like a common Brick, on the other, hoHow'd. They are B R ufed for the Conveyance of Wa- ter. 3. Feather- Edg'd Bricks which are like the common Sta- tute-Bricks, only thinner on one Edge, than the other, and are ufec for penning up the Brick-Pan nels in Timber-Buildings. 4. Triangular Bricks. 1. Thofe from their Dimen- fions are, the Great and Small or Statute, and Didoron, Tetra^ doron, and Pentadoron. 2. Great Bricks, are twclvdj Inches long, fix broad, and three r thick ; the Weight of one is a bout tiftcen Pounds, fo that : hundred will weigh fifteen hun- dred Pound, and a ihoufand of them fifteen thoufand Pounds. 3. Thofe from Cuflom, are Statute and Cogging- Bricks. Cog^t:-}g- Bricks are ufed foi;|| making the indented Work un-|| dcr ihe Coping of Walls built i' with great Bricks. 1 4. Thofe from the Method of |> maki.ncr, are Pbce and Stock- 'j Bricks. -Place- Br'cks, are fuch > as are made in a Place prepared ' on purpofe for them, near the Building they are to be ufed in. Statute- Bricks, or fmall common. Bricks, ought to be nine Inches' long, four and a half broad, and two and a half thick. 5-. 1 hofc from the Place,where, or by whom are Dutch, or Fle- r-.'xf/h^ thefe are ufed in paving Yards, or Stables, and for Soap- BoilcTs Fats and CiitcrMs. 6. Thof.; from their Ufo, are Buttrefs or Ptlujler, Coping and ^Paving- Bricks. Buttrefs or "Ti- lajlcr Bricks, which are of the Time Dimenfionsiwith the Gre.^t Bri.ks, only they have a Notch at one End of half the Breadth of the Brick. Their Ufe is to bind th* \ B R B R the Work at the Pilafters of Fence- Walls which are built of Great Bricks. Copin^z,- Bricks are ibrm'd on Purpofe for Coping- Walls; Paving-Bricks^ or Tiles, are of fcveral Sixes in feveral Counties and Places. 7. Thofe from Accident, are Clinkers.^ Samel or Sandal. Clin- kers nre fuch Bricks., as are gla- xed by the Heat of the Fire, in making. Samel or Sandal- Bricks., are fuch as lie outmoll in a Kiln or Clamp, and confequently are foft and ufelefs, as not beipg thoroughly burnt. Of all which, I fhall treat in their Order, I. Compafs-Brich.^ are, as has been faid, of a circular Form ; and their Ufe is for fteyning of Walls; which is pcrform'd in the Manner following: A go(^d Bed of Clay is firft laid for the Bottom, and then it is pav'd with caramon or Statute- Bricks., only laid down, and well ffctled on it ; which being done, the Compafs-Work is begun with Compajs Bricks., and as the Courfes are carried up, they ram Clay in behind them, (Room be- ing left behind for that Purpofe,) which caufes all the Bricks to pen tight and clofe together. An experienced Workman fays, he has done this Sort of of Work, where the Walls have gone but a little Depth in the Ground, and in a loufe and open Mould, where the Water has Jen brought in by Concave- Bricks ; which held very well for thirty Years. As to the Price of thefe Bricks ., it is not certain; but they are not much dearer than common or Sta- tute Bricks ; but the Perfon who has them made for his Ufe, is ufually at the Charge of a Mold, made according to the Circum- ference of hisVVall. 2. Concave or Hollow- Bricks. Thefearc like ctmmon or Statute- Bricks on one Side, but have a Concavity or Hollownefs, on ther, which is femicircular. This Hollownefs is about three Quarters of an Inch deep, and an Inch and half broad, fo' that two of thefe Bricks being placed with their Hollows to- gether, they are like a Pipe of an Inch and half Bore. Thefe ^r/V ^7 are ufually about twelve Inches in Length, four and a half in Breadth, and two and a half in Thicknefs. /^s to the Manner ~ of laying them in the Ground.^ it is ufually done in Clay : But it fhould be carefully minded, that no Trees, Bufhes, or Brambles, be fuffcr'd to grow over where thefe Bricks are laid for the Conveyance of Water, nor yet very near them ; bccaufe their Roots are apt to get in betwixt the Joints of the Bricks, and there to fpread them- felves with Kibrous Roots, which meeting together like a Ball of Flair in the Concavity, will in Time ftop up the Paffagc, and hinder the Currency of the Wa- ter. Which Inconvenience could it infallibly be prevented, it would be the cheapeit Way of convey- ing Water to a Houie; for Bricks to the Value of feven or eight Shillings, willdoabout (ixRods; and fnppoline; the Vi^orkriianfiiip in digging the Trench, laying the Bricks., Charge of the Clay, and ramming up again, to be ns much B R liiuch more, oneRod would coll buc two Sliiiliiigs and two Pence*, or two Shillings and eight Pence; and would not be one lixrhPart of the Charge or" Leaden Pipes, and altogether as ferviceable, it not more ; becaufe they would laft (as may be faid) for ever : And preterrable to Lead, if (as we may fuppofc) the Vruii. would not hurt thefe , whereas it fre- quently burlh Leaden Pipes. For though the Water flioald be fro- zen up in them, and wc may rea- fonably fuppofe that the Ice would then, by expanding iifelf, open the Joints of the Bricks ; yet it is as reafonable to fuppofe, that afccr the Froft is gone, they will come together in their due Places, by the natural Gravity of the Earth; for then there will be no foiid Body betwixt the Joints to hinder the Bricks from cloiing again. And as to A'der Pipcs^ altho' they be much cheaper than Lead^ thefe of Bricks will not come to much above (if any thing at al!) half the Price of Alder Pipes. As to the 'Price of thefe concave Bricks: They have been fold in Kent for four Shillings /'c-r Hun- dred, and in SnfJ'ex for three Shillings ; two Hundred of thefe Bricks^ being a Foot in Length, will lay fix Rods, 3. Cor aj fin- Bricks^ arc a fort of Bricks in Ufe in fome Parts of SnJ'ex, for making their Tooth- ing or IndiMUed Work under the Coping of Walls, which arc built of great Bricks. They arc in Length about ten Inches, in Breadth four, and in Thicknefs two and a half, and are ufually fold at the Price of ccmmou Bricks. B R The Ufe of thefe arc to lay on the fops or Wails, jvAl undei the Copi^ig Bricks .^ in an oblique Pofiiion ; fo that one Corner o Angle projects over about twc Inches and a hair' on one Side and che oppofite diagonal Angl at the other, and projedhasmucl over tiie other Side, 4. Copiy/ar Bricks.^ are to b( ufed with great Bricks in build ing Fence- Walls ; and are much ufed in fome Pares c^f SaJJex. As to the Size and Form thefe Coping Brick'i.^ they are ij follows, ViZ. They are aboui twelve Inches fquarc, and foui Inches and a half thick, having one Side flat, or plain, and twc flat Ends; and the two Edges and upper Side, are comprehended under one curvilincal Surface; the two Edges conliiling of two Boultins, joined by two Cafe- ments, or Hollows to an Allra- gal, which is the Top of the Bnck in this Form — , Their ufual Price is from twelve to fii- tcen Shillings /Ji-r Hundred. | f. Dutch or Plcraijb Bricksj are in Length about lix Inches! and a q'larter, in Breadth twa' and a half, and i.i Thicknefs one and a quarter; or, as fome whol have meafured them fay, fix In- ches long, three broad, and one thick. They are of a pale Co lour, inclining to Yellow. They are commonly ufed here in England for paving Yards and Stables, for which they make good Pavements, and are very lading; Jind being laid ed-^'c-ways, are nc.aer and (Ironger than com mon Bricks., and look very hand- lomcly, efpccially if laid Her- ring-bone F'afiiioii. They B R B R They muft be laid :n Sand. They arc alfo ufed in making Fats and Cillerns for Soap- Boilers. 0{ thefc Bricks^ which are fix Inches and a quarter long, and two and a halt" broad, allowing a quarter of an Inch for thejoints, 72 will pave a Yard Iquare ; but if they be fet on Edge, it will take up about 113 to pave a Yard fqnare. But of the other Size, of fix Inches in Length, three in Breadth, and one in Thicknefs, fixty-three being laid flat, will pave a Yard fquare ; but being fet edge-ways, it will require one Hundred and fixty-five to do the fame. Thefe Bricks are commonly fold at London at two Shillings per Hundred. 6. Clinkers^ are fuch Bricks as have much Nitre or Salt-Petre in them; which, by reafjn of the Violence of the Fire, runs and glazes them. 7. Didoron^ a fort of Bricks ufed by the Ancients ; in Length two Spans, or a Foot and half, [the Word Swpov, Doron^ be- ing Greek for a Span, or the Space between the Top of the Thumb and little Finger ex* tended,] and a Foot in Breadth, Thefe were the fmalleft fort of Bricks ufed by the Greeks in their private Buildings; but for their publick Buildings, they had two larger Sizes, as you will find hereafter, called T'etradoron^ and Pentadoron. 8. tcather-ed^d Bricks^ are a fort of Bricks formerly ufed in Kent and SitJJ'ex \ they are of the fime Size as common Bricks^ but are made thinner at one Edge than they are at the other, on purpofe to pen up their Brick Fannels (as they call them) in Timber Buildings, and were commonly fold amongft the Sta- tute Bricks for that Purpofe. 9. Great Bricks^ are a fort of Bricks that are twelve Inches long, fix Inches broad, and three Inches thick. The Weight of one of thefe Bricks has been found to be fif- teen Pound ; fo that one Hun- dred will weigh one thoufand five hundred Pounds, and one Thoufand 1 5-000 Pounds ; which amounts to fix Tons, thirteen Hundred, three Quarters, and twenty Poun ds ; and fo one Hun- dred and fifty will be a Ton Weight. 1 hefe Bricks are ufed in build- ing Fence- Walls, together with Pilafter or Buttrefs Bricks^ and Coping Bricks. Thefe Walls are no more than fix Inches thick, except at the Fiiajiers., whej'e they are twelve; and it is ufual to fet a Pilafter at every ten Feet. There is a Wall, about nine Feet high, built with thefe fort of Bricks., that ftands very well, that has been built near thirty Years. Thefe Walls are reckon'd by fome to be m.uch cheaper than thofe of a Brick and half, or fourteen Inches of Stutjcte Bncks. Stt Wails. Thefe Bricks are fold by the Thoufand at forty Shillings the Thoufand, or four Shillings the Hundred. 10. Paving Bricks: Of thefe there are various Sizes, accord- ing to the Fancy of the Work- man, and the Cuftom of the Places- B R Places. Mr. Leyhourn fays, they arc fix, eight, ten, and twelvcln- ches fquare, and arc fold from Note^ That Bricks of B R fix to twenty Shillings per Hun- dred. Some call them Tiling- Bricks. laches fquare, will pave a Yard fquare. Paving- Bricks^ are made in Sur~ ry, and feveral Counties in Eng- land, of three f>.'veral Lirgenef- fes, viz. twelve Inches fquare, and an Inch and half thick ; ten Inches fquare, and an Inch and quarter thick ; and eight Inches fquare, and one Inch thick : Hi- ther of which Sorts being polifli- ed or rubbed with Oiarp Sand on the Surface, and well-joined, and the Sides rendred equal, by hack- ing them with a Brick-Ax, and rubbing them with a Rubbing- Stone with fharp Sand, makes an excellent Pavement, very hand- fome to the Sight, cfpecially "when laid Arras-ways. There have been made in Snf- fex'Pavi fig -Bricks fix Inches and a half fquare, and an Inch and fe- ven Eighths thick; two ofvv'hich have weighed ii /Z'. fothat a hun- dred of them would weigh 5')'o//'. and a thoufand, ■^fOoli>. and confequently, four hundred and feven of them would weigh a Ton. Some have been made in Srsf- fex nine Inches fquare, which were ufdally fold for Sj. per Hundred. An experi>;nced Brick-Maker fays, that he had made Paving- Bricks of Clav, fifteen Inches fquare, but found muchl'rouble to prevent their warping. Thefe Bricks, when burnt, were of a pale red Colour ; as were alfo f()me which he made l]\ Inches fquare of another fort of Clay, fome Miles dillantfrom tne former. He like wife lays, that Paving Bricks made of Loam, are red- ded in Colour, when burnt; but ought to be made of better Earth than comrmn Bricks, though they feldom arc by thofe who make them for Sale. He adds, that befide the Good- ncfs of the Earth, in Pavtng- Bricks, there ought to be a great deal of Care taken in the drying them, to hinder chem from warp- ing, and that when they have been dry'd, in drefiliig thcmfmooth and ilraight, cfpecially on the uppermolt Surface, and alfo in paring the Edges ilraight, and a little under, making an acute Angle with the upper Side, and in feeing that they be ex.iclly fquare before they are put into the Kiln to be burnt. The common Price of nine or ten Inch Paving-Bricks is from 8x. to 1 2 J. a Hundred in the Country. Thole of ten Inches have been bro'ight by Water trom Surre\\ to Seaport Towns in Kent ^u gin to fet them upon thole which Tverc firft laid on the Hack, by which Time, they will be a little dry'd, and will bear the others, being molded of very fiiii^ Earth. By that Time they come to let a Second, or Third, ^^. At which Time, they cater them a little, (as they call ir,) to prevent their reeling: And when the Hack is of a proper Height, they cover them with Straw, after the fame Manner, as they do 'Place- Bricks., ti'l they arc dry enough for Burn- ing. This, they fay, being more Trouble than the other Way, viz. of making Place-Bricks , for making and burning (belides the digging of the Earth,) they have 6.r. a thoufand, whichis i /. more than they ulually have for making 'Place- Bricks ; but they are under a NecefTity to make them after tnis Manner ; or elfe if they were laid abroad in a Place to dry, as the Place-Bricks are, the Quality cxf the Earth is fuch, that they would built to Pieces. There is an Inftancc of this, which is related by an experien- ced Brick and Tile-Maker, (who was ufed to work \n Kent and SiffJ'ex^^ who being fcnt tor to llnmfurd in E£ex., to make a hun- dred thou land of i)V/V^j, he unad- vifcdly, not knowing the Quality of the Earth, having (truck about athouliind, they being fet down to dry, after the Method of Place-Bricks., and lain till about Ten a-Clock, the Sun beginning to fhine very hot, the whole thoufand of Bricks burlf to Pie- ces, fo that he was forced to throw them av/ay, and go to work afrefn ; and thaching them (i. e. covering them) with^Stravy till the next Morning, and then raking it off, the Bricks did very well, when they came to be fet on the Hack; and after they had been burnt, were curious red Bricks., which would ring, being Itrack with any hard Thing. At this Place, they made none but Stock-Bricks before he found out the Way of making Place- Bricks of this Earth. 1 6. Statute.^ ^mell.,OT Commou Bricks. Their Dimenfions, viz. oi the Mold, according to the Statute, ought lo be as follows, viz. nine Inches in Length, four and a half in Breadth, and two and a quarter in Thickncfs with- in. Bricks made in aMoldofthefe Dimenfions (the Earth being firft well-temper'd) being dry'd and burnt, will be leller and lighter ; yet they fluink but little inThick- ncfs, lefj in Breadth, and fcarce any fhing difcernable in Length. As to the Weight of Bricks., that js uncertain, there being a great Difference in the Gravities of Earths ; yet in common, a fin- g!e B R B K f^le Brick will weigh about five Pounds, and contain ninety Cnbick Inches ; and from fome Molds, a hundred. Four Bruks being meafured, and weighed, each being nine Inches long, four and a quarter broad, and two and one Third thick, weigh'd twenty - two Pounds ; fo that a lingle Brick weigh'd five Pounds and a half, fl hundred of which, at that Rate, would weigh five hundred and ■ifty Pounds; and a thoufand, five thouHuid fire hundred Pounds ; and about four hun- dred and feveii would be a Ton weight. Thefe were Snjfex Bricks^ of which they ufuaJly reckon five hundred to the Load; which Number of Bricks^ according to this Proportion, will weigh a- bout twenty-four hundred and a half. Thefe Bricks are often ufed in paving Cellars, Walli-Houfes, Sinks, and Fire-Hearths, and the like ; thirty of which made, ac- cording to the Statute, will pave a Yard fquare,and three hundred and thirty of them, a Square of an hundred Foo^, being laid the iiatWay, and notfet edge-ways; for then it will require near as many more. It has been found by Obfer- vation,that thirty-two Bricks laid flat, will pave a Yard fquare ; andfixty-four fet on Edge will do the fame. It ii alfo found by Experience, that four thouiknd dx hundred Statute-Bricks will be required to make a fnperficial Statute-Rod of Brick- Work of a B.ick and half thick, and confequently fe- ventecri hundred to the Square, and an hundred and fifty- five to the fnperficial Yard, on a Wall of a Brick and half thick. As to the Price of thefe Statutt or Cowmon Bricks^ it is various, according to the different Places ; for they have ditTeicnt Prices iii different Parts of the Kingdom; which is not all neither, for Bricks in the fame Kiln, fnall have a different Price, according to the Dilhncc the Mafter of the Brick- Work is to fond them ; and alfo fome Contideration is to be had of the Price of Fuel, and Workmen's Wages. Mr. Leyhoicra fays, he never knew them cheaper than gs, nor dearer than 18/. delivered inany Part of LoKdoM. Statute or Common Bricks^ have been fold in fome Parts o^ Suf- fex and Kent, for 16s. a Thou- fand, laid down within two Allies didant from the Kiln ; and at other Times, they have been fold at 20/. a Thoufand. At another Place in Suffex^ they are fold at 25' j. aThoufand, if laid down within two or three Miles diftant from the Kiln : Whereas within twelve or fif- teen Years they have been fold for 20 X. a Thoufand. Burfince the Beginning of the lare Wars, the Iron-Works in that Part, have confum'd fo great a Quantity of their Wood," that Fuel of late Years is grown a fourth Part, or more, dearer than itu[ed to be ; for which F^eafon, they have lince raifed i\\Q.\T Bricks to 2.^s» a Thoufand. Mr. H'inoi; fays, that in Rt^t- land. Bricks are but 12/. aThou- land at the Kiln. [As to the Price of making Sta- tute-Bricks^'] the common Price G 3, ' iii B R B R in the Country, is 6d. a Thou- land for the Molder, ^d. for the Bearcr-olf, and ^d. tor the Digger and i emperor ot" the Eartii, fit for Ufe; and the Dig- ger of the Eurth lor making it ready, after it is digged, theDig- ging not being rcckon'd into the Making, Molding, Bearing ot!', ^c. and Burning, the ufual Price is yj. a Thoufand. Mr. Leyburn informs US, that about London they allow the Molder ^d. fd. or 6 d. a Thou- fand; and that Bricks made at Home, will Hand the Maker of them in (beiides the Value of the Earth,) betwixt y andOf.^er Thoufand. But it will be more in feme Parts of Ke»t and SuJ/ex. 1 7. Tetradoron^ a fort of an- cient Grecian Bricks^ which were three Feet or four Spans in Length, and one Foot in Breadth, being one of their larger Size, with which they built their pub- lick Buildings, Tr'tangyJar Bricks. Daniel Barbara.^ Patriarch of /i^uilia^ in his Comment on ^itruvius^ re- commends another Form of Bricks^vtz. Triangular ones, eve- ry Side a Foot long, and fomean Inch and half thick: Thefe, he obferves, would have many Con- veniences above the reft. As, Firll, being more commodious in the Management, Secondly, of Icfs Expencc. And Thirdly, of fairer Shew; adding much Beauty and Strength to the Mu- ral Angles, When they fall grace- fully into an Indented Work. Sir Henry H-^otton wonders they have never been brought in- 'to Ufe, being recommended by fo ereat an Authority. [The Method of burning ^r;f^j.]The Bricks ox Kiln being fet, and coverM< with Pieces of Bncks^ they firft put in fome Cord or great VVood to dry them with a gentle Heat or Fire ; and this they continue till iheBricks are pretty dry, which is known by the Smoak's turning from a whi- tilli, darkilh Colour, to a black tranfparent Smoke ; they then leave off putting in Wood, but proceed to make ready for burn- ing, which is perform'd by put- ting in Bufh, Furze, Spray, Heath, Brake, or Fern Faggots ; but be- fore they pat in any Faggots, they dam up the Moutn, or Mouths, of the Kiln with Pieces of Bricks^ (which they call Shin- log,) piled up one upon ano- ther, and clofe it up with wet Brick-Earth iniiead of Mortar. 7'his Shinlog they make fo high, that there is but juilRoom above it, to thrull in a Faggot betwixt one Foot and a half, :nid two Foot; for the whole Height of the Mouth is but three Foot, The Mouth being thus fliin- logg'd, they then proceed to put in more Faggots, till the Kiln and its Arches look white, and the Fire appear onthcTop of the Kiln, and the Kiln and Allies below begin to change from a white to a greyifli Colour ; then they iiacken the Fire for fome Timc^viz. for half an Hour or an Hour, that the Fire or Heat may afcend to the Top of the Kiln, by the Motion of the Air in at the Mouth; and alfo that the lower Ware may fettle and cool, and not be burnt more than that above it. Thus B R B R Thus they continue to do, heat- ing and ll.ickening alurnutely, tiW all the Ware is thorougiily burnt; which will be CDinmonly in a* bout forty-tight Hours, As to the cooling of Kilns of Ware, fome unsltilfuf Burners do, as foon as the Ware is burnt, immediately (lop, up the red of the Mouth of th« Kiln, which ivas left open above the Mouth of the Shinlog, which caufes it to be long a cooling; by which Means a Kiln will be ordinarily a Fortnight or three Weeks in fetting, burning, cooling, and drawing: Whereas an experien- ced Burner has affirmed,he has fet, burnt, cool'd, and drawn a Kiln a Week, for feveral Weeks fuc- ccflively one afcer another ; but then he never llopped up the re(t of the Kiln's Mouths above the Shinlog, but left it open, for the Air to go in and cool the Kiln of Bricks. He adds alfo, that fix hundred of Faggots will burn a Kiln of ten or eleven thuufand Statute- Brifks. And Mr. l^'iftg lays, that a Chaldron of Coals will burn four thoufand two hundred Bricks. By the foregoing Method, a Kiln of Bricks may be burnt fo equally, that thofe on the Top fiiall be burnt as hard as thofe at the Bottom : So that an ex- pert Burner affirms, he has burnt feveral Kilns of Tiles and Bricks together, about three thoufand Bricks., and ten or eleven thou- fand of Tiles, and has not had above fifty wafte, broken and Sandal Tiles in all : Whereas fuch Brick-Burners as continue ?heir Fire without any Inter- miffion, render their lower Brickf extreme hard, and thofe on the Top, Samel-Bricks, or Tiles : Nay, v\ hat is worR% they can fe the lower ones to run fo, by exceflive Heat, that they are al- moft united in one entire Body ; 1(3 that they are forced to gee them outu ith Wringers, (or Iron Bars,) and each Bolt of Tiles Ihall be one entire Mafs. About London.^ they burn their Bricks in Clamps built of the Bricks themfelves, after the Man- ner of Arches in Kilns, with a Vacancy between each Brick''s Breadth, for the Fire to play through ; but with this t)iffe- rence, that inftead ot arching, they fpan it over, by making the Brick's projett one over another on both Sides tiie Place for the WoodandCoaUto iiein,till they meet, and are bounded by the Bricks at the Top ; which clofe all up, proje&iiig over inwards, till they meet in the Middle; which they will do in about three or four Courfes of Bricks in Height. The Place for the Fuel is car- ried up Ifraight on both Sides, or, which is the fame Thing, upright on both Sides, till it is about three Foot high; then they fill it almolt with Wood, and lay a Covering of Sea-Coal over that ; and when that is done, they over-fpan the Arch: But they (frew Sea-Coal alfo over the Clamp, betwixt all the Rows of Bricks \ for they ai^ not laid contingent in their ver- tical Rows ; and one Courfe of Bricks is laid one one Way, ancj another, another ; fo that there are fmall Interftices through all B R B R the Bricks, for the Coals to be Arewed into. When this is done, they fire the Wood, and that fires the Coah', and when all is burnt, they conclude the Bricks ace burnt enough. Mr. Goldman obferves, that B:'':cks wiil have double the Strength, if, atter one Burning they be ftcep'd in Water, and burnt afrcfli. If the Earth be to fit, it muft be temper'd with Sand, and that trod out again, firft by Cattle, afterwards by Men. Bricks made of common Earth melt, nay, often vitrify, by too much Heat : For which Reafon, the Kilns are made of Stones, which will themfelves calcine, that the Vehemence of the Fire may be broken : Befides which, they nfually place other Bricks made of an Argillons Eartii, which would nielt next the Fire. What Quantity of Earth will make arhoufand Bricks'i Some fay, that a Load of Loam (a Load being twelve Eufhels) will ma'cv' about two hundred Statute-Bricks \ and if fo, confe- quently five Loads will make a thoufmd: Alfo that nineteen Load will make fixteen hundred Q^ Great Bricks', and twelve will be fufficient for a thoufandof the fame. Of the Choice of Bricks. Plinv ndvifcs in chuiing of Bricks for building, to procure (if it can be) fuch Bricks as are two Years old at leaft. There are generally in all Kilns, or Clamps, Bricks of three Degrees in Goodnefs. The firtl: and bed Sort are fuch as lie next the Fire, {viz. thofe arc bcft for laftlng,) which have as it were a Glofson them, which proceeds from the Salt- petre which is inherent in tlicm, and which runs, and glazes them, by Means of the Violence of the Fire. Thele are called Clin- kers. The fecond, and mofl general Sort for building, are thofe which lie next in the Kiln, or Clamp, to thofe Clinkers before mentioned. The third, and word Sort, are thofe which lie on the Outlides of the Kilns and Clamps, where the Saltpetre in them is not di- gerted for want of due Heat. jAnd thefe, when they come to be expofed to the Weather f )r fome Time,- will moulder away into Duft. Thefe are called by Bricklayers, Sar/jel or Sandal- Bricks. It is an Obfervation, that whiifl Bricks are burning, thole on the Inlide of a Clamp are the worft of all. Mr. li^orlidj^e, m his Syjlemd Agricultural is iur exciting the Brick-Makers to try their Skill in making a Compofition of Clay and Sand, to form in Molds, Window-Frames for Houfes of different Forms and Si'zes ; and alfo Chimncy-Pieces,and Frames for Doors, (s^c. in feveral Pieces made in Molds, that when they have been burnt, they may be fet together with a fine Cement, and feem to be but one entire Piece ; by which Means all manner of Stone- Work now ufedin Build- ing, may be imitated : Which would very well fupply the De- ficiency of Stones, where they are cither wanting, or fcarce and dear ; and at the fame Time, lave B R B R iave a great Dcr.l ofTimber now 11 fed in Briclc-Buijdings, and ap- pear much more compleat and beautiful, and be ot' greater Strength, and more durable for Iartin;:r, than Timber or ordinary Bnck. iVud one would imag!n# it ve- ry practicable, as may be per- ceiv'd by the Earthen Pipes made fine, thin, and durable, for the Conveyance of Water under Ground at Portfmouth in Hamp- Jhire^ and by the Earthen Backs for Grates and Chimneys, for- merly made by Sir John W'tater^ at Charin^-Crofs. Which are evident and fufficient Dcmon- llrations of thePoffibilicy of ma- kings Work fine, thin, and light, for Tiles of a large Si'z,c and Thick nefs, either plain, or cur- ved, and of making larger Work in Molds, and by burning them for Doors, Windows, and Chimney-Frames. This, fays he, is one of the mod feafible and beneficial Ope- rations that 1 know to be neg- ledcd in England. Another Author fays, he real- ly thinks much migh: be done as to making of Cliimney-Pieces, Stone-Moldings, and Architrave- Doors and Windows, and Ar- chitraves, or Fafcia's for Fronts of Buildings. If Men of this Profeffion would but apply their Minds to find out fome good Compofition of Earth, and a Method of managing it well in molding, burning, ^c. It may be queftionable, whe- ther a Compofition of Earth, fomething like to common Crockers Earth, would not in fome Meafure anlwer the Pur- pofe, fiace it appears plainly, that what Form foever they put their Earth into, the fame it retains after drying and burning, altho' Crocks, and fuch like Things, are form'd very thin. Now foppofe that Chimney- Pieccs, or the like, were made in Molds, and afterwards dry'd and burnt, if they were not thought fmooth enough when they were fet up, they might be polifh'd with fliarp Sand and Water, or a Piece of fharp Stone and Water. Or if Care were taken of fuch Things as thcfe (which are for Ornament, as well as Ufe,) when they were half dry, or more, in the Air, they might be polifh'd over with an Inftrument for the Purpofe of either Cop- per, Iron, or fome hard Body, and then left to dry till they were dry enough for burning, if fo, 'tis probable, they would not need imich polifliing afterwards. It is likewife as probable, that Ingenious Workmen might make very handfome and beautiful Chimney-Pieces, Stone-Mould- ings for Doors, C55^c. fit for No- blemens Houfes, and all others who would be at the Charge. Thefe might be glaz'd, as Potters do their fine Eartherii Ware, or elfevein'din Imitation of Marble, or be painted and anneal'd with Figures of various Colours, either Hiftory, Pcr- fpedive, or the like; which would be much cheaper, if not alfo as durable as Marble it- felf It is not, fays a certain Author, the Want of Materials, but Wane of Skill, and Diligence in ma- naging them, that makes our Englijb Buildings m the leaft Mca- Q 4 furs B R B R ^: fare inferior to any of thofe in foreign Countries. A certain EHgl'tjh Ambafiador made this Obfervation, That we oncht not to bedifcouraged with our ignoble Materials for Buil- ding, which we ule in Englan^.^ in Comparifon with the Marbles of Afia ^xw^Numidta: For, fays be, I have often view'd with much Plcafure, at Ft^nice, an Anti-Porch after the Greek Man- ner eretlcd by Andreas Palladto^ upon eight C^-lumns of the Ro- man Ordtr, the Backs of Stone without Pedeftals, the Shafts or Bodies of mere Brick three Foot and a half in Diameter below, and of Confequence, thirty-five Foot high, than which, he laith, his Eyes never beheld any Co- lumns more ftately of Sione, or Marble. The Br'icks being firll form'd in a circular Mold were cut before they were burnt into four Quarters, or more Parts, and afterwards, jointed foclofely and nicely in laying, and the Points to exadly concentred,^ that the Pillars appeared to be of one entire Piece. [Things worthy to be ob- ferved ill buying and laying of Bricks.'] I. As to buying. The fc- venth Number will be a fufli- clcnt Dirc&ion to any Wori^- man, (who docs not underftand it.) to chufo good Bricks. And in the i6th Section of Bricks, viz. under the Head o( Stat-ute- Bricks, there are Dire61:ions as to the Number of Bricks^ that will make a Square or Rod of Work ; though 'tis impolIjit)le to he exa6lly certain to a very fcvv ; bccaufc, Firft, the Workman's Hand may vary 'm laying the Mortar. Secondly, many^r/V/\f may warp in burning ; and the Seller will bring you feme fuch. Thirdly, Some will be broken and fpoilcd in the Carriage. Fourthly, you will often find the Tale deficient, if you be not ex- traordinary careful. And befides this, when Bricks aredear, and Linie cheap, and you put your Work out by the Great, or by Meafure, and the Work- man is to find Materials, he, ex- cept he bewell looked after, will ufe the more Mortur, and the fewer Bricks, making large Joints, which is a Del'edt in any Build- ing. ir. As to laying Bricks, which is a Tiling of no fmal-1 Confe- quence in any Building, in order to the Well-working and Bond- ing of Brick-Work (or as it is called by fome Workmen, Breaking' of Joint,) conduces very much to its Strength. It will not be therefore improper to add fjme pu-ticular DireifionsJ concerning ic, wiiich have been recommended by experienced Workmen. I. Tdke Care to procure good flrong Mortar. See Mor- tar. ' 2. If your Bricks are laid in Winter, let them be kept and laid as dry as pofllblc. If they arc laid in Summer-Time, it will quit Cod, to employ Boys to wet them ; becaule being wetted, they will unite much better with the Mortar, than if they were laid dry, and will render the Work much Hron- gcr. But B R B R But if it fliall beobjcacd, that if the BuiMip.g be larjz,c, it will be a great deal of Tnnible to wet all the jBr/V/'r, by dipping them in Water ; and alfo that it •will make the Workmens Fin- gers fore in laying them. To prevent thefe inconve- niences, Water may be thrown on each Courfe, of Bricks after they have been laid ; as is (liid to have been done by the Order of the Ingenious Mr. Robert Hook^ the Surveyor at the Building of the Pb\l/icia»'s-Co!kxe in li arwkk- hane. 3. If Brtch are laid in the Summer-Time, don't fail ro co- ver them, to prevent thv:ir drying too faft ; for if the -M'>rrar dry too hallily, it doth not cement lb firmly to \\\?7VX\r, and two Inches broad, and lay- ing it on the lad Toothing- Courfe, to bear it, or a Brick- Bar, pur upon the lad Toothing, will bear it till the next Quoin is fet upon it, and then the Bat may be taken away. 6. The lame Inconvenience, at an upright Quoin in a Brick and half Wall ; where it isufual to lay a Clofer next the Header, on both Sides of the Walls ; and in ^o doing, 'tis Joint in Joint all the Length of the Wall, except by Chance, a Three-quarter Bat happen to be laid. \\-\ order to avoid this Incon- veniency, and by that Means to make the Wall much firmer, lay a Clofer on one Side ; but lay a Three-quarter Baton theStretch- ing-Courfe, and join a Header next B R B R next to the Header, at the Quoin in the Heading -Conrfe. 7. Airo in two Brick -Walls, it will be the bed Way in Stretching-Conrfes, in which Stretching is laid on both Sides the Walls next the Line, to lay alfo Stretchiiit^ in the Middle of the Wall, and Clofers next to each Srrerching-Courfe which lies next the Line. [What Number of Bricks may be laid in a Day.] A Bricklayer and his Labourer (all. their Ma- terials being ready) will lay in Day about a thoufand Bricks^ in whole Work, on a folid Plain ; and fome dextrous Bricklayers will lay twelve, and fomc fifteen hundred. [Of Facing Timber-Buildings "vj'wh Bricks.'] This may be more properly called Cafing ; it being covered all over on the Outfide with Bricks^ fo that no Timber is to be feen. The Manner of per- forming it. Is as follows ; viz. Ail betwixt the Timber and the Wall Is a Brick'' s Length thick, (or Nine-Inch Brick- VVall,) but againft the Timber, the Wall is but four Inches and a half', or a half Brick thick, befide the Tim- ber. But experienced Workmen do not approve of this Method ; becaufe the Mortar does Co much corrode and decay the Timber. An experienced Bricklayer fays, that in pulling down Work at Ericij^e- Place., (which is one of the Lord Mergavenny'^ Country Seats,) the Timber wasextream- ly corroded and eaten by the Moftar. BRICKLAYERS WORK. What.] In the City of London., ^c. it conlifts of feveral Kinds, viz. Walling, Tiling, Chimney- Work, and' Paving with Bricks and Tiles. But in the Country, tis com- mon for the BricklayersTx-x^tlo comprehend thofe of the Mafon and Plaifterer alfo: But I fhall here confider it only as to the particular Branches of Walling, Tiling, Chimney-Work,Pavin;4, [As to writing a Bricklayet's Bill-] A Bricklayer's Bill 'may be made after the Method fol- lowing : M)\ B R B R Mr, Wr L L T A M B L A K E w E Y ^j" Bill of Materials had of, andlVork done, by Thomas Hailing, Bricklayer ^ June 5. 1732. For eight thounin4 cf Bricks, at 12/. per M. For four thouland of Tiles, at 20^. "per M. For fineen Hundred of Lime, at 12 x. fer C. For Fonrteeii Load of Sand, at 2/. 6d.fer\i. For five Hundred of Nine- Inch Paving- Files, at '} 1 1 s. per Hundred 5 For thirty Ridge-Tiles, at \d.\, per Piece r or three Weeks and two Days Work, for my-^ felf, at 3 X. per Dion 5 For tvventy-nve Days Work and a half for my ? Man, 2X, 61a'. per Dier,i S For a Labourer, twenty-rivc Days and a half, at"? I J. 8^. fer Diem 5 Theii Sum Total is . But if Bricklayers do not work by tbfe Day, then they write their Bills after another Manner : For then they either undertake the Work by the Great, viz. to do all, and to find all the Materials belonging 16 Bricklayer'* s-lVork\ or elfe they are to do it by Meafare, and to do all the Work, and to find all the Materials, at fuch a Price, by the Rod, for Walling; by the Square, for Tilitig ; and by the Yard, for Paving, ^c. But if the Bricklayer docs not find any Materials, he may then work by Meaflire ; and in this Cafe, his Bill may be made after the following Manner, viz. for fo many Rods of Walling, at fo mxichper Rod, zsfc according as he has made his Agreement, /. J-. d. 4 16 4 00 9 00 I 15* 2 15- 04 4t 3 00 3 03 9 I 18 30 12 5- i Sometimes Chimney- Work is agreed for with. the Bricklayer^ by the Hearth; either only to find the WorkmanlTiip, or that and Materials too ; and in this Cafe, the Bill is made according to the Agreement, There are likewife other Things which come into a Bricklayer's Bill viz. all kind of Ornamental Work in Brick ; which is ufually fet down and rated at fo much per Foot, or at fo much per Piece. Or there maybe aSumof Money uUow'd over and above the Price or Va- lue of the Rod-Work ; and then the Ornamental Work will be included in it. You are to underhand by or- namental Work, Arches, either Straight, or Circular, over Win- dows w B R B R dows or Doors ; Fafcia's, eithei" wirh, or without Moldings ; Ar- chitraves, Round Windows, or Rubb'd Returns, Friezes, Cor- nices of all Sorts, Water-Tables •wrunghf, and Water- Courfes : All which are valued by the Foot, runninj^ Meafure. Fo thefe may be added Bafe- Ivlouldings, and Plinths, and the the Splaying of the Jaumbs of Windows and Doors on theln- fide of Buildings, Ain< Pilalkrs, Peers, Pedi- ments, Grotto's, and Rullick Quoins. j"ne(e five lall mentioned are valu'd -at To much per Piece, ac- cording to the Largenefs and Goodnefs of the Work and Ma- terials. An■. *■'/. q^ s. f. d. a. s. d q. 1 I 2 D I 3 -d ^1 I '■'•' 2 I I o rt 4 I o :; I I f 1 ^ 3 I 3 u^ 6 -. I c 2 I O S-l ^■' ' U 7 2 I I 2 3 8 3 I 2 3 a* 9 3 I 3 3 i rt .J — j;:: lO 2 4 c O II 2 I 4 2 rf 12 10 •2 2 5- 1-1 13 I 2 2 5" I 3 I 2 jo 2- 3 3 ^' ? ? , U. x6 2 jo 3 I 6 3 O 17 2'o 3 i 7 18 310 3 2, 7 - 2 3 IQ I 3|o 3 3 7 c z 2C 2 ojo 4 1 8 2 a. 21 2 OiO 1 4 I 9 o 22 2 1 4 i 9 I u a. H ^3 26 2 2 i|o 2 4 3 5" 9 3 10 I -> 2 30 5" I 5- 2 10 3 11 27 2 3;o ^ 3 II 3 28 0,0 6 o I 2Q 3 iO 6 I I 2 30 3 .|o 6 2 I I 3' 3i 3 .jo 6 3 I 1 2 3 2 7 c>!^ I 3 3 ^P 7 I'l 2 I B R B R «j/^ Rod 10 X. 30 X (40 J- l5'0x. ■ t-i- t+ od 15-.. 22X 6ri.!30X 37 -f 6^. ° 8 4 O -tf n 2 8 I 3 7 4 f 3 8 1 1 r<-^ M 2 10 2 3 10 c 4 9 9 6 o -a 3 15 i6 3 I 2 4 2 )" 2 2 10 S 3 4 2 4 6 >" 7 2. I £ 2 (L> IT 3 6 ■> 4 9 S II 1 II 10 2 ber of 1 iS 19 3 9 3 5" I 6 4 1 12 8 2 4 f 4 6 8 Ci 13 4 a 20 4 3 5- b ^ I 14 2 3 21 4 6 6 G 7 6 If 22 4 8 I 6 -> C 7 9 ■^1 If 7 2 2-^ 4 10 2 6 6 8 I 2 16 3 o o o 25 f I 2. 6 10 8 6 2 i":^ 5- 3 3 7 I 8 10 1 17 8 2 (SJ l6 5- 6 ^1 7 1 9 1 i« 6 2 h 28 5 9 6 3 c 7 9 9 1 19 4 2 3 10 I 29 5 :; 3 4 10 S I 10 30 6 y I :^ 7 10 8 I I S 2 5 8 I S ji 1 1 I -> I 2 3 2 ^2, 5 10 29 2 II 5* 2 I 2 II • 1 ^3, 7 I H9 6 ojii 10 1 ■^1 I J 9 Ti;, B R B R The Explanation of the preceding TAB L E. Firft^ At the Head of the Ta- b'e, over each Column, is the Price of one Rod, three quarters of a Rod, half a Rod, a quarter, and half a quarter of a Rod. Scir>ndly^ In the firlt Column is the Number of odd Feet, from one dcfccndin^ to thirty-three; and againft thefe odd Feet, in the I other Columns, flands the Price I or Value which the odd Feet come to, at the feveral Rates over each Column. The Method of ufing ft is as follows : Find the Price /'fT Rod agreed on in the Head of the Tables, and juft under it you have the Price of three quarters, half, a quarter, and half quarter ; and under them, in the fame Columns, you will tind the Price of any Number of odd Feet from one to thirty- four, or one Eighth of a Rod. EXAMPLE I. At ^\^ theRod^ vjhat is the Value of three quarters^ an half a quarter^ and half-qu-arter of a Rod^ and thirty'three Feet ? /. The Price of the whole Rod is The three quarters is -7- The half is The quarter is The half quarter is The thirty-three Feet is s. o I)- lO S 12 II d. O o o o 6 lOi The Sum is 13 14 04: EXAMPLE II. At il. 10 s. per Rody uihat comes thirty Feet to 1 Look at the Head of the Ta- fs. /\d. 7; which is the Price of ble for SOS. and you will find 30 Feet, atjoj. perRod. EXAMPLE III. What comes 25* teet to^ at 4I. i^s. per Rod> Becaufe you cannot find 4/. find what 25- Feet comes to at 15- J. at the Top of the Table, lox. per Rod, which is \od. ^; therefore firft find out what 25" and in the next Place, what 25- Feet comes to at 4/. per Rod, Feet comes to at yx. per Rod, which will be 7/. and \d, next which is ^d- \, H Set BR BR Set them down as follows: /. s. d. 2^ Feet at 4/. per Rod is ■ 07 i 25- Fee: at ioj. per Rod is o o iii ij Feec at j-/. /^-r Rod is . o o 5^4; The Sum is 08 5" EXAMPLE IV. If^hat comes 29 Feet to at 7I. ics. per Rod'\ 29 Feet at 5- /. per Rod is 29 Feet at 2/. lo/. fer Rod is — The Sum is • — /. s. d. 10 S S ii If / - EXAMPLE V. ir^at comes 32 firi^ to at 6 1. 17s. 6d. per Rodl 52 Feet at 5-/. per Rod is 32 Feet at i /. per Rod is 32 Feet at IOJ-. per Rod is 32 Feet at ^ s. per Rod is 32 Feet at 2/. 6^. per Rod is - The Sum is — /, s. d. 11 lok 1 I li- 7 .->- 16 ri A Tlble B R B R A Table for reducing Brick-Work of any Thick- nefs, to the Standard Thicknefs of a Brick and half. ^- Brick. I ririck. li -Br ck.l 2 ! Bricks. /<:. ^ . /^. li. 4L JP li. 6) F.^R. I 22 I Oiiartcr 22 4f I 2 Quarters 4^ 1 22 2 2 45 3Qa:irtcr"- I I 2 C I I 22 2 4;r I o}i 22 ^ i 2 4^- I I 22 2 02 2 45- « ^ I c 2 C 3 0! 4 > a 4 I I 22 2 2 45 4 ojy I 22 ^^ 3" I 2 4:r 3 I 22 5" 0! 6 2 45 O (L) 6 2 c 4 6 q| 8 7 2 I 22 4 2 45" •7 / o| 9 I 32 U2 82 2 45 5- I 22 8 10 2 45" 93 o c 9 o'l2 103 I 22 6 2 45" [O o!i3 I 22 ex, 113 2 4^ 7 I 22 II 014 2 45- :3 124 8 12 016 « 13 4 I 22 8 2 45 '3 0.7 I 22 C 14- 4 2 45' 9 1 22 '4 1 s 2 45" 15 r f> c ro c li" 020 1 o 16 r I 22 10 2 4f 16 1 21 I 22 ^ I7p 2 45 ri I 22 17 o|22 2 45" O I S;6 1 12 iS 0|24 on -73 196 I 22 12 2 45- f9 Oils 1 22 C^ 20|6 2 45 13 I 22 10 o|27 2 45- 21 7 14 021 \ ¥ H a B R B R A Table for reducing Brtck-Work of any Thick- nefs, to the Standard Thicknefs of 2i Brick and half. 1 2Bricks7. 3 Brick s. SBrickbi. 4b ri.ks. /? (5). /•. R (5) F R 6) P R o-'. /-" <=^_ =^ ■x^ 1 Quarter I 4)- 2, T 22 2 4)- 2 Quarters 3 22 I I 4f I I 22 3Quar tcrs I I c I 2 I 3 c- 2 1 I 2 45 2 c 2 I 22 2 2 45- _J 2 3 I 22 4 4 2 45 S I 22 3 5 c 6 7 c 8 4 6 2 45 8 9 I 22 lO 2 4f U-, 5 h I 22 fO II 2 ^\> 12 I 22 O o 6 10 C II '4 16 u 7 1 1 2 45 14 16 I 22 18 2 45" ^. 8 ^3 I 22 16 18 -> 4f 21 I 21 -J •03 9 15- C 18 21 26 i 4)- 10 16 2 4f 20 1 "1 I 22 II i;^ I 22 12 c 2f 2 45'J29 0,32 I 22 t5 12 20 C 24 28 t c 13 21 2 4) 26 30 1 -i;34 2. 45- o ex. H 23 I 22 28 c 32< 2 45';37 I 22 ly i)' C 30 c 35- ■40 16 26 2 4^ 3^ c 37 I 22 42 2. 4^ Q 17 28 I 22 ^4 ^.9 2 4f 4f I 22 o o o i& 19 30 C 3^ 42 48 31 2 4)-3S 44 I 22 fO ■^ 4? e^ 20 33 I 2240 46 2 4)- f3 I 22 ai 3)' 041 Q 49 ^6 A B R B R A Table for reducing Br ic/z-lfork of any Thick- nefsj to the Standard Thicknefs of a Brick and half. 4 Brick .SM5-P ricks. )I3 ricksT. A'. ^ ^\7 8124 o ( 16 ^ 4^ ^9 I 22 9|27 o (.. 30 c 33 lO 30 c. 33 I 223^ 2 45- 11 33 " c 36 2 4-r 40 I 22 12 36 c 40 44 13 39 43 I 22 47 2 45- ^ 14 42 46 2 4f 51 1 22 5 15- 4f fo SS SJ j6 48 { f^ I 22 y8 2 45- C3 o u to O 17 iS 19 51 5-4 ( c f6 6q i 43 62 66 I 22 S7 6; 1 22 69 2 45- »J 2060 c 66 2 4^73 I 22 21 63 i ( 70 077 Pi TU« B R Tioe ExpLiiution of the Table. Ac the Head of the Table, is fet the Tnicknels ot" the Wall, in Bricks and half Bricks, from half a Brick ia Thicl:neli,to li\ Bricks thick. tn the firft Column is placed the Number of the Rods con- tain'd in any Wall, from one quarter of a Rod to twenty-one Rods ; and againtt thofe Num- bers, in the ouitr Column, (lands the Quantity of Brick-l^^ork^ in Rods, Quarters, and Feet, which a Wall con:ains of any of thefe Thicknellcs, at the Head of the Table. EXAMPLE I. If a W'lll u>o>i the Superficies •>»tuiyi tivclvc R.ods.^and':t be three Bricks and a hjif tn Thichnejs., I'QVJ many P^ods dies that I4'uii contai\xoien {o as to bear Waggons with tl',e heavieil L^ads for fevcral Weeks ; and upon (he Thaw happening, fuch Mountains of Ice daflied againll the Piers, as fliook them, and canfed feveral Arches to fall down. But nevcrthciefs, the third Pile on Av'gnion Side, with the Chapel o'l Si. Nicholas W:.\\i':Y the Situation of Places and Circumftiucs 'nQteQ.'iy^B/-idges. Some Diftieulties are to be met with. Wiiereas Pailadio directs, l^iat in order to build a Bridge, Firfi, To make choice or that Place in a River that has the lealt Depth ot" W^ater,to the End that it may be hitting ; and that the Foundation may be even and firm, as Rock and Gravel- Scone, Secondly, l^hat thofe Places be avoided, where the Water turning, makes Vortexes or Whirle-Pools, and where the B.utom is i'ol't Sand or Gravel ; becaufe thete Matters are eafily carry'd away by the Violence of great Waters, which commonly alter the Bed of a River, and fap the Foundation of the Piers, and are often theOccalionofthe Ruin of Bridges. Thirdly, and L«7/?/y,The Stream of the Water mutt be (Iraighr, and without Elbows or Sinuoli- ties in the Banks; becaufe thefe Turnings and Windings will come in Time to be dettroy'd by the Force of the Current, and the Bridges will become infula- ted, and v.'ithout Epaulments ; and bcfides, that there will be amafs'd in thefe Places a thou- fand filthy Things which the Ri- ver B R B R er will carry thirher ; which be- n^ (lopp'd by the Piers, will at a(t cho.ik up the Opening of lie Brioi/^e. AH ihefe Ditnculties which Pciliiidio mencious oi'cen, happen o be ill a Place where one would )roje6t a Bridge ; and ic is the ^ddrets of an Ariiil to lunnount hem by Art, The Btid;ie called Pont-Nem"^ land that of the ThuilU'ries^ had never b>-en ercded in the Places where they are, if all thefe could have been hud: But when one can have his Choice, it will be very well to follow PaJhidiu^s Advice. This Author, beliJe<;, Hiys thar there are two Sores of Bridges ; the one made of j Wood, and the other of S:one. Thac wnich is erected over Ithe Torrent called C/J/z/c-??^ at the 'Foot of the y?//>fj-, between the Cities of Trent und BajU'ane in Ital)'^ is form'd by lix equal Bays of Joifts, and carried up entirely to [he Length of near ieventeen P^aihom, between the Abutments built upon the Brinks of the Ri- ver. Ftg^.l. LMate I. The Joifts lying along upon the Beams, ana being cover'd, make the Flanking or Floor- ing and Way ol: the Bridge. S^e the Figure's. Palladia lays, that there is no Bridge made ufter the fecond Manner. ScePIaiel. Fg- U, Although we are aflar'd there is one inGermafty. And inEltlct, M. B/o}7dcI^ who relates all that Pulladio has faid, alfures us, that he has feen the like at Nerva^ a City belonging to the King of Svjeden., in the Q\x\i oi Finland^ in the Baltick- Sea. The Affemblage of the Third, is that of a Scheam- A-rch, TheDivilions are unequal in Number ; and it has at each End along Brace at theEnd bLlow, iu the Wall of the Abutment. The Fourth Figure is in the Form of a Vault, or Mold for an Arch ; and the Afiem^ages between the two Poincons are difpofcd atter the Muiiner of Voulfcjirs. The Divilions are in Number unequal, that there may be one Voulluir in the Mid- dle, ferving as a Key. Says M. Blondei, if there were another Aliemblage equal to that of the Bridge underneath ir, the Work would be infinite- ly llronger.. Upon this Notion, it was pro- jected, to make a H ridge crofs the River Seine., overagainft the Seine., above St. Cloudy to abridge the Way of l^'^erfailles. As to Stone- Bridges.^ Palladio obferves four Things: I. As to the Heads of Bridges^ or their Abutments \[. As to the Piers. III. As to the Arcades. IV. As to the Pavement upon the Arcades. The Abutments ought to be very folid, and to be made on fuch Places of the Rivers that are rocky, hard Gravel, or good Ground; otherwife, they mult be fecured by Art, with other Piers, or other Arches. The Piers ought to be equal in Number, to the End that there may be one Arch in the Middle, where commonly the Water has the greatcit Current ; which ren- ders the Work ftronger, more equal, B R equal, nnd more agreerible to the Sif^ht ; tlu'l'\)imd;uions ought to be laid at that i ime of the Year, during wiiich the Waters are at the li'wel}, as in Autumn: And if the i'oundaiion is rocky, hard Gravel, or Stany Ground, the fird Stones of the Foundation may be laid without hollowing or digging any deeper. But if it be foft Sand, or Gra- vel, then it will be proper to c:ir- ry it oft", till vou come to find a iblid or firm Bottom; or, if this be too ditficult, you mull; at lealt carry ort'one Part of it, and pile the reft. But in the firft Place, that Side of the River where you are to work, mult be inclos'd in Dams; and the Current mult have its Liberty on the othci Side. As to the Piers, they ought not to be lefs in Bigneis than one lixth Part of the Breadth of (he Arcade ; nor commonly more than a Fourth. '["heirStnidiure ought to be large good Stones, well joined together wit.'i Cramps of Iron, or other Metal ; to the End that by this Encliainment, they may be as one e;itire Stone. It has been a Cuitom to make Advances or Projednres at the End of Piers, at Right Angles ; nnd fometimes in Semicircles, the better to throw oit the Wa- ter, and to ircfill «hc Shocks of Trees, or other Things, which the River carries when it is lari;^c. Thirdly^ The Arches ought to be made of very long Stones, nnd well jointed. Thofe are the flrongx-'ft, that are femicircular ; becaufe they bear entirely upon the Piers, without pudiing the cue againft the other. B R When one is conftrain'd by the too great Height, the Arches may be dimini(hV, or made Scheain- Arches ; ib that the perpendicu- lar Height upon the Line of their Chord may be one Third of the fame Chori^; in which Cafe, tiie Abutments muft be extreamly well fortify'd. After this, Pclladio gives the Deiigns of fome antique ^r/W^c"/, or of his own Invention. The fiift is that of R'an'r/it^ built by jiugujlui^ over a R.'ver twenty-nine Fathoms bioad, made wi:h ine Arches ; thethree middlemoft: are equal, and each twenty- five Feet; and the two others, but twenty Feet ; theA- butments are each levc;i Foot and a half; the Piers are eleven Feet; and the Arches femicirci'la''. •'Fhc IV('jc£lure of ttie Piles rifes no higher than the Imp'.)fts, above which are Tabernac'es and Niches for placirg of Sta- tues. The whok Length of the W')rk Is crovvn'd with a C( riiicc; and above that, a Pa- rapet, adorn'd from its Zocle, its B-ife and Cornice, v ith Tuf- can and maflive Work. He aftet wards gives the Dc- fcription of the Bridge over the Bach'tgiiaKe^ ot (ixteen Fr.choms wide, compos'd oi three Arches, each twent^-tvvo ^'oot and a half; the Abutments, two Foot and a half m Breadth, and the Piers five Feet. The Arches are Schcam ones ; and thjit Height is one Third of the lame Chord, as well the mid- dle Arch, as the other two. Fie alfo gives an Account of the Bridge \^[ Rcro»e^ whofe Ri- ver is fixicen Fathoms wide. The Bndgf B R B R ErJJgels compofed of three Ar- ir: I'hat the Piers ought to be chcs'; that in the Middle, being equal in Number and Size, iweuty-uine Feet; and the other ThcM'r Breadth fl)ou!d be one two, twenty-five eiieii; the A- Third of that of the Opening of j^utments of wiiich, are but three the Arch. That there muit be T^oot and a halt, and the Piers, before the Piers Juttings-out in five Feci ; their Projcfture, at the Form of the Prows of Gal- Right Angles; the Arcades are lies, againit the Current of the bchcum ones. Water; which ]uctings-our, in Palladia alfo gives the Dcfign their Proje6h\re, jiiult have one of a BnU^e iifter his own Man- halfofthc Breadth of IhoPieritfelf; ner, over a River thirty Fathoms and which mull be railed above •wide, between the Brinks of the greatcll Heights that the Wa~ the River, and the Abutments, ter rifes ; and that ihfre mull be whicl) con fills of but three Ar- made on the other Side, otiicrs ches; that in the Middle, being in T'orm of Poups; which will ten Fathoms, and the two others, notbedifagreeable, if their Points eight apiece; the Piers two Fa- are cut off, and made more blunt thorns, or one Fifth of the than the other. Breadth of the great Arch. He fays, it will not b« amifs, Ihc Arches are Scheam ones, if on the Right of the Juitings- and their peipendiculur FJeight out, there be Counterforts on above tlie Impolts, is one Third each Side, or Pilailers reaching of their Breadth. up the Height of the r'r'ui^e^ the Leon Baptifla Albert tells us, better to fufiain the Flanks ; and that the Parts of a Bruige^ are their Breadth below, not to be the Piers and Arches ; and the Icfs than two Thirds of that of Pavement above the upper Part the Pier; the Import of the Arch of the Brid/j has a large Way ought to be entirely out of the for the Pallage of Cattle and Water: The Ornaments of the Waggons; and little Banks on lonick or rather Doric Architec- each Side, for the Conveniency ture. of Foot Palfengers, inclos'd on Scrlio tells us, that at Punt the Outfide by their Bread- Sixtus^ the Piers have oneThird Works, or Parapets. of the Breadth of the great Ar- In fome Places, he fays, Br/W^^j ches; the greatcll Arch but half are cover 'd, as antiently //<^r/<2«'j a Circle of Height (jf one Sii- Brid^e :it Rome was, now call'd teenth of the Diameter. Po»t St. jK^efo^ which was the At 'PoKt St.Any^eh.^ the Piers fintft and mofi mignificent of them all ; the Ruins of which cannot be beheld without Vene- ration. As for the Strudure of a Bnd^e^ he fays, it mu(t be al- lowed the iame Breadth as the grand Highway that abuts upon are one half of the great Arch, and is fcmicircular; the Bandeau, or Head-Bund, the Height of one Ninth of the Diameter of the Arch ; the Piers bear upon a grand Bafe, or Patten of the Pillar, in Form of a Zi;cle quar- tered, raifcd fomc Feet above th : otd'n:^ry B R B R ordinary Level of the Water, by a Projv.'<51:ure on the Outlidc, round the whole Pier. Its Spur, or Counterfort, is a Semicircle, which riles to the Middle of the Arch ; a fqiiare Pilalter above its Par:ipet, with Pede{l;ils, at equal Dift;inccs ; which forveto lullain, according; to the Opinion of AlhcrtH^^ the forty-two Columns which tup- pore the Covering of the Brtd^e^ the Arches being femicircular. The Br-d^e dc Qjt.itro Ciipi^ a;i- tiently Fubr'tcms\ of which the Author relates, that there are but two Arches remaining, which are eqnnl and femicirj^rular, have a Pier the Breadth ofti^e Arch, with a Spur,or Counterfort, round it, and a Niche above. The Bandeau of the Arch is ruflick, and its greatcft Height is one Tenth of the Breadth of the Arch. \PontM'!h'::is has femicircular Arches, born upon Impnlls of the Height of one Third ofthcir Diameter ; the Piers are half the Breadth ; and upon them, there are Niches withon: Ornaments. M. Blondel^ of the Roynl J- cademy rf Sciences^ an accompiifli- ed Man, cnuled to be buiit at A'ainfes, upon the Ch.ve-fitc^ near the Place where the Ebb of the Tide commences, a Bridge of Stone, in the Yenr 1665-; the Piers of this Bridge are in Pro- portion, ns 3 to 8, as to the Breadth conipar'd with the O- peni'ig of the Arches ; the Pier at the End, towards the Pout Levis^ and which fervcs for an Abutment, has one S-'xth of the greateft Width ; bixaufe it is to - tulbiii on that Side the Pulh of all the Arches, (which are Schcain ones.) in ord.r to carry the Keiglit of the Impods above the common Height of the Warcrs of the River, without making any Alreration of the Level of the Old Bridge. Ti'.is is in a Manner the S;b- fl:;nce of whai the moll celebra- ted^ Archirecls have given us in Writing, as to the Proportion of Bridges; but no body has given us as yet the dcmonltr.ative Rea- fons : They have not acquainted us with the Fufts of their v o- lumns; what Meafures we fliill give eithec to the one or the other; which may be helpful to us in imtatinsj t'lem : Thev have given us no Reaion why they do after that Manner, ra:her tl.an anv othc'-. The ablcfi Archirc^s are not agreed amoMg themf;;!vcs ns to the Proportions they give to Buildings, not only as to the'r Solidity, but even not in refpccf :o their Ornaments. So true it is, Thar Arts and Sciences are ftill imperfed:. All thefc depend upon a certain Taite and certain ideas that Men have had different from one another, and in different Ages. So many Archit.-cis, fo many d'ff.'rent Man^iers. It may be feen, as to all that hns been before related, they give us no Reafon why they make their Piers, their Abutments, their Arches, ^c. of fuch a Largcnefs, or fuch a Thick nefs and thofe who now work ac cording to thefe ancient Exam pics, know no more than th Authors themfelves, for what Reafons they do fo. They f B R B R They condu6t thcmfclvcs on- ly by Ideas that they cannot de- mon (trate ; but which appear to he imitable, by the Example of lb many others who have fuc- ceeded other w i Lc ; for which Rea- fons they fay the Work ii beau- tiful and Iblid, becaufe the Pro- portions between the Parts which compole it, are there obferv'd. Although I have made a dili- gent Search into this Affair, lays M. Gautier, I have not found what has fatisfy'd^^e. It were to be willi'd thatfome accomplillVd Perfon would fet himleU' upon the folving of thefe Difficulties, in order to render them eafy to the Pub- lick. M. De la Hire, of the Royal Academy of Sciences ^h^S labour'd for this Purpofe; but thofe^vho are not fo learned as himfelf, cannot comprehend him, for want of being acquainted with Algebra , he having exprelled himfelf iaTcrms drawn from this Science; which, Workmen, and Perfons of but a moderate Share of Learning, know little or no- thing of, and confequently un- derhand not how to be profited by them. Of the 'Projection of Bridges. The Sieur Gautier^ Archite6t, Engineer, and Infpeftor of the Bridges to the French King, fays, in his "Traite' des Ponts^ there arefo many Things to be known in relation to the building of Bridges^ either of Carpentry, or Mafonrv, that it is hard to find one Man that is equally qualified with the Knowledge ot them all. And it is fufficient in a Work of Confequence, if many Perfons can be found, who, all of them together, underftand well what is bcft to be done. A Carpenter or Mafon of Ex- perience, cannot be to highly prov'd. Thefe two Perfons are ordinari- ly the Head, the Workmen, the Arms; and a well-accomplifli'd Engineer, or Infpe<5lor, the Soul of the Work, for either the carry- ing on, and the ready Execution or good Manner of it. And it is impoffible, this Conduftor, who fhall be an Engineer, Archi- teft, or Infpeflor, be fo fitly qualify 'd for that Office, as that he may be depended upon, unlefs he knows alfo the working: Part. ^ Nor is it pofllble, he fhould know the working Part, if he does not know the Parts and Materials to be ufed in the Work ; and alfo the Utenfils, Scaffolding, Plummets, Engines for raifing great Weights, Pit- Wheels, Pumps, Buckets, ^c, for emptying and clearing the Foundations, Dams, l^'c. of lb many different Forms ; the Man- ner of piling the Foundations great Borers for boring the Rocks according to their Confii'fence ; Centres, or Molds for Arches, Affemblages, the Cut of Stones, and an infinite Number of other Things which cannot be fore- feen : So that for thecredting of a confidcrable Bridge^ he ought to be a Perfon of univert'il Knowledge, and not ignorant of any Thing that relates to thcMy- ftery of Architedure, which fip- pofes the Knowledge of all thofe 'VJ B R B R thofc Things, if he would fiic- ceed. When any one projedts a Bridge^ he ought to begin 1. With making an cxri- ther of Mafonry, or Carpentry ; ■with the Number of Arcrics, and Quantity of Piles, Bays,cr Joifts. He mult always lay down the Bridge over the River upon the Square, and never Wanting. 3. He mull:, upon this Plan, trace a Line which dial I cut the Bridge in the Middle, and there found the Depth of the Water from Fathom toP'aihom, or from two to two, or from three to three, according as there Hiall be Occnlion. This Sounding is to be made either by aPo'c, divided into Feet, at the End of which is a Leaden Weight, according as the Cur- rent oi the Water Ihall require. If this fliall not be fufficient, he muft make ufe of a Cannon- Bail, put into a little Bag, tyed to the End of a Cord, which has been before divided into Feet and Fathoms. He mult make ufe of thefe, or other Methods, which fliall be found to be moll proper, accord- ing to the Rapidity of the Water that is to be furmounted. All this is to be done by means of a Boat, which may be con- cluded \n difierent Manners; ei- ther by a Cable, which is carried a-crofs the River, or by other Cords made fall to Trees, or .Stakes on the Bank, or to Stakes drove down for that Purpofe ; round vvhich the cable that is to hold it is to be many Times turn- ed, and flacken'd, according as Occafion requires, to guide tlie Boat more to one Side than the other. 4. The Soundings of the Wa~ ter being made, and fetdown on the Plan, they fcrve for making a Profile of the River, which marks or fets out the Depth of the Water that has been found ; and the Line under the Water, whether it be fandy or rocky, to which Attention muft be given, marking the Diflerence on the Profile.^ Upon this Profile is marked by a Line the D^pth of the Water, at the loweft it is at any Time of the Year, which the Bridge-Mailers of great and navigable Rivers will acquaint you with; and the Peafants or inhabitants of the neighbouring Places to fmall Rivers, will in- form as to the Height of thofc Inundations, which have hap- pen'd in their Memory. There may alfo be drawn in the Profile, which fhall fhew the a Mean of the Height of the Wa- ters. All thefe Lines being drawn by a perfect Level, parallel the one to the other, may be waflied with a Water Colour. 5-. The Profile being thus railed, a Sounding-Iron may be made, of a convenient Length, for founding below the Depth of the Water, the Ballall, or Sand; and no Certainty can be attained till this is done, and the Depth of the Water be known ; And, ill J B R B R in order to this, there are two Metliods ufcd, either by a Sound- ing Ii)ftrumenr of Iion, made on purpofe, having a large Ring at its Hoad tor a Crowning, crofs which there goes the Arm ot' a Borer, larger or fmaller, in or- der to turn it v/ith ; and having at the Top a Head to be driven down, to make it enter till it comes to a firm Bottom below the Sand«. This Sounding-Iron is made pointed and barbed at the End with four Angles ; fo that being bored or forced through the Sand, or Part of the Rock, or Iblid Ground, that it meets with below the Sand, by being turned feve- ral Times, in order to bring up in the Hollows of the Barbes fomefmall Quantities of the folid Ground it meets with, and thus being drawn up, the Quality of it is to be entered down in the Memorial that is previded for this Purpofe, in order to know what kind of Ground the Bot- tom is. There are Inftruments for founding of another fort, which have a little Pocket in the Form of a Snail-fhell at the End in the Shape of a Borer, which receives noLhing but Sand in turning one way, and the Earth under the Sand by turning it the other. Thefe Sounding Inltruments mull be all of one Piece, that they may be as ftrong as may be; Ibmetimes they are adjufted ac- cording to the Hardnefs or Eali- nefs of the Ground to be pene- trated ; fometimes they are of no Ufe, efpecially when the Sand is too grofs, and meets with Flints that the Sounder cannot remove. Vol.. I. In this Cafe, they make ufe gf a Stake of Oak made round, of the ihaicell Piece of a Tree of three, four, five, or fix Inches Di- ameter; which liavingdctermin'd to what Depth of the Earth they would found, they arm with a Lardoir, or pointed Iron at the End, for removing the Flints; with a Ferrel at the Head, to be able to refill the Strokes of a Beetle with two or three Helves, with which the Sounder is driven down. All this requires a great deal of Pains, Care, and Expence too; but the Satisfattioh of doing the Work well, and making a faith- ful Relation of it on the Profile, of the Depth of the Sand or Gravel that is to be piled, or which onght to be removed for the Foundation of the Piles, in order to fettle the Dams necef- fary, will make amends for them; and fo long as a Perfon is igno- rant of this Depth, he can neither projcft a Bridge^ nor know how to compute the Expence, fince he cannot tell what Timber it will take up, nor what Precautions ought to be taken for lecuring the Work. 6. When a Knowledge of the Confiftence of the Ground has been obtained, as whether Sand, Earth, Rock, ^c^ then a perfon may proceed with Safety upon the Profile he has made, to lay down the Projcftion of the Bridge^ whether of Mafonry or Carpentry; then the Length and Thickntfs of the Piers and Piles may be known, according as the Foundation mufi be more or lefs in Depth. I This B R B R 7,This being done,andtheHcight finifli the Work in a certain otthe iiigincli Inundations beiiig Time, before the R.iins of A"- known Iry thelntorinationof the tiimn. which make Rivers ovcr- antientcrt neighbouring Inliabi- flow ; a'^d a manv Precautious tants,]Vlarksaretobemadeatthi'; are mcelT.ry to betaken, that can- Height; and fuppofing three Feet not well be enumerated, upwards to be the IntradofTe, or inward Face of the Arches of the Brid<[e that one would lay down a Frojedion of, and alfo the Bays, Joifts, Beains, ^^c. of a Wooden 5r;Vi^'f, which is tie fame : The Work may be fo regulated, that it may be known to v hat For a B'id^e of Carpentry. The Builder mull inform him- felf from whence the Timber mud be had : if it be found and good ; the Time for procuring it; the Civirge of ir, as to what it will coft, laid down at the iTiuft be carried. all the Materials mav be ready in 8. The next Thing to be done, Time, to begin the Work with- is to provide the Materials which out Hinderance, and to be able arc to be employ 'd in the Work, For a Stone Bridge. It ought to be confidered from whencetheFreeStonemay behad, its Difiance, the F.alinefs or Dif- ficulty of cutting it, its Carriage, its Nature, as to its being ftrong or weak, in regard to the Effort it is to fuftain, being prelfed by the Reins of the Arches, if it will be able to fuftain the g:«ion of the River. Weight ; for there is feme Stones A^ thefe are neceflary for the to finilh it before the contrary Scafons for the compleating of the Bridge commence. The Breadth of Bridges are to be regulated according to the Multitude or Throng of People who pafs over them, end the large Streets or Roads that abut upon thcni : The Ht-ight and Breadth of tlie Arches, accord- ing to the Commerce and Navi- fo tender, efpecialiy having been but lately taken outof theQuarry, as one may fay bleeding, that they will crack, fplit, or fliiver to Pieces. As to the Lime, it is to be conlidered from whence that is to be had, its Nature, and when it takes hold, whether as foon as it is ufed, or a long Time after; the Wages of Workmen, the Chcapncfs and Conveniency of having Provifions, the Conve- niencv of the Place, and Num- ber of the Workmen required to laying down an exaft Projection, To thefe may be added, other Things necelTary, according as the CircLimftances of the Place fhall require, and according to the Pifcretion of the Miiter-Builder. Of the Largemfs of Bridges, in Proportion to the ^antity of Water they rniifl receive ivhen Inundations happen. It has been already faid, when any one lays down the Projecti- on of a Bridge, he mull inform^ liimifilf as to the Quantity of Waters B R B R Waters which pafs in the Uivcr over which the Bridi^e \s to be bui!r, in order to make the Ar- ches, the crois B'-'anis-, Joirts,^^^-. of a fufficicnt Largcnds, to be able to give them a Currency. Tht common Rule is tomalce the IntradolFes of the Arches at the Places of the Keys; and the crofs Beams or Joilb of the Bridges of Carpentry, three Feet higher than the highest Inunda- tioiis. This Rule is not obferv'd in all the Arches of a ^r/(^^ 391 "^ Js'Sl it overflow 'd twice. ►^CfPi twice. Ill B R B R r it w.is like r. Deluge 6qo< duriiiJ twice ov^i- ^ J C flovvius- 'n (^ this laft 7;(;c'r ovcr- . '^ ]^ fiow'd twice. *c /^Vespasian. SjVNerva, "C J^\drian. '^ -\ A.N'TONiNus Pius. •£ ^Marcus /. urelius. -, V.Mauritius. K. rG. III. Gregory II. Adrian I. Nicolas I. Gregory IX. Nicolas III. • Urban VI. in 1379. ^•< Martin- V. SiXTUS IV. •Alexander VI. LeoX. Jlfment VII. h Paul IV. in 15-57. PiusV. and SixTusV. 15-89. £ VClementV. in 159S. The Water under the Arches of a Briaj^e fhould never be for- ced, fo as to caufe any Difor- ders orTurbulencies under them, more than they ordinarily have at the Banks of the River within which they ordinarily flv)w ; if there be given to thefe Arches between the i'icrs a Palfnge equal to thar the River had in ics natu- ral Bed, fo that if its Breadth, for Example, were one hundred Fa- thoms, the Void of the Arches becween the Piers and the Abut- ments fhould have the like Breadth ; to the End, that the Fridion or B.^atiiigof the Water againft tlic Piers of the Brid^e^ when biii't, be equal to that w: ioh they made on the Ban/fs of the Rivcr beiose the building of I lie 'WuPie. A Budge may be made equal to the Brcad'h of the Ri\er, by making cheii Abntments to enter the Lind beyond the Banks of the River, as much Sp see as the Piers ( ccupy in its bed, ard by that M^'.nis rendering the Pref- fure of the Water under the Ar- ches equal to what they were be- fore the building of the Bridge. Of the Rapidity of U^atcrs under Bridges, a?i'd the Means to a- "Void it. It is certain, that the Piers o Bridges don't become deftitute of Gravel, nor oftener fall to Ruin , by any l^hing mcu-e, than by the Rapidity of thofe Waters which undermine their Foundations. If the Current of a R'lver can be dimin idled, it is certain tha the Piles of a Bridge wiill not be in danger of being fo cften over- thrown : And there are but two Ways of lefP-ning the Curienr of Rivers; the firlt is by lengthen- ing their Couil'e, in making them circulate in a Plain, if it be pof- Hble, and the great Turnings and Windings that they are m.ide to have, diminifl)ing their Declivity, caufes them to lole their Force, by Reafon of their great ^^.ompafs. This is the Means that the An- tients made ufe of, in rendciirg their Rivers navigable, wlu^rt- the Difpofitionof theCouniry w n d permit it, they bting unacq.v i c- ed wiihthe Aitofni; kii gSin-c s. But this JVlcthcd is not pi i^ti- cable in (lopping thcC^iM !' o: 3 River, at a Place w 1 cic u Are is Occaii jii ior a Fringe. I3 Tli< B R The fccond and lad Method of^diminifliing the Courfe or Cur- rent of a River at the Place of a Bridge^ and which is what the Antients knew nothing of, is by flopping fliort the Funds of the moll: rapid Rivers, by R.ows ofBanks, Stakes, or Piles, which cut the Curreat ofthe Water iit the Bottom of the Bed, and raile it to what Hcii^ht onepleafes. Waters augn^ent and diminifli in Rivers, in Proportion to their greater or lellcr Declivity ; which they find in gliding in their Bed, ■which they hollow or wear by li; t e and liitle : From the firlt Ages that they have begun to flow, they hol- low them more and more every Day, according to the Force they have of carrying along the Sand and Stones in their Inun- dations. All thefe Bodies defcending, rub or wear the Banks of the Rocks, which contain thofe Ri- vers, and aggrandize them, or bring them to that L-irgcnefs in which we fee ti^.cin at this Day. It is in common at thefe rocky Places, where the Rivers are moil kept in above, and the moft quiet or fmooth ; and from whence they pnfs with greater Rapidity, becaufe of their Fall. Thefe Rocks h.ave given Men the Notion, and par them upon imitating them, and rendering Rivers calm and navigable, ar- tificially, bv Retentions, fo as to make the Waters lofe their Ra- pidity on their Surface, by giv- ing it to them underneath by their Fall, which they have to leap from above theSluice made by Art. And this is the Method that ought to be ufcd to hinder tiiu wafking away of the Foua- B R dation of a Bridge^ when it is not ft)unded very low. The Bridge of Conrjan^ in Langued'C^ one of the fineft Bridges in this Province, upon the River /hide^ in the Diocefe of Narbonne^ has fliaken, or fal- len by this Default. Rivers may be made to flow wi;h more or lefs Rapidity, as they are more or lefs pent up. I fhail cxplnin myfelf. When a Projection of :: Bridge over a River is made, it is certain that the Piers of Mafonry, or the Rows ot Piles or Stakes that are projeftcd there, dimi- nifli the Bed of a River over which a Bridge is to be made. Now fuppoling this Diminu- tion to be but one Fifth ; we may conclude for certain, that when Inundations hnppcp, they will hollow the Bed one fifth Part more thnn they did before the building of the Bridge ; becaufe the Waters gain in Depth what thev have lolf in Breadth. Again, it is certain that the Bed oi a River having been ren- dered narrower by one Fifth, t'le Waters which are always the fame in Quantity in their Cur- rent, from their Sources to the Sea, being divided into threii Streams or Rivulets, or re-uni- ted into Rivers, pufs with grea- ter Qaicknels by one Fir'th, in the Place where they are con- tracted within a fmaller Coni- pafs, in order to erccl a Bridge there, and by Confcquence, wa(h away the Foundation ; from whence they have more Hold by one Fifth; and they hurry away with this firlt Filth with the grea- ter Quicknefj, the Flints, ^c. and fuch other Bodies, whicfi they B R B R they had not Force enough to carry alonji: with one Fifth lefs of their Weight, or the (^uick- neCs of tlicir Motion, which I efteem as equal the one to the other. If the Current of an en- tire River be retrench 'd the one half" of its whol? Length, there is DO Doubt but that the Waters which this River contain'd be- fore, would flow with a double Rapidity; and, on the contrary, that they would diminifh their Quicknefs by one half, if they fhould be enlarged one half more than they were. For Example: The Pont Ro ty or Swiftpefs, and Weight; the lame Waters palluig under 'Pont Royal of the Thailleries^ would carry a Flint of two Pound Weight, according to the Proportion of the Greatncfs ot the Opening of the Arches of the one Bridge and the other, and the Retrenchment of the Waters at the Time of their Overflowings. All thefe Notions are cflen- tial to a Man who projeds a Bridge. If we would examine further the Force Waters have upon Bo- dies of the fl^me Matter, but of ^^/f, or the Royal 5rzV^^ of the different Bignelles, the Realbn Thuilleries in Paris^ over the Sc'r/ie^ fcventy Fathoms long, its Piles bar the Breadth of the River, diminifliing it about one Twelfth- there is no Doubt to be made, but that the Waters pals onel'welfth quicker through will ealilybe perceived, why they carry away Sand fooner than Ballaft ; and the latter, than Flints, than great Blocks of Stone, although all compofed of one and the fame Matter. And when it fliall be known, the Arches, than they pafled be- that the Movement join'd to all fore the Bridge was made For the fame Reafon I con- clude, that jPo^^iVe^/f, above that of ihtd htiHleries ^ being, for Exam pie, twice as large as that of the Thuilleries in the Opening of its Arches ; for they have about ninety-fix Fathoms void Space in their Length; whereas thofe of the Bridge of the Thuilleries have not above fifty-fix ; the Wa- ter of the Seiae^ which palfes through both thefe, at the Time of great Inundations, muft pafs flower by one half at PontNeuf^ than it paffes at that of the7Zv«7- leries. And, in fine, if the Waters of the Seine carried a Flint but of one Pound Weight, under Pe7n Neuf^ to the moving of which, they contributed all their Rapidi- thefe Bodies different in She., takes Inch as have the moll: Sur- face, in refpecl to their Weight, that the Ballaft, which is the lar- gcll, the Water raifes rather the firrt than the lall, a Perfon will not be furprized at all thefe Fffeds, and will prefently fee the Reafon of it. Thus Sand having more Sur- face, in refpeft to ir? Weight, than the Ballalt which is larger; the Water raifes the firll looner than the lall, becaufe it has more Hold of ir. ' It may be feen by this, that the more Bodies are diminilh'd, the more their Surfaces are aug- mented ; which, in refpccl to the Movement, having fcarce any Thing but Surfacej and very Hu!e of Body, they bee ir.e n> I 4 " ' ^^^-tj B R 1 light, that the leaft Motion car- jijs them away; us isfccn when '■■cy are reduced intoDiift: And Goij, for Example, being re- duced into Lea\es, is carried away by the leait Puff of Wind. This, which has been already faid, being known, we fliallnext pals to the other Means ufed for the building of Brid^^es-^ which is the lowering of the Waters of the Rivers. Of Lovjerwg the Waters of Ri- vers^ and the Manner of divert- ing them^ for Liymg the Foun- datio;is of a Bridge. When it is intended to work upo.i the Foundations of^Bridge^ the moll proper Sealbn of the Year mult be taken for this Work, as the Summer-Time, afcer the Sn«iw has been all melted. If the RivLT, in which Piers are to be ere6i:cd, is firuaced be- tween two N4c»untains, and the Courfe of it cannot be pombly diverted, and carry'd througli a Plnin. rhe Architeftmufl content himf^il' vvi;h Ir.ying the Founda- tion by fixMig firtt one Pier by Dam«, or Wattr-Stops of Piles, which may direct the Current of the Waters of the River to the oppollte Bank, or fo that it may run round the Woik. He muft render the Waters calm in that Place where he would ercft the Piers. After the Waters of a River have been fo diverted, as to have fixed one half of the Piers of the Foundation, then the Current of the Waters are to be turn'd to that Side which has been crcfled by another Dam, contrary to the firfl, that has been B R demolifh'd, in order to finilTi the other Side of the Bridge. When this has been contriv'd, the Architeft mulf examine if there be any Mill-Dams below, which may raife the Courfe of the Waters, which he ought to caufe H) be broken down in the Place of the Bank, or Dam ; which will be leaft prejudicial, or will do the lead Damage ; and to give the River a Curren- cy that Way, to lower the Wa- ters as much as may be. T hefe Ruptures are made by ftripping the Dam or Dike of all its Straightenings, or narrow Paf- fages ; and ot all thofe Things that retain the Water in one Place. Where any Opening has been made, there fliould be nothing lett but Piles and Stakes, to be ableto be us'u for the fluuting in thefe Openings after the Piers of the Bridi^" h we been fixed, and rai~ fed higher than the Waters of a Miii-U.im or Pond. But when the Water of a Ri- ver, over which you would ereft a Bridge, may be eafily diverted or turn'd off; as when an Ifland or llkt is to be met with, and that the River may be diverted with one of thefj Currents ; this l-aci.icy does i finit^'ly forward the Work: Ai.d it is the larrie, when there happens to be a Plain, w here the River has a large Ex- tent; when there is any Inunda- tion, and afterwards reneats a- gain into the former Channel, where it is- reduced again to its common Quantity ot Waters; then the Foundation of the Bridge may be piled the whole Extent of the Plain where the River does not run, w^hen its Waters are at the loweft ; and when B R B R vvncn the Found:.tions of thefe Spaces are laid, a Canal is made through all that Fart which is fi- nidi'd, through which, the Cur- rent of the Waters may by little and little be dcriv'd, by very lim- ple Works, according to the Dif- pofiiion of the Places, by cutting the Current of the River -.iS deep as may be, and in that Place of its Courfe where it has leaft Depth. As ii" I have but three Foot Depth of Water to engage with, to divert the Courfe of a River, and to conducl it into another Channel, made by the Hands of Men, I make ufe of other very eafy Works, without Piles, ac- cording to the Difficulty to be cncountred in that Place. Thefe eafy Works are nothing but Racks, in Form of Ladders, which carry the Surfiice of the Water ot the River which is to be turn'd; which are placed on the Side perpendicularly and vertically crofs the Courfe of the • Waters, overagainft and a little below the Channel of Derivation, whichhas been niadeby Art, into which the River is to enter into a new Bed. There are made many Ranges of thefe Racks, which do thus crofs the River in Form of a Mole ; and a- crofs all the Va- cuities of the Bars, the Waters pafs without Interruption. The Sides of thefe Racks be- ing fad bound with Cords, at their Croffings at the crofs Quar- ters of the Timber, and at the Difchai-ges which fecure them on all Sides, the Channel of Derivadon being hollowed, and ready to receive the Waters of the River, many Fafcines are I thrown between two of thefe Racks, good Store of which have been provided beforehand, at the Foot of the Work ; or of Flints or Stones, for to make them fink to the Bottom of the Racks; which will caufe the River to fwelf, and conltrain it, by little and little, to enter into the little Channel prepared for it. Andone may have the Satisfac- tion to fee, according as theordi- naryCourfe of iheRiver is ubfiruc- ted, and the Waters befn.; abridg'd of their ufual Current, will in- creafein thenewChaimel of De- rivation ; fo that this la(f being commonly but one Tenth, or one Twentieth of that of the River that has been ftopp'd, it may be perceiv'd vilibly to grow larger, and the Water to carry along with it all that it meets in its Way ; as Rocks which they could not remove out of the Way; Stumps and Roots of Trees, that the Workmen were not able to get out of the Way ; fo that by that Time the Waters have paf- fed that Way for twenty-four Hours, it becomes fpacious, and proper to receive all the Waters of the River, were they twice as many as they really are. This Method, fays M. Gau- tier^ I made ufe of twenty- five Years fince, upon the River de Nejie^ in the Plain of Jvcntig- nan^ which empties itfe'f into the Garonne^ at the Foot of the Upper Pyrenees^ at Alonirejaux; Where the Mafts could not float, but againlt the Rocks ; which render'd every Day the Ra- gers in Danger ot periling, and where a great many had before peri(h'd, running no Risk in croffing B R B R crofllng the Plain; with Works of Billafl; z^amd which Planks as eafy, and even flighter, than I may be nailed, which may force had turned the Courfc of the the Water to paf<; under them /^ude^ in the Lower '■Tyrenees^ with the greater Weight, and within the fame Bounds, and in confcquently With the grca- as many Places as its Courfe ter Rapidiry ; and bv that Means, changed, efpecially where thele remove and hoiiovv the Heap of iimple Works were conftru£led. Sand, which it would be verv Laftly^ I alfo made ule of the laborious to take away any other fame Expedient in turning the Way. River Orb above Bcfiers^ for the And alfo loaded Boats may be Ule of a Mill ; where I had five Foot of Water to turn otf. The Sides of thefe Racks are nothing but Trees cleft wich ufed for the fame Ufe; which fallen'd with Cords, and placed on the Places that are to be clear- ed of thcDailaft, by letting them lie there ibme I'ime, the Water Wedges, and bored in the Man- which thefe Boats prefs over ner of Ladders. them, by (topping the Courfe of Elm, or Poplar, C!rV. are Trees the River, caufes it to pals with proper for this V/ork. The a Rapidicy according as thev are Holes are made with a large more heavilv loaded, fo that at Boring-Iron, or wich Imall Chif- Length the Waters hollow a Bed lels, about the Space of ten or for themfelves. twelve Inches the one from the All ti^efe Methods are made other. ufe of, more or lets eafy, accord- And the Bars of thefe Racks ing as Occalion requires, which are only Pieces of Wood, and the Prudence of him whodireds the Ends of Branches of all the Work makes nfe of, as he .Sorts of the lilceTrees, made in- to Stakes, from two, to three Inches Diameter, more or leis; for you mult have of all Sorts. Lajih, The Waters of a Ri- ver may be lower'd one or two Feet, in refpcct to its Fail, by hollowing the Bed finds molt for his Purpole, that he may have the ieaft Trouble to pile the Foundations of a Brici^e^ having the lefs Height of Water to lower. When a Perfon has laid down the Proic6tion of a Bruize^ ei- ther of Carpentry, or Malbnry, Vex this Purpufe, fo much of over any conliderable River, and the Sand is cleared away at the there is a Difiiculty in biinging Sides of the River as is judg'd to the Place the Materials for necelfarv, in order to enlarge it the Work, the Ways necef- by lowering the Waters; for this fary for bringing them ate to be is certain, the more it is enlarged, prcpar'd. the more are the Waters lowei'd. For a BriJ^e of Larpentrv, a Alfo a Number of Stakes may larg- Boat is uled ; upon which, be Ituck in thole Places, where Scaif.lding is erected, or ai F.n- thc Curreiit of the Water is not gine is placed, and [a Sonrttti] very rapid to clear the Bottom Inftrument proper lor ramming *" ' down B R B R down the Piles ; to xvhlch Boat are brought in oiher klTer Boats, the Piles, Plood-Gates, Stones, Pianks, and other Materials.^ 1. Of vvhatThickneisorSub- Ibnce thcButmcnts of all Sorts of Stone-BfiJgts ought to be, or •what Proportion they ought to bear to the Arches, and the Weights they are to fupport, a. What Proportion the Piers or Piladers ought to bear to the Apertures or Heights of the Ar- ches, and the Weights they are laden by. 3. What ought to be the Length of the VoulToirs, from their Lntradojj'e to their Extra- doQe^ or from their inner P'aceto their outer Face, for Arches of all Sizes, quite up to their Key- Stone. 4. What Sort of Arches fixed upon one and the lame Diame- ter, would be capable of fultain- ing the greateft Burthens, and the feveral and ex^6t Degrees of Strength, whether they be of an Elliptical, Circular, or Third Point ; or Gothick^ and carried up to what Height you pleafe. Theib Principles, which are here to be laid down, muft be well known and indubitable. Which Principles mud be ex- plain'd by evident Terms, and in a known Language, that they may be intelligible to every body, and lie open to their Judgment. Now it will require no extra- ordinary Genius to comprehend what I have to offer towards the clearing up of the four Difficul- ties here propofed; and I am not without Hope, that the mea- nelt Workman, who has but common Senfe on his Side, will unravel and demonftrate what I have here to advance. FirJ}^ By theAfliftance of com- mon Senfe, and by the Help of Pome fmall Smattering in Phy- ikks, and fome Skill in Argu- ment together, you may readily comprehend the Combination or Conjunftion of the feveral Ma- terials employed in the building of Arches and Vaults : For they will give tounderftand.that were it not for the feveral Methods of fquaring or cutting of Stone, or for the Mortar which binds them together, it would be altogether impoffible to conftrud an Arch of any Sort. The Anticnts only praftifed the firft Method above, in their finefl: Works, without making ufe of any Mortar; as may be feen in the Archivolts of their Arches, whofe VoufToirs have no Mortar at all between their Joints. An Example of this is ftill vi- fible in the antique Aqueduct Du- gard^ in han^nedoc^ and elfcr- where; and alfo in the Amphi- theatre at Ni[mes\ where the Joints of the Stone are perfv.^ftly free from Mortar ; as aUb in the Vauliing of the Temple of Dia- na at the fame Place. But thefe Examples are not al- ways to be regarded or follow- ed, and efpecially where rhe Smalnefs of the Materials (fuch as Bricks) do abfolutely require to be firmly bound with Morrar, to ftrengthen the Work, and ro enable it to ftand. Secondly^ It "will bs neceflary, that you'fho'uld be vvclleiy.wgh \ B R B R acquainted with Staticks, to know that whatever turns upon an Axis, after the Manner of the Scales of a Balance, whofe Brachia are either equal or un- equal, will never be ra aquiii- hrio with another Body, ir that Body be not of equal W'eignt with the Body at firll prc;pofed ; or if by a reciprocal Dillance from the Centre or Ax's, it b^ not brought to have a Preffure downwards, to counter-balance the Preflure of its oppofite Weight. B\ the Knowledge of this, we pr)viJe agaiiift the PuHi or ImpuMion of Arches, by keep- ing them within due ijoands, by the Alii ita ice of forces of a Pi)vver tqual to their Pufh or Effort to fpread or part afun- der. Thirdly, Y u are to have Re- courfe to Mcchauicks, to judge of the Scrcngrh of all thele B'>- dics, and the Power of 'noviiig Forces ; and in what R rp.ci, und after v/hat MantiC', thtfe Bodies , which are tuppirt- ed or born up in ihe Air, ii6t upon th'.fe that are Mxed upon Earth, and which are looKcd upon as immv'ViabU; fi.'ch as the Arch oT a Brid-e, • r a Vault, which iiave very vai io-JS Powers upon the Butments and Piers vvh.ich fnpporc them, and which arc fuppofed to be immoveable. And upon this Account, a Knowledge of Stone-Cutting is receOary '; by which you may^ determine the fcveral Powers ot the VoufToirs, oneupon another: For there is no VoulFoir, which being differently inclin'd, (though it may be cut by the very fame Moulds,) but what acts in a Manner peculiar to itfcll, upon thofe upon which i; is placed, or upon which are placed over it; io thai (hey a 1 ad differcnily, according to tie aiffcreut Incli- nations oi their PLiiu'S. t'otirthiy^ Geometry will be nevcilaiy'' for the right Under- ftanding of thefe four Propofi- tions, tnat you m ly be aoie to determine or calculate the Sur- faces and f(»lid Content of thefe Bodies in Qjeltion, thereby to ome at ineir Powers, ar.d to compare themvvith one ano- ther. A final 1 Portion of thefe above Ipecified S:ienres, adi..g in Concert aiih cutimonSeuie, \\'\:\ be riiffic.'er.t ror the clear c incLi\ing of v.hit i fliall here advance. 1 iTiall omit nothing that can coiitnbu'e t > render vv hat i have to fay plain and i,.relliiiib;e to Perfuns of the m.anelt Cap;iuty, for w^oni aloiic 1 have under- taken tiiisTask. l^he Learned M. De la Hire pretends to have demonilriued iViQ Pufh tf Vaults, and deier- min'd rlieTfiickr.efsof PieJruits wivch Iup;.orr ihem. The Vau'ts in his Work are Arches of Brn'^es\ and the Pie- droics are the Culees or Abu:- meuts. It is, fays he, a Problem, that is one of the nioll cifficult in Architediire, roknow the Force of Piedroirs (^f Vaults for fuf- taining their Pufh; and Archi- tedls have not yet found out any certain Rule for determining it. This Problem appertains to Me- B R B R Mechanicks ; and by the Help of that Science, we may be able to Iblve ir, by making fomeSup- po(ition«, which are agreed upon as to the Conflrudion ot thcf^ Sorts or Works. ' The Pufh of Vaults, is the EfF.-rt that all the Stones which are form'd, cut into Quoins, ana called Voulloirs, make to remove or diiperfe the Jaumba- ges or Piedroits which fuftain thefe Vaults. And aschufePerfons whohave been lefs bold in their Enterpri- ses, have allovv'd an extraordi- nary Force to thefe Piedroits, to render their Works the more du- rable, as has bc;en the Pradtice of m.41: of the Ai ti^nts , and others, on the contrary, have been too daring in making their Piedroits too weak, and fo deli- catv.', as not to feem to be able to fupport the incumbent Weight; 1 have thought it neceffary, by the Help of Geometry, to fcarch after a Rule by which we may arrive at a Certainty, in deter- mining the Force or Power that they o ght to have. It hab been g^'nerally obferv'd, that when the Piedroits of a Vault are too weak to fuflain the PuOi of ir, the Vault cracks or fplits about the Middle, be- tween ics Import and the Middle of the Key-St'.ne; and therefore it may be fuppofcd, that in the upper Half of the Demi- Arch, the Voulloirs are fo firmly uni- ted the one with the other, that they form, as it were, out one en- tire Stone: And upon this Sup- pofition, and the Solidiry of the Foundation on which thefe Pie- droits are placed, the Demonllra- tioii of the following Rule is eftablifh'd. See Pa^e 70. of the Memoirs of the Academy in the Tear ijii. M. Dc la ///>(? enters upon the Bufinefs, gives the Figure of a Vault of which he undertakes to ihew the Pufh, and determine the Largenefs the Piedroit ought to have that is to fupport it. Upon which, our Author M. Gautter remarks as follows : 1 own lugenuoufly, fays he, that I have not Genius enough to comprehend it. 1 have never been able to follow his Opera- tion, as he has compofed it; and I look upon all that he has told us, as what ihofe who are but half-learn'd,and efpecially Work- men, are not able to compre- h.^nd : For if Algebra, rrom which he borrows his AfTiftan- ces, be abfolutely neceffary to be known, in order to conceive what he fays, I believe, fcarce any Stone-Cutter, Mafon, or Architett, for whom IVeatifes of this kind ought to be rcndrcd as eafy as poflible, will be any Thing profited by it; becaufe flich Perfons in common, don'c apply themfelvcs to that Science, as unnccelHiry to their Profefiion,. and their Time being wholly ta- ken up in the working Part. If M.T)e la Hire had well folved thefe Difficulties, in fuch a Manner as had rendred them intelligible and eafy to thofe who are employed in Buildino-^ as he was ab'e to have done, be- ing better qna!ify*d for it than any Man, he w^ould have done a Work very much defired, and Would have prevented me. We find in the Memoirs of tie Royal Academy of Sciey?ce'^ in the il'ar 1704. upon the Fisjurc B R B R of the EytradofTe or outward Face of a circular Vau)t, whofe Voailbiis are i:i(t-i:'.litbrto^mox\g thcrnfelvcs, that a Vault, oraSe- niidrcular Arch, being placed up- on liie two Piodroits, all the Stones or Voulfoiis which com- pofe this Arch, being nude and placed, one with the other, i^o ih, t their Joints being prolong- ed, ail meet tc\gether ac the Cen- tre (^f the Arch. It is evident that all thcfe Vor,{ibir<: f,uve the Form of a Coin larger ubove than below ; by Vertue of which they reft, and are ivilhinM by one another, and reciprocally rellft the Etiort of their Weight, which would incline them to fall. TheVoulIoir in the Middle of the Arch, perpendicular to the Horizon, and which is called the Key, or Key-Stone of the Vault is luflain'd on both Sides bv the VoulToirs next to it, ex- aftly as by inclined Planes ; and confequently the Etfort it makes towards falling, is not equal to its Weight, but is a certain Pnrt of it, by lo much greater, than the inclin'd Planes which fuftain it are ihs lefs in- clin'd. So that if they were but never fo Utile inclin'd, that is to fay, perpendicular to the Horizon, as well as the Key of the Vault, it xvould tend to falling by its own Weight, and would not be any more fodain'd, but would a6hi- allyfall, if the Cement, which fs not here conlider'd, did not hinder it. The fecond is fufla'n'd by the third, which is on the Right or iycfc of the Key of the Vault, :.^ fallained by a third VoufFDir; which, by Reafon of tlic Fomi of the Vault, is neccfliirily more inclin'd, in refpc6t to the fecond, than the fecond is in rel'ped to the fiift; and confequeiitiy the fecond VoufToir, in the Etibrt it makes towards falling, exerts a lefler Part of its Weight than the firft. For the fame Reafon all the VoufToirs, beginning from the Key of the Vault, proceed al- ways exerting a lefs Fart of their whole Weight : And, m fine, this laft, which is placed upon a Horizontal Surface of a Pie- droif, does not exert any Part of its Weight; or. which is the lame lliing, makes no Effort towards falling, becaufc it is en- tirely fnflained by the Picdroit. If you will have it, that all thefe VoufToirs make an equal Effort tow'ards falling, W'herc they be in tcqmlibrio^ it is viiible, that every one, from the Key of the Vault, to the Piedroit, do continual !v exert a Idler Part of their whole Weight. Fhe firft, for Example, exerting but one Half, the fecond one Third, the third one Fourth, cTf. there is no other Way of making thcfe different Part- equal, butby augmenting in Proportion the Wholes of which they are Parts ; that is to fay, that the fecond VoufToir be heavier than the firft, and the third than the fe- cond, and fo on to the lall ; which ought to be of an infinite Weight, 'that it may make no Effort towards falling ; and that one Part being void of Weight, may not be equal to the finite Efforts of the other V^ouffoirs, at leaft, that this Weight be not infiin'tcly great. To B R B R To have a clearer Idea of this Matter, there needs only a Re- fie<5lin^ upon this, that all the Vouflcjirs, except the Inft, can't let any other Voiifroir fall with- out its being rnifed ; and that they refill this Elevation to a certain Point determin'd by the GrcatneA of their Weights, and bv the Part of it which they ex- ert; that there is none bnt the the lafl VoulToir, that can futu-r another to fall, without beint^in fome fort elevated or rnifed it- felf; and that only p''ding Ho- rizontally, that the Weights, as far as they are bounded, bring not a Refinance to the Horizon- tal Movement ; and that they do not begin to have there any finite one, but as when they are conceived as infinite. M. De la Hire, in his Treaufe of IMechanicks, printed in 1695', has demonftrated, that this was the Proportion upon which the Weight of the VoufToirs of a Semicircular Arch are to be aug- mented, to the End that they may be all in aquilibrio. Which is the fureft Difpofition that can be given to a Vault, to make it durable. Tiii this Time, Architcds had no certain Rule, and wrought in the Dark, or by Guefs. U-wc number the Degrees of a Quadrant, or quarter of a Circle, from the Middle 01 the Key of a Vault, to a Piedroir, the Extre- mity of each Voufloir will ap- pertain to, or be Partof an Arch, bv fj much greater as it is far- ther difiant from the Key. According to M. De la Hire's Rule, the Weight of oneVouf- foir muft be augmented above that of the Key, as much as the Tangent of the Arch of this Voullbir exceeds the Tangent of the Arch from the Half of the Key ; the Tangent of the laft Vouflbir neceflarily becomes infinite, and foconfequentlydoes its Weight. But as Infinity has no Place in Pradice, fo the Matter comes to this,To load the h; ft VoufToirs as much as pofilble, to the End that they may be able to rcfift the Effort the Vault makes towards Splitting ; which is what is cal- led the Pufh. M. Parent has made an En- quiry what ftould be the out- ward Bending, c r the ExtradoflTe of a Vault, whofe Intrado/Ie, or interior Face, is a Semicircle ; and all the V\)ufToirs in aquili- hio by their Weight, according toM.lJe U Hire's Rule. For it is manifefl, that all theft VoufToirs, unequal in a cer- tain Proportion, would bear or puiTi outw^ards a certain regular Curvature. He has not found it but by Points, but in a very plain Man.ner. So that by his Method a Vault may cafily be conftrudted, of which one may be fure, that all the VoufToirs will be /» aqui- librio. One confiderable A-dvanrage may be gain'd by the Inquifuioii of M. Parent^ is, that he has at the fame Time difcovered the Meafure of the Pufli of a Vault, or what Relation this Pufh has to the Weight of the Vault. He only knew, that this Ef- fort was very great, and there- fore oppofcd to it great Mafles of B R B R of Stones or Abutments, rather too llrong, than too weuk; but we knew not prccifely what Proportion to keep to: But this, we niav come to a Knowledge of at prefcnr, that Arts always are improving by the Help of Geometry, ^e. See, by what Rnles, all thofe "U'ho have been Builders, have conduced themfclves, or have been gui.ied by others until this Time, in making Fiedroits for the Support of Vaults, as well as the Abutments of Bridges. The Learned Father Dcran^ in his Treatifc 2?f ia Coup des (PJerres^ and M. Blandel^ Archi teft to the King of Fr.'nce^ as skilful Men as any the prece- ding Age has afforded, in his Treatife of Archirefture pro- ceeded on thefiinic-Footas thofe who fiicceedcd them. In anv kind of Vault or Arch of a 5r/Wsj^ what focver, fay they, either ElHprick, Scmicircu'ar, or of the third Point, and a P ^^ the Straight Arch cannot fhove or pufh the Wall GD be- yond the Axis CA; and thus AD will be the Thicknefs of the Butment and Piedroit, or the Walls which are to fullain the Impulfion or Pufh of the Plat- band or Straight Arch ; which, indeed, is more frequently ufed \\\ Civil Strudures, to fupporc Platforms, Ceilings, or Roofs of Galleries, or other Palfages a-crofs a Court; and in Chur- ches, to ferve for Tribunes, than tor Bridges. There is a very fine one in the Church of the Je- luits at Nifmes^ which was con- llrufted by the Diredion of the Father Mourgues^ and after the Delign of the late Sieur Cuhijol^ who was a very skil- ful Archited, to which he gave lefs Height at BE than what we allow here; whether it was, that he was afluredof the Soundnefs or Solidity of the Stones, or the Truth of the Work, l^c* As his Delign is per- fedly bold, I fhall here give lonie Account of it. The Platband or Straight Arch wc are here fpeaking of, is four Fathoms, two Feet, and fix In- ches in Length ; the Stones of it are one Foot in Thicknefs ; their Height BE is two Footto- wards the Key, and at each End AGCH. They begin with two Foot four Inches. This Platband or Straight Arch had a Rife about fix or feven Inches at B, when its Stones wete fet tjgcrhcc K 2 til o I B R B R upon fhc Centre ; but it after- wards Tank down three Inches, when its Joints came to fettle, upon the taking away of the Centering or Stay ; fo that at t'lib Day, it rifcs about four In- ches above H. The Pradice of this Sort of Work, and a Knowledge of the Soundnefs or Kardnels of the Stone, arc what mull guide you in reguhitii;g the Height BE; but for want of fuiftcicnt ExpcrimenLs, we are ilill in the Dark as to this Matter; there not having yet been found out any Rule in Mcchanicks to determine it. The skilful Architect mnft do in this according to the belt ot his Knov/ledge: If he fucceeds, he will be cllcem'd and ap- plauded ; but if he fails, he is dcfjiifed and laughed at. However, by repeated Expe- riments, and Pr(xjfs of the ConiUience of Stones, it would not be impofiiDle to afccrtain ibme fure Rules, with regard to this Matter. For it is of the greatefl Im- portance to know the diffe- rent Solidity and Firmnefs of Stones, and other Bodies, which vary confiderabiv, according to ttieir feveral Climates, and Grains, that we may be able to proportion their Subllaiice to the Efiorls, Prellures, or Piiflits of Straight Arches, or others, which being once cilculated {viz.) the Weights of the F.rtoris of the Bodies, which the Muunffs of the Plat- bands of tl-.e Vouilbirs of Arches arc to UUhnn. We ma . imagine the Strength 'if ii^^niis we are to vS'i by ta- king a Piece of them of a Cu- bical Inch in Dimcnfion, that IS, in Form of a Dye, and by loading it with Weights, till it difperfes, and yields to the Preifurc of its fuper-incumbent Burthen ; from whence fomc certain Rules may be ellablifh- ed with regard to this Matter. Thus, If fuch a Cube of Stone, as we have mention'd, fuppotts a Weight a Thoufand or a Million of Times heavier than its own Weight, and bigger than itfelf, we will allow it but one quarter of that Reliliance or Force, when we come to apply it to the Building of our Works, whether they be Piers, or Brid^es^ which are to fuftain the greateit Burthens; or whether they be VoufToirs of Vaults, or Archi- volts of Bridges:, which are the Parts that give or exert the greated Efforts or Pufh, as well as Stones of Straight Arches, whether they are to fupport Towers, or Steeples, cfr. - Thus I allow three Fourths of the Strength of thofe Bodies, to make Amends for the Im- pcrfe6lions of the Work ; for there is no Man whatever that can fet or join them together in any Building, with that exadl Arrangement in which they were placed by Nature in the Beds or Strata of the Quarries from whence they were raifed. Clumfey joints, ftuffd up with Mortar, and Shells, which do not bear throughout equally, and confequently yield to the Prellure of the fuperincumbent Weight, is the Rcafon why Buildings every Day fplit and Icitlc from the Difference of the Binding, B R BR Bindiiifj^, which is not equally linn in all its Farts ; fioni whence nril'c very difagreciible Deformi- ties, and Eve-fores, as well as very prejudicial Accidents to the Work itfelf. The Joints between B and C of the Platband or Straight Arch, are indented, (fPlate If. which are Ibmetimes ordered after a very different Manner ; for there are thofe who like a plain uniform Joint beft, fuch as you fee between Band A ; but this depends upon the Skill, or at lead the Fancy of the Archited: For the more complex Joints are (fay fome,) the more they are confus'd, and the more fubjctt to Defeds ; but the more limple and plain they are, the truer and ftronger is the Work ; as thofe Joints be- tween AandB, which are plain. Wiiat I have here offered by Way of difcovering the feveral Degrees of the Strength and So- lidity of Materials, is fomething like the Experiment made by the GcMtlemen of the R)yal Aca- demy of Sciences^ upon a twifted Cord, compofed of twenty Yarns or Threads; each of thefe Yarns, when fingle, were capable of fuftaining one Pound Weight without breaking ; but being twifted together, and converted into a Cord, they could not bear up a Weight of twenty Pounds ; for it broke wich a Weight of between fixteen and eighteen 'ounds. For it is impoffible for luman Art to twill thefe twenty ifarns fo nicely together, as that .11 of them ftall fulUin an equal Share of the Burthen fufpcnded by them, when in a Cord; fo that fome of them loaded with a "Weight fuperior to their Strength, they are all in general unequally or difproportionally laden ; from whence it muft ap- pear, that they muft be unable to bear the Weight of the twen- ty Pounds before mention'd. Thus fuppoling a Cubical Inch of Stone to be able to bear a hundred Pound, it would not from thence follow, that ten fuch Cubes would fuftain a Bur- then of a thoufand Pounds ; bc- caufe a Mafs or Body of thot Weight would not bear alike upon all the Ten; wherefore fome of them being more hea- vily laden than others, they would all be crufh'd one after another ; from whence happens the flying or breaking of the Stones of an Archivok, and of all Bodies; which are not upon an Equality throughout the whole Plane of their Superficies, or Beds. The following Table gives the Proportions of the Length of the VoulToirs, or the Heightsjof the Archivolts,as they can be ga- thered and afcertain'd from the bed Authors Works of Antiqui- ty ; which cannot be reduced to an cxadl Geometrical Dcmon- dration, and has been merely calculated from the Experience of the more folid or coarfe Con- fidence of Stones; upon which Point, this whole Article turns. So that Phyficks bear a grea- ter Share of this, than cither Mc^ chanicks or Geometry. K ^ U'hat B R B R What ought to he the Largenefs of 'Piers in refpe^ to the Open- ings of the Arches^ and the Weights they fuftain. The Size of Piers ought to be precifely dctcrmin'd according to the Spring or the Arches. No Fcrlbn yet has laid down nny certain Rule as to this. I fhall relate what ihemoftaccom- plifh'd Architeds have told us in relation to this Matter. Leon Baptijle Albert would have the Piers of a Bridge be equal in Number and Size, and their Largcnefs, one third Part of the Opening of the Arch. Palladto fays, the Piers ought to be equal in Number, to the End that there may be one Arch in the Middle, where there is commonly the greateft Cuirent of the Water. That the Piers ougb.t not to belefs than afixth Part, nor com- monly more than a fourth Part of the Width of the Arch. He next gives fome Examples of antient Bridges^ and fays, that thofe of the ancient Bridge of Rimr/ii are eleven Feet, and the Opening of the Arches twenty- five Feet : T hat the Bridge of Bachiglione, which is alfo an- tient, the Piers are five Feet, and the Arches thirty in their Open- ing : That the Bridge over the Kerone has its Piers alfo five Feet, which fupport an A.rch whole Opening is twenty-nine. He, after this, gives the Pro- jection of a Bridge ; where he makes the Piers two Fathoms wide, to fupport an Arch whofe Opening is ten Fathoms. Serlio fays, that the Piers at 'PoTft Sixtus at Rome^ have one Third of the Width of the great Arches; that the Piers or the Bridge of St. Ayigelo^ formerly Adnan^ s- Bridge .^nxc one Half of the Breadth of the grand Arch, which is a femicircular one. That at the BiiJge of Quatro- Capi^ Tarpems^ or anticntly Fa- hricius, the Piles are alfo one Half of the Breadth of the fe- micircular Archts: And, in fine, that the Bridge ihilvius^ at prefent called Ponte iMole^ the Piers are there half the Breadth of the Ar- ches. M. Blo-^det n\:ikes the Piers of his Bridge of Xai^tes as three to eight, in refptct to the Opening of the Arches . The Piers of the antient Bridge Du Gard are two Fa- thoms wide, and fupport three Arcades, two of which are at Bottom lixteen Fathom of the Opening of a Height of near twenty- five Fathoiii; which is an imnienfe Weight upon fo fmall a c::pace as two Fathoms. We are allured that the Towers of Nutrc-Dame^ at Paris .^ are but thirty Fathoms high. If fo, they are not riifcd higher than the PoAt de Card.^ but about fevew Fathoms. j The Piers of Pont Neuf^ a(l Paris., are but fifteen Foot wide. or thereabouts, at the Mailer Arch. Thofe of Pont Royal, on thi Thuilieries., are but two Fathoms; one Foot, fix Inches, or there: abouts, and fupport an Arc! of twelve Fathoms, opening t, the middle one. Thofe of Pont Neuf in Tot, /o!-ife, are four Fathoms wide, c thereabpuiSj and fupport Arch( B R of Opening from fifteen to fix- tcen Fathoms, or tluMeabouts. Too great a Variety in all thcfe VVorks, gives us Ground to think, that Authors have not yet obfcrved any certain or ge- ne; al Rule, founded upon de- monrtrable Priiiciples for crta- blifliing the Piers oi Bridges. Bat ncverihJefs, one may draw from all thefe Models fomething that may be fcrvice- able to us on Occafion ; it is not to be doubted, but that ihefcable Architects, who havccondu6led all thefe Works, had a Reafon for all the Projedions of thefe Piers, before tbeyerefted them. I do not all doubt, but that a Pier of two Fathoms wide, wholly built of large Blocks of hewn vStone, as is that of the Antique Pont Degard^ which bears more, perhaps, than any other in the World befides, will nor be fufficient to fupport the Efrbrtofan Arch of an Open- ing of twenty Fathoms; when another Pier of four Fathoms will not fupport an Arch of ten, which lliall be conftrucled only of hewn Stone, and the Infide of the Body of the Work of limplc rough Walling, or Shards or Pieces of unhewn Stone. This would break fooner than thefirft: this would heap up all the Weight of it s Charge or Load, and the lafi would be immove- able. It is upon thefe Principles, and the ufing Materials more or lefs folid, and differently arran- ged, which we fhould have Re- gard to, and determine as to the Width of Piers in all Sorts of Bridges^ The fame Materials ufed in different Counuies, fome of B R which have a firmer Confidence than others ufed for building Gates of Cities, Fortifications, Towers, Steeples, Bridges, ^c. might be examin'd, in order to gain from thence t)\e Advantage one defires for projecting a Bridge., greater or fmaller, in thefe Places. And although by all thefe Ex- amples I have form'd a Rule for determining the Piers of all Sorts of Bridges., according to the fore- going Tables, wnich is one Fifth in an Arch of ten Fathoms Opening ; a larger or leffer Breadth may be allow'd to Piers, in regard to the greater or leffer Solidity of the Materials that are made ufe of. With this Remark, that if the Bed of a River is very wide, then a greater Breadth may be al- low'd; becaufe there is no need of fearing of penning up the Waters, in Cafe of Inundations, but on the contrary, in the Beds of Rivers that are too clofe pent up and ftraighten'd, it will be of great Importance, not to give the Piers of Bridges which one builds, but as little Width as can be, that we may be able to fupport without Fear the Load of the Arches; efpecially when at the fame Time we are ty'd up by the unfavourable Difpoli- tion of the Places. In conftruding the following Table, I have obferved the Pro- portion of one Fifth of the Width of the jpiers, in refped to the Openings of the Arches, from thofe of twenty Feet Opening, and upwards ; and thofe which are under ten, a fmall Arch of three Feet Opening, and even to that of one Foot. It is found by this Table, that fl Pier ought K) be one Foot ten Inches wide for an Opening of three Feet ; and one Foot fix In- ches for an Opening of one Foot; which may be praftifed upon any Common-Sewer, or on any Stream of Water, how fmall foever, whofe Piers are made all of hewn Stone, when by Rea- fon of the bad Situation of the Place, we (hall be obliged to it ; and the Whole is proportion'd not only to the Mafs of Mafou- ry, which the Pjcrs ought to fupport, but alfo to the Stream of Water that is to pafs under it. As we cannot come at the Knowledge of the Solidity of the Materials, but by making Trials, in order to know how far their Effort will be able to fu (tain the Weight that they are to be charged with. Experiments may be made, as in the preceding Chapter, upon which this Table is fram'd; fince there is no Rule, which exaftly determines the Breadth of the Piers more after one Maimer than another. The Table which I have given of the Breadth of the Piers of all Sorts of Arches, from that of twenty Fathoms Opening, is proportioned as well as poflibly I could doit, from all that has been done ; on which I have thought proper to make Obfervations as to this Matter. IVhai Bearing l^oujfoirs (houJd have from their Intradojfe or interior Curvtiy or Face of the yirch^ to their Extradoffe or txterior Curvity tu Arches of 4tll Large Jteffcs^ to the Place of the Key-Sione. Scs :vhat the inoftable Archi- tefts havefaid, who have written on this Matter. M. Blondel fays, thaj they have not fo folid Stone at Paris ^ for the building of Bridges^ as the Romans have in Italy. And that to fupply'^this De- {t^^ they have made at Pont Neuf and ^he Thialleties^ Vouf- foirs of £ great Length, and at the fame Fiine very well fecu- red by the Returns and Courfes of the Croflcttes, to make an infinrtely greater Binding, and to take a much better Hold. The Bridge of Touloufe may, without Difficulty, be put upon a Foot parallel with the fined in Europe. Neverthelefs it is built with nothing elfe but Bricks, except that at the Angles or Heads of the Arches, there are fomeRows in the IntradolTe, or interior Face of the Arch, where hewn Stones are us'd ; which are certainly no more than the principal Parts of it? Ornaments ; and it may be laid, that although the Arches which arc about iixtcen, and fo many fathoms the Opening, are, for all tlr«at, made only of Brick, fnuated in the Cut, according to the Bearing which VoufToirs and Pendants (liould have. After th;it Manner, that this Difpofnion, fo well eftablifli'd together with good Mortar, which they ufed, and that makes the Binding,formsa Work which feems to be all of one Piece, al- though compofcd of very fmall Alatcrials. And this istheReafon that the Arrangement join'd to the Soli- diiv of tliefe Materials, is the Caufc of the Whole of its Good- ncfs. Leon- B R Lco»-Biipl't(la Alhcrti fays, that the Height oV the Hcndbaiid or Fillet ot Arches in coiiliderable Bridges, \\\\\c\\ is what ihc French callVoulVoirs, or their Bearing Irom the liitradoirc to their Ex- tradoHe, when they are thus de- termin'd on their Exiradolfe Ar- ches, ought never to be Icfsthan one i'ificcnth of the Width of the Opening ofthe Arches which they form. It is upon this, I havecflablifh- cd the Column of Vouflb'rs in t^z lollowing Table, fuppoling the Mafonrv to coufill entirely of large Blocks of very hard hjwn Stone. And it is upon the fimc Prin- ciples, that the antitnt Bridge Dugard was made. But neverthelcfs I have not omitted to determine the fame VoulFoirs, when there are none but fofc or tenderStones to be ufed. Palladia fays, that the Voul- foirs of the Arches of Bridges fliould be made of very long and well jointed Stones, but does not determine their Length. Wh-^n he fpeaks of the Bridge of Rimini^ whofe Arches are fe- micircular, the VoufToirs, where the Headband has one Tenth of the Opening of the Arches, which are twenty Feet in Dia- meter. In that of Bachigliotie^ whofe Arches are Scheain ones, that in the Middle of the Opening of thirty Feet, the Height of ns Headband is one Twelfth of the Diameter ; and the Space above the Key-Stone ot thegreat Arch, which is between the Headband and the Cornice, is equal to half the Headband. B R In the ancient Bridge of Re- ranc^ as the two before mention- ed upon an Arch of an Open- ing of twenty-nine Feet, the Headband has the fame Pro- portion as the preceding. In a particular Defign which Palladia gives of a very fine Bridge which he has projeSed, the grand Arch of which has ten Fathoms for the Diameter [flatted] makes not the Head- band, or the Length of the Vouf- foirs, but one Seventeenth ofthe Width of the grand Arch, and one Fourteenth of the fmallcr, which have an Opening of eigiit Fathoms. See what Serlio fays as to the ^.ilatir/t Bridge aiRome^ antient- ly called Senatorius^ he remarks, that the Headband of the Arch at its greateft Height, is one Twelfth of the Breadth of the Arch. As to the Bridge of Quatro Capi^ antiently called Fabricius^ of which there are but two an- tique Arches remaining, tiie Headband of the Arches which are of the Ruftick Form, and whofe VoulToirs are the one longer than the other alternate- ly, that which has the mofl Bear- ing, is oneTenth of the Breadth of the Arch. The Bridg: Milvius has its Headband in Projedure, in Form of a Plinth quite plain, and whofe Height is one I'enth of the Diameter of the Arch. This is the Subllance of all that the nio(t accomplifiied Ar- chitefts have left us as to the Proportions of Voulfoirs. A TABii B R B R A Table of the Proportion of all the principal Parts of Semicircular Bridges^ from an Arch of one Foot opening to an Arch of twenty Fathoms, or one hundred and twenty Feet ; the Differences of their Culees, or A.butments, Piers, and Vouffoirs. The Open- Cu ees or A VouflToirs ofVouffbirs of ings of Ar- ches. bucments. \ Piers. hard Scones fott Siones. j 'fc Inc. Lin. Feet. ft- Inc. Lin .Ft, Inc. Lin. Ft. Inc. Lin. I 2 6 6 I 6 I 6 1 6 2 2 9 I 8 I I I 7 2 3 4 2 3 II 2 6 c I 2 10 I 1 I 2 6 I 8 I 9 4 6 8 H 3 4 6 2 2 I 2 6 I 10 6 3 7 2 4 ^ 3 2 8 6 7 3 9 6 2 6 I 3 6 2 8 4 2 8 I 4 2 I 9 4 2 6 2< 10 I 4 6 2 2 3 lO 4 f I 3' i 3 II 4 6 9 1 D I n D r 5" 6 i 4 6 12 4 8 6 3 2 6 I 6 2 4 13 4 9 9 -^ D 9 I 6 6 i 5- 2 6 14 f 3 5- I 7 If 5- I 9 1 6 ") I 7 6 2 6 9 16 5" 3 6 J 7 6 I 8 2 7 17 )' 5- 1 3 8 9 T 8 6 2 8 18 f 6 ' 3 9 I 9 2 9 19 5- 7 9 -> 10 3 I 9 6 2 9 -1 20 S 10 4 I 10 2 9 6 XI 6 II 4 2 S I 10 6 2 9 9 22 6 4 4 5- I II 2 10 ^3 6 6 6 4 7 I II 6 2 10 3 24 6 9 7 4 9 7 2 2 lO 6 ^S 7 6 r 2 6 2 10 9 26 7 3 5" s 2 S 2 I 2 II 27 7 6 6 r 5- 2 I 6 2 II 3 28 7 9 s 7 2 2 2 II 6 29 7 II 7 s 4 7 2 2 6 2 II 9 3'^ 8 3 6 023 3 B R B R The Open- c^iees or A- VouiToirs of.Vouflbirs of ingsotAr-j bucme.us. ches. 1 Piers. J lard Scones, foft Stones. Feet. ft. L,c. Lin. Fr , Inc. Lin.'Fc. Inc. Lin. tr. Inc. Lin. | 31 b ^ II ) 2 5-1 2 3 61 3 10 32" 890 65-0240! 3 I 8 33 8 11 670 246 326 34 9 2 7 ^97 250 330 3S 956700 2 5* 6 3 3 10 36 9667 26 260 340 3^ I 9 9 6| 7 5- 266 3 4 6 oj 7 7 270 3 S 39 2 ,03 1797 1 7 6 356 40 J 8 0' 8 280 3 8 41 ] on 3! 8 2 5 1 8 10 3 8 10 4^ ] I 2 bi 8 5- 2,98 3 9 8 43 ] I 5- 6; 8 7 2 10 6 3 10 6 44 ] [I 8 II 8 9 7 2 II 4 3 II 4 45" 46 [2 09 300 400 12 3 3; 9 2 5 3 10 4 10 47 12 6 8; 9 5" 3 I 8 4 I 8 4^ 12 10 9 7 326 426 49 13 11 9 9 7 3 3 4 430 SO 13 4 010 c 3 4 4 3 10 Si 13 7 s'lo 2, 5 3 4 10 4 4 8 52 13 10 810 5- 3 S 8 4 5-6 ^■s 14 I 610 7 3 6 6 464 ^4 14 4 II 10 9 7 3 7 4 472, 1 ss 14 8 on c 380 480 J° 14 II 3I11 2 5* 3 8 10 4 8 10 J7 5^ If ^ Sii s 3 9 8 4 9 7 15- 5- 6 II 70 3 lo 6] 4 lo 3 S9 60 61 62 66 57 68 69 15 8 11 16 16 3 3 11 9 7 3 II 4 12 0| 4 c 12 2 5: 4 IC 4 II 2 > 5 ) J- 10 16 6 8 16 9 6 12 s oj 4 I ^ 12 7 Oj 4 2 ( > 5- I 8 55-26 17 11 12 9 7j 4 3 . } 5" 3 17 4 13 0, 4 4 c 3 5- 3 10 n 7 3 13 2 5-j 4 4 IC 35-48 17 10 8 18 I 6 18 3 II 13 5 o| 4 5 ^ 13 7 0; 4 6 13 9 71 4 S 35-56 6564 4 5" 7 2 70 18 6 CI14 346 058c 71 i8' II 3 14 2 5481 05 8 IC ) 72 19 3 S 14 5" 049 8 f 9 y r 73 19 5- <^ 14 7 4 10 6j 5* lo : \ 74 19 8 II 14 9 7 4 II 4I 5" II ^ I 75 20 C ^15- 05- oj 6 ( 3 76 20 3 : llif 2 5-5- 10^ 6 IC 3 B R B R Th« Op»n- ingj of Ar- ches. 1 Culcci orA- Piers, VoufToirt ot,Voufl"oirs of bu imenti. hard Stones.' fofi Scone r. 1 F«ef. Ft. tnc Lin. Ft, Inc. Lin. Fc. Inc. Lin. 'Ft. Inc. Lin. 1 ( 77 20 6 815- f S I i i 6 I 8 78 20 9 6is 7 c S 1 6 (626 79 21 11 15- 9 7 S 3 A 630 80 21 4 c 16 S 4 c 6 3 10 81 21 7 6 16 2 s 5" 4 ic 648 82 21 10 8 16 f S S ^ 65-6 83 22 I 6 16 y S 6 6 664 84 22 i ^^ 16 9 7 S 7 A 672 % 22 8 17 S 8 c 680 86 2i 11 3 17 2 j- 5- 8 ic 6 8 10 87 i3 2 5 17 5' S 9 8 6 9 7 88 i3 f 17 7 S \o 6 6 10 3 89 ^3 8 II 17 9 7 f II 4 6 II 2 90 24 18 60c 700 91 i4 3 3 18 2 5- 6 10 7 10 92 i4 6 8 18 5- 6 I 8 7 I 8 9? i4 9 6 18 7 6x6 726 94 if II t8 9 7 5 3 4 7 3 95- ^S 4 19 640 7 3 10 96 if 7 3 19 2 5- 6 4 10 7 4 8 91 25" 10 8 19 r 65-8 7 5- 6 98 26 I 6 19 7 667 764 99 26 4 II 19 9 7 5 Z 4 7 Z ^ 100 16 8 20 680 780 lOl 16 II 3I2O 2 5- 6 8 10 7 8 10 102 103 27 2 8;io 5- 698 6 10 6 7 9 7 i7 5- 6,20 7 7 10 3 104 i7 8 1 1 20 9 7 6 If 4 7 II 2 105- 28 021 700800 106 28 3 3^1 i J 7 10 8 10 107 28 6 8j2i ^ 7 I 8 8 I 8 108 28 9 621 7 726 826 109 26 II 21 9 7 7 3 4 8 3 c no i9 4 022 740 8 3 10 iir 29 7 222 2 J 7 4 10 848 112 29 10 822 5- 7 5- 8 85-6 113 3<^ I 622 7 766 864 114 50 i ^^'' t2 9 7 ^ Z 4 872 irr 30 8 0: 13 780 880 116 50 1 rr 8: ^3 ^ S 7 8 10 8 8 10 117 Ji 2 8: ^3 S 7 9 8 8 9 7 irS : >i 5- 623 7 7 10 6 8 10 3 1 19 : 51 8 II 23 9 7 7 II 4 8 II 2 110 ■: > n 0,24 800900 B R B R N.B. That which I have freqvently rendered here^ Headband ot Fillet, M. Gauticr cxprejjes by Ban- deau, vjhich is the common Englifh, according to A. Boyer : But M. Gautier makes it the fame as Intra- dolle ; which he explains to be the interior Curvity of a i^^auh^ Archy or P'^ouJlJoirs of a Bridge. Experiment. In order to be fully confirm'd in what I have here advanced concerning the Pufh or PreiTure of Arches, Vaults, the Length of Voulloirs, or the Height of Archivolts, (ays M. Gautier^ I had Rccourfe to the following Experiments. 1 got a fmall Semi-Arch ot ten certain Meafures in Diame- ter, and femicircular, as in the \zi\ Table. This Semi-Arch I compofed of nine Vouffoirs (See Ftg. II. AB CD, Platel.) which were made of Wood, and turn'd k up againft a Wall in ABE, as againd an immoveable Key upon the Half-Centre BCE. Having thus placed the nine Voulfoirs CB upon the Half- Centre CB, I loaded them behind with other Pieces of Wood, equal to them in Bulk, and alike in Weight : I then placed nine more one upon another, after the fame Manner, as you may fee in the Figures FG, and be- hind them, I ranged the four others at H I. This done, I uncentred the Semi-Arch EBC, and it remain- ed unmoveable in the Pofition you fee it in the Figure I. 1 afterwards took away the Pieces of Wood which form the Butmenr, and keep in the Reins or Sides of the Arch one after another, beginning at the Top, according to the Numbers 9»8, 7,6, J-, I, 13, 4, 12,3; fo that there remained but the four undermoft, viz. 11,2, 10, 11 ; which four fupported the Semi- Arch without falling, ABCD; But as foon as I began to re- move the nth, theVouflbirs fell afunder. This Experiment gave me to underftand, in the firft Place, that the Mafs of Stone- Work, which the Sides or Declivity of Vaults are laden by, ferve them for a Support to keep the Vouf- foirs in aquilibrio^ that they may not deviate or depart from the Curve form*d by their Centre, and likewife that their ftrongell Pufti is in that Place. 2. Though this Experiment was made with Pieces of Wood (which confequently were very light,) that had nothing between their Joints to keep them toge- ther, they neverthelefs keep each other up by means of their Mould or Cut; the Pattern of which 1 had given to a Joiner to make them by. Thirdly^ This Experiment con- firms me in the Opinion, that \^ we made our Archivolts without any Mortar, Cement, or Cramps, in Imitation of the Antients, and afterwards ran a kind of tine Mortar, or Cement made of pul- vcriz'd Stones into the feveral Abrcuvoirs, the Work would be much more durable ihva \t can B R B R be with thick beds of Mortar, •which yield to the immenic Weight of the fuperincumbent Stones. Fourthly^ From this Foot of the Semi-Arch I railed tiie Per- pendicular CK, and found that the Voufloirs BC. which are in- terfered by the Line CK, never attempted to fall afundcr till the Part of the Butment CH was inade lighter than the Semi-Arch CB, which confirms whatUaid before. Thus the VoufToirs, together with the Materials they are la- den with, ought to be in aqui- itbrio with the Butment, which you would have to refift their Pu(h, or the Work muft infallibly fall to pieces. I have calculated the above Table, in order to make thefe Things familiar to Perfons who are ignorant of Geometry. Which of the feveral Sorts of Arches, fixed or ereded upon one and the fame Diameter, would be capable of fuftaining the greateft Weight; and in Pro- portion their Etforts or Pu(]ies are to one another, whether they be Scheam, Elliptical, Semicircu- lar; or, in Ihorr, of the third Point. If due Attention be given to what I have already laid down, it may be allow'd, that the Pufhes of all Arches of ditferent Degrees of Flatnels, are to the Weight by which they are laden, as their Icveral Degrees of In- clinations are to the Breadth of the Butment which is to iecurc them; and it will alfo be found that thofe, whole Pulh is the lealt inclin'd, (or oblique.) will be able to fullain greiicr Burthens i than thofe which border upon the (Iraight Arch, which is the vvcakeft of all. Let us fuppofe the ftraight Arch (A, Fig. L Plate II.) to be a Beam tranfporced or re- mov'd to AC, Fig. IX. Now it is certain, that if in this Situa- tion it was laden with a Weight of ICO Ik and it fliould happen to break it, it would neverthe- lefs be able to bear not only a Weight of 100 /^, but alfo a Weight infinitely greater, if it was raifed perpendicularly, as AB. But I Hiall pv.t the Cjfe here, that it would bear 200; and therefore 150 being the main Proportional between 100 and 100, or between the firlt Pufh (as we will call it) and the fe- cond, it will be found that the Beam, being elevated to 45- De- grees in A_D, it will bear that Weight, (-z//^.) i^oil;. form'd as a femiciicular Arch. if you lovi'er it down to AF, to form the Elliptical Arch, it will be found, that if you take the main Proportional between the femicircular Arch AD and the Beam (or Hraight Arch) A C, which is AF, the Ellipfis AV will bear but iiy. in fliort, the main Propor- tional between the femicircular Arch, which is 15-0, and the Power or Force of AB, which 200, will be 175-, and that will be e.xprcllly the Strength of the Gotb:c Arcn A E. Fhus the higher an Arch is carried up, the llrcnger will it be; and the flatter or lower it is, the weaker. This Argument may be de- termined to the niceftExadnefs, when B R B R when you (hall have difcovered or agreed upon the Difference of the Strength of a Beam, when laid down like a (Iraight Arch, as AC, and when ercded per- pendicularly AB. From this Demonftration I infer, that the Gothic Arch is ftronger than the femicircular, the lemicircular Arch ftronger than the elliptical, and this laft than the ftraight Arch. This Figure JX. in Plate II. helped me to make an Experi- ment, whereby to find theWeight of all forts of Bodies at diffe- rent Inclinations, as may be Ic: rr.ed from the following Pa- ragraph. Of the Weight of Bodies at dif- ferent Inclinations^ and the Manner of calculating it. A Body AB, (Plate II. Fig. II.) uniform throughout its whole Length, Breadth, and Thicknefs, no matter whether round or fquare, wcigh'd loo upon the Point of Support A, and eredt- ed perpendicularly, as AB. Bat when this fiime Body AB was laid down horizontally, or on a level upon the Points A and CE, which were equidillant from the Centre or Middle, and Extremities of it, it preffed upon the firft Point of Support A with a Weight of 5-0 only ; becaufe as the whole Weight is equally fupported by the Points A and C, the whole Weight aforefaid is equally divided between them : Thus, as it bears 5-0 upon A, and 5-0 upon C, the Sum of thofe two Numbers is 100 the whole Weight. When I alter'd the Pofition of this Body AC, by giving it an Elevation of 45- Degrees in AD, I found that weighing in the whole 100 Parts that prefled up- on D with a Weifcjht of 25- only ; wherefore ic muft prefs upon A with a Weight of 75-, in as much as the Sum of thole two Numbers gives 100, the whole Weight which was to be. I then made two other Expe- riments, by elevating the afore- faid Body from AD to 67 i in E, by deprefling or declining to 22 Degrees f \n F ; upon the Point E it prefTed with a Weight of iii only, the Point F with a Weight of 37 7 ; and confe- quently I found that E A, at an Elevation of 67° 30', prefling after the Rate of 12 7 only upon the Point E, mull prefs with a Weight of 87 T upon its Point A; and alfo that AI-', at an Elevation of 22° 30' mud prefs upon its Point A with a Weight of 62 ^. And thus you will find it in continued Proportion by fubdividing the Parts BE, ED, DF, and FC. From hence I calculated a Table; which fliews that the Bo- dy AB prefTes the greater upon its Point of Support A, the higher it is elevated above the Level AC in F, or towards I), Ij'c. and inverfely, that the afore- faid Point of Support A is the leaft prelled the more the Body AB quits its Perpendicularity, and is inclined towards EDF and C, and lb on, beneath the Level AC, by a reverfe Politiop, indeed, but, however, m the very fame Proportion. la B R In order to this, I have fup- posM the Body AB to be uiii- torm throughout its whole Di- menfioiis, and to weigh loo equal Parts, (no matter whether Pounds, or any other Weight,) nnd to be one hundred equal Parts in Length. Having laid down this for a Foundation, I found no Diffi- culty in inveltigating the Effort and Power of all Bodies what- ibever, more or lefs inclin'd, ■whether in Lines or Curves ; for by reducing the Curves ti (Iraight Lines, or at leaft by fuppofing the Curves to be equally fupport- ed by the Extremities of their Chords ; and by comparing the Chords with one another, [ re- folve the Strength and Weight of all Arches and Vaults, of whatfoever Figure they be, whe- ther regular or irregular. But you mull previoufly con- fult the following Table, where it will be feen, at the firft Co- lumn, the various Degrees of the Inclination of Bodies, whofc Weight we would calculate. You mud again fuppofc the Body to weigh an hundred Pounds, or any Thing elle, or any other Number, which an- fwers to the equal Parts into which it is divided, and the In- clination of the Body fhall ue determined by a certain Number of Degrees. This being premifcd, let there B R be an Arch of any other inclin' Body, to whofe Weight or Pre( lure at the Key you wouh know. Let us fuppofe it to be the Hal of the femicircular Arch, (Fig, [ Pla:e I.) whole Prefllire' o. Weight you would know at the Key E; calculate the Stone or Brick Work E H A of the Semi- Arch, which you may ealily do by a previous Knowledge of the Weight of a cubic Foot of ei ther of thole material?, and you may come to the Knowledge of the relh For fuppofe that EHA weighs 97j'o //a the Half of which will be 4575'/^. but the Chord of the Semi- Arch is at an Inclination of 45-*^, therefore (from the Table below,) f-iy, If 5*0, the laft Number or Term, gives the Weight of zf, at an Inclination of 4^ Degrees, how much will 4875-, the Half of the Weight of rhe whole Triangle A HE, give? And it will come come out 2,437 j-; lb that the Body EH A, weighing in all 9-5-0, will weigh at the Key at an Inclination of 4)^ 2437 y ; which lall Number being fub- Itraded from 975'o, it will be found to weigh or pufli at the Foot or Couifmet "312 5. It is after thisIVlaimer that you are to determine, with regard to the Strength of Burtrelles, for the Support of Vaults, Wails, / A Table D G H F/a I. \^ __Ji^ /^ 7 -"><■■• y./.^. / Q ■1=1 » ■ , N C T i A N r -B >l S'. i ^ G A I c^^W ^ i-Mi/y i«i-H I^hIP' (D|c E 'II W/7/./y B R B R A Table of the Proportions of the Weights and Pufhes of Regular Bodies, at all De- grees of Inclinations. The Number of Qiiantities of an inclin'd Body to be determined. De^. lb. Dz.'Deg. lb. Oz.iDeg. lb, < 3z. Deg. lb. Oa. I O 8f M 13 y 47 :i6 ^ 70 38 i 2 I I 2f 13 1 48 26 6 9 71 39 ^ 3 I ii i 26 14 V 49 2.7 2 c) 72 40 4 2 y i7 ij- C 5-0 27 i 73 40 \ 1 2 6 28 15- i 5-1 28 9 74 41 I 6 3 I 3 |!29 16 ^;3o 16 I 9 (S Q 5-2 28 S3 29 8 9 f 1< 41 i 76 42 9 8 4 ^31 17 9" 7 ^4 30 > 77 42 % 9 5- 032 17 9 5 ff 30 h I 78 43 I lo 5- y 33 18 Q 7 5'6 31 79 43 I II 6 1 34 18 9 n 31 9 6 80 44 ^ 12 6 2. 35- 19 A V ^8 32 flSi 4^ ? 13 7 2 36 20 f9 32^ 1 §2 45" 9 14 7 9 37 20 i 9 60 33 i 83 46 f i^ 8 1 38 21 4, ^^ 33 18446 i i6 8 39 21 6 9 62 34 ^,%47 ? 17 9 y 40 2i 2 "^3 3S J8647 i 1 8 lo < 41 22 7 9 64 35- ^8748 1 19 10 V I 42 2^ i. 65- 36 i 88 48 1 20 II 9 43 23 A 9 66 36 fi89 49 ^ 21 II y 2 44 24 f <^7 37 90 yo 22 12 4r 25- o|6S 37 7 9 23 12 ^ 4^ 25- 9^:69 3S 9 Vol. I. Draw-Bridge^ B R B U Draw-Bridge^ is one that may be drawn or taken up by Means of a Sweep, or Counterpoiie, and which l"huts up againft a Gate. There are others with Pitfals and Beams, fuliained by two large Stakes fifteen Koot high ; one Part of which lowers as the other rifes. TO BRING UP, a Term ufed among Workmen, efpecial- ly among Carpenters, when they are talking with Bricklayers : Thus they fay, Bnrig up the Foundation fo high ; Bring up fuch a Wall; Bring 7ipx.ht:iZi\\m- neys, ^c. which is as much as to lay. Build the Foundation fo high, Build the Wall; Build the Cliimneys, ^c. BROAD STONE, is the fame with Freeftone ; only this is fo called, becaufe raif- ed broad and thin out of the Quarries, viz. not more than two or three Inches thick. As to itS'Ufe : The Ufe of this Sort of Freeftones, which are called Broad- Stones^ is for paving Court- Yards and Paffi- ges, and before Shop-Doors, as in Walks or Paths in the City oi London^ to feparate them from the Highway. As to their Price : If the Breadths and Lengths are pro- mifcuous, then the common Price for fitting and laying the Stone in Mortar, from 6 ^. to 8 d. per Foot fquare, or from 4/. to 6s. per fuperficial Yard. But fome of thcfe Stones arc cut into perfed Squares, likePa- ving-Tiles, but much larger, as eighteen, twenty, or twenty- four Inches fquare or more ; but as thefe are neater, fo they are Nearer j fooie Pavements ofthefc t being worth i^d.per Foot ; anc if the Scones are good, and well polifh'd, as they ought to be foi Kitchens, Dairy-Houfcs, Brew Houfes, t^c. they will be worth, 15-, or 16 d. per Foot. Spanish BROWN is a dark? dull Red, of a Horfe-FieOi Co lour. It is an Earth tlut is dug; out of the Ground : But there is fomc of it p!e:ifnnt enough to the Eye, conlldcring the Decp- nefs of it. It is ofgreat Ufe among Pain^ ters ; being generally ufcd as the firft and priming- Colour, which they lay on upon any kind of Timber- Work, being cheap and plentiful, * and a Colour that works well, if ft beground fine; which may be done with lefs La- bour, than fonie better Colours do require, l^hat wiiich is of the deepert Colour, ai^d the freeft from Stones, is thebeft. The other Sorts arc not fo good to give a Colour to the Eye, but yet they fervc as well as any other for the Priming Colours, to feafon the Wood to lay other Colours upon. BUFFET,? a little Apart- BUFET, 5 m^'^-'» f<^Parated from the reft of the Room, by flender Wooden Columns for placing'^China, Glafs-Wnrc, ^f. Called alfo a Cabinet. The Biijfet^ among the hi- lians, C&Ucd Credeijza,\s inclos'd within a Balullrade, Elbow- high. BUILDING, is ufed to fig- nifv both the Conflruding and Railing of an Edifice; in which Senfe, it comprehends as well the Expences, as the Imvention and Execution of the Dclign. In B U B U '^k III BusW^g there are three 'fillThings to be coniidered , viz^ '°',Firft, Commodity or Convenien- *xy. Secondly, Firmnefi' Third- iftk;iy, Delight/ i To accomplifh which Ends, ^'SJSir Henry l4'utton conliders the ;iJiwhoIeSubje£t under two Heads, in? •&/>;. the Seat or Situation, and ; is (he Work. ^ I. As for theSeat: Either that of the Whole is to be coniider- ed, or that ot'iis Parts. 2. As to the Situation, Regard is to be had to the Quah'ty, Tem- perature, and Salubrity or Health- fulnefs of the Air; that it b.- a j;ood healthy Air, not fubjedt to ■'oggy Noifomenefs from adja- cent Fens or Marfhes; alfo free from noxious Mineral Ex ha la- ions : Nor fliould the Place want he fweet Influence of the Sun- Seams; nor be wholly deftitute Df the Breezes of Wind, which vill fan and purge the Air ; the Vant of which would render it ke a flagnated Pool, or ftanding iake of Air^ and would be very inhealthy. Pliny advifes not to build a !]ountry-Houfe too near a Fen r Standing- Water; noryetover- gainft the Stream and Courfe of River ; becaufe the Fogs and /lifts which arife from a large liver, early in a Morning, be- )re Day-Light, cannot chnfe at be very unwholefome. Dr. Fuller advifes chiefly to lufe a wholefome Air : be- lufe, fays he, the Air is a Difh ne feeds on every Minute; jid therefore it had need be fa- brious. \Cato advifes, that a Country- joufe have a good Air, and not lie open to Tempefts, feated in a good Soil, and let it exceed therein, if yoa can; and let it Aand under a Hi 11, and behold^tiie South, in a healthy Place. As to CommodioufnefS) or Conveniency, Sir Henry U-'otton advifes, that the Houfe or Seat hive the Conveniency of Wa~ ter. Fuel, Carriage, ^r. that the Way to it be not too lleep, and of an incommodious Accefs, which will be troublefome botli to the Family, and Vifitants. And as for the Conveniency of being fupply'd with Necclfaries, it fliould not be feared too far from feme Navigable River, or Ann of the Sea. Wood and Water, fays Dr. Fuller^ arc two Staple Commo- dities. As for Water ; the Want of it is a very great Incouveniency, the Detriment of many Houfes to which Servants mull bring the Well upon their Shoulders. And as to Wood ; where a Place»is bald of Wood, no Art can make it aPerriwig in Hafte. Optical Precepts^ or Maxir/if Such I mean, fays Sir Henry iVot- ton^ as concern the Properties of a well-chofen Profpe6t ; which may be itiled the Royalty of Sight. For as there is a Lord- fhip (as it were) of the Feet whereon a Man walk'd with much PleafUre about the Limits of his own PoflefTions, fo there is aLordfhip likewife of the Eye which being a ranging and impe- rious (I had almofl laid) uiurp- ing Senfe, cannot endure to be circumfcrib'd within a fmall Space, but muft be fatisfy'd both with Extent and Variety : Yet on the other Side, I find vail and in- definite Profpe£l:>, which dro\V;i L i all B U all Apprchenfions of very remote Objcdis condcmn'd by good Au- thors, as if fome Part of the Pleal'are (whereof we arefpeuk- ing) did thereby peridi. 'Agrecablenefs and Pleafant- nefs of Profped is to bevalu'd. Dr. Fuller fiys, a Medley View (fuch as of Land and Wa- ter, at Gree-avjich) beft entertain the Sight, refrcfliing the weary Beholder with Change of Ob- jects: Yet, fays he, 1 know a more profitable Profpecl, whire the owner can only fee his own Land round about him. And to this Head of Situation, he adds, as follows : A fair Entrance with an cafy Afcent, gives a great Grace to a Building, where the Hall is a Preferment out of the Court, the Parlour out of the Hall ; not (,as in fome old Buildings.) ivhere the Doors are io low, that Pigmies may (loop ; and the Rooms fo high, ti:at Giants may (land a-tiptoe. , A political Precept : That great Architect Sir Henry IVotton fays. One private Caution, which I know not well how to rank among the relt of the Precepts, unlefs I call it political, is this, viz. By no Means to build too near ?. Great Neighbour; which were to be as unfortunately feat- ed on the Earth, ^% Mercury is in the Heavens; for the molt part ever in Combudion or Obicu- rity, under brighter Beams than his own. Contrivance. : The Situation being tix'd on, the next Thing in Order, is Contrivance; which bc'ng a Hiing of great Moment in thii Atfair of BKildi:-7^^^ before ft is emred upon, it will fc« nc- B U ceflary to give fomx few general} Precautions. Firfl, let no Perfon, who in tends to build a SrrudUuc that! fhall be either ufe.^ul orornamiCn- tal, begin it without the Advice or Alfiilance of a Surveyor, «i Maflcr- Workman, who under- ftands the Theory of Bmldiytg^ and is capable of drawing a Draught or Model according to the Rules of Art. In a Draught (which may ferve inditfcrently well in fmall Build ings) there ought to be the Ich-;; nogrnphy of eacii Moor, and al-'> fo the Orthography of eachFacell of the Btiildiiig^ VIZ' the i-'ront,! the Flanks, aiid the Rear. But if the Artisan be well vers'd in Profpcdlive, then more than one Face may be rcprefcnt- cd in one Diagram Ucnogra- phically. In contriving thefe Deligns,: whether by Draught or Model.1 the Quality of the Perlon, foij whom the Edifice is to be ered-' ed is to be conlidcrcd, in regard to the Ichnogrsphical Plots elpe-i ca'ly, I For Noblemen have Occafioi: for more Rooms of Oflice, thai: other Perlbns of a meaner De-I grec. All which ought to be defign'd according to their mof convenient OccnHons ; witf' their Lengths and Breadths ac cording to Proportion. Like wife the Ichnography of al Chimneys, both as to the Lengtl^ and Breadth of the Hearths* Jaumbs, Bed- Places, and Stairs and the Width of all Doors, an( Windows, in each Contignatioi or Floor. And if it be required, inTinf I bcr Buildings, the Lengtb Breadth B U B U Brcadih, and Thick neCs of Ground-Plates or Cells, Brcll- Summcrs, (and in all, whether I'inibcr, Brica, or Scone Build- i}7gs,) the Dimcn/ions of Sum- mers, Giruers, Trimmers, or J Gifts. AHo in the upper Floor, the Scantling of Dragon -Beams, Raifuns, or Railing-Pieces, or Wall-Plats, ej'f. And alfo the Thicknefs of Partitions, Walls, <^c. in Brick or Stone Fabricks. All which, and all other Parts (whether \\\ the Ichnogrnphy, or Orthography} of Build'mgs^ ought to be reprefented; as alfo Ovens, Stoves, Broilers, Fur- naces, Coolers, Fats for Brew- ing, zsc. with their juft Mea- fyres to the beft Advantage, as to Convcnicncy,Health,Strength, and Ornament. All which Dimenfions ought to be fct in the proper Places to which they belong in the Dia- grams in CharaQers ; becaufe if the Schemes be not very large, it will be very difficult to take the Dimenijcjiis of the fmallcr Parts nicely, if not of the great ones themfelves ; for it will fcarcebe prat'ticable, to take ei- ther of them to an Inch, nor perhnps, to two, three, or four Inches, according as the Dia- , gram may be in Amplitude. In the Orthographical Schemes , there muft be true Delineations and Dimenlions of each Face, and all its Concomitants, as Doors, Windows, Balconies, . Turrets, or Cupola's, Chinmey- Shafts, F"afcias, Ruftick Quoins, Architraves, Friezes, Cornices, Pedinaents, Pilalters, Columns, Shells over Doors, Lanthorns, and all other Ornaments. If it be a l^imber Buildir,g^ all the Members in that Face ought to have their feveraJ Si- zes in Gharaders, and true Po- litions by the Scale. As for Example: The Ground- Plates or Cells, Introdaces,Brell- Summers, Beams, Principal Pbfts or Braces, Quarters, Prick- Po(h, orWindow-Pofts,Jaumbs, or Door-Pofts,. or Puncheons, King-Pieces, or Joggle-Pieces, Struts, Collar- Beams, Door- Heads, Principal Rafters, Shread- ings, isfc. The Ichnography, Orthogra- phy, and Stenography of the Stair-Cafe may alfo be delinea- ted, and all its Parts, as Hand- Rails, Rifers, Nofeing of the Cover or Top, String-Board and Mouldings on it, as Car- tQuzes, Ballufters, Pendents, eff, with their true Pofitions, Forms, and Dimeniions; all which, if they be carefully done by an ingenious Surveyor, a Workman will hardly be like to commit any Blunder. Sir Henry Wottun advifes as to this Matter, as follows: Ftrjl^ Let no Man who in- tends to build, fettle his Fancy on a Draught on Paper or Vel- lum of the Work or Defign, how exaSly foever delineated or fet off in Perfpedive, without a Model or Type of the whole Strudhire, and of every Parcel and Partition, either of Pafte- board, or Wainfcot. Secondly^ Let the Model be as plain as mav be, without Colours, or other Beautifying, leaft the Ij ^ Pleasure B U B U Pleasure of the Eyes preoccu- pate the Judgment, Thirdly^ and Lajll\\ The big- ger this Type is, fo much tne better it is : Not that I would perfwade any Man to fuch an £normity as that Model made by AntOKio Labaco^ot St. 'Peter^s Church in Romc^ containing twenty-two Feet in Length, lix- teen in Breadth, and thirteen in Height, which coft four thou fand one hundred and eighty-four Crowns, the Price of a reafon- ab!e Chapel ; yet in a Fabrick of forty or fifty thoufand Pounds, there may very well be thirty Pounds expended in procuring :m exa61: Model; for a little Pe- nary in the Premifes, may eafi- 3y create fome Abfurdity or Er- ror of a far greater Charge in the Profecution, or at the Conclu- lion of the Work. What Sir Henry Wotton here advifes, is very requifice, efpe- cially for large and fumptuous 'Butld'inii^ either pubiick, or pri- vate ; but it is not worth the while to be at the Charge of a Mode) for every little Dwel- Ifng-Houfe which Men build for their own Conveniency. I fhall here add as to the Con- veniency, what is recommended by Sir Henry IVotton^ that the Chief Rooms, Studies, Libraries, l^c. fliould lie towards the Eaft; that thofe Offices which require Heat, ns Kitchens, Brew- Houfts, Bake-Houfes, and Diltillatories, to the South ; thofe which re- quire a cool frefh Air, as Cellars, Pantries, Granaries, to the North ; as alfo Galleries for Paintings, Iviuf^ams, ^c. which require a ileady Light. He tellsus, the anticht Greeks and Ro'nans generally luuntcd the Fronts of their Houfcs to- wards the South; but the" mo- dern Italians vary much irom this Rule. And, indeed, as to this Mat- ter, Regard muft ftill be had to the Country, each being forced to proride againft its Incoiive- j niencies : So that a good Parlour \ \n JEgypt^ n-Jght make a good Cellar in Rngland. The Situation being fixed on, and the Delign and Contrivance deiign'd, the next Thing to be confider'd, is the Work itfelf ; under which the principal Pares are firll: to be confider'd ; next, the Acccilbries and Ornaments. Under the Principals are, firft, the Materials ; next, the Form or Difpofition. As for the Materials, they are either Scone, as Marble, Free- ftone. Brick for the Walls, Mor- tar, i^c. or of Wood, as Fir, Cyprus, Cedar for Poftsand Pil- lars of upright Ufe ; Oak for Summers, Beams, and Crop- Work, or for joining and Cou^ ( nc6tion. i As to theFormorDifpofitioni; of a Bmld'ing^ it is either fimple, • or mix'd. The liniplc Forms are either circular or angular ; and the circular ones either compleat, as juft Spheres; or deficient, as oval ones. The Circular Form is very commodious, and the molt ca- pacious of any, ftrong and du- rable beyond the reft, and very beautiful ; but is the mod chargeable of all others ; and much Roono is loft by the Bend- ing >1 B U B U }ng of the Walls, when it comes ro be divided into Apartments, btfidts an ill Diflribution of Ivighr, unlefs k be from the Centre of the Roof. For thefe Reafons, \t was, that the Antients ufed this Form only in their Temples and Am- phitheatres, which had no need of Compartitions. There are the fame Inconveniencics attend- ing Oval Forms, without the fime Couveniencies, being iefs capacious. As for Angular Forms, Sir Henry l^Fotton obfcrves, that Building neither loves many nor few Angles. The Triangle is condemii'd above all others, as wanting both Capacioufnefs and Firmnefs ; as alio not being ca- pable to be refolved into any other regular Figure in the in- ward Particionsbefides its own. As for Forms of BuiUtng of five, fix, feven, or more Angles, they are much fitter for Fortifi- cations, than Civil Buildings. There is indeed, a celebrated Buiidmg of Vigmla at Caparole^ in the Ki'jure of a Pentagon; but the Architecl had very great Difficulties to grapple with as to the Difpoficion of the Lights, and the faving the Vacuities. So that fuch Buildings intern rather for Curiofity than Conve- niency. At^d for this Reafon, Redangles are generally cho- fen, as being a Medium between the two Extreams. But then Authors are in Dif- pute, whether the Re6tangle ftiould be anexad Squar^^ or an Oblong. Sir i/ewry /fWe» pre- fers the Oblong, provided the Length exceeds not the Breadth by more than one Third. As to Mixed Forms or Fi- gures, a Judgment may be made o( them horn what has been al- ready faid of fimple ones; only that they have this particular Dc- fe6f,that they offend againft Uni- formity. _ Indeed, Uniformity and Va- riety may fcem to be Oppofites; But Sir Henry IVotton obfcrves, that they may be reconciled ; by Infiances in the Stru6ture of the Human Body, where they both meet together. Some obferve, that in build- ing Houfes long, the Ufe of fome Rooms will be loft ; and they will take up more for Entries and PafiTages, and will require more Doors: And if a Building be a Geometrical Square, if the Houfe be any Thing large, the middle Rooms will want Light more, than if they were built in the Form of an H, or fome other fach like Figure, unlefs there be a Court in the Middle of it: Which was the Method of building great Hou- fes in former Times. Some much commend this Way ofbuilding an Houfe in the Form of a R-oman H : For they fay, this Form makes it ftand better, and firmer againft the Winds ; and that the Light and Air coines to it every Way, and every Room is nearer one to the other. Some approve of this Form very much ; becaufe in it, the Offices may be remote from the Parlour and Rooms of En- tertainment, and yet in the fame Houfe, which may ferve very well for a Country Gentle- man's Houfe. B U In Buildings of this Form, fome propofe the Difpofition of the Apartments thus : In the Frc nt of one of the long Part of the H, is to be the Kitchen, theBake-Houfe, Brew- Houfe, and Dairy-Houre. In the fame Part behind it, the Hall, in the Middle of the H, which feparates the Parlours which are in the other long Part, and Rooms of Enttrtaiirment from the Offices. Thus much for the firft grand Divilion, viz. the Whole of a JSuildin^. As lor the Second Divifion, or the Parts of a Bulldiijg^ they are comprized by Baptijla Jilbcr- ii^ under five Heads, -viz. the Foundation, the Walls, the Aper- tures, the Compartitions, and the Covering. I. As for the Foundation, Vi- iruvius orders the Ground to be dug up,to examine its Firmncfs, that an appearing S ^lidity is not to be truftcd, uuKfs the whole Mold cut through be found and folid : 'Tis true, he docs not fay to what Depth it ought to be dug. But Falladio determines it to a jlxih Part of the Height of the Building. And this is called by Sir Henry Wottoyi.^ the Natural Foundation, whereon the SabftruiSlion or Ground-Work is to (tand to fjpport the Walls ; W'hich he calls, the Artificial Foundation. This then is to be level ; the Joweft Ledge or Row of Stone, only clofe laid with Mortar ; and by how much the broader it is, by fo much will it be the better; but at Icuft, it fliould be twice rhe Breadth of the Wall. Some advife, that the Mate- B U rials below, be laid jufl as they come out of the Quarry; fuppo- fing that they have the grcattft Strengfh in their natural Poilure. De Lorme enforces this by ob- ferving, that the breaking or yielding of a Stone in thi^ Part, but the Breadth of the Back of a Knife, will make a Clettofmore than half a Foot in the Fabrick above. As to Pallification, or Piling the Ground-Pint, which Vitru^ ^ vius does fo much commend, I fhall fay nothing here, becaufe that is requilite only in a moill marfhy Ground; which, for Buildings friouldncverbechofen :i Nor, perhaps, are there any In-' fiances of Pallification pra6lifed,i but where they were obliged to: it by Neceffity. A-S tor Walls, they are either entire and continued, or inter- mitted; and thelniermilfions are are either Columns or Pilalfcrs.* Entire or Contihued Walls' arc, by fome, varioufly dilliu guilfi'd, according to thcQuili ty of t.ie Materials, as they are either Stoiie, Brick, (sfc. other only coniider the Polition ol' the Materials, as when Brick or fquare Stones are laid ir their Lengths, with Sides oi Heads together; or their Point; conjoined together like Net Work. See M.^sonry. 1 he great Laws of Wallinj are. Fir ft. That the Walls flanc perpendicularly to the Ground. Work, the Right Angle beinjj the Ground of all Stability] Secondly, That the mafliefl an' heavielf Materials be i\\q lowefli as fitter to bear than to be borr Thirdly, l^hat the Work dim nifh in Thicknefs, as it rife; bot s ' \ B U B U both for the Eafe of Weight jind Apartments, i^c. Sir Hettry Eipence. Fourthly^ That cer- //'W/'^w lays down thefc Pre! i mi- tain Gourfcs or Lodges, of more naric;:. That the Archircd do Strciii^th than the relt, bo inter- never fix hi^ I'aiicy on a Paper- laid like Bones, to fultain the Draught, be it let oft" never la Fabrick from total Ruiu,ir Ibme exa£lly in Porfpedive, much Ivfs of the under Parts chance to on a mere Plan, without a JVlo- decnv. Fifthly, and Lafily, That del or Type of the whole Struc- the Angles be tinnly bound, they tare, and every Part of ir, either being the Nerves of the whole in Paftcboard or Wood. Fabiick : 'Which are ulually for- 1\ the Compartition iif.lf there tify'd by ihe//rf//jiJj" on each Side are two general Views, v^z. the Corners, even in Brick the Gracefulnefs and Uf-Uilnefs BuilJiiJgs^ wich fquared Stones; of the Dillribution for Rooms of which V.dd both Beauty and Office and Eriteitainmenr, as far Strength. as the Capacity of it, and Nature The intermilTions of Walls, of the Country will allow, as has been before mcntion'd, T.\ie Gracemlnefs will con- are either Colums, or Pilalkrs; fill in a double Analogy or Gor- of which there are five Orders, rcfpondency. ^-"V^, Bec/v-een viz. the Ttifcan, JDor'ic^ luuic, the Parts and the Whole; by Cori-^tbian^ and C/.mprfite. All which are dilfiniSily treated un- der their refpeCtive Articles. ' Columns and Pilalters arefre- wlnch a large Edifice Ihowld have large Partitions. Entrances, Doors, Columus, and, iii Ihort, all its Members large, propor- queiuly form'd Arch wife, both tional to the Buildin;:^. for Bcviuty and Grandeur. The fecond Analogy is be- As for Apertures, thty are ei- tween the Parts themfelvL-s, not ther Doors, Windows, Stair- only confidering their Lengtns Cafes, Chimneys, or Conduits and Breadths, as we Ip^uk of for the Suillage, e^f. All which Doors and Windows. But here, you m.ay fee conlidered under favs Sir //^«rv, enters a tin'ra Re- thcir proper Heads. ped of Height, a Point ; 1 con- And as to the lad. Art fefs. laiih he, fcarce reducible to (hould imitate Nature in thefe any general Precept, ignoble Conveyances, and con- The Antients determined their ceal them from the Sight, where Rooms which were oblwng, by a running Water is wanting, in- doable their Breadth, and their to the moft remote, loweft,and Height by half their Breadth and thickelf Part of the Foundation, Length added together, with lecret Vents palling up When they wou'd have the through the Walls like a Tunnel Room a perfc6l Square, they to the open Air. Which is re- made their Height half as much commended by all iht It alMns^ more as their Breadth : But the for the Difcharge of noifome Moderns difpenfe with thefe Vapours. " Rules, fometimes fquaring the As to Compartitions orDiftri- Breadth, and making the Diago- bution of the Ground-Plot into iial of it the Meafure of the Height B U B U Height, and fometimes more. This Deviation from the Rules of the Ancients is afcrib'd to A/. Sometimes they fquar'd the Breadth, and doubled that fquare Number; and taking the Root of that fquare Number, for the Height, and fometimes more ; but feldom lower for the Breadth. But what is here mention'd is fcarcely now praftifed, unlefs it be in a Nobleman's Houfc; "who will have a Hall, C5'<^- higher pitch'd than the reft of the Rooms in the Building ; and fometimes a Dining-Koom; or clfe, for the moft Pure, all the Rooms of a Floor are of an equal Height: And this feems to be the moft commodious Method; becaufe in this Cafe, there is no Lofs of Room, as there muft necelTarily be, where one Room is open almoft to the Top of the Houfe, as may be obferved in fome old Buildifjgs ; and then the Floor of the fecond Story will lie level and even, and not in the old Method of Steps out of one Room into another. As to the Height of Rooms, that is various amongft us, ac- cording totlie Perfons tor whom they are built, and the Cuftom of the Place. In the Country, common Timber Buildiugs are ufually about feven Feet one Third, or eight Foot at the moft, betwixt the Floors. The fecond Sort of Houfesin the Country is about nine Feet between the Floors ; which for the moft part is the Pitch of the Rooms at Tunbridge-ll'ells . The third Sort in the Country, {'uiz,. in Kent and SujJ'ex^ are Gentlemens Seats; which for the moft part are tenor twelve Feet high, fuch as are new Buildings. But in old Stone Buildings.^ 'tis common to be much higher, VIZ. fourteen or fixteen Feet. By Aft of Parliament, for building of Loudon., there were reckon'd four Rates ot Houfes, viz . The The The R'^*^ ^^SFoot V5- at Difcretion, Zffc. 1 X Rates, Cellars ^6 I 2 (in Height, be- ^6 i3r'twixt ^ '"" 4) Floor 'and Ceiling. Rate, Firft Story. and a half Foot at Difcretion, b'V. Foot at Difcretion, ^c. The B U B tr The fecond Confideration, as to the Compartiments, is the Ufefulnefs ; which confifts in having a fufficicnt Number of Rooms of all Kinds, with their proper Communications, and without Diftradtion. Here the chief Difficulty will be in the Lights and Stair-Cafes. The /^ntients were pretty eafy as to both thefe, having general- ly two cloifteied open Courts; one for the Women's Side, and the other for the Men. Thus then rhc Reception of Light was eafy into the Body of the Build- hg^ which mull be fupply'd a- mong us either by the open Form of the BuildiKg^ or by graceful Refuges or Breaks, by terraffing; a Story in danger of Darknefs, and by Abnjours or Sky-Lights. As for cafting the Stair-Cafes, it may be obferved, that the Ita- lians frequently diftribute the Kitchen, Bake-houfe, Buttery, ^c. under-ground, next above the Foundation ; and fometimes level with the Foot of the Cel- lar, railing the firft Afcent into the Houfe fifteen Feet, or more ; which, befides the removing of Annoyances out of Sight, and gaining fo much Room above, Foot and a half, at Difcretion,cs''^. Foot and ahalf at Difcretion,$ifr. Foot and ahalf high atDifcretion,$3^f^. adds a Majefly to the whole Fa- brick, by elevating the Front. Sir H. Wotton obfervcs, that in England the natural Hofpita- lity will not allow the Buttery to be fo far out of Sight ; befides, that a more luminous Kitchen, and a fhorter Diftance, are re- quired between that and the Di- ning- Room than that Compar- tition will admit. In the Diftribution of Lodg- ing-Rooms, 'tis a popular and antient Fault, efpecially among the Italians^ to caft the Partitions fo, that when the Doors are all open, a Man may fee through the whole Houfe; which is founded on an Ambition of fhewing a Stranger all the Fur- niture at once; which is an in- tollerable Hardfliip upon all the Chambers, except the innermoft, into which a Perfon cannot come, but through all the reft, unlefs the Walls be extreme thick for fecret Paffages : Nor will this fuffice, unlefs there be three Doors to each Chamber, a Thing incxcufuble, except in hot Countries. Befides, it is a Weakening to tht Building; and the Necelfity which it occafions, of making as many B U many common great Rooms as th'-re are Stories, wnich devour a great deal ot Room, which migi.t be employ'd in Flaces of Rctre-it; and alio mud likewife be d'.rk, as running through the Middle oi the Houfe. In the Compartition, the Ar- chited will tiave Occalion for frequent Shifts, throu\:,h which his ^)wn Sagacity, more than any Rules, mult condudt him. Thus he will , be frequently put to flruggle with Scarcity of Ground ; lometimcs to damn onelloom for the Benefit of the reft, as to hkie a Buttery under a Stair- Cafe, ^c. At other Times, to make thofe the moft beautiful which are molt in fight, and to leave the reft, like a Painter, in the Shadow, t^c. As for the Covering of a Building, this is the laft in Exe- cution, but the fitft in Intention : For who would build but to fhdter? In the Covering or Roof, there are two Extremes to be avoided ; ivhich are the making it too heavy, or too light. The firit "will prefs too much on the un- der Work ; and the latter has a more fecret Inconvenience; for the Covering is not only a bare Defence, but a Bond or Ligature to the whole BuiUing. Indeed of the two Extremes, a Houfe top-heavy is the VTorft. Care ought to be taken, that the Prclturc be equal on each Side: And P.illadio wifhes that the whole Burthen may not be laid upon the (mtward Walls; but that the inner may likewfe bear their Share. The Italia;!! are very curious in the Proporticn and Graceful- -. B U nefs of the Pent or Slopenefs ; and divide the whole Breadth in- to nine Parts, whereof two ferve for the Height, or highcft Top or Ridge from the lowelt ; but in this Point, Regard mult be had to the Quality ot the Region : For, as PaJladio intimates, thofe Climates which fci^r the falling of much Snow, ought to have more inclining Pentices than others. As to the Accefi^ories or Or- naments of a Building^ they are fetch'd from Sculpture and Paint- ing. As for Sculpture, Care ought to be taken that there be not too much of it, efpecially at the firft Approach 9i a Building ; or at the Enterance, where a Doric Order is much preferable to a Corinthian one ; that the Niches, if they contain' Figures of white Stone, be not colour'd in their Concavity too blacR, but rather dusky, too fudden Departments from one to another being dif- pleafing to the Sight. Fine Sculptures ought alfo to have the Advantage ot Nearnefs, andcoarferofDilt^nce; and like- wife in placing the Figures aloft, they fliould be inclin'd or lean a little forward, becaufe the vifual Ray extended to the Head of the I'igurc is longer than that reach- ing to its Feet, which will nc- ceflarily make that Part to ap- pear farther oft'; fo that in order to reduce it to an erect Poiture, it muft be m.ade to ftoop a little forwards. But M. Lc Cierc docs not al- low of this Inclination, but will have every Part in its juft Per- pendicular. As B U B U As to Painting; the chief I hings that are to be regarded are, that no Room have too much, whicii will furfeit, ex- cept in Galleries, Ijc. that the belt Pieces be placed where there are the fc.velt Lights. Rooms with leveral Windows are Ene- mies to Painters ; nor can any Piftures be feen in Perf'edion, unlcls illuminated, like Nature, with a iingle Light. That in the diipofing of them Regard be had to the Pollure of the Painter in working, which is the molt natural for the Polture of the Spcftacor ; and that they be fuiced to the Intention of the Rooms they are iifed in. To make a Judgment of a Buildings Sir Henry IVooton lays down the following Rules. 1. That before a Perfon fixes upon any Judgment, he be in- formed of its Age ; that if the apparent Decays be found to ex- ceed the Proportion of Time, he may thence conclude, with- out farther Inquilition, that ei- ther the Situation is naught, or that the Materials or Workman- fhip are too flight. 2. If the Bti'iWmghz found to bear its Years well, then let the Viewer run back from theOrna- msnts and Things that Itrike the Eye, to the more eflential Mem- bers, till he is able to form a Conclulion, that the Work is commodioi-s, fiim, and delight- ful; which are the three Qualities of a good Buildings which have been laid down at firft, and a- greed on by all Authors. This he accounts the moft fci- entifical Way of judging. FnJJ'ari propofes a third, viz. by pafling a running Examina- tion over the whole Buildin^^ according to the Stru6turc vl a well-made Man ; as whether the Wall (tand upright upon a clean Footing and Foundation; whe- ther the BuHdiMg be of a beauti- ful Stature; whether h appear well burnilh'd as to rheBreau.h ; whether the principal Enterancc be in the middle Line of the Front or Face, like our Mouths; whether the Windows be fet in equal Number and Diftance on both Sides like our Eyes ; whe- ther the Offices are ufefully diitributed, ^c. like our Veins. Vttruv'ms recommends a third Method of judging, fumming up the whole Art under thefc lix Heads. 1. Ordination.^ or the fettling the Model or Scale of the Work. 2. Dtfpfitton.^ i. e. the jufl: Expreffion of the firit Delign of the Buiidi^g^ (which two Sir Henry WoUon is of opinion he might have fpared,) as belonging rather to the Artificer than the Cenfurer. 3. Eurithmy^ i. e. the agree- able Harmony between the Length, Breadth, and Height of the ievcral Rooms, zd'c. 4. Symmetry^ or the Agree- ment between the Parts and the Whole. 5". Decor^ which is the true Relation between the Building and the Inhabitants : From whence Palladia concludes, the principal Enterance ought never to be limited by any Rule; but the Dignity and Generofity of the Matter. 6. DiJlrihutioM, i. e. the ufeful calting of the fcveral Rooms for Omcc?, B U fi U Offices, Entertainment, or Plca- fure. The laft four of thefe are al- ways to be run over, before a Man palfes any determinate Cen- Rooma of Entertainment, rtnd Windows on theSiJe for Dor- mitories. Secoyidiy\ A<> toCipacioLifnefs • A Houfc had bcnt.:r be too little fore: And Sir Henry Wotton for a Day, than to big Tor a Year ; fays, are fufficient to acquit or therefore Houies ought to be condemn any BmUifig what- proportion'd to ordinary Occa- €ver. iions, and not to extraordinary. Dr. Puller prefents us with It will be eaf}cr borrowing a two or three good Aphorifms, Brace of Chambers of a Ncigh- or general Maxims, for Contri- bour for a Night, than a Bng of Vance in Buildings which are as Money for a Year .■ Therefore follow : Ftrfl^ Let not the common Rooms be feveral, nor the fcve- ral Rooms common ; that the common Rooms fliould not be W% a Vanity to proportion the Receipt to an extraordinary Oc- caSon ; as thofe do, who by overbuilding their Houfcs, dila- pidate their Lands, fo that their private or retired, as the Hall, Ertatcs are preffed to Death un- ( which is a Pandocha;um,)GalIe- der the Weight of their Houfe. ries, yf,_ which are to be open ; Thirdly^ As for Strength and the Chambers, Clolets, k^c. retired and private, provided the whole Houfe be not fpcnt in Paths. Country-HoufesmuftbeSubllan- tives, able to ftand of themfelves, not like City BuiLfuigs^ fjpport • ed and flanked by thofc of their Light (God's eldeft Daugh- Neighbour, on each Side ter) is a principal Beauty in a By Strength, is meant fuch as Building ; yet it lliincs not alike may relitl Weather and Time, from all Parts of the Heavens An Eaft Window^ gives the Infant Beams of the Sun, before they are of Strength to do any Harm, and is offenlive to none but a Sluggard. A South Window, in Sum- mer, is a Chimney with a Fire in it, and flands in need to be skreen'd by a Curtain. In a Weft- Window, the Sun grows low, and ever familiar towards Night in Summer- Time, and with more Light than Delight. A North Window is beft for Butteries and Cellars, where the Beer will be four, becaufc the Sun fmiles upon it. Thorough Lights are bcft for J but not Attacks ; Cifiles being out of Date in England^ except on the Sca-Coalls,^minon Rate of Bmidiyigs^ laft longer than ihj Grouivl-Lcale ; and that is ctjmm.only about fif- ty ordixty Years, x^nd if there happens to be a long Continu- ance of exceffivc Heat in Sum- mer, or of Cold in Winter, (though, indeed, thofc Extreams happen but feldom with us,) the Walls being thin, become at Ia.lt f ) penetrated witli the Air, thit it mult needs make the inhabi- tants uncafy. But then this Manner of build- ing is very much to the Advantage ot Builders, and fuch Trades as have Relation to them ; for they fcurce ever want Work in fo large a City, where Houfes arc here and there always either repairing or rebuilding. Again, the Plailter'd Ceilings, ' which arc fo much mere ufed in England^ than in other Coun- tries, B U B U iiies, do, by their Whitenefs, make the Rooms much lighter, and are alio excellent againll the Ravages of Fires; they alio (lop the Paiiagc of the Dull, and lelfcn Noiic over Head, and ren- der the Air fomcthing cooler in Summer- Time, and warmer in Winter, becaufe they keep out cold Air better than Boarded Floors alone can do. Dr. Fuller fays, he who alters an old Houfe, is ty'd as aTranf- lator to the Original, and iscon- fin'd to the Fancy of the firft Builder. Such a Man would be unwife to pull down a good old Building,perhaps, to ere6t a worfe new one. But thofe who ere6l a new Houfe from the Ground, are worthy of Blame, it they make it not handlbme and ufe- ful, when Method and Confu- lion are Doth of a Price to them. I fhall here propofe a cheap Contrivance in buildings which feme approve of, vtz. - Raife the Walls with Bricks, where Bricks may be had, ma- king firm and ftrong Quoins, at the Corners of the Houfe, of fuffici'.Tit ■ Strength to fupport the F" loots and Roof, or the main Beams of it ; the Walls may be built fquare, and the Walls between them, built of the fame Materials, and work'd up together with the Quoins, leaving one Half of the extraordinary Breadth of the Quoins without, and the other, within the Wall, whereby there will be much Charge fav'd, both in Materials and Workman- fhip, and yet the Builamg be firm and ftrong. Vol. 1. Some General Rules to he observed in building. Thefe which follow, were eliablilh'd by Ad of Parliament, before the Kebulld'.ng of the ^CX" X^j o^ London after the Fire. P»'ll^ In every Foundation within the Ground, you mult add one Brick in Thicknefs to the Thicknefs of the Wall next the Foundation to be fet orf, in three Courfes equally on both Sides. Secor.dly^ No Timber muft be laid within twelve Inches of the Forclide of the Cnimney- Janmbs. Thirdly^ That all Joifts on the Back of any Chimney, be laid ■with a Trim.mer at fix Inches Diftance from the Back. Fourthly^ That no Timber be laid within the Funnel of any Chimney, upon Penalty of ten Shillings to the Workman, and tea Shillings every Week it con- tinues unreform'd. '/(fif^j'Thatno Joifts or Raf- ters be laid at greater Diftances from one to the other, than twelve Inches; and no Quarters at greater Diftance than fourteen Inches. Sixthly^ That no Joifts bear at longer Length than nine Foot. Seventhly^ That all Roofs, Window-Frames, and Cellar- Floors be made of Oak. Eighthly^ That the Tile-Pins be made of Oak. Ninthly^ That no Summers or Girders "in Brick Euildings^ do lie over the Heads of Doors or Windows. M 'TentkW^ B U B U TentUy^ Thar no Summers or whereas Mortar cats and cor- Girdersdo lie lefs than ten In- rodes it, ches inro the Brickwork ; nor no Some Workmen pitch the Joirts Ids than ci^ht laches, and Ends of Ti.nber which h'e in that they b'' laid in Lome. the Walls, to preferve them from Alfo fomc advife that all Tar- the Mortar, fels for Mantle- Trees to lie on. As tothefurveying of5«/W/»^, or Lintels over Windows, or I fliall touch briefly on it. As Templets under Girders, or any to the Method by which theMan- othcr Timber, which mull lie in ner and Form of taking Dimen- the Wall, be laid in Lome, which fions, will appear, that is, as is a great Preferver of Timber ; follows : Itloe Survey of a Building ereilcd by Henry Gaines, for Mr: William Blakeway, TheThuknefs of the IValls (as b)< Agree- ment^ Brick and half at ^\. per Rod. For Mortar and IVorkman- Jhipy the D'tmenfioas VJcre taken as follows: Feet. Tarts- 1. The Length of one Side 40 S^Ia q q From the Foundation to the Railing 16 co 5 '^ 2. The Breadth at one End 17 16? o The Height to the Crofs-Beam 16 5-0 S ^^3 ^4 ■3. A. Partion- Wall within 17 16 Height to the Firll Story 10 5-0 4. The Length of the other Side 39 33^ ., From an old Wall, to the Raifing 7 oS^'^ ^ 5". The Breadth at the other End 17 o^ From the Floor, to the Crois-Beam 4 83 ^ 6. A Water-Table, 30 Foot reduced to 7 yo^ From the Foundation, to theTable 3 16 5 7. ASetting otf onthe otherSideofthe 7 .>? o,, 15 g:> Houfe $ -^ 8. A Gable End 66 j 66 o iSo 18 i II 2 ■'o The total Area or Conwnt of thefe' Dimen lions i^7J 17 'Tarticitlart FU B U Particulars to be deduced. i. One Door-Cafe Broad High 2. Another Door Cafe Broad — . High 3. A third Door-Cafe Broad High 4. A Window-Cafe Broad High f. Another Window-Cafe Broad Deep The Total of thefe Deduftions Taken from the whole Content There remains due Feet. Part!* 8 66|g^ 58 9 42S 4 33^32. 7 4iS^ 13 4 33?-,, 34 4 ^^l^o ^5* 4 50^ 4 ^°^20 4 5-0? 2^ 176 ss ^S7S 27 1398 72 Which reduced into fquare Rods, is five Rods, thirty-eight Feet ; and fo, according to the Contradt, there will be due to the Brick- layer If/. 8 J. 3^. Mr. f^e». Maudey gives us the following Method of furveying Buildings^ and takingDimenfions, and fettingthem down in a Poc- kec-Book. 2. Before you begin to fet down the Dimenfions, it will be proper to divide the Breadth of the Page into fo many feveral Columns as you fliall think you fhall have Occafion for, either with Lines drawn with Ink, or a Pencil. Your Pocket-Book Ihould be of the broadeft Size, viz. four In- ches broad ; which may be divi- ded into four Columns. 2. Before you fet down any Dimenfions, you muft firft fet down the Names of the Matters of the Work, and the Work- men ; alfo the Place where, and the Day of the Month, and Date when you meafure. As for Example : Suppofe yoa are to meafure GlaiieK Work : Then you muft obferve, if it were glazed with fquare Glafs, you muft write Squares over the Dimenfions ; and if there is any. Part or all inQuarty-Glafs, yoa mud write Quarries; that whea you come to make the Bill of Meafurement, you may exprefs them feveral ly; becaufe theyare of feveral Prizes. For the clearer Underttanding of this^ I fhall give you this Bill of ^eafurement of Glaziers Wqrk, as follows: Ma Ctaiing B U B U Squares. ProduSis. F. I. "P. F. I. P. I 7 6^S 5' " 3° Squares. ^roduds. F.I. P. F.I. P. 4 ^ o7 x: ? 2 o5 4" 6 lltl '^ ^ - I 6 oS 3 f I t o}«« 9 » ^ ^^ 3 . 3 2 I 0^ , , I 8 6?C2)7 2 4 \ o^^)7 ° c 60 5" II 45" 4 9 An 'Explanation of the Column. they amount to but very little in Value, unlefs theie be many and In the firfl: Column, towards large Articles of them to be ad- the Left Hand, are the Dimen- ded together, fions of Glnzings done with N. B. When you are taking Quarrels; which are to be cafl; Dimtnlions, and fetting them up by Crofs Multiplication. See down in your Pocktt-Book, Multiplication. whether of the Work of a Gla- In the fecoiid Column, are 2ier, Carpenter, Bricklayer,erf. the Products of each Dimenfion you murtrcm^-mber to leave eve- jufl: ngainft it; ry other Column vacant, that In the third Column, you have when you have fet dcuvn all the the four Dimenfions of Glazing Dimenlions in the Book, (which done with Squares ; and in the is to be done bcfoie you cafl any laft, you have the Produd of up, and which is to be done in each Dimenfion juft againfl it. another Book, or Sheet of Pa- At the Bottom of the fecond per,) the Produft of each Pair of Column, you have the Sumtotal Dimenfions may be entered of the Produdls oi the Diitien- down juft againft them, as is to lions done with Quarrels, which be fcen in the foregoing Ex- is 60 Feet, J- Inches, and 1 1 Parts, amples. At the Bottom of the lafl Co- If there be another Perfon to lumn, there is the total Sum of meafure againll you, and there the Products of thofe Dimen- fliould happen a Miftakc in ei- fions of the Glazing that was iher of your Cartings up, this done with Squares, which is 45" fhould becorrcftedby one Read- Feet, 4 Inches, and 9 Parts: As ing over the Dimenlions to the for the odd Parts, they fignify other looking on his Book, that but little ; if they be left out in the Error maybe found out and the Sum total of Meafuremeat, redlify'd, that both the Accounts may agree exadly together. When B U B U When you make your Bill of Name to it, at the lower End of Meafurcmsnt, you muft fet your the Bill. Att Example of a Bill of Meafurement. Glaziers ITork dofie for A. B. of Stepney, hy C. D. of Ratcliff. Mcafiired ]\inQ zi^ ^733- For fixty Foot five Inches of Glaiingdone with? i ^ iA Quarrels, at 5'^. pfr Foot 5 For forty-five Feet and four Inches of Glazing c ^ ^ ^ i^ done with Squares, ?i\. yd. per ¥ooi. ^ Meafured the Day andTear Sum total is 2. H 3 * . abovevjritten ^ by E. F, The Method of taking the lumns, yet in the Menfuration Dimenfion of Bricklayers Work, of Biicklayers V/ork,it will not which is the moft troublefome be neceffiry to divide the Page of the Work of any Artificer into any more than three Co- concern'd in Buildmg\ I Ihall lumns; one large, for the Appel- give an InlUnce ot it lations, and two fmaller, for the Although I before ad vi fed to Dlmcnlions; the other for the divide the Page of your Meafur- Produdts : ing Book into four Parts, or Co- As in this Example following : ^ppdlatiom Dimen. 'Troduds. Br. 3 Br. 3 Ft. In. Ft. In- Bafis of the Front and C if o? ^ ,>, ,_ „ Rear \ o 6$ ^ ^ ^ Br. ik Br. Ij From and Rear ^^i o\^^^ ^^^ ^ 2Br.^ z Br. ^ Bafis of both the Flank- > 36 i").^ ^a , M 3 ^ppcllm»S)L B U B U Both the Flauks appellation. ^imen. "Produds. 2 ^r. 2 Br. Ft. In. 2 Br. 2 Br. The Wall between the<;ii 5^ Chimneys ^ 9 loS^^^ "^ ^ ' ■* ■ m The Falling-back of both ^ <' 07, Chimneys ^ > ^K^) 4<^' o 2 or. 2 r'r. The four Jaumbs S^ °^^,>( ,^, II o>v The Fore-Part or Breaftsl 11 6?, ^ '" of both Chimneys J 5- oS^^^ ^^^ c- Having fet down the Dimen- theDeduftionsfor the Windows i?ft -nit Jv^ i\^ ^°" "'^^ ^^°"' ^ith their Produas. mult m the next Place let down *the DeduaioTts. appellations. Dedua. Produas. zBr.i 2 5r. i ^A /;?. Ft. In. The four Window ^ ^ ^^(^3 ,^^ ^ ' ^Br.\ 2Br.i The two Doors S ^ '^Id^ -,, ^ i 4 o^^^J 1^ o The B U B U The next Thing vou have each feveral Thickiiefs of the to do, is, to add the Products of Sum, Tbe 'ProduSts of the feveral ThichieJJ'es. ^Er. 2 i Br. z Br. l i Br. i Br. ^S o 555 o 36 1 556 2 7SS 8 161 o 115' o 1071 8 113 40 o The feveral Produds of each Thicknefs being added, in the lirft column on the Left Hand, is 25- Feet of three Bricks. In the fecond, 586—2 of 2 4 Bricks, Novir to find thefe Produ(5ls, fee Crofs Muhiplicatioft., N. 2. Having found the total Sum of the Produds of ihe Deduc- tions, each total Sum mud be fubtra£led from the total Sam of the Produds of the Dimen- fions that are of the fame Thick- nefs. E.^r. The Deduftions in A B, 104 73 00 00 The Total Produfl in ^ j^^ ^^ 2 ;t Br. is — — — 5 Which 176 Feet of 2 ^ Brick- work, being contained in the Windows and Doors, muft be fubtraded from the 5-86 Feet 2 Inches, being the total Produ6t of all the Dimenfions of that Thicknefs, viz. 2 i Bricks, i'/;^;. 2 i Brickwork. This is manifeft to Reafon, becaufe when the Dimenfions of the Front and Rear were taken, the Whole Lengrh was taken over the Doors and Windows, not allowing an Abatement for them. N. B. Whatfoever Doors or Windows, or any other Vacan- cies, are meafured over when the Dimenfions were taken, you mud remember to dcdud them out of the whole Produ6l of the Dimenfions of the fame Thick- nefs, wherein they were fitu- ated. In order to render this plainer, take the following Example : The Doors and Windows be- ing in 2 J Brick-Work, you muft fet down the total ProducEl of all the Dimenfions of that Thick- nefs, which is 5S6 02 Total Produft-J .e Dedudtions/ - Thicknefs, >i :S The Total Produd of all tl of that which are to be fub traded, is- 79 00 The Remainder is 410 oa The like muft have been done, if there had been any other De- • M 4 dU(^iQnj B U B U duftions in any other Thick- nellcs : All fach Dedudions mud have b'^en fubtradted from the Produds of the Dimcnfions, before you went about to re- duce your Thickncircs to the Standard Thicknefs of a Brick and half. More of this Nature, viz- of llirve)ing Bu'tldr/igs^ or taking Dimcnlions, Is'c. may be fcea nndcr the Heads Carpenters Work, Joiners, Bricklayers, Plaftercrs , * Mafons , Painters , Thatchers, ISc. Of meafuring Baildtngs. I (hall in this Place only mention the Artificers relating to Build- ings who ufually work by iVlea- furc; which are, F/r/?, Brick- layers ; fecoiidly. Carpenters ; thirdly s Plafterers ; fourthlw, Painters ; fitbly^ Glaziers ; Jixfh- ly^ Joiners ; and feventhly^ Ma- Ibns. Some of which work by the fapcrticial Yard, fome by the Rod, Ibme tne Square, and ibnit: by the Foot: Of all which Works theDimenlions are takci; either with a ten-toot Rod, or a five-foot one ; or elfe with a two-foot Rule, and fomeiimes with a Line. But however the Dimenfions are taken, they are generally fet down in Feet, Inches, and Parts of Inches ; or elfe in Feet, and centelimal Parts of Feet ; which lall Way is the eaiiefl: caft up : And as to the Centeiimal, i. e. hundredth Parts, the follow- ing Table will fhew them. A Table B U B U A Table of Centefimal Parts for every Inch, and quarter of an Inch, in a Foot. I Quarter of iQuaitcibOi q C^Liaf t'. I i(.(, an Inch. ;in Inch. "' '"'-■• Inches. ICO Part of a Foot. 100 Part of 100 i^art or a Foot. I a Foot 1 CO : - . o . oo • 02 -4 . Oj I . o8 . 10 . 12 ) 2 2 . i6 .18 .20 . 21 3 . IS • 27 -29 ■ 3' 4 ' 33 • 3T 37 \ 39 1 . 42 • 44 4S 47 6 7 . J2 . 60 S3 62 55" 64 8 . 66 . 68 70 7i 9 lO II I Foot • 75- . 83 . 92 . 100 • 77 . 85- • 94 " 79 87 96 bi 40 98 To fct down any No.mber of Feet, Inches, and Parts; as fup- pofe 43 Feet, 6 Inches, and 3 quarters; you mufl; firft fetdown 40 Feet with a Period or Com- ma after it thus, 40, and then look in the firfl: Column for 6 Inches, and at the Head of the Table for 3 Quarters, you will find SS i which fct down be- yond the 40 to the Right Hand, and it will (land thus, 40,5-5. Of the Daluing 0/ Buildings. In order to the cftimating the Charge of erefting any Houfe, as near as can be, or to value one that is already built, to come pretty near the Truth, provided it be built of Brick and Timber. i/Z, Find the Dimcnlions iti Length, Breadth, and Height, in relped to the Number of Sto- ries. ^dly. By the Length and Breadth, iheQuaiiiity Oi Squares upon each Floor may be lound; and alio the Squares of Roof- ing m Carpenters Work, and alfo of Tiling in Bricklayers Work. 3a/)', By the Height you may give a near Ellimate of the Rows of Brickwork contain'd in the Walls round about, and in the Partition Walls, if there be any; and alfoin theChimntys. Then, ^thly^ Confider how many Fairs of Stairs, and of what Sort. Stbly, B U BU ^thJy^ What Number of Par- tirions of Timber, with Doors. 6thly^ What Timber Fronc, -jthly^ What Number of Win- dow Frames, and Lights. 8.'%, What Iron Work. ^thty, What L.ad, ^V. Of which fee the particular Heads Mr. Leybourn puts the Que- ftion, What will be the Charge of ereSing a Building of Brick Walls and Timber, wUch flrall be 20 Feet in Front, and 44 deep, and lor the Front to be fhorter than the Flanks, and to confift of Cellars, three Stories, and Garrets, which is one of the fe- cond Rate Hoafes. Now fup- poling the Piice of Materials (in Londuii) to be as follows, viz.. For /•Bricks per Thoufand I Files /Jt-r Thoufand I Limc/'£'r Hundred oad — 1 imbcr fer L' ^if Hundred V Laths /^rBindle — I ijimc/'£'r Hu •x oaiid fsr Vi'Xc Oak or Fir 1 j Deal Boards )3d /. s. d. CO 16 00 01 Of 00 00 10 00 00 03 CO 02 ly 00 07 10 CO CO 01 c6 Ai for ^kllerers WorK For For /. "Lathing, Plaflering, Rendring, and V\i ' - O i v\ ith White and Size, yer Yard _;> iLatliing and Plaftering /'f; Yard . Plaftering and Sizing per Yard Smiths Work. Iron for Balconies per ]■>. Folding Cafcments /Jrr Pair Ordinary Cafemeats /^c-r Piece 01 02 For J}ainUng. Window Lights — — Shop Windows, Doors, Pales, /'«•/• Yard 00 CO 10 QO CO 06 I s. d. 00 00 Of CO 16 CO 00 04 06 /. s. d. 00 CD c6 CO 01 CO Now, fays he, from thefe Rates of Materials for Buildings and for VVoikmanfhip, fuch a Hoafe will amount to about 360/. which is about 41 /. per Square. Mr. Phillips propoles the fol- lovving Method to find the Va- lue of a Bmldifjg^ viz. Suppofe a Honfe to be one Rod, or fix- teen Feet and a half in Front, and two Rods deep, back in the l-"lanks, the Compafs of this Houfe will be fix Rods : And if thisHoufeftands in a high Street, having a Cellar, four Stories, and a Garret, (which is one of the third B U ,third Rate Houfes,) the Height thereof will be fifty Feet, or three Rods ; fo that there will be eighteen Rods of Brickwork in the Walls, which may all be reduced to a Brick and a half thick, and (fuppofing each Rod of Brickwork to contain 45-00 Bricks,) will coft about 7/. the building, viz. Bricks, Mortar, and Workmanfhip ; then the whole eighteen Rods of Brick- work will coft about 126/. ■ The Timber Work for Floors, Windows, Roofs, t^c. about as much more. ■ The Tiling, Plafkring, Lead, Glazing, and Painting will be about as much more ; fo that the Whole will amount to 378/. The Allowance for the Party- Walls will very well pay for the Chimneys ; (o that this Houfe cannot amount to above 400 /. 'the building, which is not full 13/. per Square: But this is a very great Price, in comparifon of Mr. Leybourrt's ; but he fays it will be worth more or lefs, according to the Market Pi ice of the Materials. The Friendly Society of Lon- don for infuring Huufes, h-ve two Rules by which they value them, viz. Either by the Rent, or Number of Squares contain- ed on the Ground-Plot. ' The lafl: is the general Rule by which they value all Buildings ; "which is grounded on an A6t of Parliament for rebuilding the pity of London^ made about y^»- »o 18. Car. II. The Bnildinq^s of the City of London are valued according to their Rates, of which Rates there are four, m= B U Fir/1 Rate 2 Second Rate Third Rate Fourth Rate 3 (Stones, 4r and i Cellars, ^ arrets. And the naked Bnilding or Shell of a Brick Houfe (the Floors being finiOied) is thus valued, by the Square or 100 Feet in the High-Streets, viz. Fir ft Rate 2f /. Second Rate 35- 7'hird Rate 45- Fourth Rate jo ''^ per Square. But thefe may be augmented at the Dilcretion of the Survey- or, or according to the finifhing of the Houfe. Vitruviiis^ Lib. 1. Cap. 2. de- termines iix Confidtrations, in order to the judging or cenfuring of a BuHdiKg^ viz. I. Ordination. 1. Difpofition-. 3. Eurythmy. 4. Syr/imctry. j-. Gracefulness. 6. ^Dlftribution. The two firft of thele might have been very well fp.ircd, fuice he feems to mean no more by Ordination, than but a well- fettling the Model or Scheme of the whole Work ; nor any Thing by Difpojitioit^ but a neat and full Exprefflon of the lirft Idea and Defign of the Building., which feems more properly to belong to the Artificer than the Ccn- furer. The other four are fufficient to approve or condemn any Building whatfoever. Eurithmy is that agreeable Harmony which is between the Length, Breadth, and Height of all the Rooms of the Buitdiag^ which will be very pleafmg to Beholders j B U B U Behf^ldcrs; which is always fo to al!, by a fecret Power, that is in Propoirioi). Here it ni;iy be proper to ob- feivo, that though Excefs of Hfi^-ht is the leait Error of Of- fci cc t>nt ran be committed a- gai- It th'.' Sight; yet even that Erioi is no where of fmal! Im- P'Tf.uice, becauCeit is the great- cll Trel"p;ifs upon the Purfe. Symme/ry , which is a dne Proport'on of e;ich Part, in re- f'P'.tt .() itie Wiicle; whereby a great Butiding fliould have large Apar.mcDts or Rooms, great Lit^hts or Win'iows, great Stair- Cafv.s, great Pillars or Pilafters, ^c. Ill fhorr, all the Members and Parts large, in Proportion to the BuUdtM^. Vox as it would be but an odd Sight to fee a large Man wich little Legs, Feet, Arms, Hands, ^c. Co alfo would it be un- comely to fee a large Building conliliing of little Apartment's, L'ghrs, Srair- Cafes, Entrances, C5f. and fo, on the contrary, it will be as odd to fee a little Man "wichiargeLimbs; thefamc willit be in a linal i Building fo contrived, as to have large Rooms, large Stair- Cafes, large Lights, large Entrances, ^c. But regain, as it is an unbe- feeming Sight to fee either a great or little Man with fome of his Limbs or Parts proportiona- ble to his Cody, and others fome fo little, as if they did belong to a Pigmy ; and others fo large, as if thty did belong to a Giant: So would it be equally as ugly and offcnlivc to the Sight, to fee a fmall Houfe have fome of its Parts monftrous, viz. large in fome Parts of the Apartments, and by confequence others muft be as fmall, .or elfe fome muft be annihilated, and fo confe- • quently will be wanting ; or j large Stair -Cafes, large Win- > dows, and large Doors, or any \ other Parts larger than they ought 1 to be, in refped to the Symme- > try of the Parts with the Whole. It is likewife unfeemly to fee ' fome of the Parts too little, and not proportionable to the whole Structure, as to fee a Man with one leg proportional to his Bo- dy, and the other very fmall, or to have one Eye of a Man, and the other of a Bird. Many Errors are committed by Workmen in Symmetry, for want either of due Conlidcra- tion, or Skill. Sometimes it may be obferved in the Courfe of cenfuring, that aDoor or Chimney has been fo mifplaced, either to the Right or Left, as to fpoil the intended U(e of a Room : And though fometimes it is not totally fpoil- ed, yet it (hews the want of Con- trivance in the Artificer. Sometimes you may obferve a Chimney fo fituated in the Angle of a Room, (which though it was deligned for Conveniency, becaufe it could not well be car- ried up otherwife from the Chim- ney below it,) yet this Chimney fliall in fome meafure fpoil the intended Ufe of two Rooms, viz. that in which the Chimney is, and the next adjoining to the Chimney Jaumb, Thus two Chambers have been in great meafure fpoiled by a Chimney being fct in the Angle of the inner one, the Door com.ing in- to it from the Chamber without, jult by one Jaumb, and of con- fequencQ B U B U fequcnce that whole Chimney was carried a Foot too far out in the Room, which might as well have been carried farther the other Way, by v.'hich Means the Door was pUiced too far to- wards the other Wall ; fo that the Partition Wall, by this Means, was made fo narrow between the other Wall and the Door, (at the Chimney Jaumb,) that it was thereby rendered untit to fet a Bed in againft it, though it was the fitted; Place in the Room for that Purpofe. Sometimes little diminutive Stair-Cafes are made in a hand- fome fpacious Strudure ; and, on the contrary, in a fmall or middling Houfe, Stair-Cafes fo large, that if you fee them be- fore any other Apartment, you might well conjecture that the Rooms of that Buitdwg were proportionable to the Stair- Cafe, twice or three Times larger than you find them. Nay, perhaps this fhall not be all the Error ; for thefe Guefs- Workmen do fo manage the Matter, as to fpoil the Conve- niencies of Clofets under them, j (for any other Convcniency ;) '. though it be now the Fafhion to to make fome little Convenien- cies under a Stair-Cafe; for Clo- fets are accounted an Improve- ment in our Way of Buildinfr. X Sometimes you may obferve an ill Pofition of Lights, (or Windows) to a Stair-Cafe, not out of Neceffity, but Want of Skill and Contrivance. And again, as to Lights, (or Windows,) you will fometimes fee an ill Pofition, as well as an irregular Difpofition in them, viz. either in regard to Ucifor- mity, or as to fecuring them from the Weather; that is, wiicn they are placed too near the SuiiaoL uf the Buildings chat the Waiis ^io not projed over ihcm, the D>.t;(.r to carry the Wet irom th^m, which r-ins duwn the Wails in flormy Weather. And then again, as to Ui.'f -r- mity in placing them, it h me- timcs fo happens, chit they C;in- not place them on the Girrets cx- a6liy over thofein theStoiics be- low; and therefore when they will not be brought into Unifor- mity with thofe below them, they ought to be placed as uni- formly as polTibly can be within themfelves. This has been obferved in a Fabrick which flood in the Form of a Roman Capital L, ha- ving two Fronts on the Outlide of the L, confronting two Streets which crofs one another at Right Angles : The Foot or fhort Part of the L in theB?/i/<;//;?g-,was not fo wide, butthat itmightbefpanned by oneRoof;butthelongP^ri wns too wide to be fpanned by one Roof, unlefs it were carried up a great deal higher than the otherP3rt,which would have been very unfightly : And therefore, three Roofs were fet on the long Part of the L, parallel with that on the fhort Part ; fo that there were three Gutters, and four Ga- ble-Heads, on that Part which was the long Part of the L; and in each of thefe Gable-Heads, there was a Window. Now according to the Divi- fions of the Apartments in the Stories below, the Windows ia them would not fit, to be placed (any of them) perpendicular un- der the Middle of thefe Gables, the B U the Workman thinking to ren- der it ibmething nearer to Uni-^ formitv, places three Fourths of thele Windows all towards, nay, very near one Side ot the Gables, pretending, they were without Doubr, nearer direftly over the others; and therefore it was near- er to Uniformity,whcreasat the fame Time, they are farther i'rom it: For by this Means they are not in an uniform Pofition, nei- ther in refpe^t to the Stories be- low them, nor yet within them- felves; which lalt they would have been, if they had been pla- ced i.i the Middle of each Ga- ble, and would have been more decent and handfome, borh with Regard to the Front without, and the Room within. Thcfe, and many more are the Blunders committed for want of (Contrivance or a gocd Judgment as to Symmetry. I (hall only add, that it ought to be obferved, whether Doors have their due Symmetry as to the-'r Dimenfions, as well as their Po- iitions, viz. 1 hat they be not too high, as if they were for a Barn, nor too low, as if they were made for Houfcs in Sophia in Bulgaria ; where both Jews and Chridians have their Doors of their Houfes but a little above three Foot high ; wliich are there- fore fo contriv'd, becaufe the Turks fhould not bring in thrir Horfcs ; which they would do, and make ufe of them for Sta- bles in their Travels, if it were not for this Contrivance. This, as well as all other Parts of a ^/i/WK'^, ought to be analo- i;ous to the reli of theFabrick- i (hall next fpcak of B U Docof or Becomingnefs, or rather Suitablenefs ; which is the keeping a due Refpeft between the Inhabitantand the Habitation. Whence 'Palbdio concludes, that the principal Entrance was not to be regulated by any certain Dimenffons, but by the Dignity of the Mafter; yet to exceed ra- ther in the more, than in thelefs, is a Mark ot Generofity, and may always be eicofed with fome noble Emblem or Infcription. Dijlribumn^ is that ufeful Calling, or Contriving of all Rooms for Office, Entertain- ment orPleafure, which has becii already fufficiently treated of under this Head of Budding. Thefc are the four general Heads vi^hich every Man ought to run over, before he pretends to pafs his Judgment upon a Building.^ or undertakes to cen- fiire a Work that he views. Dr. Fuller advifes rather to believe any Man than an Artifi- cer in his own Art, as to the Charges of a Building., Special- ly, if cither himfelf, or any Friend of Ills, is to be concern'd in the Building that is dcfigned to be err(^ed: Not but that Builders can tell nearly the Charge, when they know the Delign,' but it is very rare that they will give a jull Eftimate of it according to their Judgment; becaule they think if they fhould acquaint a Gentleman with the fullExpence at firlf, it would difcouragehim from profecuting it ; and for that Reafon, they footh him up, 'till it will coft him Ibmething confiderable; after which, he mull go through with it, or lofe what has been expended. The B U The Spirit of Building firft poilefb'd People after the Flood ; which thencaufed the Confuiioii of Languages, and fince, the Confufion of many a Man's Eftate: Ana hence, when feme Perfons would vvifh a Curfe up- on one with whom they are an- gry, they wifli them to be polTef- fed with the Spirit of Bmld'f/jg^ or, as others term it, the Italian ^Plagtie. BUST, 1 in Sculpture, fff ^. BUSTO, S is a Terrri ufed for the Figure or Portrait of a Perfon in Relievo, fhevving on- ly the Head, Shoulders, and Sto- mach, the Arms being lopped off; which is ordinarily placed on a Fedellal or Confole, Felibien obferves, that though in Painting, one may fay, a Fi- gure appears in Bujlo^ yet it is not proper to fay, in aBuJi. The BuJ} is the fame with that the Latins call Herma^ from the Greek Hermes^ Mercury^ the Image of that God being fre- quently reprefented in this Man- ner by the /Athenians. Bujl is alfo ufed, efpeciallyby the Italians^ for the Trunk of a human Body from the Neck to Hips. I3UST, or 7 ^ Pyramid, or BUSTUM,SPile of Wood, whereon the Bodies of the De- ceafed were antiently placed in order to be burnt. BUTMENTS, ^o^ Bouter, French^io abut or terminate any Thing] are thofe Supporters or Props, on or againft which, the Feet of Arches reft. Alfo lit- tle Places taken out of the Yard or Ground-Plot of a Houfe,for a Buttery^ Scullery, i^c. B U BUTTERY, in the Houfes of Noblemen and Gentlemen, is the Room belonging to the Butler ; where he depcfircs the Utenfils belonging to his Office; as Table-Linnen, Napkins, Pots, Tankards, GlalTes, Cruets, Sal- vers, Spoons, Knives, Forks, Pepper, Muftard, i^c. As to its Polliion, Sir Henry Wotton^ fays, it ought to be pla- ced on the North Side of the Building, which is defigned for the Offices. We, in EngUyid^ generally place it near the Cellar, W-^. the Room commonly juft on the Top of the Cel!ar-Stair.«. BULLEN-NAILS, are a Sort of Nails with round Heads and (hort Shanks, lin'd and lac- quered. There arc feveralShes of them. They are ufed in hanging Rooms, fetting up Beds, cover- ing of Stools, Chairs, Couches Desks, Coffins, ^c. ' BUTTRESS, a kind of But- ment built Arch wife, or a Mafs of Stone, or Brick, fcrving to prop or fupport the Sides of a Building, Wall, ^f. on the Out- fide, where it is either very high, or has any confiderable Load to fuftain on the other Side, as a Bank of Earth, ^c. They are alfo ufed againft the Angles of Steeples, and other Buildings of Stone, i^c. on their Outtide and along the Walls of fuch Buildings, as have great and heavy Roofs, which would be fubjed to thruft the Walls out, if they were not thick, if no Buttrejfes were placed againft them. BnUrejfes B U Buttreffes are alfo placed for a Support andButmcnt, againllthe Feet of fome Arches, that are turn'd acrofs great Halls in old Palaces, Abbeys, is'c. and gene- rally at the Head otSione Build- ings, when there are brgeCroc- kct Windows; and they aie al- fo placed for Butments to the Archis of thefe Windows. The Theory and Rules of Butirejjes are one of the 'Defide- rata \\\ Architefture ; but it is not improbable, bat that a faga- cious Archited and Mathema- tician, who would apply himfelf diligently to examine into the Matter, might bring it within the Bounds or" Reafon and Rules, •whereby it might be known very near, of what Size, and confe- queiuly of what Weight, aBut- trefs or Butmcnt ought to be ; which muft be various, accord- ing to the Dimenlions and Form of the Arch, and the Weight ■which is luper-incumbent on it. As to the Weight of the Ma- ■terials, both on the Arch, and in the Butirefs or Butment, it is not difficult to calculate. But it may probably be objefted, there may be a fenfible Difference as to the Strength and Goodnefs of the Mortar ; which may in a Mca- fure compenfite for the Weight of the Ltittrefsox Butments; for where there is a (Irong firm Mor- tar ufcd, of lefs Weight (or Mag- nitude,) of Brick or Stone, fliall be capable to rcfiii the Prellure of an Arch with its fuperincum- bent Materials, than where the Mortar is bad and weak. To which it may be anfwered, it would not be difficult to make B U Experiments of the Strength of Mortar, both as tothediredand oblique Force, by fhoving of it our of its Pofition, or pullingit i the (horteft Way from its Adhe- rents, I mean, by lifting it di- redlly up. It feems to be very feafible, and it would certainly bevery ufeiul, to try what Butment would be rcquifite for Arches of all Di- mcnfions or Fv)rms, whether Straight, Semicircular, Skeen or Scheme, or of the Third or Fourth Point, or Elliprical, C5r. Seethe Article Bridges. Dr. Hook^ Geometry Reader in Grejbam College^ in his Trea- t'fe of Heliofcopes^ did promife to publifh fomething to the fore- going Pupofe, whether he ever did do it, I know not; but what he promifed in that rreatire,v,'as as follows : viz. A true Mathe- matical and Mechanical F"ormof ail manner of Arches, with the true Butment neceilary to each of them, a Problem, faith he, which no Architedtonick Wri- ter hath ever yet attempted, much lefs perform'd. A rreatile of this Nature would be cxtreamly ufeful for the want of a certain Rule in A-rching, with its necef- fary Butment, hath often proved the Ruin of fome Struftures which have been of no fmall Charge, as to Bridges, b'c- Ofthe^rice of Building Buttreffes. If this Work be not put out to be done by the Day, it isufually done by the Cubical Foot. Some reckon the Workmanfhip at two Pence Halfpenny per Cubick Foot, which, reckoning the Ma- terials, C A C A lerials and Workmanfhip may be done for about 6d' and -jd. ■a Foot. C A CABINET, the mod retir'd Place in the fined Apart- ment of a Building, fet apart for writing, (ludying, or prefcrving any Thing that is precious. A compleat Apartment conlifts of a Hall, Antichamoer, Chamber, and Cahinet^ with a Gallery on one Side. Hence we fay, a Cabinet of Paintings, Curiofities, ^c. CABLED -FLUTE, fuch Flutes in Architedure, as are filled up with Pieces in the Form of a Cable. CALCULATION, the Aft of computing feveral Sums, by adding, fubtradingi multiplying, and dividing, ^f. CALiDUCTS, a kind of Pipes or Canals, difpofed along the Walls of Houfes and Apart- ments, ufed by the Antients for conveying Heat to feveral re- mote Parts of the Houfe, from one common Furnace. CALOTTE, in Architefture, a round Cavity, or DeprefTure, in Formof a Cap or Cup, lathed and plaiftered, ufed to diminifli the Rife or Elevation of a mode- rate Chapel, Cabinet, Alcove, ^c. which, without fuch an Ex- pedient, would be too high for other Pieces of the Apartment. CAMBER-BEAM, a Piece of Timber in an Edifice, cut Arching, or Archwife, or with Vol. L aji Obtufe Angle in the Middle, commonly ufed in Platforms, as Church Leads, and on other Occafions, where long and ftrong Beams are required. A Camber- Beam being much ftroh- ger than another of the fame Size; and being laid with the hollow Side downwards, (as they generally are) they repre* font a kind of Arch. CaMBRLNG. TheSeamea fay a Deck lies Carnhring^ whea it does not lie level, but higher in the Middle, than at either End. CAMES, the fmall flender Rods of Call Lead, of which the Glaziers make their Turn'd Lead. For their Lead being caft into flender Rods, of tv/elve or fourteen Inches in Length, are called Cames\ and fometimes they call each of thofe Rods a Came^ whpcb, when it has been afterwards drawn through their Vice, makes their turn'd Lead. CAMERATED, vaulted, or arched. CANT, aTerm ufed by fome Carpenters of a Piece of Tim- ber, when it comes the wrong Way in their Work, they fay. Cant it^ /. e. Turn it about. • CANTALIVERS, Pieces of Wood fram'd into the Front or other Sides of a Houfe to fuf- tain the Mould'ng and Eves over it. Thefe feem, in Effect, to be the fame with Modilions, except that the former are plain, and the latter carv'd; they are both a kind of Cartouzes, fet at equal Diftances, under the Co- rona of the Cornice of a Build- ing. ; As to the Price of making, Mr. Leybourn fays, they arecom- N monly C A C A monly made by the Piece, at dif- ferent Rates, according to the Curiofity of the Work: And fome Workmen fay, they have 2 J, 6d. for making and carving each. Bat they will carve them in London for twenty Pence _f^r Piece. As for their Painting, Mr. Leylfourn likewife tells us, they are ufually painted by the Foot, running Meafure, i.e. by the Nu-nber of Feet in Length only, at different Rates, according to the Curiolity of the Workman- Ihip. And fome Workmen fay, they have commonly is. per Foot for the Cornice, if plain "without Carving, and 3/. 6ci. per Foot with the Cantalivers. CANFiNG-Sl'AIRS. See Stairs. CANTONED, in Architec- ture, is, when the Corner of a Building is adorn'd with a Pila- fter, an angular Column, Ruftick Quoins, or any Thing that pro- jedh beyond the Naked of a Wall. CAPITAL, [of Caput, L, the Head] is the uppermort Part of a Column or Pilafler, ferring as the Hecld or Crowning theraof, placed immediately over the Shaft, and under the Entabla- ture, Capital of a Colur/jn.^ is proper- ly that whofe Plan is round. Capital of a Pllafler., is that whofe Plan is fquare, or atlcaft refti lineal. The Capital is the principal and ellential Part of an Order of Column, or Pilafter: It is of a different Form in the different Orders; and is that vvhichchiefly diUisguiilics and charadteriies the Orders. Such of thefc as have no Ornaments, as the Tuf- can and Doric, are called Capi- tals with Mouldings, and the reft which have Leaves and other Ornaments, Capitals with Sculp- tures. The Tufcan Capital is themoft fimpleand unadorn'd: Its Mem- bers or Parts are but three, -viz. an Abacus, under this an Ovo- lo, or Quarter- Round ; and un- der that, a Neck or Colarino ; the Neck terminates in anAftra- gal, or Fillet belonging to the Fuft or Shaft. M. Le Clerc fays, this Capital only confifts of three Parts, an Abacus, a Quarter-Round or Bouhin, and a Gorge or Neck, which terminates under the Quar- ter-Round in a Fillet; the Aftra- gal underneath belonging to the Shaft. The Charaaer of the Capital whereby it is diPiinguifhcd from Xht Doric, cjV. is, that the Aba- cus is fquare, and quite plain, having no Ogee, or other Mould- ing ; and that there are no Ari- nulets under the Ovolo. ^ It is true, Authors do vary a little as to the Charader of the Tufcan Capital' yignola gives the Abacus a Fillet, inftead of an Ovolo. yitriivtus and Scamozzl add an Aftragal and Fillet between the OyoIo and Neck : Serllo., only 3 Fillet; and FhUander rounds the Corners of the Abacus. In the Trajan Column there is no Neck, but the Aftragal of the Shaft is confounded with that of the Capital. l^he Height of this Capital is ihe fame with that of the Bale, C A ijiz. one Module or Semidlame- ter. its projcfture is equal to that of theCindture at the Bottom of the Column, viz. five Eighths of the Module. According to Fiiruvius, the Height of ihtT'ufcan Capital (by the Aftragal at Bottom) muft be half the Diameter of the Body of the Column below. And this Height being divi- ded into three Parts; the firfi: jmd uppermofl: Part goes to the i^bacus (which is a fquare or fiat Moulding ;) the fecond Part goes to the Boultin nnd Fillet under it; theBoultinis aquarter of a Circle; the Fillet, a narrovi^ flat Moulding ; and this Part is Subdivided into four Parts ; three of which go to the Boultin, and one to the Fillet; and the third and laft Part go to the Neck, which is flat and ftraight. Again, the Neck is divided into two Parts, one of which is the Breadth of the Aftragal un- der it (which confifts of a Semi- circle and a Fillet under it.) The Aftragal is again divided into three Parts, of which, two go ro the Semicircle, and one to the Fillet. The Projedure of the Capital is to be the half Part of the Dia- meter of the Body of the Co- lumn below. The Aftragal projefts in a Square. Scamozzi makes the Height of the Capital by the Aflragal at the Btittom, alfo half the Diameter of the Column below ; and this Height being divided into fixty Parts, twenty of them go to the Abacus or Plinth (aS- he calls ir,) G A fifteen to the Echinus or Half- Round (which is called the Boultin, by J/'itruznus^) and five to the Rondel or Bead-Mould- ing (which is a Semicircle.) three to the Lift, (which by Vitruvius is called a Fillet,) and fcventeen to the Ncclc or Frieze. Again, feven fuch Parts go to the Ron- del of the Aftragal, and three to its Lift. Valiadio alfo makes the Height of the Capital half the Dia- meter of the Body of the Co* lumn below {viz- by the Aftra- gal, which is by none of them reckon'd a Part of the Capital^ though properly fpeaking, it ought to be fo accounted ;) and this Height he divides into three equal Parts, the uppermoft of which goes to theAbacus (which by him is alfo called the Dado or Dye,) the next Part goes to the Ovoloor£c/:'/V/^/ (which by Vitrtivius is called the Boultin.) the other Part he divides into feven, one of which he makes the Liftella (which l^iiruvius calls the Fillet) under the Ovo- lo, and the other fix Parts go to the CoUarino or Neck (which is alfo called by him the Hypo- trachelium,or Frieze of the C«- pital. The Doric Capital has three Annulets, or little fquare Mem- bers underneath the Ovolo, in- ftead of the Aftragal in thtTuf- can^ befides an Abacus, an Ovo- lo, and a Neck, in comm.on with the Tufcan ; and a Talon, Cy- ma, or Ogee, with a Fillet over the Abacus. Authors alfo vary as to the Charadlers of this Ca^ pital. N Palladia, C A C A Palladio^ Figfiola, ^c. put Ro- feS under the Corners of the Abacus, and in the Neck of the Capital. ritruvius makes the Height of the Capital (by the Altragal at the Bottom) equal to half of the DiiinictcT of the Body of the Column below. And this Hei;:ht being divided into three Parts, the fir(l and lowermoli gotstothe Neck, the next to theBoultin (under which I'crm, fever al Members arc com- prehended ;) and this Part is by him delcribed in two Forms ; the firll of which is a Boultin (as 'tis defcribcd btfore,) and three Fillets under ir, and the other is a Boultin, and an Altra- gal under it ; and this Part is divided into three Parts, two of •which go to theBoultin, proper- ly fo called, and the other to three Filles, or to the Allra- gnl. The Fillets are all of an equal Size: In the iVitrngal, the Fillet is one Third of the whole. The tliird and uppermod Part ef the Crtp/'/rf/is again divided into three, tlic two lowermoft of which go to the Squ^ne, and the other to the Cymatium (which is an Ogee with the Hollow downwards,^ and a Fillet over ir. An Ogee is a Moulding which bears fomeRcfemblancetoan S ; which l^iirtivius makes of two quarter Circles joined together; and this Cymatium being alfo divided into three Parts, two of them go the Ogee, and one to the Filltr. The Allragal under the Capi- tal h equal to on» half ot the N«ck. Scam«zzl makes the Capital of the fame Height, and divides it into fixty Parts, three ot" which go to the Fillet of the Cymatium, five to the Ogee of the Cyma- tium, twelve to tie Square,four- teen to the Boultin, five to the Rondel, and two to the Fillet of the Allragal under the Boultin, and nineteen to the Neck. The Allragal under the Neck contains ten fuch Parts, (ix and a half of which go to the Ron- del, and three and a half to the I'"illet. Thefe are defcribcd ac- cording to Vitruviiis''% Terms, Scarnozzi noi mentioning any of them. \PaUtjdio like wife makes this Capital of the fame Height, as f^itr/ivius, and divides it into three Parts ; the uppermoft of which, he tubdividej/ into five Parts, two of which he allows to the Cymatium, and is fubdi- vided again into three Parts, one of which he gives to the Liftel- la or Annulet, and which by Fi- trnvifis is called a Fillet; aiid the other two to the Cima re6ta, (which is an Ogee, as here de- fcribcd ;) and the other three of the firft Subdivifions of this Part go to the Abacus, which by (■^iiruvius., in this Number, is called the Square. The fecond of the three grand Divilions of the Capital is lubdi- vided in three Parts, two of which go to the Ovolo or Echi- nus (which is by f^itruvins cal- led the Boultin ;) and the other to the Annulets under it, which arc three, and are all eqnal. The third princ-pal Hypotra- chelium or Prize L, (which is by Fitrnvifts called the Neck.) The C A C A The Aftragil under the Neck is as high as all the three Annu- lets. The Ionic Capitals compofcd of three Parts: An Abacus, con- fitting of an Ojjce; under thiJ, a Rind, which produces theVo- lutes or Scrolls, the moft effen- tial Parts of this Capital; and at the Bottom, an Ovolo or Quarter-Round : The Aftragal under that Ovolo belongs to the Shaft: The middle Part is cal- led a Rind or Bark, from its fuppofed Refemblance to a Bark of a Tree, laid on a Vafe, whofe Brim isrcprefented by the Ovolo, and feemingto have been flirunk up in drying, and to have been twifted into the Volutes. The Ovolo is adorn'd with Eggs, as they are fometimes called from their oval Form, the the Greeks call it E^ivo^. The Height of this Capital^ M. Perrault makes eighteen Minutes; its Projcdure, one Module, fcven Tenths. The Ditferenccs in the Cha- rafter of this Capital ^ow moft- ]y from the different Manage- ment of the Volutes, and coii- iift in this: That in the Antique, and fome of the Modern, the Eye of the Volute does not an- fwer the Aftragal of the Top of the Shaft, as Fitruvius, and fomc of the Moderns make it : That the Face of the Volutes, which ufually makes a Flat, is fame- times curved and convcxed fo that the Circumvolutions go ad- vancing outwards, as is frequent in the Antique. 2. That the Border or Rim of the Scroll in the Volute, is fome- times not only a plain Sweep, ^$ N it ordinarily is, but the Sweep is accompany'd with a Fillet. 3. 'J'hat the Leaves which in- vilt the Balulter, £re fometimes long aiid narrow, fometimes lar- ger and broader. 4 That the two Faces of the Volutes are fometimes joined at the outward Corner, the Ba- lufters meeting in the inner, to m;ike a Regularity between the Faces on the Front and Back of the Building with thofe of the Sides. 5*. That among the Moderns, fine* Scar/iozzi, the lo?j!c Capi- tal hisbeeu altered, and the four Faces mide alike, by taking a- way the Balufter, ajid hollowii^g all the Faces of the Volute in- wards, as in the Compofite. 6. That Scamozzi, and fome others, make the Volutes to fpring out of the Ovolo, as from a Vale, after the Manner of the modern Compojite: Whereas in the Antique, the Batk pailcs be- tween the Ovolo and Abacus, quite ftraight, only twilling at its Extremities, to form the Vo- lute. 7, Lajily, That of late Years, the Sculptors have added a little kind of Feftoons,fpringing from the Flower whofe Stalk lies on the Circumvolution of the Vo- lute ; and fuppofed to reprefent the Locks of Hair hanging down both Sides of the Face. The /o»/V, according to K/- truv:us, is made thus : Divide the Semidiameter of the Body of the Column below into eighteen Parts, take nine fuch Parts, of which, three muft go to thcCy- matiujTi, one ro the Fillet, and two to the Cima or Ogee under N 3 i«i C A C A it; then take four Parts for the Trochilus of the Volute or Scroll [the Trochilus is that Member irom whence the Scroll begins] thence take four Parts from the Boultin, which is the fourth Part of a Circle, and which mufi: be carved with Eggs and Anchors Then take two Parts for the Aftrugal is carv'd "With Eggs and Anchors ; then take two'Parts for the AlUaga' under theBoultiu: The Aftni- gal is carved with Beads, and has a Fillet on each Side of it, each one fourth of the Whole : Then the fix Parts remaining muft go to the half of the Vo- lurc below. Then take eight more fuch Parts, which mart go to mfike the Remainder of the Frizc or Neck of the Cupital ; and three more fuch Parts for the Aftragal, under the N^ck of ■which one Part goes to the Fillet. PrJlad'io's Defcription of this Capital agrees with that of I'l* truviui ; and Scarnozzt'^ is fo blind, that 1 believe fcarce any are the wifer for it. M. Le Clerc fays, the moft efTential Part of this Capital is the Volute ; which feveral Ar- chiteSs imagine to have been in- tended to reprcfent the Rind or Bark of a Tree inclofed be- tween the Abacus and Quarter- Round, having its two Extremes twilled into Scrolls, and thofe two Scrolls bound with a large Rope in the Middle ; which comes pretty near the Figure that the Antients gave on the two Sides of the Capital. Other Architecis confidcring that this Capital bears fome Rc- fcmblance to the Head-Drefs of a Greek Lady, believe it to have taken its Origin from thence ; But this being a Matter of no great Ufe, we leave every one to judge of it as he pleafes. The Capital of the Antients being found improper in angu- lar Columns, by reafon of the Diverlicy of its Faces, Scamozzi compofed a ncv/ one with four fimilar Faces. Som.e Architeds, however, won't allow the Volutes to fprirg out of the Vafe of the Capital.^ but will have them con- fifl of one and the fame Rind continued under the Abacus ; which, by this Means, will :r • pear the better fupporied ; an i'.: fiance of which xve have in tn j Five Orders of M. 'Perutult And th-r/ would have Reafon on their Sides, were there the fame gO(^d Tafte in this, as iu :he other "Dclign ; but a^ that can't be, we mall be contented wiiii the other, which is ealily de- figu'd, and has a beautiful Ap- pearance. 'Tis true, the new Abacus, which it has in his 49ih Figure, being better proportion'd to the Largenefs of the Volute than that oi Scamozzi^ renders it more graceful ; befides, that it is fur- ther inrich'd with little fclloons falling from the Volutes, which fome modern Sculptors have been pleafed to add. He obferves, that when there are Eggs cut in its Quarter- Round, their Number fhould be 24; and the Shaft or Fuft fhould be channelled with an equal Number of P'lutings. He adds, we fometimes alfo cut Pearls and Olives in the Altragal, over iheOvolo, though it: C A C A (t belong to the Shaft : But were the Capital made of a Matter diftcrenc from that of the Shaft, then muft the Artragal be con- tidcred as a Bauguette, making Part of the Capital, and not ot the Shaft : To which lafl the Fillet underneath would be left; were \t otherwife, the Capital would be but poorly terminated by its Ovolo or Quarter-Round ; beHdes that, it would be too flat and fquab. He adds, that the Antients having made the Balulter of this Capital very (hort, there h fome Difficulty in adjufling the Vo- lutes to the Quarter-Round in the Capitals of the Pilafters. This has occafioned feveral Archite6ls to flatten or diminifii the Convexity of the Quarter- Round ; which is a very confi- derablc Irregularity, which they might have avoided, by lengthen- ing out the Baluder, fo as to go beyond the Quarter- Rsund ; at the fame Time making the Cir- cumvolution of the Volute ad- vance a little further. However, fays he, if a Perfon has a mind to follow the Guftom, he means, if he chufes to diminifli the Convexity of the Quarter- Round, as is here done, he com- mits a Fault, that has good Au- thority on its Side: Which, how- ever, he would do well to avoid, efpecially as it may be done without much Trouble. A Difficulty of the fame Kind may be met with in the Quarter- Round ot the modern Capital^ which our Architefts have like- wife diminil"hed, in order to re- ceive the Volutes more favou- rably, which fliould further have a Curvity, like that of the Aba- cus; but from which a man is under a Necefllty of receding and of opening the Volutes, fo as to be above the Quarter- Round, after \i has run perpen- dicularly acrofs th^ Face of the Pilafter: And the fame, he fays, may be underitood of ihc Roman Capital. The Corinthian Capital is much the richeft ; it has no Ovolo, and its Abacus is very ditfercnt from thofe of the Tufcan^ Doric, or Io»ic ; as having its Faces cir- cular, hollowed 'inwards, with a Rofe in the Middle or each Sweep. Inftead of Ovolo and Annu- let, here is only a Brim of a Vafe; and the Neck is much lengthened and inrich'd with a double Row of each Leaves, bending their Heads down- wards, and between them fmall Stalks ariling, whence fpring" the Volutes, which do not re- femble thofe of the lo^iic Capital ; and which inftead of the four in the Ionic, are here iixteen ; four on each Side under the four Horns of the Abacus, where the Volutes meet in a fmall Leaf, which turns back towards the Corner of the Abacus. The Leaves are divided, each making three Ranges of lelfer Leaves, of which they are com- pofed ; each le/Ter Leaf is again m.olt commonly parted into five, and are called Olive Leaves ; but fometimes into three, and are called Laurel Leaves : The middle Leaf, which bends down, is parted into eleven. In the Middle, over the Leaves, is a Flower fliootin^ out between the Stems and Volutes, like the Rofe ifl the Abacus. N 4 Th(i C A C A The Hd.'^ht of this Capital is two Modules -j, and its Projec- ture I J. The Diuerencej in che Cha- racter of this Capital are, that in Vttruviui^ fltc. the Leaves are ill the Form* of the Acanthus ; whereas in the Antique, they are more ufaally Olive Li^aves. 2. That their L"a\es are ufu- ally unequal, and the undermoft commonly being made the tallcll ; biu fometimes the fliorteft; tho' they are fometimes all equal. 3. Sometimes the Leaves are TUtfled, fometimes quite plain : The firft Row generally bellies out towards the Bottom; but at other Times they are ilraight. 4. Sometimes the Horns of the Abacus are fharp at the Cor- ners, which feems to agree to the Rules oi Vitruvius \ but they are more ufually cut off. 5-. There is alfo fome Diffe- rence in the Form and Size of the Rofc. 6, The Volutes are alfo fome- times joined to each other, and at other times wholly feparate. 7. Sometimes the Spires of the Volutes continue twiAing, even to the End, in the fame Courfe; and fometimes they arc turned back again, near to the Centre, in the Form of an S. According to ^'timvius^ the Height of this Capital (by the Aftragal at the Bottom ) is equal to the Diameter of the Body of the Column below, one feventh Part of which goes to the Abacus, which confifts of aBoultin, a Fillet, andaPlinih, [which is no other than a larger FillPt.] The Abacus being fubdivided mto three parts, one of them goes to the Boultin, and a third Part of the next goes to the Fil- ler, raid the red to the Plinth. The Height of the Altragal below the Cap.ta/j is one twelfth Part of the Diameter of the Bo- dy below, and is divided into three Parts ; of which the Fillet contains one, nna the Boultin two. Scaynozzi makes this Capital in Height i \ of '.he Diameter of the Column ; vvhici. being di- vided into 75- Parts, four of ihcm go to the Boulcin, one to the Fillet, nine to the Plinth, and the rclt to the Neck- PalLidio makes this Capital equal in Height to the win>;e Diameter of the Body of liie Column below ; and one lixih Part more, which is allow 'd to the Abacus, by which he is fap- pofed to mean all theMouldi.igs above the Acanthus Leaves. The Leaves of this Capital^ M. Le Clerc fays, are in Num- ber 16, 8 in each Row. Each Leaf, fays M. Le Clerc ^ is divided into feven or nine Plumes ; two of which, or to fpeak more properly, one whole and an half on each Side go to form the Return or Defcent. Sometimes the Return cvnilifts of three Plumes almoil intire, each Plume being divided ac- cording to the Nature of the Leaf, Upon this he remarks, that the Leaves of the Capital are or- dinarily thofe of Olive, thofe of Acanthus, or thofe of Smallage; but he gives the Preference to the two laff, and particularly when the Corinthian is raifed over any oti>er Order. For C A C A For its Leaves being flat and plain, they refleft mure Liglit than the others, which are more wrought and uneven; for which Reafon the firft have a better Hf- fett, when feen at a Diftance, than the laft; which arc only fit to be viewed near at hand. He likewife oblVrves, that in making the Leaves either of this or the Rryman Capiul^ great Care mufl: be taken that they be well defigned ; particularly, that di- viding them into Plumes, thofe Plumes don't run too far off from one another, but fhall all together appear to form one fingleLeaf; which mud nor be too narrow towards the Top, that each Plume dired to its Ori- gin, ^c. Without luch Precau- tion, rhe Leaves will lofe all their Gruce and Beauty. Jt a Cjri-fithian Order were to be placed very high, as in the Lanthorn of a Dome, he would rather chufc not to divide the Leaves of its Capital at all, but to prelerve the Mafs intire. In fome Cup'uals we find Leaves that are finely wrought, which ncvcrthelef> are of an ex- treme ill Taik^, ns thofe of Olives, for inftance, in fomc Pi- lafters. This, he fays, he men- tions for the fake of thofe, who, having no great Share of Judg- ment, think they can't fail of doing well, if they do but imi- tate what they find in Buildings of Reputation. The Cor/ipojite Capital is fo called, as partaking of the Done in its Quarter- Round, of the Ionic in its Volutes, and of the Corinthian in its double Row of Leaves underneath, which are in ^umber i6 M. Le Clcrc fays, the Leaves he gives it are of Laurel, which not being much edged or in- dented, are lefs delicate ; and for that Reafon more fuitable to the Volutes of this Capital, which are tolerably maflive, but agreeable to the Modilious of the Entablatures. In the Middle of the Abacus, is a Flower, and under thi? Horns, Leaves which return up- wards, as in the Crnnthian r But inftead of Stalks in the Curmthi- «>?, the Compojite has fmall Flowers, which lie clofe to the Vafeor Ball, twilling round to- wards the Middle of the Face of the Capital^ and terminating in the Rofe. The Height of the Compofu? Capital is two Modules one Third, and its Projedure one Module two Thirds, as in the; Corinthian. 1. The Differences of the Charafter of this Capital con lilt in this ; that the Volutes wnicH ordinarily defcend and touch thfe Leaves, are in fome Works of the Antique feparated from tliem; that the Leaves which are gene- rally unequal in Height, the lower Rank being the tulkll, are fometimes equal. 2. That the Volutes of the Moderns generally fpring out of the Vafe; whereas they do in the Antique ordinarily run ftraight the Length of the Abacus, over the Ovolo, without ftriking into the Vafc. 3. That the Volutes, whole Tiiicknefs is contraded in the Middle, and enlarg'd above and below ill the Antique, in the World; C A C A Works of the Moderns have their Sides parallel. 4. That the Volutes which have been hitherto made, as the/ folid, both by the Antients aud Moderns, are now nradc much lighter, and more airy; the Folds ftanding hollow, and at a Dif- tance the one from the other. This Capital^ called tne Cok'z- fofue or Ro.niti^ is made and di- vided by Vitrnv'.us^ Sccim'izz't^ and Pallad'to ; except that the Carving of this is different from that. SomeArchicefts diftinguifhthe *Tufcan and 1)or'ic Cufitals^ which have no Ornaments, by the Title of Capitals (jf Mouldingi ; and the three other, which have Leaves and Ornaments, by the Title of C.-ip:ia's of Sculpture. An AnguUr Capital^ is a Ca- pital which bears the return of an Entablature, at the Corner of the Projedure of a ?>onti (piece. Capital of a B.iilufter., is that Part which crowns the Balkilkr, which fometimes di)cs fome- what refemble the Capitals of fome Columns, and particularly the Ionic. M. Lc Clcrc gives the Capital of the Spanijh Order eight large Leaves, (Imple, but a little wav'd with grena'x Staiks, or Flowers rifing among them, which may be managed in various Manners, according to the various Places where this Order is ufcd. The Horns of the Abacus are fupported by little Volutes ; the Middle of the Abacus being a- dorned with a Lion's Snout in- flead of a Rofe, which noble Animal '\^ the Symbol of Spain.^ and exprefTes the Strength and Gravity, as well as the Prudence of that Nation. In the Friezes over. this Capi- tal may be added a rerrellrial Glooe; with Cornucopia's, Palms and Laurels, which are lignili- caur Ornaments that explain thcmfelves. Capital of a Iriglyph., is the Plat-band over the Triglyph ; V/hfch Vitrttvius calls 'Iccnia. AUb a Triglyph fometimes docs tne Office of a Capital to the Doric Pilafter. Capital of a Nich^ is a fort of little Canopy made over a fhal- low Nich, which covers or crowns a Statue. CAR -^ A kind of rolling CARR C Throne ufcd in Tri- CARRE 3 umphs fr,r Victories, in which the General; fits and in the fplendid Entries of Princes. CARACOL, a Term fome- tjmes ufed in Architefture for a Stair-Cafe, in a helix or fpiral Form. CARCASE, is the Shell or Ribs of a Koufe, containing t!ie Partitions, Floors, and R::itcrs made by the Carpenrer; or it is the Timber Work (or, as it were, the Skeleton) of a Houf , before it is lathed and phillered. It is Othcrwif; called the Framing. The Price of Frar.iing. Some Workmen fav, that the Price of Framing the drcafe of a Houfe, (in the Country) is about eight Shillings per Square, if the Workman pay for the ia wing of the Timber ; and if he does not, about four Shillings and Six- pence per Square. CARIATIDES or CARIA- TES. See Caryatides. CARINA^. C A C A CARINA, a Term ufcd in antient Architecture, a Name given by the Romans to all Buildings in the Form of a Ship, [from Carina^ the Keel of a Ship,] as we Hill ufe the Word Nave for No/vis^ a Ship, the middle or principal Vault of our Churches, becaufe it has that Fi- gure. CARPENTERS If'ork, in a Building, includes the Framing, Flooring, Roofing; the Foun- dation, Carcaie, Doors, Win- dows, ^c. Of Carpenters Work: The fe- veral kinds of it, (in relation to Building) with their Prices and Methods ot meafuring them, ^c. are too many to be comprehend- ed under this fo general a Term as Carpenters IVork ; for which Reafon they (hall be referred to their Particulars, (as Framiag, Flooring, Roofing, i^c.) The Meafuring of Carpenters Work. Carpenters IVorks^ which are meafurable, are Flooring Parti- tioning, or Roofing; all which are meafuredby the Square often Feet long, and ten broad ; fo that one Square contains loo fquare Feet. I. Of Flooring. If a Floor be 5-7 Feet 3 Inches long, and 28 Feet 3 Inches broad, how many Squares of Flooring is there in that Room? Multiply 5*7 Feet 3 Inches by 28 Feet 6 Inches, and the Pro- dud is 1 63 1 Feet, ^c which di- vide by 100, (this is done by cut- ting off two Figures towards the Right Hand with a Dafh of the Pen,) and the remaining Figures are the Quotient, and the Figures cut off are Feet : Thus 1 631 di- vided by 100, by cutting off 31 from the Right Hand thereof, the Quotient is 16 Squares, and the 31 cut off is 31 Feet. See the Work bath by Decimals, and alfo by Feet and Inches. SI 28 25* S 2862 x8oo 114^0 S 1631.62 S F. /. 11 1 4^6 28 7 6 7 16I31 7 6 Facit 16 Squares, and 31 Feet. Note^ That j is the Decimal for Half of any Thing, 25- is the Decimal for a Quarter, or 3 In- ches i and 125" is the Decimal of 1 Inch and half, or ^ ; be- caufe 3 Inches is a quarter of a Foot, and 5- is the Decimal of 6 Inches ; becaufe 6 Inches is half a Foo:. Example C A Example 2. Let a Floor be :J'3 beet 6 Inches long, and 47 J-eet 9 Inches broad; how ma- 47-75- C A ny Squares are contained in that Floor ? i3«75' 143^5- J 3^75- 2515-4.625- F. /. ^3 6 47 9 371 212 . 26 9 13 4 6 ^3 6 2^15-4 7 6 Facit 25- Squares, and 54 Feet. By Scale and Compares. In the firit Example, extend your CompafTes from i to 28.5-; and that Extent will reach from 57. 2f ro 16 Squares, and near a third Part. In the fecond Example, ex- tend the CompalTcs from i to 47.75. and that Extent will reach from 5-3.5- to 25- Squares, and a- bove a half. Of ^art'tttoHing. Example i. If a Partition be- tween Rooms be in Length Sx Feet 6 Inches, and in Hei^h 12 Feet 3 Inches ; how many Squares are contained therein ? The Length and Breadth be- ing multiplied togetner, the Pro- dud will be iclio.625; '.'.hich divide by 100, (as before hasocen fhewn,) and the Anfwer is 10 Squares 10 Feet ; the Inches or Parts in thefe Cafes. 12.25- 82. 5" 6125- 2450 9800 io[io.625 T. /. 82 6 12 3 990 20 7 6 icjio 7 6 Each lO Squares 19 Feet. If C A If a Partition between Rooms be in Lengthi 19 Feet 9 Inches, and in Breadth 11 Fcer 3 Inches; how many Squares are contain'd therein ? 61.75- II 2f 45-87-r 18350 2175- 9175- C A The Length and Breadth being multiplied together, the Produtt is 1032 Feet; which divided by 100, the Anfwcr will be 10 Squares and 32 Feet. F. 91 II /. 9 3 1009 22 3 II 3 10I32 2 3 Of Roofing. It is a Rule among Workmen, that the Flat of any Houle, and half the Flat thereof, taken with- in the Walls, is equal to the Meafure of the Roof of the fame Houfe; but this is when the Roof is true pitch'd; for if the Roof be fnore flat or deep than the true Pitch, it will Mea- fure to more or lefs accord- ingly Example i. If a Houfe with- 18.25- 44- S 91.25- 7300 730c Flat 812.125- Half 406 12I18 By Scale and Compajfes, In the tirft Example of Parti- tioning, extend the Compaffes from I, to 12. 25-, and that Ex- in the Walls be 44 Feet 6 Inches long, and 18 Feet 3 Inches broad ; how many fquare Feet of Rooting will cover that Houa Defign in CARTOON, 5 Paincing,made on llrong Paper, to be atter- wardscalkcd through, andtranf- ferred on the freih Plaifter of a Wall, to be painted in Fref- co, CARTOUCHES, 7[ofar- CARTOUSES, >toccio, I- CARTOUZES, ^'.altan ] an Ornament in Architeftare, Sculpture, ^c. reprelentiiig a Scroll of Paper. It is ufaally a Table, or fiat Member with Wa- vings, on which is fome Infcrip- tion, or Device, Ornament of Armoury. Cypher, or the like. They are fometimes made of Stone, Brick, Plaifter, Wood, cs'c. for Buildings. The C A C A They are, in Architefture, often much the fume as Modi- lions ; only thcfc are fet under the Cornice, in Wainfcotting, and thofe under the Cornice, at the Eaves of a Houfe. Perrauh fays, Cartouch h an Ornament of carved Work, of no determinate Form, whofe Ufc is to receive a Moito or Inicrip'-i'tn. CARTRIDGES, in Archi- tea ire, as fom;; Workmen call them, arc rhe fame as Cartou- CARYATIDES,^^ [fo called CARIATES, 3 from the Caryatids a People of Caria] are in Architc6turc, a kind of Order o.- Columns or Pilaftcrs, under the Figures of Women dref>' i in lont; Robes, after the Manner of the Carian People, and lerving inflead of Columns to fupport the Entablement. Vitruvttis relates the Origin of the Caryatides. He obfjrvcs, that the Greeks having taken the City of Cnria^ led away their Women Captives ; and to per- petuate their Servitude, repre- fented them in their Buildings as charged with Burdens, fuch as thoie fupported with Co- lumns. M. Le Clerc, aptly enough, calls thefe, Symbolical Columns and tells us, that the antient Greeks had a Cuftom in the Co- lumns of their pablick Buildings, to add Figures and Reprefenta- tions of the Enemies they had fubdaed, to prefcrve the Memo- ry of their Vidories. That they having reduced the rebellions Cariaas to Obedience, and led away their Wives Cap- tives ; and that the Lacedemo- n'tayis havihg vanquifh'd the P^-r- fians at Platcca^ they were the firft Subjeds of thefe Columns \ which have preferved to late Po- sterity both the Glory of the Conquerors, and the Difhonour of the Conquered. And hence originally came the Names Caryatides^ and Per- fian Columns; which Names have been fince apply'd to all Columns made in human Fi- gures, though with Characters very different from one another. M. Le C/erin the general C.'EMENT,Cof the Word, CIMENT, 3lignifies any Compofuion ot glutinous, oc O 5 tenacious C E C E tenacious N;'.ture, proper for binding, uniting, and keeping Things in Cohciion. OmciU^ \\\ x^rchitcftnre, is a {Irong Sort of iMortar, ufed to bind or ftx Bricks or Stones to- gether for foine kind of Mould- ings; or in cementing a Block of Bricks (as vhcy '.cail it;) for the carving of Capitals, Scrolls, or the like. It is of two Sorts ; one called Hot Cement^ and the other Cold Cement \ becaufe the Hot Cement is m.vde and ufed with Fire; and the Cold Cement is made and ufed without Fire. To make the Hot Cement^ take half a Pound of Bees-Wax, an Ounce of line Brick-Duft, an Ounce of Chalk-Duft or powdered Chalk ; fift both the 13rick-Dun and Chalk through a fine Hair-Sieve, (the Brick and Chalk may be beat in a Mortar, before it is fifted .) Let all thcfe be boiled together in a Pipkin, or other Earthen V'tllcl, for about a quarter of an Hour, keeping it continually fb'rriiig uith a Piece of Iron or Lath, then take it off, and let it (land for four or five lUinures, and it is fit for Ufe, The Bricks which are to be ccir.ei;ted with this Kind of Q- ynaa^ mviil be made hot by the Fire, before the Cement is fpread on them ; and after that, bctub- bed.to and fro one upon another, after the fame Manner that Joi- ners do, when they glue two J3oards together. The Cold Cerr.cnt is Icfs ufed ; and 13 nccounted a Secret known • bat ro few Bricklayers. It is made after ihe following fyjawner ; ■ ■ Take a Pound of old Chcpirc Checfe, pare of the Rind, and throw it by, then cut or grate the C^heefe very fmalj, put it in- to a Pot with a Quart of Cows P^ilk; let it (land allNight,and in the Morning, take the Whites of twenty-four or thirty Eggs, and a Pound of the bcft uii- flack'd or quick Lim.e, and beat it in a Mortar to a very fine Powder, (ift it in a fine Hair- Sieve, put the Cheefe and Millc to it in a Pan, or Bowl, and flir them well together with aTrowel or fuch like Thing, breaking the Knobs of the Cheefe, if there be any, then add the Whites of Eggs, and temper all well toge- ther, and it will be (it for Ufe. This Cement will be of a white Colour; but if you will have it of the Colour of Brick, put in- to it, either fomevery fine Brick- duft, or fome Almegram, but not too much, but jlifl enough to give it a Colour. CENTRE, [in Geometry ] of a Circle, is a Point in the Middle of a Circle, or circular Figure, from which all Lines drawn to ihG Circumference, are equal. Centre of a P aralleh^ram or ^oh^on^ is the Point wherein its Diagonals interf ft. Centre of Magnitude is a Point equally remote from the cxtream Parts of a Line, Figure, or Body; or the Middle of a Line or Plane, by which a Figure or Body is divided into two equal Parts. Centre f>f a Sphere is the Poln t from which all the Lines drawn to the Surface, are equal. Qntr^ C H C H Centre ofun EllipJJi is that Point where the two Diameters, the Tranfverle, and the Conjugate, interfed each other. Centre of Gravity^ in Mccha- nicks, is a Point ivithin a Body, through which, if a PJane pal's, the Segments on each Side will equiponderate, i. e. neither of them can move the other. CENTRAL, fomething rela- ting to a Centre. CHALK, a white Subftance ufually accounted as a Stone: Though Dr. SUre thinks there is not lufticient Reafon for it; iTnce it having been examin'd by the Hydroftatical Balance, it is found to want much of the Weight and Condltence of a real Stone. Chalk is of two Sorts, the hard dry ftrong Stone, ufcd in making Lime; the other is a fofc unftuous Chalk, ufed for manuring Lands ; eafily diiTolv- ing with Rain and Froft. CHAMBER, in a Houfe, or Building, is any Roomlituate be- tween the lowermod (excepting Cellars,) and the uppermolt Roonic, So that there are in fome Houfes two, in othersthree or more Stories of Chambers. S'\T Henry If'^otton direifs, that the principal Chambers for De- light be lituated towards the Eart. As to the Proportions; The Length of a well-proportion'd Lodging fliould be the Breadth and half of the fame, or fome fmall Matter lefs; but fiiould ne- ver exceed that Length. As for the Height, three Fourths of the Breadth will be a tit Height. 'Palladio dire6is x.\\:\i Chambers, Antichambers, and Halls, either i3at, or arched, be made of the fol- lowing Heights. It they be flat, he advifes to divide the Breadth into three Parts, and to take two of theiit for the Height of the Story from the Floor to the Joift, as in the Figure. Let the Figure rcprcfent the Chamber, and whofe Height you would find, v^hich fuppofe to have in Breadth 24 Feet within the Work, which fhall be divided upon the Line A B into three equal Parts within Points, whers is mark'd the Numbers i, 2, 3, each Part being eight Feet ; two of each Parts fhall be the Height of theChamber, ef<^- to wit, iix- teen Feet from the Floor to the Joift. If you would have it higher, the Breadth mnft be divided into feven Parts, of which take five for the Height. O C H Let the Figure be of the fame ^icadth with the foregoing, to C H wit, twenty-four Feet wlrhin the Work, which fliall be divided upnn the Line AB into feven e- qual Parts; take five ot them to make the Height of the Story AG and B D, and the faid l^eight will be fcventcen Feet two Inches from the Floor untq the Joirts. Or divide the faid Height into four Parts; and three of ihofe Parts will likewilegive a greater Height, Let the Figure be of the fame Breadth, viz. twenty-four Feet within the Work ; which divide upon the Line AB into four e- qual Part?, three nf whicli you mud take for the Height of the Story, which will be eighteen Feet from the Floor to the joift. 'f'hc Height cf the Chatnhirs of iht fecond Story (hall be a ^velfth Part lefs than the Cham- Ijers below; as fuppofe its firfl Story be fixtecn Ftet from the Floor to the Joift, divide the fix- teen Feet into twelveequal Parts ; and take eleven of them, which will make fourteen Feet eight Inches for the Height of the ie- cond Floor to the Joifi. Again, fuppofe the firft Story be fcventeen Feet two Inches, and in twelve equal Parts ; take eleven of them which will make fifteen Feet, feven Inches for the Height of the fecond Story from the Floor to the Joifi. If yon would make above the Second Story and Attic^ or third Story, the fecond muil always be divided into twelve equal Parts ; nine of which will give the Height from the Floor to the 13oitom of the Joifts. C H C H In the building of Chambers^ Regard ought to be had as well to the Place of the Bed, which is ufually fix or feven Feet fquare; and the Paffagc, as well to the Situation of the Chim- ney; which, for this Confidera- tion, ought not to be placed juft in the Middle, but diftant from it about two Feet, or two and a half, to the End it may make Room for the Bed; and by this Means the Inequality is little difcern'd, if it be not in Build- ings of the Breadth at leaftof 24 Feet within the Work; and in this Cafe, it may be placed jufl in the Middle, CHANCEL [fo called, of CancelU^ Lettices or crofs Bars, wherewith theChaj^cels were an- ciently encompafTed, as they are nov/ wirh Rails] a Part of the Choir of a Chuvch, between the Altar, and the Communion-Ta- ble, and the Baluftrade or Rails that inclofe it; where theMini- fter ftands at the Celebration of the Holy Communion. CHANNEL in Architedure, is particularly ufed for a Part of the/c/Wf Capital, a little hollow'd, in Form of a Canal, lying un- der the Abacus, and running the whole Length of the Volute, inclofed by a Liftel; or it is otherwife defcribed to be that Part of the /oa;V Capital, which is under the Abacus, and lies open upon the Echinus or Eggs, "which has its Centres or Turn- ings on every Side, to make the Volutes. Channel of the Larmier is the Soffit of a Cornice which makes the Pendant Mouchette. Channel of the Volute^ in the lomc Capital, is ,the Face of its Circumvolution, inclofed by a Ui\c\. CHANTLATE, in Building, a Piece of Wood fattened near the Ends of the Rafters, and pio- jeding beyond the Wall to fup- P ort two or three Rows of Piles, Fo Placed, to hinder the Rain Water from trickling down the Sides of the Walls. CHAPEL ? A fort of little CHAPPELS Church, where an Incumbent, under the Deno- mination of a Chaplain, of- ficitcs CHAPLET, a String of Beads, called Paier-nofiers^ ufed in the RomifJj Church. CHAPLET, in Anhlteiiure, is a fmall Ornament cut or car- ved into round Beads, Pearls, Olives, and Pater-nofters, as is frequently done in Baguettes, A Chapkt is, in truth, little elfe but z Baguette^ inrich'd with Carving. CHARGE, inPainting. Over- charge is an exagerated Repre- fentation of any Perfon, where- in the Likenefs is preferred, but ridiculed. The Method is to pufii out and heighten fomething already amifs in the F"ace, wheher by way of Defect or Redundancy : Thus, V. gr. if Nature has given a Man a Nofe a little larger than ordinary, the Painter falls in with her, and makes the Nofe extravagantly long ; or if the Nofe be naturally too (hort, in the Painting, It (hall be made a mere Stump; and fo of the reft. CHARNEL, a Building, a kind of a Portico or Gallery, ufually in or near the Church- Yard, over vyhich were anticnt- ly C H C H ly laid the Bones of the Dead, after the Fkfh was totally con- fumed . CHESNUT. The Horfe^ Chefnut, fays a certain Author, ought to be univerfally propa- gated, being ealily increafed from Layers, and grows in goodly^ Standards, and bears a inoll glorious Flower : It is much ufed for Avenues mFratice^ and was brought into theie Parts of Europe from Turkey^ and has been raifed from Nuts brought from thence; which grow well with us, and in Time to fiir large Trees, full of Boughs and Branches, green - leaved , and itreaked on the Edges ; with Threads in the Middle, that in their native Country turn to Chefnuts; but rarely with us. It is valued for the fair green Leaves and Flowers ; and for want of Nuts is propagated by Suckers: Its Naire comes from the Property of the Nuts, which in Turkey are given to Horfes for their Provender, to cure fuch as have Coughs, or are broken- ivinded. Mr Chome] fiys, that nothing fecms to him more agreeable, or that would bring more Profit to a Country, than Cbefnnts planted in Rows, well managed, and kept in good order; which would not oniV be pleafnig to the Eye, but the Flower would be ngree- able to the Smell, and the Tafte in Time will aUo be gratified. Thcfe Trees are of quick Growth, they rtioot up in a lit- tle Time, and their Leaves, which are very fair and beautiful, will form a Shade, which will invite People to retire under them. In fome Places he tells us, that CheJMut -Trees grow like Oaks, and make Fortlt Trees ; they likewife plant them at a Foot Dillance one from the other, like young Oaks for Cop- pice and Underwood ; but this is rarely done, becaufe they are not good for burning, by realon of their crackling 'n\ the Fire, and Aptnefs to burn Peoples Clothes that fit at it. As to the particular Ufes of ChefKHt Timber, they are next to the Oak, moft coveted by Carpenters and Joiners ■ and for- merly moft of ourantientHoufes in London were built of it, there being a large Forcft of them not far from this City in the Reign of our King Henry U. h makes the befl Stakes and Poles for Palifadoes,. Pediments for Vine Props and Hops; it is alfo proper for Mill-Timber and Water- Works, or where it may lie buried. It is fo prevalent againft Cold, that Chefnm-Trees defend other Plantations from the Injuries of the feverelt Frolts. The Chcyiut-Tree is alfo pro- per for Columns, Tables, Chflh, Chairs, Stools, Bedlfeads, and Wine-Casks, and thofc tor o- ther Liquors, giving the Liquor the lead Tindure of the Wood of any whatfoever ; and having been dipped in fcalding Oil, or well pitched, is extremely du- rable. It will look fiir with- out, indeed, when rotten with- in ; however, the Beams give warning of a fall of a Houf^ by their cracking. The C H C H The Coals of this Wood are excellent for the Smith, foon kindled, and as foon quenched. CHIMNEY, that Part of a Room, Chamber, or Appart- ment, ■wherein the Fire is made. Chimneys confift of thefe fol- lowing i^arts : The Jaumbs or . Sides coming out perpendici- I larly, fometiines circularly, erV. l| from the Back, the Mantletree, " which rells on the J.iumbs; the Tube or Funnel which conveys away the Smoke; the Chimney- Piece or Moulding, which is on the Forelide of the Jaumbs over the Mantletree, and the Hearth or Fire-Place. 'Palladio lays down the follow- ing Proportions for the Breadths and Depths of Chimneys on the Infide, and for that Height to the Mantletree. Chimneys in 1 Breadth. Height, Depth. Halls, 6, 7, or 8 Feet. 47, or f Feet. 2 7 or 3 Feet. Chambers, 5-i,6,or7Feet. 4, or 4^ Feet. 2, or 27 Feet. Studies and Wardrobes. 4, 4i, or 5" Feet. 4, or 41 Feet. 2, or 2-^ Feet. Wolfius orders the Breadth of the Aperture at Bottom to be to the Height as three to two, to the Depth as four to two. In fmall Apartments the Breadth is three Feet, in Bed- chambers four, in larger Apart- ments five, in fmall Banquet- ting Rooms five and a half, in large fix. But the Breadth muft never exceed two and a half, Icfl: there being too much Room for Air and Wind, the Smoke be driven into the Room : Nor mull the Height be too little, left the Smoke mifs its Way, and be check'd at firrt fetting out. 1 he fame Author advifes to have an Aperture, through which the jiiternal Air may, on Occa- fion, be let into the Flame to drive up the Smoke, which the internal /Wr would otherwife be puable to do; Some make the Funnel twifi;« ed, to prevent the Smoke's dc- fcending too eafily ; but the bet- ter Expedient is to make the P'unnel narrower at Bottom than at Top, the Fire impelling it up more eafy when contradted at the Bottom ; and in mounting it finds more Space to difengage it- felf, and therefore will have Icfs Occafion to return into the Room. Mr. Felibien orders the Mouth of the Tube, or that Part joined to the Chir.iney-Back^ to be a little narrower than the reft ; that the Smoak coming to be re- pelled downwards, meeting with this Obdacle, may be prevented from getting into the Room. Fo prevent fmoaking Chim- neys^ "Wii. Lucar advifes to leave two Holes, or make two Pipes in the Chimneys one over the Other on each Side, the one fio- P'«S C H C H ping upwards, and the other downwards ; thro* thefe Holes or Pipes, lays he, the Smoke will eaiily pafs out of any Fun- nel which way foever the Wind blows. Philip 'D'Ormc advifes to pro- vide a hollow Brafs Ball, of a reafonable Capacity, with afmall Hole in one Side tor the putting in Water, to be hung up in the Chimney^ at a Height a little a- bove t'he greateft Flame, (with the Hole upwards,) by an Iron Wire that (hall traverfetheC^/Vw- ney a little above the Mantle- tree ; where, as the Water grows hot, it will rarefy and drive thro' the Aperture or Hole in a va- poury' Steam, which will drive up the Smoke that would other- wife linger in the Funnel. Some think it would be bet- ter if this Brafs Ball were made with 2 fliort Nofe to fcrew ofl' "Vvheij it is to be fill'd y/ith Wa- ter ; and then the Hole at the End of this Nofe need not be bigger, than that at the fmall End of a Tobacco-Pipc. It alfo may be proper to have two of thefe JBalls, one of v/hich may fupply the Place of the other when it is exhaufted ; or, upon Occafion, to blow ihe Fire ill the mean Time. Others place a kind of move- able Vane or Weather-Cock on the Fop of the Chimney^ fo that what Way foever the Wind comes, the Aperture of theO'/f^- «cs will be skrcen'd, and the Smoke have free Egreis, Indeed the bed Prevention of a fmoking Chimney fecms to lie in the proper placing of the Doors of a Room, and the apt falling back of the Back, and due ga- thering of the Wings and Bread of the Chimney. Rules about Timbers near Chimneys : It is a Rule in Build- ing, that no Timber belaid with- in twelve Inches of theForedde of the Chimney Jaumbs ; that all the Joirts on the Back of any Chimney be laid with a Trimmer, at fix Inches diiPance from the Back; that no Timber be laid within the Funnel of any Chim- ne\. Chimney Hooksy are Hooks of Steel and Brafs, put into the Jaumbs of Chimneys^ into each Jaumb one, for the Handle of the Fire Tongs and Fire Pan to rcll in. Their Price: The Steel Hooks are about i s. the Pair, and the Brafs about 2j. the Pair in Lon- don. Chimney 'Jaumbs.^ arc the Sides of a Chimney.^ commonly Hand- ing out perpendicularly (but fometimcs' circularly) from the Back, on the Extreipities of which the Mantletree relts. See Corner-Stoxe. Chimney-Piece.^ is a Compofi- tion of certain Mouldings of Wood or Srone, ftanding on the Forelide of the Jaumbs, and coming over the Mantletree. The Price : Chimney-Pieces of Free-Stone, wrought plain, are worth lOJ. but there may be fuch Mouldings wrought in them, as with their Coves, and other Members, may be worth 20, 30, or 40 .f, fer Piece. Chimney-Pieces of Egyptian Marble, or black-fleak'dMaj-ble, or of Rome^ or liver-coloured Marble, (of an ordinary Size,) are worth twelve or fourteen Pounds per Piece. Chimney' C H C H Chiwney-Pieces of Wood, are iilfo of different Prizes, as from ten to twenty Shillings a Piece, more or lefs, according to their Size, Goodnefs of the Stuff, and Curiofity of Workmanfhip. The Price of painting Chim- Key-Pieces : They are ufually painted by the Piece, at about two Shillings each, more or lels, according to their Magnitude, and Goodnefs of the Work. In the Year 1713 was publidi- ed a Fre'/ich Book, intitkd, La Mechanique du Feu ; or, The Art of augmenting the Effefts, and diminifliing the Expence of Fire, by M. Ganger, which was Iince publitlied in Enghjh by Dr. Defagaliers ; in which the Au- thor examines what Difpofitions of Chimneys are moft proper to augment the Heat ; and alfo proves geometrically, that the Difpofitions of parallel Jaumbs, with the Buck inclined as in the common Chimneys , is lefs fitted for receding Heat into a Room, than parabolical Jaumbs, with the Bottom of the Tablette hori- zontal. He alfo gives feveral Con- ftrutlions of his new Chimneys^ and the manner of executing or making them. Of meafuring Chimneys : Brick- layers commonly agree for build- ing of Chimneys by the Hearth ; yet they fometimcs work them by the Rod, as in other Brick- Work, and then their Method of taking the Dimenfions is as follows : If you arc to meafure^a Chim- ney rtanding alone by itfelf, with- out any Party Wall adjoin'd, then girt it about for the Length, and che Height of the Story is the Breadth ; the Thicknefs mud be the fame the Jaumbs are of, provided that the Chimney be wrought upright from the Man- tlerree to the Cieling, not de- ducing any thing for the Vacan- cy between the Floor (or Hearth) and the Mantletree, becaufe of the Gatherings of the Brcaft and Wings, to make Room for the Hearth in the next Story. If the Chimney-Back be a Party Wall, and the Wall be meafured by itfelf, then you muft meafure the two Jaumbs and the Breaft for a Length, and the Height of the Story for the Breadth, at the fame Thicknefs the Jaumbs were of. When you meafure Chimney- Shafts^ girt them with a Line round about the leaft Part of them for the Length, and the Height will be your Breadth. And if they be four Inch Work, then yon muft fet down your Thicknefs at one Brick- Work ; but if they be wrought niffe Inches thick, (as fornetimes they are, when they (tand high and alone above the Roof,) then you muft account your Ihick- nefs one Brick and half, in con- fideration of Wyths and Parget- ting, and Trouble in ScafFold- ing. It is cuftomary in moft Places, to allow double Meafure for Chimneys. For Example : Suppofe the following Figure A B C D E F G H I K L to be a Chimney that has a double Funnel towards the Top, and a double ^hzii, and is to be meafured according to double Meafure. I firft begin with the Breaft. Wall IL, ai]d the two iVngles LK C H LK and HI, which together are eighteen Feet 9 Inches; then I take the Height of the Square HF twelve heet iix Inches, which multiplied together, pro- duce 234 Feet 4 Inches, Iix Parts for the Content of the Fi- gure F G H K. As for the Square Da E^, the Length of the Brealt- Wall, and two Angles, is four- teen Feet fix Inches, and Height Da nine Feet; which multiplied together, make 130 Feet ii\ In- ches for the Content of the Part Da EL Then the Height of the next Square feven Feet, and ihe Length of the Breaft-Wall and two Angles is ten Feet three Inches; which multiplied toge- ther, produce feventy Feet nine Inches for the Content of the Square Be c d. The Compafs of the Chimney Shafts is thirteen Feet nine In- ches, and the Height iix Feet Iix Inches ; which multiplied toge- ther, produce eighty-nine Feet four Inches, fix Parts, the Con- tent of the Shafts. The Depth of the middle Fet- ter that parts the Funnels is C H twelve Feet, and its Width one Foot three Inches; which mill- HL :i.K tiplied together make fifteen Feet the Content thereof. F, I. 18 9 The Work. 12 6 225- FGHK 9 4 6 ^34 4 6 F. 9 6 X>a Y.b 130 6 18.75- 12.5- FGHK 937> 37yo 157)- Produa i34-375- 14 S Va El; 130 s F. L C H C H F. /. 10 3 7 Be Ccl 71 9 F. /. 1.^ 9 6 6 82 6 6 10 6 The Shaft 89 I 12 4 /. 3 6 The Fetter i^ 272") 1082 (3 Rods. 68) 266(3 quarters. Rem. 6x Feet. When the five Produds have been produced together, the Sum is to be doubled, and that double Sum is the Content of theO^/^z- Key in Feet, according to the double or cuftomary Meafure ; which Feet mult be reduced to Rods, as direded in reducing Feet to Rods. So the Feet in the foregoing Ivxample being reduced to Rods, (the Thicknefs being fuppofed one Brick and a hall,) it makes three Rods three quarters, and lixty-two Feet; that is, four Ryds wanting two Feet. This 10 If 7 Be Cd e Sh^ft " 11 -IS 6.S 6H7S Szso Th 89 37f 1.25- 12 i5'.oo /: /. p. FGHK 234 4 6 'Da Eb Be C< 130 6 o 71 9 o The Shaft 89 4 6 The Fetter 15- 00 The Sum 541 o o The Double 1082 o o is all the Meafure that can be allowed, when a Ch'nnncy ftands in a Gable or Side-Wall ; in which Cafe the Back of the Chimney (here not mentioned) is accounted as Part of the Gable; but if the Chimneys ftand by thcmfelves, as all Stacks of Chim- neys in great Buildings do, in fuch Cafe it is all Chimney- IVork^ and therefore ought to be mea- fured double on all Sides. The Price : Chimneys are fome- times meafnred and paid for by the Rod, like other Brick- Work; and fometime.« by theFire-Hearth, ac € H C H at fo much per Hearth, and the Price is various, from 20 to jo j. per Hearth. Mr. H-^tfj^^ fays, that building of Ojim>te\'s for ordinary Build- ings, with Architrave, Prize, and Cornifh, is worth from if to 20^. fcr Hearth, according to their Height andSubllance; and with- out Architrave and Frize, from JO to 20. He adds, that in great Build- ing'; they are ufually done by the Feet, fiz. at about 6 ^f. per Poot. They are commonly built in London^ and fome other Places, for about fifteen Shillings a Hearth ; and fome fay, they have twenty and twenty-five Shillings fcr Hearth for building in Suf- fcx, M. Ganger has given us anew Treatife of Chimneys^ and has ihewn a Way how tci build them for the moli Conveuiency. He lias flicwn you how you may readily light a Fire, if you haveitalways blaze, what Wood you (hould burn, how to warm you you on all Sides, though never fo cold, and and yet with- out fcorchiig; how always to breath frefh Air, and of what Degrees of Height you pleafo ; how to keep the Room ever free from fmoaking,aud without any Damp ; and how to put out a Fire that hascatchcd the Funnel of a Chimney in a Moment. All thefe Conveniencies dc* pend upon the Difpofitionof the Hearth, Jaumbs, and ihe Fun- nel upon an Iron or Copper- Plate, apply'd in fuch a Manner, that it leaves a void Space be- hind, through which the exter- nal Air that fliould go into thi Room, paiTes, and warms, upoi a Trap which fervcsinllead of a Pair of Bellows, uponaBafcule or Swipe, virhich is fitted to the Funnel of the Chimney ; and the particular Way of forming tht upper End of the Funnel ol fome Chimneys. A Model of a Hearth andJaKmhs for ihe Imreajt of Height. Suppofe the Space between the Extremities of the Jaumbs, taken on the Side of a Room be 4 Feet, and the Depth of the Chimney twenty Inches, which is the common Size oiChimneys j and if there are thofe which are larger or fmaller, they increafe or diminifk the Lines by which they would determine. Take a Beard, fuppofe ABj h a^ four Foot long and twenty Inches broad, whofe Sides muil be drawn by a Rule one upon another, or a liquare Draught made in the Middle of M of the Side B^, mark the Length MC eleven Inches, and fromC, mark upon the fame Side, the LeugthCG, which muft be four or five Inches long. From the Point H, draw H/', by a Rale upontheLineGH A: From the Point G, draw alfo C/, by your Rule upon the Line BM, upon the Point P, where thefe two Lines drawn by the Rule, meet as in a Centre; and from the Dllhnce PH, or PC, defcribe the Arch HC: Do the fame Thing on the other Side Mb^ in order to dafcribc the Line cha. Then I? C H C H Then, within three Inches of this rectangular Figure, trace another, as at Z, 3 Inches long, and f.vo and a halt broad. Thefe two redtangular Figures ought to anfwer to the Middle M of Cf, cut off the Draught upon the Board marked AH, C^, cha; and fo you will have your Model for the Chimney. The Great Re6langie X will ferve as a Model for the Afli-Pan, which murt be dug in the Hearth, of a convenient Depth, if you have a Mffid to have one. The imall reftangular Figure Z ferves to be a Model for a Pair of Bwilows of a new In- vention, The Hearth is to be opened here; and this Opening is to yield a PaiTigc to the Wind that comes from the Street, or fome other convenient Place, by the Means of a Funnel or Pipe con- cealed m the Floor of the Room. '^Fhis Hole or Opening is to be furnifiied with an Iron, or Copper Frame; to which isfaft- ened a fmall Trap-Door, that fhuts clofe, and lies open to- wards the Fire; the Sides of the Frame and Trap are madeflope and Bevel-wife; on the Side op- polite to the Turning- Joint or Hinge, with which the Trap- Door is fattened to the Frame, is placed a fmall Burton, that you may lift this Trap-Door with the Tongs ; and you mav put on a Button; There will be below on both Sides the Trap, a fmall P:irt of a Circle, whofe Centre mutt touch the Hinge, that the Wind may not get out another ^Vay than before, and towards tlie Fire, when the Trap -Door Vol. I. is lifted up ; and to the End it may be kept open to fuch a Height as you think proper, and yield more or lefs Wind : Two fmall Springs mult be fiillened under the Frame, each ot which muft reft upon fome Parts of the Circle, and prefs them fo, that the Trap-Door may be kept up. Let the Bottom ot the Ta- blet or litrle Board be placed pa- rallel to the Horizon, according to its Breadth, or Level thiit Way ; for it may be arched ; and it muft not be above ten or twelve Inches diftant from the Bottom of the Chimney^ to the End that the Funnel of the Chimney may have no more Breadth in that Place, If the Funnel is loofe, you muft have Languets or Tenons on the Sides, in fome Parts of the Circles, from the Top of the Jaumb to the Floor, In building or forming the Bottom of the Chimney^ fo that the Air may come into the Room hot, you muft make ufe of a lingle Copper or Iron Plate or Back made of feveral Sheets about four Feet long, and three and a half high ; furnifli'd with feveral Iron Bands, which muft be five Feet broad, and not fo high by ten Inches, as the great; apply them to it in fuch a Manner, that the firft Band may reach from the Top to with- in ten Inches of the Bottom, that the fecond may have the fame Diftance from the Top as the firft has from the Bottom; that the third be placed in the fame Manner as they firft, are reprefented in the Fitft Fi- gure. P Jt C H C H It would be convenient, ifyou Room may be augmented ordi- can,to hollow the Wall as much minifh'd, according as you part- as is neceflary, that the Back ly flop, or open the Hole, which may not be too forward; but be need be but two Inches Diame- that as it will, there mnft be ter. made, as it were, two Gutters an Inch deep in the Wall, which in:iy anfwcrtheTenons that may enter in, which are to be filled with very trcfn Mortar, and a Space mud be left between the Wall and the Back, four Inches deep. h would, perhaps, be more convenient to make a C;n'lie or Box of Iron, furnillied withTe- nons of the Dimenfions afore- faid, and to fallen it in the Bot- tom of the Ciyy.-finex ; you may alfo order as many little Cells as you pleafe, but there muft not be fewer than ten or twelve In- ches Diftance between the Te- nons ; and Matters muft be fo contriv'd, that the fecond little Cell be bigger than the fifft,and the third tlian the fecond and fo of the reft. This Box fliould have but two Openings; one at the Bottom, at D; and the o^her on the op- pofite Side above, at R.. In fr.iming the Ch'r/nney^ you muft make a Condui'r-Pipe, which muft be open to a Street or Court, and be aljout a Foot fquare; this Pipe will convey the cold Air as far as D, yet not without the Ufe of the particu- lar Liftrument at R before de- fcribed. From D, it enters into the Box, where itruns winding- ly through all the Cells form- ed by the Tenons or Lan- guets ; It grows warm there, and comes out at the Hole R, at the Corners of the Tablet ; in- fotnuch, that the Heat of the If you have a Mind to heat feme particular Part of a Room, fuppole a Perfon fick in Bed, you may appiy a Tin Pipe to this Hole, by which you may alfo convey the warm Air into ano- ther Room ; perhaps, a Leather, or Paftebonrd one may do. Lajll%\ if the Heat i^ not fuf- ficient, you may caufFthe little Cells of this Box to pafs under the Hearth, and under the Ta- blet. When once the Work de- fcrib'd is underftood, there will be no Difficulty to make it fcrve in all Pans of the Hearth, where you think it may contri- bute to increafe the Heat. But ifyou cannot poffibly be able to adjurt the little Cells in the Bottom of the Cb'tmney^ you muft content your felf to do it in the Jaumbs, under the Hearth and little Bonrd. As to the forming of the up- per i'art of the Chimney^ to pre- vent its fmoking, you muft firft obferve, that your Chhnney be not communded by any Thing; that is, that there are no Buildings about it higher than the Funnel : You muft alfo place your Fun- nels one by the Sides of another, as thecommonPradiceis. Sup- pofe that the f\innel within be thirty Inches long, and the Breadth ten, make a Ledge of two Inches, lloping underneath, quite round and within ; the Opening will be no jiiore than twenty-fix Inches long, and fix broad; divide this Length in- to C H C H to three Parts by two Partitions, each of four Inches; the lower- moftPart of which will defcend Anglewife into the Pipe; each of the three Openings will be fix Inches Square. Make three curtail'd fquare and hollow Pyramids, the Bafis of each of which within will be eleven or twelve Inches fquare, and the Height from twelve to fifteen Inches ; divide this upper Opening by a fmall Languet of two or three Inches in Height, which you are to place diffe- rent Ways: You are alfo to ap- ply and fix thefe three Pyramids near one another, over the three Openings you have contriv'd on the Top of the Funnel of the Chimney. If the Opening of the Ch'irnne'i is too fmall, which is fcarcely to be fuppofed, you muft: leiTeu the Apertures of the Pyramids , and if it be too big, you muft enlarge them, or in- ftead of three, ufe four. Thefe Pyramids may be made of Tin, Clay, or Poiters Earth, bak'd, as you do other Earthern Ware. You may fit a Cap to thefe • Pyramids, made i:i fuch a Man- ner, that being higher, ic may ferve to fufpend a Body above the Opening of the Pyramid, made in the Form of a triangu- lar Prifm, one of the Angles of which rnuft be turned towards the upper Openings of the Pyra- mids, and the Smuak gets out thro' the Sides. It will be beft to make all thofe Pieces of Tim The Swipe is an Iron-Plate, placed in fome Part of the Fun- nel of the Chimney: It fhouldbe eiaclly of the Length and Breadth of that Place, where you put it, that it may flop it exadly. To the Middle of this Swipe two Trunnions or Knobs are to be fitted, which are put into the Wall; by the Help ot which, you may fit ic where you pleafeto have it; and draw it with two two Wires that are falteaed to both Ends. This Swipe being (liuf, keeps the Heat in the Room, when the Fire is covered, and there is no Smoke: It likewife hin- ders the Smoke ot the neighbour- ing Chimneys^ to enter in, as it very often happens when there is no Fire in the Hearth: You may likewife ufe it to extinguifh ir, when a Chimney is fet on Fire, having no more to do, than to take out the Coals or hot: Embers, and (hut the Swipe. The Wood moft proper to burn, is that which is called Float- Wood; which has lefs Heat, and burns Quicker than new Wood. Float, Beech, or Bakers Bil- lets, burn fafter than the other. Green Wood will not burn fo well as dry ; it grows black in the Fire, caufes much Smoke, and is hard to be lighted. White- wood, and the Poplar, Birch, Afpcn, '^c. are the worft of all Woods to burn. If there is a Diftinction to be made between Oak, young Oaks burn and heat much, the old grows black in the Fire, makes a fort of fcaled Coal, that yields no Heat, and is foon put out. P 2 Thus G H Thus in ufing OaK for Firing, you mult chufe Billets of three or four Inches Diameter. The Oak, whofe Bark is taken off for the Tanners Ule, burns well enough, but yields very little Heat. Yoke-Elm burns well, makes a good Fire, and a good many red-hot Brands, which laft long. The bed of all Woods, is new Beech, which makes a good clear Fire, and bat little Smoke, when well ordered: it yields a good deal of Heat, and many good Embers. CHISSEL, an Inflrument much ufed in Carpentry, Joine- ry, MaConry, Sculpture, &c. Chijj'els are of different Kinds ; and have different Names, ac- cording to the different Ufes they are apply'd to. As, 1. The Former^ which is ufed in Carpentry and Joinery, firft of all before the 'Parin^^ Chijfel^ and juft after the Work is Icrib'd. 2. The Paring ChiJJ'el which has a fine fmooth Edge and is ufed in paring off, or fmoothing the Irregularities, which are made by the Former. This is not (truck with a Mallet, as the For- mer is, but is prelled with the Workman's Shoulder. 3. I'he Skcvj-Former^ which is ufed in clean ling acute Angles with the Point or Corner of its narrow Edge. 4. The Morttce-ChiJJel^xvhxch. IS narrow, but very thick and llrong, to endure hard Blows ; and 'tis cut to a very broud Ba- fil; its Ufe is cutting dccpfquare Holes in Wood tor Mortices, C H S. The Gouge \ which is a Chijfel with a round Edge, one Side of which ferves to prepare the Way for an Augre; and the other to cut fuch Wood aS is to be rounded, hollow'd, ^c. f. Socket-Chijfeh \ which are chiefly ufed by Carpenters, ^c. having their Shank made with a hollow Socket at Top, to re- ceive a ftrong Wooden Sprig fit- ted into it with a Shoulder. Thefe Chijj'els are alfo diftin- guifh'd according to the Breadth of the Blade, into Half-Inch Chijfels^ quarter of an Inch ChiJJels^ ^c. 7. R'ppitJg ChiJJ'el ; which is 1 Socket Chijfel^ an Inch broad, ha- ving a blunt Edge with no I3alil to it, for ripping and tearing two Pieces of Wood afunder, by for- cing in the bliint Edge between them. CHOIR, is that Part of a Church, Cathedral, ^c where the PrieflSjChorifters, and Singers fit. ^ TheC^o/V is diflinguifli'd from the Chancel, or Sanduary, where the Communion is celebrated; as 'alfo from the Nave or Body of the Church, where the People aiTifl. CHORD [in Geometry] is a Right Line connecting the two Extreams of an Arch ; or it is a Right Line terminated at each Extream in the Circumference of a Circle, without pafTmg through the Centre, and dividing the Cir- cle into two unequal Parts called Segments, as the Line A Bin the Figure. The I' M I'/a/^' JZZ c c A / s^^ M C G B /if:'.. J J '' 1 ^ 1 L..---\h i 1 ^ 1 tl A C I C I The Chord of an Archh a Right Line drawn from one Extremi- ty Jof an Arch to the other; cal- led alfo the Subtenfe. To make a Line of Chords for the Menfuration of the Quantity of jifjgles. Firjl^ Draw a Right Line at Pleafure, as AB, and from any Point, as D, raife the Perpen- dicular DN, and "compleat the Quadrant DNBof any given Magnitude. /?^ ,r^N ^X m " s. \ N *■ cL \ \ \ /bX '- '• . i '■ x i) Secondly^ Divide the Arch N B into ninety equal Parts, and then fetting one Foot of the CompafTes in B, and extending the other to the feveral Divifions of the Arch, transfer them to the Line AB, as 'the feveral Divifions of the Arch, and tranf- fer them to the Line A B, as the feveral pricked Arches L 10,20, 30, 40, ^f. exhibits ; which will compleat the Line of •Chords requir'd. N.B. The larger thefe Scales are made, the better they are for Pra£tice. CHURCH, is defined by Da- .•viler^ to be a large Veffel extend- ed in Length, with Nave, Choir, ^Ifles, Chapel, and Belfry. /I Simple Church, a Church fo called, having only a Nave and ^ Choir. A Church with IJles is one which has a Row of Porticoes iii Form of Vaulted Galleries, with Chaplcts inthePourtour. Church in aCreck Crofs is one the Length of whofe Crofs is equal to that of the Nave; fo called, becaufe mofl: of the Greek Churches were built in this Form. Church in a Latin Crop^ is one whofe Nave is longer than the Crofs, as mod of the Gothick Churches. Churchin Rofondo, one whofe Flan is a perfed Circle, in Imi- tation of the Pantheon. CIMA, orSIMA, a Member or Moulding; called alfo Cy- matium, and Gula : Which See. CIMBLY. See Pedestal. CILERY, a Term in Archi- te6lure, fignifying the Drapery or Levage that is wrought upon the Heads of Pillars. CIMELLARC, in Archi- te6lure, is a Veftry, or Room, where the Plate, Vclbnents, and other rich Things belonging to the Church, are kept. CINCTURE, ? i.e. a Girdle CEIN TURE, S in Architec- tefture, a Ring, Lift, or Orlo, at the Top and Bottom of the Shaft, at one End from theBafe, and at the other from the Capi- tal. That at the Bottom is parti- cularly called /ipophyges, as if the Pillar took its Height from it ; and that at Top, Colarin, or Collar, or Colicr^ and fometimes Annulus. The CinSlure is fuppofed to be in Imitation of the Girts or P 3 Ferrils, C I Ferrils, which where ufed by the Anticnrs to ftrengthen and prc- fcrve the priir/itive Wooden Co- lumns. CIPHER, ^one of the Nii- CYPHER,S "1^1.^' Charac- ters or Figures, in this Form o. The Cypher, in itlelf, implies a Privation of Value; but when placed with other Chara£lers on the Left Hand of it, in the com- mon Arithmetick, ic fcrves for an^meiiting each of their Values by^ten; and in Decimal Arith- metick, leflens the Value of each 1' igurc at the Right there- of in the frme Proportion. CIRCLE, is a plain Figure coniaiii'd under one Line, which is called a Circumference, unto which all Lines drawn from a Point in the Middle of the Figure, call'd the Centre, and filling upon the Circumte- rence of ir, are nil equal the one to the other. The Circle con- tains more Space than any plain Figure of equal Compafs. Problem I. h^'.h the Diame- ter and Cii'cumfereiice to find the Area. T'he RULE. Every Cirde is eq lal to a Pa- rallelogram, whofo Lcngih is z= to half th-? Circumference, and the Breudth equal to half the Diameter; therefore multi- ply half the Diameter, and the Product is the Area of the Cir- cle. Thus if the Diameter of a Circle (chat is the Line drawn crofs the Circle thri>ugh th.e Centre,) be 22. 6 and iftiieCir- cumierence be 71, the Half of 71 is 35". f. and the Flalf of 22.6 is 1 1.3, whicli multiplied toge- ther, the Produd is 401. ij", which is the Area of the Circle. CI 35-5' HalfCircumh 11.3 HalfDiamet. 1065' 25-5- 401.15' Demonstration. Every CWcUvca^ht conceiv'd to be a Polygon of an infinite Number of Sides, and the Se- midiameter muft be equal to the Perpendicular of facli a Poly- gon, and the Circumference of the Circle equal to the Periphery of the Polygon ; therefore half the Circumference multiply'd by halt the Diameter, gives the Area as aforefaid. Or (with P. Ignatius Gcflort Pm-Jics,) every Circle is equal to a Redangle Triaii^le, one of whofe Legs is the Radius, and the other a Right Line equal to the Circumference of the Circle: For fuch a Triangle will be greater than any Polygon in- infcribcd, and lefs than any Po- lygon circumfcribed (by the 24th, 25'th, 26th, and 27th Articles of the For.rtb Bookof his Elements of Geometry'^ C I C I Geometry) and therefore mud be equal to the G>f/- cle, as EB, DB, G B, CD, 4. A Segment, Sc6lion, or Portion of a Circle^ is a plain Fi- gure or Superficies contained under a Right Line (which is lefs than the Diameter.) and Part of the Circumference, cither greater or lefs than a Se micircle. As for Example: The Right Line H I cutting off tlie upper Part of the Circle HDI, does tiiereby divide the whole Grc.V into two unequal P^rts, which are called Segments, Sedions, or Portions; as HDI, the lefTer contained under the Line H 1, and Part of the Circumference HDI, which is lefs rh.m the Semicircle ADC and HCI un- der the Line HI, and the re- maining Part of the Circumfe- rence HECI, which is greater than the Semicircle ECG. )-. The fourth Part of a Circle^ as EBD, or DBG, cTf. is cal- led a Quadrant, being contain'd under tvvoSemidiameters(which are called the Sides) and the lourth Part of the Circumference, which is called the Limb of the Quadrant. 6. A Seftor of a Circle is a Figure contained under two Se- miuiametcrs, (as BF and BE,) and Part of the Circumference FE contain'd between the Cir- cumference of every Circle is fuppofed to be divided into 360 equal Parts, which are called Degrees; therefore as a Qua- drant is one fourth Part of a CircU\ the Degrees contained in it, are 90 ; and a Semicircle therefore contains 180 Degrees. 8. Every Degree of a Circle is fuppofed to be fubdivided in- to 60 equal Parts, which are called Minutes ; therefore one Fourth of a Degree contains if Minutes, half a Degree 30 Mi- nutes, three Fourths of a Degree 45- Minutes, ^c. 9. All Right Lines (lefs than the Diameter,) which divide Cir- cles into Portions as HI arecal- led Chord-Lines, or Subtenfe Lines,0f thofeArches,which they lb fubtend ; becaufe they fubtend both SegiTients, that is, the Line Hi is common as well to the Segment HE CGI, as to the Segment iHD I. 10. Thofe Parts of the Cir- cumference of GW/^J, which arc contain'd between the Extreams of Chord-Lines, as HDI, or EDG are called Arches, or Arch-Lines. II. The C I C I 11. The Complement of an Arch to a Quadrant or 90 De- grees is fo much as an Arch wants of 90 Degrees : As for Example, the Complement of theiXrchGI is the Arch lD,and the Complement of the Arch H E is HD; alfo in Number of Degrees, the Complement of 40 Degrees is yo Degrees ; becaul'e that 40 Degrees is lefs by 5-0 Degrees, than 90 Degrees: So likewife is 40 Degrees the Com- plement of 5'o Degrees, and 10 Degrees the Complement of 80 Degrees ; and the like of any other Quantity of Degrees what- foever. 12. The Complement of any Number of Degrees and Mi- nutes to 90 Degrees is the Quan- tity of Degrees and Minutes which are wanting to make their Sum 90 Degrees compleat. As for Example: The Com- plement 27 Degrees 16 Minutes, being fubtradted from 90 De- grees, the Remainder will be 61 ' degrees, 44 Minutes; and the like of any other Quantity. 13. The Excels of an Arch, greater than a Quadrant, is fo much as the faid Arch exceeds 90 Degrees. As for Example : The Excefs of the Arch EDI is the Arch D I ; becaufe when the Arch E D (which is a Quadrant) is ta- ken from EDI, the Remainder is Dl, which is the Excels more than the Quadrant EHD. 14. The Complement of an Arch lefs than a Semicircle, is fo much, as that Arch wants of a Semicircle or 180 Degrees. As for Example : The Arch % H is the Complement of the ArchHDG: So likewife is CEH the Complement of the Arch HD, and HDG is the Complement of the Arch H E. To divide the Circumference of the Grcle CAED into 360 equal Parts or Degrees, by wiiith the Quantities of all Angles are meafured : t'trfl^ Defer ibe aC/r- cle of the given Magni;ude, as AC ED, and draw the two Dia- meters C E and AD at Right Angles, to each other through .A. its Centre; then will the Circum- ference of the Circle be divided into four equal Parts, at the Points CAED, and confe- quently the Circle into four Quarters, each of which is cni- led a Quadrant, as A B C, or A BE, l!fc. Secondly^ Make A 3 and E6 equal to the Radius B E, or A B, then will the Arch A E be divi- vided into three equal Parts, each = 30 Degrees. And here obferve. That as this Divilion of the Arch AE was made by the Radius AB be- ing fet from A to 3, and from E to 6; therefore it is plain, that as thereby the Arch is divided into three equal Parts, each con- taining a Third of 90 Degrees, the Radius AB mult =60 De- grees of the Arch AE. There- C I C I Therefore hereafter, when the iladius of a Circle is mention'd, thL- Arch of 60 Degrees is to be iinderllood by it at the fame Time. 7^/W'y, With the Compaffes flivide E3, 36, and 6 A, each into three equal Parts ; and each of thole Parts into ten equal Parts (chere not being yet any Geomeincal Method of di- viding an Arch otherwite,) then will the Quadrant A E be divi- ded into 90 equal Parts ; and confequentiy if the other three Quadrants ACB, CBD, and BED, be divided in like man- ner, the VVholp will be divided into 360 equal Parts, as required. it is by the Number of Degrees contained in every Arch of an Angle, that its Quantity is niea- fured. Thus the Quantity of the Right Angle ABC is 90 De- grees, the Acute Angle 6BE 60 Degrees, and the Obtufe Angle CB6 120 Degrees; that is the the Arch cr Quadrant CA 90 Degrees, and the Arch A 6 30 Degrees ; which taken together, ai c = 1 20 Degrees. Hence 'tis plain, that all Acute Angles contain lets than 90 De- grees, or a Right Angle, and all Suppofe the Circle ABI to be fourteen Feet Diameter, then I N A C G Obtufe Angles more than ninety Degrees, and lefsthan a hundred and eighty Degrees, or tvi'o Quadrants, which taken toge- gether, are = to a Semicircle ; therefore a Semicircle contains a hundred and eighty Degrees. If from the Points, 8, 7, 5-, 4, 3, 2, I, of the Quadrant there be rigiu Lines drawn to the Centre B; and if on the Centre B. another Circle be de- fcrib'd, as the Circle FHGK, the Quadrant HG will be divi- ded by the Lines 8B, 7B, 6B, l^fc. unto the like Number of equal Parts or Degrees, as the Quadrant A C ; wherefore 'tis plain, that all Circles^ either great or fmall, have their Cir- cumferences alike, divided into three hundred and iixty equal Parts or Degrees, and each of thofe Degrees are fuppofed to be again divided into fixty equal Parts called iMinutes. Every Circle is nearly equal to a Parallelogram, whofe Length is equal to half its Cir- cumference, and Breadth to the Semidiametcr: Or every Circle is equal to the Parallelogram, whofe Length is equal to the Diameter, and Breadth to eleven Fourteenths thereof. fay, that the Oblong BHIM, whofe Length BH is equal to ^ 7 S j& L 74" 22, the Half of the Circumfe- Breadth HM, to the Semi^; reucc of the Circle A EI, and diameter BL, is equal to the Pa- rallelograirB C I C I rallelogram ACIK, whofe Length CK is equal to the Di- ameter A I, and the Breadth to eleven Fourteenths thereof. For HM, which is equal to feven Feet, being multiply'd in- to B H, twenty-two Feet, the Produd or Area thereof is one hundred and fifty-four Feet. And again, A I the Diameter fourteen Feet, being multiplyed into A G T^: thereof, viz. eleven Feet, the Produftor Area there- of is one hundred and fifty-four Feet, as before. Therefore thofe two Paral- lelograms are equal, and either of them nearly equal to the Area of the Grf/^ A Bl. N.B. /« the preceding Figure^ there Jho7ild have been a Cir- cle defcrib*d on B, as a Cen- tre^ whofe Diameter is B A. Corollary i. Hence appears the general Rule for the Menfura- tion of Circles ; to multiply half the Circumference by half the Diameter. ^ Corollary 2. Hence every Semi- circle is nearly equal to the Ob- long or Parallelogram, whofe Length is equal to half the Curve or Arch, and Breadth to the Pvadlus or Semicircle; That is, the Semicircle AE I is nearly equal to the Parallelo- gram B HIM, whofe Length I M is nearly equal to half the Arch Line A EI, and Breadth H M, to the Semidiameter BI ; for the Parallelogram A CBF is equal to half the Paralellograrn ACiK. ^ Corollary 3. Hence it appears, that every C^ircle is nearly equal to that Rfght-angled Triangle, ivhofe Baf« is equal to its Circum- ference, and perpendicular to the Semidiameter thereof. For if the Side A Q of the Pa- rallelogram A QBH be conti- nued to X, and made equal to the whole Circumference AE2I, and the Hypothenufe BX being drawn, I fay, that the Triangle B A X is equal to the Parallelo- gram AQBH. For as AX is equal to twice AQ, and AB is perpendicular to AX, therefore QX the Side continu'd will be equal to BH, which is parallel to AQ, and confequcntly Q H will be bifec- ted in P by the Hyputhenufe BX. Now feeing that QX is equal to AQ, and PX to PE, and the Angles X OP, and BHP, both right-angled ; therefore the Tri- angle AXB is equal to the Pa- rallelogram AQBH; becaufe the Triangle QXP is equal to the Triangle B PH. Theorem. Every Se6lor of a Circle is nearly equal to a Paral- lelogram, whofe Length is equal to the Semidiameter of the Cir- cle^ and Breadth to half the Curve or Arch Line thereof; or whofe Length is equal to half the Semidiameter, and Breadth to the whole Curve or Arch Line thereof. Let NM X be the Sedor of a Ctrch\ whofe Arch Line NX is equal to five Feet, and Semi- diameter N M to feven Feet, I fay, that the Oblong A N N M, whofe Length is equal to the Semidiameter N M, and Breadth, to half the Arch NX, is equal to the Oblong HBVM, whofe Length V M is equal to the whole Curve N X, and Breadth, to half the Semidiameter BM. For C I CI A ^ - H — - «»«T^'" o" " ::.. V \ It jvt B X For AN, -which is equni to half the curved Line NX, z>iz. two Feet; one half being mul- tiply'd into fcvcn Feet, the Se- midiameter, the Area or Pro- dud will be feventeen one half: So likewife H B, which is equal to ihe whole Curve NX, viz. five Feet, being mukiply'd into half the Scmidiamcter B M, three Feet and a half, the Area or Pro- dud will be alfo feventeen and a half, as before. • For ns NX is equal to HB, and H V equal to BM fo alfo is A R equal to N M, and A N to lialf NX, and as all the An- gles of the three Parallelograms ANRM, OBRM, HOVR, are all Right Angles, and their refpcdivc oppofite Sides equal; therefore the two Paralleloe;rams ANOB, and OBRM, which compofe the Parallelogram A N KM, made by the Half Arch mukiply'd into the whole Semi- diameter, is equal to the two Parallelograms OBRM, and -HOVR, which compofe the Parallelogram HBVM, made by the whole Arch mukiply'd into half the Semidiameter Corollary. Hence *tis evident that the Axis of any Circle^ Semi- Circle, Quadrant, orSettor, may be found by this one general Rule, z- cle will be .0795-8 ; then the Square of i is i, and the Square of 71 (the Circumference of the former Circles) is 5-041 ; there- fore it will be Sq^. Cir. Area. Sq. Circumf. As 1 : .0795-8 :: 5-041 5-041 795« 3183Z 397900 401.16278 Area. As 88 Or thus : 7 :: 5-041 7 $8) 35-287(400.98 Area. 35-2 0870 704 76 Or as 1420 . II? ;: P4I : 401.15-. Problem C I Problem VI. By having the Diameter^ to find the Side of a Square that is equal in Area to that Circle. If the Diameter of a Circle be I, the Side of a Square equal thereto will be 8862 : There- fore As 1 : 8862 22.6 17724 177^4 C I : 22.6, the Diameter, 20.C2812 The Side of the — Square AC. Let the Diameter of the Circle EF, or GH, be 22.6 (as before) to find the Side of the Square of the Side AC, AD, e^f^r. If .8862 be multiplied by 22.6, the Produft will be 20.02812, which is the Side of a Square equal in Area to the Circle given ; for if 20.02812 be multiplied fquare-wife, that is, by Jtfelf, i' will produce 40i.i2f5'907344i which is nearly equal to the Area found in the laft Problem. You may find the Side of the Square equal, by extraSing the Square Root out of the Area of the given Circle, Q2 401. 1 J) C I G I 4o'i.i5-)20.02S7295' Side of the Square. 4 4002)01.15-00 40048)349600 320384 29216 28034 1182 801 360 21 20 By this Method of extrafting the Square Roor of the Area, you may find the Side of a Square equal to any plain Figure, regular or irregular. Problem VII. By having the Circuynfereace, to 'find the Side of the Square equal. If the Circumference of a G>- cle be I the Side of the Square equal will be .2S21 : Therefore : 71 TheCircumf. The Side of the Square. 2C.0291 Problem VIII. Having the Diameter., to find the Side of a Sqftart., ixihich may be inscribed in that Circle. If the Diameter of a Circle be T, the Side oi the Squara in- fcribcd will be fore .7071 : Thcre- As .7071 :: 22.6 226 42426 14142 14142 I5-.98046 The Side EG in- fcrib'd. Or if you fquare the Semi- Diameter, and double that Square, the Square Root of the doubled Square will be the Side of the Square infcribed: For (by Euclid \. 47.) the Square of the Hypothenule E G is equal to the Sum of the other two Legs EO andOG. "•3 C I C I "•3 "•3 " 339 113 113 fip-i 127.69 The Square of EO, which is doable, bccaufe 1 EO^OG. 25-5'. 38 Ci5".98 Root; which is the Side of the Square; 309)30^8 2781 3188)25-700 25-5-04 iq6 Problem IX. Having the CircumfereHce^ to find the Side of a Square ^ivhlch may be infcrihed. If the Circumference be i , the Side of the Square infcribed will hz .21^1 : Therefore As : I .225-1 :: 71 71 225-1 inn i5'.982i The Side of the Square EG. Becaufe that in each of the four laft Problems, viz. Vlth, Vllth, Vlllth, and IXth, there is a Pro- portion laid down, it will beeafy to work them by Scale and Com- paiTesi for if you extend the Compafles from the firft to the fecond, that Extent will reach from the third to the fourth : As in the laft Problem, where the Proportion is as 1 to .2251, fo is 71 to the Side of the Square i5'.982i. Here extend the Compafles from I to .225-1 ; that Extent will reach from 71 to I5-.98; and fo of the reft. But the fifth muft be wrought like the fourth, thus : Extend the Compafles from i to 71 ; and that Extent turn'd over the fame Way from .0795-8, will fall at the laft upon 401.15. Problem X. Having the /Jrea^ to find the Diameter. If the Area of a Circle be i, the Square of the Diameter there- of is 1.273 i*. Therefore Q3 1!^^*' C I C I Area. Sq.'D'iam. Area. As I : 1.2732 :: 401.15- 4CI.IJ- 63660 12732. 12732 5-0928 5-10.744180(22. 5-99 The Diameccr- 4 42)110 84 445)2674 222f 4509)44941 40581 45189)436080 406701 ^9379 By Scale and Compajfes. Extend the CompafTes from 1 to 1.2732; that Extent will reach from 401.15 to 510.74, eff. Then divide the Space between I and 5'io.74 into two equal Parts, and you'll find the mid- dle Point at 22.6. Or you m.ay divide the Space upon the Line of Numbers, be- twcerj 401.55 and .7854 into two equal Parts ; and one of thole Parts will reach from i to 22.6, the Diameter fought. Problem XI. Having the Area^ to find the Circumference. If the Area of a Circle be i, the Square of the Circumterence will be 1 2. 56637 : Therefore Area. C I C 1 Area. Sq.Circumf. Area. As I : 1.25-6637 ••: 40i.if. 401.15- 628318^ 125-6637 125-6637 5-026 5-48 Circumf. 5-040.999325'jo (70.9990 ^ooE. 49 109)14099 12681 14189)141893 127701 141989)1419225- 1277901 1413245-0 12779901 1 3 5-2 5-49 By Scale and Compajfes. ■ Divide the Space between 401.15- and .07958 upon the Line, into two Parts ; one of thofe Parts will reach from i to 71, the Circumference fought. Problem XII. Haviag the Area^ to find the Stde of a Square infcribed. If the Area, of a Circle be i, the Area of a Square infcribed within that Ctrck will be .6366 : Therefore Q4 As C I C I As I 401.15- .6366 .6366 240690 240690 120345- 24C690 2'5'5'-372.o9o(ij^.98 Roots ; which is the Side of I the Square fought. 25") ijf 125- 309) 3037 2781 3188) 2^620 25504 1 1 690 5 $ ThefameReafonmaybe given for the lart Proportion, thac was given belbre f ir the Proporiiim of Crdts io the Squares of their Diameters and Circumferences ; for nor only t^e Squares of the Diameteis and Circumferences are in Proportion to the Circles they belong to, but .lUb Figures inl'crib'd or circumfcrib'd, have the Squares of chcir like Sides proportional' tq the Circles they are infcribr;d in, or circumfcribed about, and alfo"io the Figures themfelves : The Square of any Side of one Figure, as the Square of the like Side of another iimi- 3ar Figure is to the Area thereof; as may be found prov'd at large in Euclid^ Sturmius^ Mathejis EuHcleata^ and other Authors. By Scale and Compares. Extend the Compaffcs from i to 401.15'; that Extern will reach from .6366 to 25'5'.37; the half Space betveenthat and i, is at 15.98, the Side of the Square. Problem XIII. Having the SJe of a Square^ to find the 1)'tameter of the cir- cnmfcr thing Circle. If the Side of a Square be i, the Diameter of a Circle^ that will circumfcribe th.it Square, will be 1. 4142 : Therefore As I : 1. 4142 :: I5'«9S ■ 1^98 113136 12727S 70710 14142 22, 5-98916 The Diameter 1 fought. Bf C I By Scale and Compajfes. Extend the Compaffes from i to 1. 4142, and that Extent will reach from 1^.98 to 22.6, the Diameter fought. Problem XIV. Having the Side of a Square^ tO find the Diameter of a Circle equal. If the Side of a Square be i, the Diameter of a Circle^ e-qual thereto, will be 1,128 : Therefore Side. iDiam. Side of a Square, As I : 1. 128 :: 20.0291 1128 C I SideSq. Clrcnmf. Side Sq. As I : 4.443 : : 1 5". 98 1 5 •98 39987 22217 4443 70.99914 Circumference. 1602328 4005-82 200291 200291 22.5-928248 Diamet. By Scale and Compajfes. Extend the CompalTes from i As i : 3.5'45'- to 1. 128, and that Extent will reach from 20.0291 (the Side of the Square given) to 22. 6, the Diameter of the Grcle fought. By Scale and Compajfes. Extend the Compaffes from i to 4.443, ^"d fhat Exent will reach irom I5-.98 to 71, the Cir- cumference. Problem XVI. Having the Side of a Square.^ to find the Circumference of a Circle that will be equal there- to. If the Side of the Square be i, the Circumference of a Ctrde that will be equal thereto, fliall be 3 5-45- : Then 20.0291 3-f45' Problem XV. Having the Side of a Square.^ to find the Circumference of the circumfcribing Circle. If ^the Side of a Square be r, the Circumference of a Qrcle., that will encompafs that Square, V/ill be 4.443 : Therefore 100145-5' S01164 100145-5- 600S73 7 1 .003 1 f 95- Grcumf By Scale and Compaffes. Extend the Compaffes from i to 3.545', and that Extent will reach trom 20.0291 to 71, the Circumference. "ia jftiu III C I C I In feveral of the foregoing Problems^ where the Diameter and Circumference is required, the Anfwers are not exadtly the fame as the Diameter and Cir- cumference of the given Circle \ but arc fometimes too much, and fometimes too little, as in the two lall ^Problems; where the Anfwers in each fhould be 71, the one being too much, and the other too litde. The Reafon of this is, the fmall Defecl that happens to be in the Decimal Fradions, they beinj; fometimes too great, and Ibmetimes too little; yet theDe- feft is fo fmall, that it is need- Iti's to calculate them to more Exaftnefs. Every Circle is fuppofed to be divided into 360 Degrees. l^he Area of a Circle is found by multiplying the Periphery by the fourth Part of the Diameter, or half the Periphery by half the Diameter. The Area is alfo found by finding a fourth Proportional to 1000.78^, and the Square of the Diameter; or to 452.35-5', and the Square of the Diameter. Circles^ and limilar Figures in- fcribcd in them, are always as the Squares of the Diameters : So that they are in a duplicate Ratio of their Diameters, and therefore of their Radii. KCircle is equal to a Triangle, whofe Bafe is equal to the Peri- phery, and its Altitude to the Rnd ius ; therefore Circles are in a Ratio compounded of the Pe- ripheries and the Radii. CIRCULAR, any Thing that h defcribed or noved in a Round; as the Circumference of a Circle^ or the Surface of a Globe. Circular Lines are fuch (Iraight Lines as are divided trom the Divilions made in ttie Arch of a Circle; as Sines, Tangents, Se- cants, ^c. Circular Numbers are fuch, whole Powtirs end in the Roots themfelves ; as 5-, whofe Square is 25, and Cube 125'. CI RCUMVOLUTIONS. The Torus of the Spiral Line of tne Ionic Volute. CIRCUS, a large Building, eitlier round or oval, uiea for the exhibiting Shews to the People. Th& Roman Circus was a large Place or Square, archea at one Ena, encompafled wirn Porii- coes, and furaiii;ed with Rows of Seats, placed afccndiug over each other. CIS l^ERN, is properly uted for a fubcerraneous Rcf.Tvoir of Rain-Water; or a Velfei mjde to ferve as a Receptark lor Rain or other Water, tor the ueccfla- ry Ufes or a Family. If you would make your Ci- jlerns under the Houfe, as : Cel- lar, which is the belt Way to preferve Water for culinary Ufes; then lay the Brick or Stone with Terra?, and it will keep Water very well, Qr you may make a Cement to join your Brick cr Stone withal, with a Compofition made of flacked lifted Lime and Linfeed Oil, tempered together with Tow or Cotton- Wool]; The Bottom fhould be covered with Sand, to fweeten and pre- ferve \X. C I C I Or you may lay a Bed of good Cifterns^ has a very diTagreeabfe Clay, and on that lay the Bricks 'Sialic, and very often Itinks. As for the Floor ; then raifc the Wall round about, leaving a convenient Space behind the Wall to ram in Clay, which may be done as faft as the Wall is raifed : So that when it is fi- for thofe Rains that fill during the Autumn, Spring and Winter, when the Weather is not vio- lent ; thefe, fay they, will do. A.nd in all fine Weather, they erteem the fmall Rains that fall nifhed, it will be a Ciflern of in the Month of May^ which Clay walled with Brick; and be- Ihouid carefully be faved, to be ing in a Cellar, the Brick will the bed, as being the purell and keep the Clay moilt, (although it lightcft, and even purify the Wa- fliall fometimes be empty of ter they found in the Ciftcm. Water,) that it will never crack. As to the Way of making Mr. U^orl'idge fays, he has Clflerns^ that is left to the Ariilt known this to hold Water per- skilled that way ; only- it may fe6lly in a (hady Place, though be obferved, the Walls fhoruld not in a Cellar. be good, and built to advantage, Thus in a Garden, or other for fear the Water fhould be lolt; Place, may fuch a GJtem be that the Infide (liould be well ce- made, and covered over, the Rain - Water being conveyed thereto by declining Channels mcnted, efpecially in the Angles, without any NecefLty of doing the fame by the Arch or Roof, running to if Alfo in or near through which the Water cannot Koufes, may the Water that falls pafs. As to the Bignefs of the from them, be conduced there- Cijier-/j^ that depends upon the to. Fancy of the Perfon, Authors fpeak of a Gflem at The Manner of bringing to- Coiiftanttnople^ the Vaults of gethcr Rain-Warer, is of Ch*.a- which are fupported by two nels made of different Materials, Rows of Pillars 212 in each fixed to the Edge of the Roofs Row, each Pillar being two of Houfcs, which convey the Feet in Diameter. They are planted circularly, and in Radii tending to that in the Centre. There are fome Perfons very fcrupulous about thefe Waters, which are received in Ciflerns ; for they pretend that they are Water into a final 1 Bafon made of Lead or Tin, in the Midft of which, there is a Hole through which the Water paffes into a Pipe that is there ; and which, before it enters into the CJiern^ helps it to fall into a Stone jiot all good, without Diftinc- Trough made on purpofe near tion ; that Rain which falls in the Cijlern. 9 fmall Quantity duruig Heats, This Trough is placed to re- and the great Rains which fall ceive the Rain that falls from prefently after great Droughts, the Roofs of Houfes, from ;ire reckoned in the Number of whence it runs into the GJfern ; thofe that are bad : And thence but, as it has been obferved be- it is, they fay, that the Water fore, 'that there is a Difference Tfirhich is fometimes taken out of to be made between the Rains thftt C L C L that fill, and which are received into thcle Conveyances, without DiRiii6tion, it is ni-cellary you Ihould know how to fave thofe that ar^ good and whulefome, and get rid of the relt; it mult be by the Means of this Trough, which has a Hole in th. Bot- tom, in a Corner, on that Side where the molt Declivity appears. This Hole muft, at the Time you judge it convenient to fave the Water, be (topped, to the End, that the Trough com;ng to be tilled up to a c tain Mace, where there is a Grace on the Side Oi the C/IcrHj it may fup- ply a Pallage for the inclofed Water to tall fn'O the Gflcrn ; and when, on the contrary, they do not value the Rains that fall, they only leave thai Hole open, fo that fo fall as the Water comes into the Tiuugh, lb Lit it runs our. There are thofe who do not ufe any fuch I'rough as this, but fuffcr the Rain to fall with- om- any D'Hindion into a fubter- rancous Place buiit higher than the C/jhrn, in which they put fome River Saiid, pretending that the Water which pafics thro' is purged of all ill qual'ties it may hjive ; and that confequent- ]y the W*{er ,;hey take out of th(iic Cijlenfs ^IQ drink, ouglu to be extrcaiTily good. CLAIR OBSCURE ? . CHIARO SCUR0 5 '" Puiniiiig, is the Art of diftribucmg fo Advantage the Liglits and Shades of a' Piece ; both with Regard ..to the eafuig the Eye, and the' Elfe6l of the whole Piece. Thus, when a Painter gives his EiL'ures a iL^ong Relievo, loofens them from the Ground, and fets them free from each o- ther by the Management of his Lights and Shades, he is faid to underdand the C'/air Ohfcure. The Chlr Obj'cure makes one of the grtacelt Divitions, or Branches of Painting ;.theWholc of a Pi6ture being refolvable in- to Light and Shadow. The Dodrinc of the Clair Ob- fcure^ may be brought under the fo]lowii]g Rules : L'tght may be coniidercd either, ly?, in regard 'to itfelf; 2-//)', in regard to its Effeds; g^V, in re- gard to the Piuce wherein it is diffufed; 4^/^/)', in regard to its Llfl", For the firft Light is either na- tural or artificial. Natural L\ght comes either immediately from the Sun, which fs brisk, and its Colour various, . acccrding to the lime of the Day ; or it is that of a clear Air, through which Light is fpread, and whofe Colour is a lirtle bluifii; or a cloudy Air, which is darker, yet rcpiefents Objects in their genuine Colours, witli Eafe to the Sigiit. Ai'iificial Li'Jjt: proceeds from Fire or Fiunie,and tinges ihe (. )b- jett with its own CoiiJiir; but the Light It projeds ivVdry har- row, and confined. For the fecond: The Effrfts' of Light are either princip;.!, as when the Rays fall perpendicu- larly on the Top of a Body, without any Interruption ; or glancing, as when it ffides along Bodies; or fecondary, \Vhich is for Things at a diltance. 3. For the Place: It is either the open Campaign, which makes Objed:s appear with great Soft- nefs ; C L nefs; or an inclos'd Place, where the Brightnefs is more vivid, its Diminution more hafty, and its Extremes more abrupt. 4. For the U fe or Application : The Light of the San is always to be fuppos'd without, and over- againll the Picture, that it may heighten the foremoit Figures ; the Luminaries themfclvcs never appearing, becaule the bcft Co- lours, can't exprefs them. The chief Light to meet on the chief Group, and as much as polTible, on the chief Figure of theSubjc6t; the Light to be pur- fued over the great Parts, with- out being crofs'd or interrupted with little Shadows. The full Force of the princi- pal Light to be only in one Part of the Piece; takihg care never to make two contrary Lights: Not to be fcrupuloully confined to one univerfil Lighr, but to fuppoie other accellary ones ; as the opening of Clouds, fjfc. to loofen fome Things, and pro- duce other agreeable Effedls. Laftly, The Light to be diffe- rent, according to the Quality of I'hings whence it proceeds, and the Nature of the Subjcds which receive it. As for Shadows, they are di- ftinguifhed, 1. Into thofe form'd on the Bodies themlelves by their pro- per Relievo's. 2. Thofe made by adjacent Bodies ; thofe that make Psrts of any Whole ; and the different Eftecls, according to the Diffe- rence of Places.. For thefirft: Since the different Effedls of Lights only appear by Shadows, their Degrees mull be well managed. C L The Place which admits no Light, and where the Colours are loil, muft be darker than any Part that has Relievo, and dit- pofed in the Front. The Reflex or Return of Light, brings with it a Colour borrow- ed Jrom the Subjc6l that refijds it ; and flits off at a greater or lels Angle, according to the Si- tuation ot the reflecting Body, with regard to the lumnous one. Hence its Effi.£l:s mull be diffe- rent in Colour, and in Force, according to the Difpofition of Bodies. Deepenings which admit ndt'^ of any Light, or reflex, muft never meet on the Relievo of any Member of any great ele- vated Parr, but in the Cavities or Jo'nts of Bodies, the F<.ilds of Draperies, ^c. And to find Occanons for introducing great Shadows, to ferve for the Repofe of the Sight, and the loofening of Things, indead of many little Shadows, which have a pitiful Effeft. For the fecond : The Shadows made by Bodies, are either in plain or fmooth Places, or on the Earth ; wherein they are deeper than the Bodies that oc- cafion them, as receiving Icfs reflex Light; yet fill 1 diminilh, as they depart further from their Caufe, or on the neighbouring Bodies, where they are to fol- low the Form of the faid Bo- dies, according to its JVlagnituce and its Pofuion, with regard to the Light. For the third : In Shadows that have Parts, the Painter mult obferve to take for a Light in t^ fhadow'd Place, the Teint "or Luftre of the light Part; and, on c L C L on the contrary, for the Shadow in the lightened Part, the Teiiit or Lulire in the Shadow : To make an agreeable Allemblage of Colour, Shadow and Reflex in the (hadowed Part, but with- out interrupting the great Ma(- ie£ of Shadows; to avoid form- ing little Things in the Shadow, as not being perceiv'd, without clofely look'd at; and to work, as it were, in the genera), and at one Sight ; never to let the ftrong Shadows againil the Light, without fofteniiig the harlhCon- traft, by the help of fome inter- mediate Colour ; though the Mafs of Light may be placed either before or behind that of the Shadow, yet ought it to be fo difpofed, as to illumine the principal Parts of the Subjed. P^or the fourth : The Effects of Shadows are different, as the Place is either wide and fpaci- ous; as in thofe coming imme- diately from the Sun, which are very fenfible, and their Extremes pretty abrupt ; from the ferene Air, which are fainter and mnre fweet ; from the dark Air, which appear more ditfufed, and almoil imperceptible ; and thofe from an artificial Light, which makes the Shadows deep, and their Edges abrupt : Or as it is more narrow and confined, where the Light's coming from tiie fame Place make the Shadow more flrong, and the Reflex lefs len- i'Me. Clair - bfcure ^ or Ch'taro- Scuro^ is alfo ufed for a Defign confiding only of two Colours, ordinarily black and white, fome- times black and yellow. Or, it is a Defign only wafh'd with one Colour, the Shadows being of a dusky brown Colouh and. the Lights heightened up with white. A CLAMP, is a kind of Kiln, built above Ground (of Bricks unburnt,) for the burning of Bricks. i Thefe Clamps are built much | after the Method that the Ar- ches are built in Kilns, w':^. with a Vacuity betwixt each Brick's Breadth, for the Fire to afcend ' by, but with this Difference, that inltead of arching, they trufs over^ or over-fpan^ as tiiey term it, he. they lay the End of one Brick about half way over the End of another, andfo till both Sides meet within half a Brick's Length, and then a binding Brick at the Top finiflies the Arch. The Mouth (at \vhichtheFire is to be put in) is left open about two Feet and a half wide, and about three Feet in Height; and then they begin to trufs over, which they do Tor three Bricks in Height, and which, with a binding Brick at the Top, will clofe up the Arch. But after they have begun to make the Place to receive the Fuel (before it is clofed at the Top,) they fill it almoft full M'ith Wood, and upon that, lay Sea- Coal; then it being over- fpainied like an Arch, they llrew Sea-Coal on all the Surfaces, and then lay another Courfe of Bricks the other Way, laying them at a little Diftance from one another, and firowing Sea- Coal upon them: A.nd thus they continue laying one Courfe one Way, and another the other, and ftrowing Sea-Coal betwixt each Courle, 'till they come to j, eight or ten Feet high, accord- ing a; C L C L ing as the Clamp is to beforBIg- nefs : When theyhavedonethis, they fet the Wood on Fire, and that rircs the Coals, which being all burnt out, the whole Clamp of Bricks is burnt. CLAMP-NiMLS, are fuch Nails as are ufed to faften on Clamps in the builctingor repair- ing ot' Ships. CLAMPING,inJoinery,C5'f. is when a Piece of Board, tlfc is fitted with the Grain to the End of another Piece of Board crofs the Grain, the firft Board is faid to be clamped. Thus the £nds of Tables are commonly clamped, to prevent them from warping. CLAY, a foft vifcous Earth, found in various Places, and ufed for divers Purpofes, of feveral Kinds and Properties. Dr. Lifter^ in ihtPhilofophical Tranfadions^ gives a Catalogue of twenty-two feveral Clays found in the feveral Counties of England\ five of which he calls Pure^ i. e. fuch as are foft like Butter to the Teeth, with little or no Grittinefs in them, viz. Fullers Earth, which he dif- tinguidies by its Colours, into yellowifh brown, and white. 2. Boles, 3. Pale-yellow C/^y, Cow (hot Clay., Dark-blue Clay or Marie. Seventeen Impure; whereof eight are harfli and dufty when dry, as Creta^ or Milk-white Clay. Two Potters Pale- yellow Clay. Potters Blue Clay ; Blue Clay^ wherein the Aftroites is found; Yellow C/SrAIRS. See Wi ^idsng-Staiks. CUCK I'i !\ a f )rt of Thea- tre, where Gunn.-Cocks fight their Bai:les. It is couunjuly a Ha life, or Hove!, cjver'd over. COENOTAPH, an empty Tomb or Monument, ereded in Memory of Some iiluftrious Defunft, "^vho periiTiing by Ship- wreck, in Battle, ^r. his Body could not be found to be in- terred or depofited in rhefame, COINS. Sec Quoins. COLAKIN, the little Prize of the Capital of the T'ufcan and Doric Column, placed between the Aftragal and the Annulets ; called by P'ttruviiis^ Hypotra- chelium. Called aUb Cindure. Colarin is alfo ufed for theOr- lo or Ring on the Top of the Shr\ft of the Column next the Capital. COLL.'VR-BEAM, a Beam fram'd crofs betwixt two prin- cipal Rafters. COLLEGE, a Place fet a- part for the Society and Cohabi- tation of Students, COLLER. See Cincture. COLONNADE,;! Periltyle, of a circular Figure, or a Scries of Columns diipofcd in a Cir- cle, and infiilatcd withinlide. Such is that of the little Park at P-^erfiilles; which conlilis of thirty-two Iokic Columns, all of Iblid Marble, and without In- cruftation. A Polxflyle Cohfjyiade is that whofc Number of Columns is too great to be taken in by the Ey^- ;u a lingle View. Such is the C jlanfjaae c f the Palace at ■SV. ^Peter at Kome^ vvr)icti con- fills )X two hundred eighty-four Columns of the Doric Order, t^c\\ ab^ve four Foot and a half Diameter, all in J'lburnne Mar- ble. COLUMN, a round Pillar, made to fupport or adorn a Building. The Column is the principal or reigning Part of an (Jrder. The principal Laws and Pro- perties of this eminent Member of Architecture, are thus de- duced. Every Fulcrum or Support is g fo miich the more perfed, as it I is the firmer, or carries thegrea- ■ ter Appearance of Firmnefs. And hence all Cohmns or Pil- lars ought to have th^ir Bafe or Foot broader than themlelves. Again, as a Cylinder, and a quadrangular Priiin are more ea- iily removed out of their Place than a truncated Cone or Pyra- mid, on the fame Bafe, and of the lame Altitude. The Figure of Columns ought not to be cy- lindrical, nor that of a Pilaftcr, pyramidical ; but both the one and the other to be contradled or dinn'nifh'd, /'. c. grow lefsand lefs like a truncated Cone, and a truncated Pyramid. For the fame Reafons, the loweft P.irts of the Columns are to be cylindrical, and tnat of Pilafters, pyramidical. Hence, again, as Co/a»7«j are more firm, if their Diameter bears greater Proportion to their Height, than if it bore a lefs, the greater Ra- tio is to be chofen where a large Weight, c o c o Weight is to be fuilain'd, and a lefs, where a lef:>. Further, as the Defign of a Column is to fupport a Wei;^hr, It muft never b:; fuppos'd v. hh- oiit an EntabUuiire: Thoi'gh a Colnmn raifed on an eminent Place, fo as to leave no Room to fear its bt;ing thrufl oat of its Place, needs no Pedeflal. The QwuxtColnmn in each Or- der is compofed of three princi- pal Parts ; the Bafe, the Shaft, and the Capital. Each of thefe Parts is again fubd'vided into a great Number of leller, called Members orMould- ings : Some whereof are eflen- tial, and found in all CotHm»s ; others are only accidental, and found in all particular Orders. Columns are made ditierent, according to the feveral Orders they arc ufed in; and likewife not only with RegarfJ rothefr Order, but alfo to the Marier, Con ltru61ion, Form, Difpolition, and Ufe. Columns, vjith Regard to Order. 'Ti^jcan Colmnn. isik*be..niorteft and mort liirtjUtioftail^ G- lurans. »'i'9#o lis \{<^i^\^S^z<^^\^l^Vi- truvim^ -(palladio^ ahil'Vigas^s^ is i'^iven Diameters or fourreeii' Modules; accwding to ScamyZ"-. zi^ fifteen Modules; to De- Lonne^ twelve Modules ; to Trajan's Cohtrnn^ fixteen Mo- dules. Its Diminution, according to Vitruv'iHs^ is one Fourth of the Diameter ; according ioFi^nola, a Fifth; and according to Tra" jans Column^ a Ninth. ^he whole Height of this Column, and the Height of each prin- cipal Part thereof^ according to fetieral Authors^ is as in the follow- ing Table, Auth. Nam. VVnok Height Pedeft. Bafe Body Capital Archit. Frieze ' -f- Cornic. mo.n^i mo.mi. mo. mi. mo.mi. mo.mi mo.mi. mo.mi. mo.mi. Vttr. Vign. Pall. Sea. 10 15- 11 15 2 20 2 20 I I Pi 30 30 30 30 6 6 ' « 30, 6 3c 30 30 30 30 30 30 3T 317 30 35 26 41 30 40 40 41 Vol. h H T.he c o The Doric Column is fome- thin^" more delicate: Its Shaft is adornM with Flutings. Its Hei<^hr, according to I'^itruvms, is from fourteen to fifteen Mo- dules ; to Scamozzi.^cwQniQcn', to Vigmla^ fixteen; in the Colt- c o feum^ nineteen; in the Theatre of Marcellus^ fifteen two Thirds. Its Diminutions, according to theTheatre o( Marcellus, twelve Minutes ; to the Coltfcum^ four Minutes and a half. lioe ixihole Height of this Column, and the Height of each principal 'jPart thereof^ according to fevcral Authors^ is as in the jollovjtng lable. VVhohjpg^^f^ Bafe hBodv- ^CapitaijArchit. Frieze Cornic lHeight| 1 I ' I 1 Autli. 1 Nimes tno.mi Vitr Vig"' Pa!L Sea. no. mi mo.mi.imo.mi. mo.mi. m .mi. mo.mi. mo.mr o 45-; o 40 o 45- o 45 o 45 o 3)- o 45" o 42 The Ionic Column is more de- licate flill, it isdillinguifli'd from the reft by the Volutes in its Capital, and by its Bafe. Its Height, according to Pal- ladio^ is Seventeen Modules and one Third ; according to Vig' nola^ eighteen. Its Diminution, in the Temple of Concord., ten one half; of Fortuna Virilis^ feven one half; of the Colifeumj ten Minutes. I'he whole Height of this Column, and the Height of each principal Part thereo^^ according to fcveral Authors .^ is as in this following Table. Nam. )y'?",^^lPedeft.! Bale \ Body Capital JArchit, Height J I I I 1 ;^^K 14 •no.mi.l Tio.muimo.mi. mo.m!. 301 8 10 o 20 o 37 i o\ 8 10 o 20 o 37-^ F^// 13 iS 2 40 o 523 7 40 o 272J o 34: Suuh^ -.^^i ^ nQ^ o .^-' 7 30' o iSj' o 3f Friezt-lCornic.l no.m' Ino.mi. o 3cl o 5-22 o 45 o )ai o 271 o 461 o 2S o 42 The c o c o The Corinth'ia-a Colnmn is the richcft and moft delicate of all the Columns. Its Capital is adorn'd with two Rows Oi' Leaves, and with Can- licoles, whence Ipriiig out little Volutes. Ics Height, according to Fi- trnvius^ and many Remains of Porticoes, Temples, i5'c. is nineteen Modules'; according to Serlio, eighteen ; to the Coltfeum^ Seventeen ; to the three Columm in the Car/ipo l/accino^ twcniy ; to the BaJiiickofAnton'r/iHs^iwQR-' Its Diminutions, according to the Temple of Peace., fix Mi- nutes and a half; the Patthson., fix and a half; the Temples of Sybil., and iv/a/?//?^, eight ; Con- fiantiae's-Jrch, feven; Porticos of Scpttmius^ fevcu and a half. I'he whole Height of this Column, and the Height of each prlyicipal Part thereof^ according to [everal Authors^ is as in this following^ Tabh. Aiuh Whole Height Pedeft. mo. mi. Bdfe Body mo. mi. Capital Archit. Frieze Cornic. Nam. mo. mi. mo. mi. mo.mi. mo.mi. mo.mi. mo.mi. ■Atr. ■■'^igii. c'all. )ca. i6 16 13 ^4 14 42--' 3 3^' 3 T- 2 30 2 30 3c gc 30 30 8 20 '8 20 I ^^ 8 f I 10 I 10 I 5 1 I IC 30 45" 36 39 37i 04 s 02 8 3I4 I I so, 046^1 The Con^pojite Column has two Rows of Leaves in its Capital, like the Corinthian ; and angular Volutes, like the Ionic. Its Height, according to Fig- nola.^ and J itus^s-Jrch^ is twenty Modules ; to Scammozi^ and the Temple of B.uchns^ nineteen and a half; to Septimius*s-Arch, Its Dmimution, accorduig to Jitus's., and SeptimiHs^s-Arcb, feven Minutes ; to the Baths of Dioclefian., eleven and oneTbVd ; to the Temple of Bacchus.^ fixty and a hajf. the c o c o The vjhole Height of this Column, a fid the Height of each principal ^Part^ according to the fe vcral Authors^ is^ as in this follovjtng 'Table. 1 Au:h. Nam. :tr. '/ign. ait. Si a. VVhult Heigh f l\>dclt. Ball- Body Capital Archit. Fr eze Comic mo.mi. mo.mi mo.m 3c 3 3-. 3L no. mi 8 20 8 2C 8 2)- 8 25 mo.mi. mo.mi. mo.mi. mo.mi. i6 6' i6 o '15 2C 15 2C 3 3 3 2t 3 2.. I I 10 52] I 10 45 I ^o^s I 5! 40 52-1 45 30 32 52i 1 45 48 It miy be here obferved, that there leans to be more ot Ca- price, than Realon, i:i that Di- verluy found in the Heights ot Coiu't-!Ks of the fame Oider in aitf^-rent Aahors; each ot" which frequently takes the Liber- ty of difpcnfing with his ovtu Rules. As for Inflance^ Fttruv.us makes the Doric Colnmm of Temples fhorter than thofe of Porches behind Theatres : 'Palla- dto gives a greater Height to G- umns fti'.nding on Pccclhils,thaii to thofe which have none : And Serlio ma-^es his Column :iXh\x6. thorter, when infulate or de- tached, than when contiguous to the Wall. Biit not \Tichftandtng the Di- verlity cquares of a Ceil- A f^.ompartimr/it Of Tiles is an Arrangement of white and red Tiles varnifli'd for the De- coration of the Covering of a \ Times, a Yard liuommeKfurahle is otherwifc. The Ratio of Comm.nlurables is rational ; that of Incoramenfura- bks is irrational. ComyrityijUrable lumbers ^ whe- ther Integers, or Fra6i;ions, are fuch as have fome other Num- ber which will meafure or di- vide them without any Remain- der: Thus 6 and 8 f ^ :^ are re- fpeftivcly by Coynmewfurable Numbers COMPASSES, or 7 is A Pair of COMPASSES 3 a Muhcmatical Inllrument uled tor the deicribing of Circles, meafuring the 'Diftances of Points, Lines, ^c. The common CompaJJes con- fift of two Branches or Legs of Iron, Bra!s, or other Metal, pointed at Bottom, and at the Top joined by a Rivet, whereon they move as on a Centre ^.,...... Hcur-Compi}JJes are fo contri- COMMISSURE, in Archi- ved on the Inlidc, as to take an tc6Vare, cff. ih;; Juint of two Extent to a Fiair's Breadth. Stones; or the Application of Geman CompaJJcs are thofe . the one to that of the other. vhofe Legs are a little bent out- COMMON, in Geometry, wards towards theTop; fo that is apply'd to an Angle, Line, or when fluit, only the Points the like, which belongs equally meet. to two Figures, or makes a ne- SpriKg-Comp^fJes^ ox Dkhlers^ cefiary Part of both. are made of harden'd Steel, the COMMON DIVISOR, m Head arch'd, which, by its Ari'.hmetick, is a Quantity or Spring, opens the Cvrr.txiJJes^ the Nnniber which exaftly divides Opening being direded by a cir- two or more other Quantities or cular Screw,faftencdtooneLeg, Numbers, without leaving any and let through the other vyork'd Remainder. -with a Nut. COMPARTITION, i n Ar- Turu-up-CompaJfes,^UttCon-' Cviite£lure, fignifies the ufeful trivance to fave tne Trouble fif and graceful X^ifpofitioa of the changing the Points- whole Ground-Plot of an Edi- CompaJJes c o c o Compnjfes of three Branches, Their Ulc is to takethree Points at onrc, and ib to form Trian- gles, ^c. Trij'ecling Comf-nJJ'es. Whofe Ufe is for trifedliiig of Angles Geometrically, Cylifidriack Compdjfes. ^I* r op or t tonal Compajjes. Beam Compajjes con lift of a long Branch or Beam carrying two Brafs Curfors ; the one fixed at one End, the other Hiding a- long the Beam, with a Screw to farten it, on Occafion : To the Curfors may be skrevv'd Points of sny kind, whether Steel for Pencils, or the like. It is ufed to draw large Circles, take great Extents, '^c. Elitptical Compajjes. Their Ufe is to dr^w Elliffes or Ovals of aiy kind. COxVlPLEMENF, in Geo- metry, is what remains of a Quadrant of a Circle, or of nine- ty Degrees, after a certain Arch has been retrenched from it. Thus if an Arch or Angle be twenty-five Degrees, they fay, its Complement is fixty-five, lince 6y and 25",= to 90. COMPOSITE Order, in Ar- chitedure, is the laft of the five Orders of Columns, focal- led, becaufe its Capital is com- pofed out of ihofe of the, other Columns. It borrows a Qaarter-Round from the Tufcan and ^oric ; a Row of Leaves from the Corin- thian; and Volutes from the Ionic. Its Cornice has fimple • M:)dillions or Dentils. Tiie Compofite is alfo called the Roman^ or luUck Order., as f • having been invented by the Ro- mans^ conformably to the reft which are denominated from, the People, among whom ihey had their Rile. This by moft Authors is rank- after the Corinthian.^ either as be- ing the richelt, or the laft that was invented. Scamozzi alone places it between the Ionic and Corinthian.^ out of Regard to its Delicacy and Richnefs, which he efteems inferior to that of the Corinthian., and therefore makes no Scruple to place it under it. In which he is fjllow'd by M. he Clerc. The Proportions of this Order are not fixed by Vitruvius ; he only marks the general Cha- rafter of it, by obferving that its Capital is compofed of fcveral Parts taken trom the 'Doric, Ionic, and Corinthian. He does not fctm to look upon it as a particular Order, nor does he vary it at all from the Coritt- thian^ except in its Capital. h\ Faft, it was Serlioy who firft added ihe Compojite Oidcr to the Four of Vitruvitis., forming it from the Remains of the Tem- ple of Bacchus., the Arches of "Titus., Septimius., and the Gold- fmiths: Till that Time, this Or- der was cfteem'd a Species of the Corinthian., only differing in its Capital. This Order being thus left undetermin'd by the Antients, the Moderns have a kind of a Right to differ about its Propor- tions, cstV. Scamozzi., and after him, M. LeC/or/V, may very' c o c o very properly be made nfe of, for this, and alio for the Ionic ^ and Corinthian Orders, efpecial- ly in Work expofed to the Wea- ther: Therefore inftead of pla- cing it here again, is fnewn the Plane oi either oftheCapitals as mentioned in the Corinthian Order. The Dimini(hing of this Co- lumn is the fame as the laft. The Height of the Capital is a Diameter and one Sixth; and being divided, give two to each Height of Leaves whofe Heads turn down a half Part, two Thirds of a Part to the Space between the Leaves and I'illet, one Third to the Aftragal and Piller, which is one Third of that, two Thirds to the Ovolo, one Third to the Space between the Ovolo and Abacus, a half Part to the Hollow^ and a half Part to the Ovolo, whofe Fil- let hath one Third thereof. The Projedion is the fame as the Corinthian. The Height of the Entabla- ture being two Diameters, is divided into fix; giving two to the Architrave, one and a half to the Frieze, and two and a half to the Cornice. The Height of the Archi- trave is divided into nine, giv- ing two and a half to the firft Face, a half Part to the Ogee, three and a half to the fecond, one Fourth to the Allrngal^ three Fourths to the Ovolo, one to the Hollow, and a half Part to the Fillet The Projection of the fecond Face hath half a Part, the Ovo- lo one and one Fcurch, and the Whole, two. The Frieze is form'd after the fame Method as the lonic^ being Part of a Circle that anfvvers to the Naked, and Projedion of the Architrave. The Cornice is divided info ten Parts, giving one Fourth of a Part to the Fillet, as much to the Aftragal ; one Part to the Ogec,another to the firft Face of the Modillions,a half Part to the Ogee, one rmd one Fourth to the fecond Face, one Fourth to the Fillet, a half Part to the Ovolo, two to the Corona, three Fourths to the Cima Re- verfa, one Fourth to the Filler, one and a half to the Cima Rec- ta, and a half Part to the Fillet. For the Projections, the Ogee hath one and half of thefc Parts, the upper Face of the Modil- lions in Front two, but is two and half in Breadth, viz. a half Part within the Naked, the Cap thereof a half Part, the Return'd Modillion four and a half, and its Cap 5-, the Corona fttvcn and a half, the Cima Reverfa eight and a ha/f, and the Wnolc tea being equal to the Height. COM- c o c o c o c o COMPOSITION, in Paint- ing, includes the Invention and Difpolition of the Figures, the Choice of Attitudes, cj'f. Therefore Compofu'ion confifts of two Parts; of which the one finds out by the Means of Hif- tory, proper Objcfts for a Pic- ture; and the other difpofes them to ^vantage. Compo0ion of Proportion fig- nificsthe comparing of the Sums of the Antecedent and Confe- quent; with the Confequent in two equal Ratio's : As fuppofe 4:8:3:6, by Compofu'ion of Proportion, we fay 12 is to 8, as 9 is to 6. Compojition of Motion^ in Me- chanicks, is an Alicmblage of feveral Dire£i:;ons of Motion, refulting from Powers ading in different, though not oppolite Lines, If a Point more or lefs, flow according to one and the fame Direc^.ion, whether that beeqna- ble or not, yet it will ftill keep the lame Right Line; the Cele- rity alone being changed, /", e. increafed or dimniifh'd, accord- ing to the Forces with which it is impelled. If the Directions be oppofite, as one ^.^r, dire6l!y downwards, the other upward, ^c. yet ftill the Line of Motion will be the flime. But if the compounding Mo- tion be not according to the fame Line of Direction, the com- pound Motion will not be ac- cording to the Line of Direction of cither of them, but a diffe- rent one from them both ; and this, either flraight, or crooked, accordmg as the Dire6lions or Celerities fiiall require. Iftwo compounding Motions be each of them equable, the Line of the compound Motion will ftill be a (In.ightLine : And this, though the Motions be nei- ther at kight Angles one to ano- ther, nor equally fwifr, nor each to itfclf equable, provided they be but fimilar, that is, both ac- celerated and retarded alike. COMPRESSION, the Aft of prefling or fqueezing fome- thing together, fo as to fet its Parts nearer to each other, and make it pofTels lefs Space. To CONG A MER ATE. To make an arched Roof, as in Vaulf;, ^c. To arch over. CONCAVE, is faid to be the inner Surface of a hollow Body, efpecially if it be circu- lar. Concave is particularly under- ftood of Mirrors and Leu fes. Concave Lenfes are either con- cave on both Sides, called Con- cavo-concave^ or concave on one Side, and plain on the other, called Plano'concave^ or concave on the one Side, and convex on the other, called concavo-convex, or convex -concave^ as the one or the other Surface is a Portion of the lefs Sphere. The Properties of all concave Lenfes arc, that the Rays of Light, in paffing through them, are deffecled, or made to recede from one another ; as in convex Glaflcs, they are infltded to- wards each other, and that the more, as the Concavity^ or Con- vexity, are Portions of lefs Cir- cles. Hence parallel RaYS,as thofeof the Sun, which by paffing .thro' a concave Lens, become diverg- ing: Diverging Rays are made to diverge VJ c o c o diverge the more, and converg- ing R;iys, eicher made to coii- verg'-" li-ls, or become parallel, or go (Hit diverging. Hence Objcds view'd through concave Lenles, appear diminilh- ed ; nnd the more fo, as they are Portions of lefb Spheres :And this, in oblique, as well as in dirccl Ray?. Concave Mirrors have the con- trary Eifcd to Lenfes : They re- fled the Rays which fall on them, fo as to make thum ap- proach more to, or recede lefs from each other, tban before ; and that the more, as the Cunca- inty is greater, or the Spheres, of which they are Segments, left. Hence concave Mirrors mag- nify Objcdls prefcnted to them; and that, in a greater Proportion of greater Spheres, CONCENTRICK, that which has the ilime common Centre wi;i\ another- Th;; Word is principally ufad in fpeaking of round Bodies, and Figures, i'/-^:. Circular and Elliptical ones, cs'f. Bat may be ufed likewifein Po- lygons, drawn parallel to each other upon tiie fame Centre. CONCLAVE, in Architec- ture, is a Clofct or inner Cham- ber. CONDENSER, in.PneuiTia- ticks, is a Machine or Engine whereby an unufual Quantity of Air maybe crowded into a given Space. They can throw in three, four, five, or ten Aimofphcres into the G>nden\ci\ ?.. e. three, four, l^c. Times as much Air as there is in ihc lameCompafs without t;ic Engine. CONDUCTS, y Suits or CONDUPTS, 3 Gutters, to convey away the Suillr.ge of anHoufe, Alfo Canals or Pipes for the Conveyance of Water or other fluid Matter. Sir Henry IVotton fays, lliat '\i\. the firft Place, Art (hould imi- tate Nature, in feparating thofe ignoble Conveyance^from the Sight ; land (where a Running Water is wanting,) they fliould be placed in the moll remote, -and loweft Part of the Foun- dation, with fecret Vents paf- iing up through the Walls (like a Tunnel) to the wide Air : Which ail L'(^/w;? Artifts com- mend for the Difcharge of noi- fqmc Vapours. A CONE, is a Solid, having a circular Bafe, and growing fnialler and fmaller, 'till it ends \\\ a Point, which is called the \'crtei', and may be nearly re- preicnicd by a Sugar-Loat. thti c o c o The RULE to find out Solidity. Its Multiply the Area of theBafe by a third Part of the perpendi- cular Height, and the Produd is the lolid Content. Let ABC be the Cone, the Diameter of whofe Bale A B is l6.s Inches ; and the Height of the CoMe DC is 15^.5- Feet. -F/V/Z, Square the Diameter 26.5-, and it will make 702.25-, which multiply by 785-4, and theProducl will be SS^Hl^Sy which being multiply'd b. 5. 5! the Produd will be 3033.407825- ; which being divided by 144, the Quotient will be .2107 jere^ the lolid Content of the Cone. ' The Operation. M4)3<^33-:ro3Cii-07 Feet 353 Content 947 I By Scale and Cornpaffes. Extend the Compafles from I3.f4 to 26.5. (the Diameter) that extend, turn'd fwice over from 5-.5- (a third Part of the Height) will at laft fall upon 21.07 P'eet the Content, Te find the Superficial Content. Multiply half the Circumfc- 26.5 the Diameter 26.5- 1325- 1590 530 702.25* Square •78H 280900 35II25' 65-1800 491 ^75* 5-5-1.541 715" AreaofBafe 5-5 fPt. of the Height 27:r773 :^75773 30335-03 rence 41.626 by the llant Height AC 198.46, and the Produd will be 8261.09596; which be- ing divided by 144, theQuotient is f7. 37 /fc'r^ the Curve Surface; to which add the Bafe, and the Sum will be 61.2 Bafe, the Su- perficial Content. 41- c o c o 41.626 198.46 2497^6 1665-04 333008 374634 41626 826i.r95-96 144) 8261.09596 (sy.^y Feet fere 3SS io6r 530 9S9 6j.20 Whole (Conr. 144) 55'i-H (3-^3 1195- 434 By Scale and Compajfes. Extend the CompafTes from 144 to 198.46; and that Extent will reach from 41 626 to 5-7 37 Feet, the Curve Suiface. Then extend the CompafTes from 12 to 26,5- (the Diameter) and that Extent turn'd twice over from 785-4 will at laft fail upon 3.83 Feet, the Bnfe; which being adacd to 57.37, the Sum \vill be 61 2 Feet, the Superfi- cial Content. DEMONSTRATION. ^ iEvery Cone is the third Part of a Cylinder of equal Bafe and Altitude. The Truth of this may eafily be conceived, by only confider- ing that a Com is but a round Pyramid ; and therefore it muft needs have the fame Ratio to its circumfcribing Cylinder, as the fquare J^yramid hath to its cir- cumfcribing Parallelopipcdon, viz. as I to 3. However, to iTiake ic the clearer, let it be confidcr'd, That Every right Cone isconftituted of an infinite Series of Circles, whofe Diameters do comiiiUal- ly increafe, in Arithmetical Pro- grelfion, beginning at the Ver- tex or Point C, the Area of itj Bafe AB being the greatelt Term ; and its perpendicular Height DC, the Number of all Terms ; therefore the Area of the Circle of the Bafemultiply'd by a third Part of the Altitude DC, will be the Sum of all the Series, equal to the Solidity of the Cone. The Curve Superficies of eve- ry Right Cone is equal to half the Rcftangle of the Circumference of its Bafe into the Length of its Side. For the Curve Surfice of eve- ry Right Cnne\s equal to the Sec- tor of a Circle, whofe Arch BG is equal to the Periphery of the Bafe of the Cone^ and the Ra- dius A B equal to the flant Side of the Cone. Which c o c o Which will appear very evi- dent, if you cut a Piece of Pa- per in the Form of a Seftor of a Circle ABC, and bend both the Sides AB and AC together till they meet, and you will find it to form a Right Cone. CONGE [in Architeaure, a Moulding, either in Form of a Quarter-Round, or a Cavetto, which ferves to feparate two Members from one another. Such is that which joins the Shaft of the Column to the Cincture, called alfo Apophyge^ which in Greek, fignifies Flight, the Column feeming to arife. Hence, by the Latins, it is called Scapus^ the Shaft of the Co- lumn. CONGES, are Rings or Fer- rils, heretofore ufed in the Ex- tremities of Wooden Pillars, to keep them from fplitting, after- wards imitated in Stone- Work. CONICK SECTION, a curve Line arifing from the Sec- tion of a Cone. CONICKS, that Part of the Higher Geometry, or Geometry of Curves, which confiders the Cone, and the feveral Curve Lines arifing from the Sections. C0N01DES,7 in Geometry, *• CONQlD, S a folid Body refembling a Cone, except in this, that inllead of a perfetl Circle for its Bafc it has an El- liplis, or fome other Curve ap- proaching thereto. CONSECl\^RY isaPropo- fition that follows, or is dedu- ced from fome preceding Defi- nitions, Lemmata, Axioms, or the like; whence Ibme chufera- ther to call it a Confequence, and others a Corollary. Vol. 1. CONSOLE [of confolider, Fr. lore-unite, join, er'^r.] is an Ornament cut upon the Key of an Arch, which has a Projec- ture or Jetting, and on Occafioii ferves to fupport little Cornices, Figures, Bulls, and Vafes. Thele are alfo upon Occafioii called Mutules, Modillions, ^c. according to their ^^orm: Some of them are Ilriated, or fluted ; others in Form of Car- touches; others have Drops, ia the Manner of Triglyphs. Thole made at the End of a Plank of Wood, cut Triangu- larwife, are called Ancones. Confoles are frequently ufed as Keys of Arches, projeding out to fupport a Vale, or other Or- nament. M. Le Clerc is of Opinion, that a Co»/o/^fhould always have fomcthing exceedingly maffive, to fuftain and ferve it as a Reft. CONSPIRING POWERS, in Mcchanicks, are all fuch as a£l in Direftions not oppofite to one another. CONTACT, the relative State of two Things that touch each other, or whofe Surfaces join to each other without any Interftice. Hence becaufe very few Sur- faces are capable of touching in all Points, and the Cohefion of Bodies is in Proportion to their Contads, thofe Bodies will ftick fafteft together, which are capable of the moft Can- tab. CONTENT, the Capacity or Area of a Space, or the Qua- lity of any Matter or Space in- cluded in certain Bounds. S The c o c o The Content of a Ton of round Timber is forty-three fo- lic! Fecr. A Load of hewn Timber contains fifty Cubick Feet. In a Foot of Timber arc contained feventeen hundred and twenty-eight cubick or fquare Inches ; and as often as feven- lecii hundred am twenty-eight Inches are contained in a Piece of Timber, be ic round or fquare, fo many Foot of Tim- ber arc contained in the Piece. CONTIGNATION, in the antient Architedure, the Art of laying Rafters {\\\ Latin^Tigna) together, and pariicuhirly Floor- ing- CONTIGUOUS, fignifies that two or more Things are difpofed fo near each other, as they join their Surfaces, or touch. CoMtiguons Angles^ in Geome- try,fuch as have'one Leg common to each Angle, othcrvvifc cal- led Adjoir.ing Angles, in Con- tradiction to thofc produced by continuing their Legs through the Point of Contadl ; which are called Oppolite or Verti- cal Angles. CONTOUR, the Out-Line, or that which terminates or de- fine: aFigure. In Architedurc, it is the Out-Line of any Mem- ber, as that of a Bafc, a Cor- nice, or the like. CONTRACTILE Force, m Mechanicks, is that Power or Property inherent in certain Bo- dies, whereby, when extended, they are enabled to draw them- feK-es lip again to their former DimenHons. CONIRAMURE, in Ar- cliitceh;re, an Out-\VaII built about the Wall o\ a City, TO CONTRAST, in Ar- chitedure, is to avoid the Re- petition of the fame Thing, in order to pleafe by Variety ; as is done in the Great Gallery in the Louvre^ where the Pedi- ments are alternately arched and angular. CONTRAST, in Painting, and Sculpture, fignifies an Op- polition or Ditference of Pofi- tion, Attitude, i^c. of two or more Figures, conttiv'd to make Variety in Painting: Thus in a Group of three Figures, when one is fliewn before, another be- hind, and a tnird fideways, there is faid to be a Contraft. The Cmtr/ifl is not only to be obfcrv'd in the Pofition of feveral Figtues, but alfo in that of the feveral Al embers of the fame Figure : Thus if the Right Arm advance the frrthelt, the Right Leg is to be hindmoft : If the Eye be diieded one Way, the Right Arm is to go the con- trary Way. Nay, the Contraft is tobeper- fu'd even in the Drapery. CONVERGING L/W? . GONVERGENTL;»e>y,S '" Geometry, are thofe which ap- proximate, or whofe Diftance becomes continually lefs and lets. Thcfe are oppofed to di- vergent Lines, whofa Diftance becomes continually greater. Lines which converge one Way diverge another. Cofivergmg Rays^ in Diop- tricks, are thofe Rays, which in their PalTsge out of one Me- dium into another, of a different Denfity, are refracted towards one another, i^o as if far enough continued, they will meet in a Point or Focus, Thus c o c o Thus all Convex Lenfes make the Rays converge^ and Concave ones make them diverge, /". e. the one infleds them tt)wards a Centre, and the other dcfleds them from it; and the more, as fuch Lenfes are Portions of fmaller Spheres. On which Properties, all the Effects of Lenfes, Microfcopes, Telelcopes, ^^c. depend. Rays coming corfuerging out of a denfer Medium into a rarer, v.g. from a Glafs, into Air, become more convergent^ and concur fooner, than if they were to continue their Motion through the firft. Rays coming converging out of a rarer into a denfer Medi- um, converge lefs, and concur later, than if they had continu'd their Motion through the firft. Parallel Rays palling from a denfer, into a raver Medium, D.g. from Glafs into Air, will become convergent^ and concur in a Focus. Converging Series^ in the Ma- thematicks, is a Method of Ap- proximation, or coming ftill i.earer and nearer towards the true Root of any Number or Equation i even though it be impolfible to find any fuch true Roots in Numbers. CONVERSE, in Geometry, ^c. A Propolition is faid to be the Converfe of another, when, after drawing a Conclufionfrom fomething firfl: fappofed, we proceed to fuppofe what had been before concluded, and to draw from it what had been fup- pofed. As for Example; Thus 'cis demonrtrated in Geo- metry, that if the two Sides of a Triangle be equal, the two Angles oppofite to thefe Sides are equal alio: Tbt Converfe of the Propofition is^ that if the two Angles of a Triangle be equal, the two Sides oppofite to thefe Angles are equal alio. CONVEXITY is the exte- rior Surface of a Convex^ i. e. a gibbous and globuhir Thing, in Oppoiition to Concavity or the inner Surface, which is hol- low or deprefs'd. A Convex Lens is either con- vex on both Sides, called ^Coh- vexo-Csnvex, or k is plain on one Side, and convex on the other, called a Convexo-Concave^ or Concavo-Convex^ as the one or the other Surface prevails, i.e, as this or that is a fmaller Por- tion of a Sphere. All Convex Lenfes inflefl the Rays of Light in their PalTage, /". e. fend them out from their convex Surface, converging fo as that they concur in a Point or Focus. Hence zUConvex Lenfes mag- nify^ i. e. reprefent their Images larger than their Objeds ; and this the more, as they are Por- tions of fmaller Spheres. A Convex Mirror reprcftntS the Images fmaller than the Ob- je61s, as a ConCave one repre- feiits them larger: A Convex Mirror refieds the Rays from it, diverging; and therefore difper- fes and weakens their Effeft, as a Convex one refle6ts them con- verging, fo as to concur in a Point, and have their Effeft in- creas'd ; and by how much the Mirror is the Portion of a (mai- ler Sphere, by fo much docs it diminifh the Objeds, and dif- perfe the Rays the more. S COPING c o c o COPING of a U^all, the Top Thefc Corbels are uOaally pla- or Cover of a Wall, made flo- ced for Strer.gth, immediately ping, to carry otf the Wet. under the Semi-Girders of a Cb/'/^g'/^er, in Carpentry, a fort Platform, and fometimLS under of Hanging over, not fquare to the Ends of Camber- Beams : its Upri^ht, but bevelling on its In which latter Cafe, they are Undeifide till it end in an Edge, nfually placed a Foot or twobe- The Pric? : Brick- Walls (of low the Beam, and have a Piece of a Brick and half thick) have Timber ftanding upright clofe to been cop'd with Stone for ^d. the Wail from the Cbr^e^ to the a Foot, lineal or running Mea- fure, the Workman drawing the Stones, into this Price. Drawing of Stones for Co- Beam. Corbel is alfo ufedby fome Ar- chitefis, for the hollow Niches or Hollows left in the Walls for piiig: A Penny a Foot has been Images, Figures, or Statues to given for drawing them, for this ftand i i. Ufe. CORBEILS [of the Lntm^ Corb':s a Basket] is a Piece of Carved Work in the Form of a Basket, full of Flowers or Fruits, ferving in Architefture to finil"h fome Ornament. CORINTHIAN Order, the fourth, or, as Scamozzi and M. Le Clerc make it, the fifch and laft of the Orders of Architec- ture; being the noblell, richeft, and molt delicate of all others. The Invention of this Order CORBELS, m zKrchittclure, \s-x^cx\\i'dioCartirf2achtis^2i\\Jthe- the Reprefentation of a Basket nian Sculptor, by moll of the fomeiimes fccn on the Heads of the Caryatides. Sometimes Corbel is ufed to fignify the Vafe or Tambour of the Cor'trdhlan Column, fo called on Account of the Re- Icmblancc it bears to a Basket ; Moderns, after Vitrnvius^ who pafTing by the Tomb of a cer- tain young Lady, over which her Nurf*;' had placed a Basket wi:h fome of her Play-Things, and covcr'd it up from the Wet with a Tile, the Whole having or becaufe it was firltUitm'd on been placed on a Root of Acan the Mode! of a Basket. thus, as ic (prung up, the Bran- CORBIL, ? is alfo ufed in chesencompafs'd the Basket, and CORBEL, S Building, for a bending down at the Top under fliort Piece of Timber, placed in the Corners of the Tiles, torm'd a Wall with its End Iticking out a Sort of Volutes, lix or eight Inches, as Occalion Hence Callt7:^achus took his ferves, inthe Manner of aShoul- Hint : The Basket he imitated in dering- Piece. The under Part of the End thus liicking our, is fometimcs cut in the Form of a Eoultin, foinetiincs of an Ogee, and fometimcs of a Face, k^c. ac- cc '■ cy plain asd tiat. rording as the Workman's Fan- :y is, the upper Side being the Bafe of his Column, the Leaves in the Volutes, and the Tile in the Abacus of this Or- der. The Corinthian Order has fe- veral Charaders by which it is diftinguilh'd from the reft. Its Capital is adorn'd with two Rows c o c o RowsofLeaves, betv/ccn "which arife little Stalks or Caulicoles, of which the Volutes are form- ed, which fupport the Abacus, and are in Number fixteen. It has no Ovolo, nor even Abacus, properly fpcaking; for the Member which goes by that Name, is quite ditTereiit from the Abacus of the other Order?, bc- ingcut with a Sweep, in the Mid- le of which is carved a Rofe, or other Ornament. VitruviHs obfervcs that the Corinthian Order has no particu- lar Ordounance for irs Cornice, or any of the other Ornaments of its Entablature; nor does he give it any other Proportions, than thofe of the Ionic Order: So that if it appears higher than the /o»/V, 'tis purely owing to the Excefs of the Height of its Capital. He alfo makes the reft of the Entablature the fame, and alfo ules iht j^litic Bafc inditterently for the one and the other. But Vitruviui differs widely in this Order from all the Ex- amples of Antiquity now re- maining: The moff beautiful of which have a particular Bafe, and the whole Order twenty Modules high; whereas the Ionic has but eighteen. Again, iis Capital is higher than that of Viiruviui by one Third of a Module; and its Entablature, which has Modil- lions, and fometimes Dentils to- gether with the Modillions, is very different from the Ionic En- tablature. Moft modern Archite6ls pafs by Vitruvi7fs\ Corinthian Ordon- nance, and follow that of the ancient Buildings; and feled from them rxcording to iheii fe- vcial I'ailes. So that the mo- dern Cori'^thian is a kind oi Com- pojite^ dithering from many of the antient Baiidiiigs, and much more iVom Vitruvtus. Vignola and M , Z.^ Clerc made the Cormrhtan Order twenty Modules in Height; yet Serlio makes it but eigliteen; and M. 'Perrault^ eighteen two Thirds, retrenching fomcthing from the nineteen of Vitruvius. M. P(?rr^/^/^ makes theHeight of the Shaft Icfs than that of the Ionic ^ by reifon of the Excefs of its Capital. The Corinthian QoXwmwby equal Parts. •Corinthian Pedeflal^ being in Ekight three Diameters, and is divided into four, allowing one to' the Bafe, whofe Plinth istwo Thirds of ii: The other Part is divided into nine, allov/ing two and a half to the Torus, a half Part to the Fillet, three to the Cymafe, a half Part to the Fil- let, and two and a half to the Ogee; and the Breadth of the Die is a Diameter, and two Thirds. The Projection of its BaCe is equal to its Height, the upper Fillet has three of thefe Parts, and the lower Fillet fcveu. The Height of the Cornice is half the Bafe being one Eighth of the whole Height; and is divi- ded into eleven, by allowing one and a half to the Ogee, a half Part to the Fillet, three to the Cymafe, three to the Corona, two to the Ogee, and one to Fillet. The Proje£lion of the Fillet has two of thefe Parts, the Cyinafe four and a half, the S J Cofona c o Corona fix mid a half, and the Whole eight and a half. The Height of the Bafe of the Column is half a Diameter, which is divided into iix, allowingthrec Fourths to the Plinth, one to the lower I'orus, one Fourth to the Fillet, a half Part to the Scotia, one to the Aftragals and JFillets (which are to he parted into fix, allo'.ying one to each Fillet, and two to each Adra- gal,) a half Part to the Scotia, one Fourth to the Fillet, and the other three Fourths to the Torus; the Fillet above the faid Foms, is equal to the others, and Part of the Column. The Prcjedion is one Fifth of the Diameter- and the upper Fillet has one of the faid liX Parts, the upper Torus, and the lelfer Fillets have one and a half, and one three Fourths are allow- ed to the Aftragals, and lower Fillet. DiminijJjwg of this Column !S one Eighth of tl'.e Diameter.^ I'he Corinthian Capital. Di- vide the Diameter into fix Parts, and take feven fuch Parts for the Height, allowing two to each Height of the Leaves (whofe Heads turn down half a Part of it) allow another Part of the Stalks whofe Heads turn down one Third of it; three Fourths to the fmall Volutes, and one Fourth to the Fillet; the large Volute is as high as the laid Fil- let ; a half Part to the Hollow, and a half Part to the Ovolo, •whofe Fillet has one Third of it. For the ProjeSiion of the Ca- pital., make a Square, each Side c o being a Diameter and half, and draw the Diagonals (See the Composite Or<;/^r,) and towards each Angle, inark a Diameter from the Centre, and draw the Cants at Rig it Angles with the faid Diagonals : Then, for the Curvature of the Abacus, make an equilateral 'Friangle, (tl-.e Part of the Square cut off by the Canes being the Bi!'-,) and the oppofi'.e A.ngle the Cntre. In the Circumference of the Co- lumn are eight Leaves, each Leaf having four Plmts, and each Phait five R ffles. The Proje6tion of their Heads is found b) a ftraight Line from the Abacus to thr:Colarino. The Pwofe is high a'^ ihe Volute, and projedts to the Side of the be- fore- men'ioned Square. '] he Architrave is divided in- to nine Parts, allow^'i-. one and a half to the firft f .!•;. . one and one Fourth to the '..^u^U Bead, two to the fecond Fa.-=, three Fourths to th. final' Ogee, two and half to the third'Face, a half Part to the Bead, one to the Ogee, and a half Part to the Fillet. The Trojedion of the fecond Face has one Fourth of a Parr, the third Face, one of thofe Parts, and the Whole, two. The Height of the Entabla- turc is two Diameters, and is divided into fix Parts, two of which go to the Architrave, one and a half to the Frizc, and two and a half to the Cornice. The Ccrniee is divided into twelve Parts, allowing one and one Fourth to the Ogee, one Fourth CO CO Fourth to the Fillet, one and two and a half. The Dentils one Fourth to the Dentils, one are in Breadth two Thirds of Fourth to the Fillet, one Fourth their Height, and the Spaces two to the Ovolo, one Fourth to Tnirds of their Breadth. the Fillet, two to the Modil- The Modillioits projeft three lions, a half Part to the Ogee, and three Fourths; and its and one Fourth to the Fillet; Breadth is one Fifth of the one and three Fourths to the Diatiiettr ; and one being in the Corona, three Fourths to the Centre, gives the Spaces. The Cinia Rcverfa, one Fourth to rcmrn'd Modillions eight and the Fillet, one and a half to a half, the Cip nine, the Co- the Cima Reda, and a half Part rona in'ne and a half, the Cinia to the Fillet. Rcverfa ten and a half, and As for the Projections of the the Whole twelve, being equal Cornice: The Ogee is one half to the Height. See the Figure, of ihefe Parts, and the Dentils CORK, c o c o G O C O CORK, aTree like the Holm iTree, refembling the fame in its Ij^eaves, Catkins, and Fruir, the 13ark ot it is light, (pungy, and of a grey Colour, inclining to Yellow. There are indeed fcveral Sorts of this Tree ; but two more re- markable, vit. One of a nar- rower, lefs jagged Leaf, and pe- rennial ; the other of a broader Leaf, and falling in theWinrer. It grows in the coldeft Part of Bifcay^ in the North r^i EfigluKd^ in Itnly^ Provence^ and South- weft Parts of France^ efpccially the fecond Species, which are the firteft for our climate. It grows in all Ibrts of Ground, dry Heath, floney and rocky Mountains, fo that its Foots run above the Earth, There arc Cups made of one fort of Cork, good for he<5tical perfon*: to Grink out of. The Egyptians made Coffins of Cork^ which being lined with a relinous Compolition, prefcr- vcd their Dead uiicorrupted. They fomttimcs in Spaixi line their StoneWalls with ir, which renders them very warm, and correds the Moifture of ihe Air. Beneath the Gr^^, or Bark of this Tree, there are two other Coats ; one of them reddiOi, ■which they ftrip from the Bole when fell'd, and is valued by Turners; the reft of the Wood iJ not only good Firing, but alfo applicable to many other Ules in Building. CORNER Stones, are two "Where they have little to cover Stones commonly of Rigate or them; and therefore we have no Fire-Stone; of vi'hich there (lands reafon to defpair of their grow- one in each Jaumb of a Chim- ing with us. ney. Their Faces are hollow in There were none of them in Breadth, being a certain ^vvet^ /rrt»f^ iij P//';/v's Time; but there of a Circle. The Breadth of ar:^ iage Woods of them Inlta/y^ fron wti: nee it is probable they Were tranfplanted hither. The- Manner of decorticating or taking otf the Bark of the Oj-rk-Tree^ is as follo^vs : They once m two or three Years (trip it in a oiy Seafon, otherwife the intercutai:20us Branches endan- ger ihe l>ee, and therefore a rainy Seafon is very periiicious to them when the Bark is off; they unwrap it before the Fire, and prefs it even, and that with Weights, on the convex Parr, and {i,Coronis a Crown- ing] is the uppermoit Member of the Entablature of a Column, or that which crowns the Or- der. The Cornice is the third grand Divilion of the Trabeation com- mencing with the Frieze, and ending with the Cymatium. The Cornice is different in the different Orders, there being as manjr c o c o many Kinds of CorrAces^ as there are diftlrent Orders of .Columns. It is moll pbin ia the I'ufcun Order. . yig77ola makes it to confift of an Ovum or Quarter- Round, an Artragal or Baji,uette, the Reglet or Filler, the Larmier, and the Talon. In the Ionic, the Members are in molt Refpefts the fame as in the Doric j except that they are frequently inriched wiihCarving, and have always Dentils. In the Doric, f^igmla makes the Capitals of the Triglyphs of ihe Frieze, with their Bandelet- res, a Talon, Mutules, or ])en- tiis; a Larmier, with its Guttas underneath, a 'ialon, !■ illct, Ca- vetto, and Rcglet. Thi Curinthian Cornice is the richcll, and is diflinguiflied by having both Modilions and Den- tils, contrary to the Opinion of V:t,-uv:us, who looks upon thefe two Ornaments as incompatible; and of yi. Le Clerc, who ac- counts the Dentils as peculiar to the Ionic In theCompofite there are Den- tils, its Mouldings carved, and there areChannels under the Soffit. The Tufcan, according to I^t- iruviHS, the whole Height of this Cjrnice is one Module and a half; which Height being di- vided into four grand Divili ms, the uppcrmoft of which goes to the BMultin and Fillet under it ; and ti-.i'? Divilion being fubdi- vidcd i::to four Parts, three of thcns go to the Boultin, and one to the Fillet. The two next grand Divifions go to the Corona, or Crown, (which is fiat and plain.) ;5nd the lowermoit grand Divitioii goes to the Cymatium ; which being again divided into three Farts, the uppermoft of them goes to the Fillet, and the other two to the Cyma or Ogee. The Projefture of the whole Cornice, as alfo of each Member thereof, he makes to be equal to its FJeight; and the under Side of the Corona he divides into ii Parts, of which he allots two to the Filler, and one to the Den- ticle, and fo alternately; for, fays he, it is fitting to have three as deep as they are large. Scamozzi makes the whole Height of this Cornice 39 Mi-> nutes, and the Height of each particular Member of it (begin- ning at the Top, and defcending orderly) isastollows: The up- per Lift or Plinth of the Cornice^ three M. the Superciiium, Lift, Tinea, or Eye-Brow, one M. and a half; the upper Cima or Ogee eight M. the Lift under it one Minute and a half ; the Co- rona or Crown 9 ^ M. the Lift i M- 7; the Cima or greater Ogee, fix M. (here is one and a half M. left betwixt for the Depth of the Dentils;) the Superciiium or Lift one and a half M. the Cymatium or liule Ogee five M. the Lift, two M. Palladio makes the whole Height of this Cornice forty- four M. of which the Lift at the Top is three and a half M. the Scima Reda ten M. the Lift under it two and a half M. the Corona ten M. the Boultin nine, the Lift one and a half, and the Ca- vetto or Hollow feven and a half M. The Doric Cornice is made by Iltruvi$ts after tv^o different Fa- fiiions; the whole Height of the one c o One is half a Module, which be- ing divided into two grand Di- vilions, one of them (viz. the upper one) is fubdividcd into eight Parts, of which one Pnrt goes to ihe Lift at Top^ and the other fevtn to the Ogee. TheothergrandDivifion is again divided into four Parts, the up- permoH: and lowermolt of which Parts go to the two Cymatiams, and the two middle Parts go to the Corona. The Lill of each of thefe Cy- matiums, is one Third of the whole Cymatium. The whole Height of the o- ther fafhioned Cormce is forty ]VJ. which being divided into nine Parts, two are to go to the two Fafcia's, one to the Thorus or Boultin above them, two to theModilions above that, two to the Crown, and two to the Cima or Ogee at the Top. The Modilions, as alfo the Crown, being divided each into three Parts, one of them (hall go to their refpedive Cymatiums, of which th(.ir Litis are each- one Thiid of the Whole. Sccv.nozzi makes the v/hole Height of this Corniic forty-two M. of which the Lift at the Top is two M. the great Ogee (even ^ M. the Lift one M. the little . '^pgee three M. the Corona eight 'I M. the Lift one M. the Cafe- j'" ment two M. the Boultin five ^^. the Lift one M. the Square *'''feven M. the Lift one M. and ^■'ihe Boultin four M. ' ^alladio^ in his verbal De- icription of this Cornice^ makes , jhe whole Height of it to ht >jt^irty-five M. But in his Figure jIt is but thirty-three M, and a quarter, of which the Lift at -fi c o Top is two M. and a quarter^ the Crma lie6ta^ or Ogee, iix M, three Fourths ; the Lift one M. the Ctma, Keverja three M. one Fourth ; the Corona eight M. the Ovolo or Boultin ftx AT the Lift one M. and the Calement at the Bottom five M. The lon'tc : Vitrnvius makes the whole Height of this Cornice about fifty- two M. and a half. He defcribcs two Cornices of dif- ferent Fafliions in this Order ; in one of which he divides the whole Height into eleven Parts; the two uppermoft of which go to theCymatium, and the Boultin under it : And this Space is again fubdivided into fix Parts; two of which go to the Fillet of the Cymatium, three to the Ogee, and one to the Boultin. The next two grand Divi- fions go to the Corona ; and the next three to the Cartoufes, and the Cymatium over them : And this Space being fubdivided into five Parts, one of them makes the Cymatium, of which the Fillet is one Third of the Whole; then one and a half of the next grand Divilion goes to the Boultin and Fillet over it, of which the Fillet is one feventh Part of the Whole. And again, one and a half of the next grand Divifion goes to the CaCement and Fillet over it, of which the Fillet is one Fourth of the Whole. And the taft grand Divilion goes to the Cymatium, of which the Fillet is one third Part of the Whole. In the Cornice of the other Fa- fhion, he divides the whole Height into fix Parts; the upper- moft of which he allows to the Ogee, c o c o Ogee, the Fillet of which is one lixthPart; the next grand Divi- fion being lubdivided into three Parts, the uppermoll of rheni goes to the Cymatium, (the Fil- let of which is one third F^irt,) and the other two to the Co- rona. T'Cncxt two grand Diviilons are lubdivided into rive Parts ; the uppermolt of which goes to the Cymatium (the Fillet of which is one third Part,") andihe other four to the Cartoufes. The next grand Divilion is fubdivided into four Parts ; three of which go to the Boul- tin, and one to the Fillet under »r. And the lad grand Divifions being fubdivided into four Parrs, three of them arc for the Cafe- ment, and one for the Cyma- tium, ot which its Fillet is one third Part. According to Scamozzi^ the whole Height of this Cornice is forty-two M. whereof the Lift at the Top is two IVl. the Cima Reda five and a half M. the Lift one l\\. the Cima Reverla two j»nd a half IVL the Corona fix and a half M. the Cima Rev-er- fa two and a half M. the Car- toufes feven M. the Boultin lour M. the Lift one M. the Square five M. the Lift one JVl. and theBoultia four M. Acccirding to '■Palladio^ the whole Height of this Cormce is forty-fix and a half M. of which the Lift at the Top is two and ia half iM. the Cima Reda feven M. the Lift one and one Fourth JM. the Cima Rcverfa three and a half M. the Corona eight M. the Cima Reda over the Modi- lions three and one Fourth M. the Modilions feven and a half M. the Lift one M. the Ovolo or Boultin fix M the Lilt one and one half, and the Cavetto or Hollow five M. The whole Height of the Cjrinth'icm Cornice^ according to yttruvius^ is about one Mod. And he defcribes two Forms of Cor- nices^ in this Order : In one of which, he divides the whole Height into five Parts ; the up- permoft of which goes to the Ogee, of which its Fillet is one fixth Parr. Then one and one Fourth goes to the Corona and Cymatium over it, of which Space the Cy- matium is one third Part, and its Fiilct one Third cf that. Then one and three Fourths of the next grand Divilions go to the Modillions and Cyma- tium over them, of which Space, the Cymatium is one feventh Part. And the laft grand Divifiou goes to the Boukin and Fillets over and under it; and this being divided into three Parts, the lowermoft goes to the Fillet ; and the other two being fubdivi- ded into fix Parts, five of them go to the Boultin, and the other to the Fillet over it. In the Cornice of the other Fadiion, the whole Height is di- vided into nine Paits ; of which the two uppermolt being divi- ded into four Parts, three of them go to the Ogee, (w hofe Fil- let is one Sixth of tne Whole,) and the other to the Cymatium over the Corona, (whofe Fillet is one Third of the \yhole,) and the next two grand Divifions go to Corona. , The c o c o The next two grand Divifions go to the Modiliions, and the Cymatium over them : One Fourth of this Space goes to the Cymatium (whofe Fillet Is one Third of the whole Cymatium) and the reft of the Modillions. The next two grand Divi- fions go to the Boultin, and the Fillet over and under ir, which Fillets are each one Seventh of the Whole. And The laft grand Dlvifion goes to the Cima at the Foot of the Cornue. Scamozzi makes the whole Height of this Cornice forty-fix and three Fourths M. of which the L'ft of the Cima Rc6la is two M. the Cima Re£ta fix and a half M. the Lift of the Cima ReverHi one M. the Cima Reverfa three and one Fourth M. the Half Round one and one half M. the Corona feven and one half M. the Cymatium three and one half M, the Mo- dillions eight and a halfM. the Lift one M. the Boultin fiveM. the Lift one M. and the Cima five M. Tcilladio makes the whole Height of this Cornice fifty M. of which two andoneThird M. go to the Lift of the Cima Rec- ta ; the Cima Reda is eight and one Third M the Lift two Thirds M. the Cima Reverfa three M. the Corona feven one Third M. the Lift of the Ogee over the Modillions two Thirds M. the Ogee 2 and t woThirdsM. the Modillions eight i-.nd a half M. the Boultin four and one Third M. the Lift one M. the Boultin five and a half M. the Lift one M. and Ogee four and a half M. The Compojite Cornice : Vl- truvius makfcS t'.ie whole Height of it equal to the Diameter of the Column above, which is a- bout fifty-two and a halfM. He alfo defcribcs two Cor^ faces of this Order of a different Fafliion ; one of which he di- vides into two Parts, the upper- moft of which goes to the Ogee (whofc Fillet is one Seventh of the Whole,) and the undermoft to the Corona and Cymatium over it ; and this Space being divided into four Parts, three of them go the Corona, and one to the Cymatium, whofe Fillet is one 1 bird of the whole Cy- ir.atium. Scamozzi makes the whole Height of this Cornice forty- eight M. and Palladia ioxiy-fivQ M. but for the Height of each particular Member, they leave us very much in the Dark. Goldman makes the Height of the Tuscan Cornice one and one Third, and its Projediure two and two Fifths M. the Height of the 1)Qric one and one Third, and its Projedure two and two Fifths. The Height of the lomc one and three Fifths ; its Projeclure two and two Fifths. The Height of the Com- pofite one and three Fifths ; its Projc6ture two and thirteen Thirties. The Height of the Co- rinthian one and two Fifths; its Projedure two and thirteen Thirties. The ProjeBnre of the CoRNiCE. 'Tis an eftabliflicd Rule in Archite6ture, that the Cornice of the Entablement have its Pro- jedure nearly equal to it5 Height : c o c o Height; and yet the Projcfture may may be lately made a little larger on Occalion, particularly where a beautitul Profile is re- quired. Cornice is ufed in general for all little Projedures of Mafon- ry or Joinery, even where there are no Columns, as the Curnice of a Chimney, a Buffet, l^c. Architrave Cornice is one that is immediately contiguous to the Architrave, the Frieze being retrenched. JM HI Hated Cornice is one whofe Projedure is cut or interrupted to the Right of the Larmier, or reduced into a Platband with a C>male. Cdiitaliver Cornice^ a Term ufed by Workmen for a Cornice that has Cantalivers undeineath. Cuz:i}ig Cornice^ a Cornice which has a great Cafemcnt or Hollow- in it, ordinarily latlied and plait- tercd upon Compafs-Sprcchets, or Brackets. JModillion Cornice^ a Cornice with Modilliops under it. Cornice is aUb ufcd for the Crownings of Ptdeftals. The Cornice^ too, is different in the diflercnt Orders: In the Tufcan, according to M. Pcr- ranlt^ it has a Platband, which fcrves as a Corona and a Cavet- to with its Fillet. In the !/9or/V, it has a Cavet- towitha Fillet, which bears with a Drip crown'd with a Square. In the lonic^ a Cavetto with its Fillet above, and a Drip, or hanging Square, crown'd with an Ogee, and its l^illet. In the Corinthian^ an Ogee with its Fillet, a Cymatiun un- der the Ogee ; Corona, and an Ogee with its Fillet. Lajlls^ In the Compofite^ a Fil- let with the Sweep over the Die, an Athagdl, a Cima with its Fillet, Corona, and Ogee Avith its Fillet. The Price: Mr.LeyhurnttXH us, forne Cornices are valued by the Piece, dearer or cheaper, ac- cording to their Largenefs, Goodnefs of the Stufi', and Cu- rioijty of the Workman fhip : Others are meafured and rated by the Foot, running Meafure, /. e. by the Number of Feet in Length only. Some fay, the common Rate for rnaking of Plain Cornices (without any Carving) under the Favcs of a Houfe, they com- monly have I /. per Foot run- ning Meafure. Mr. If'ing (itys, that Cornices are valued according to their Nature and Bigncfs. A Modil- lt:r,i Cornice of Freeftone, of eighteen or twenty Inches thick, is worth ^d. or dd. ix Foot running Meafure. And as to Joiners Work, a ModilHon Cor- nice^ with i(s carved Work, fs worth '/.r. a Foot, and a plain Modillion Cornice of twelve or fourteen Inches, will be worth 3 J. 6d. or 4/. a Yard running Meafure. Some Workmen fay a Wtck Cornice is worth 2 j". 6 J. per Foot. CORONA, -^in Archi- CORONES, (^izQimn. is CROWN, ra large CROWNING, .>tlacnrong Member of the Coryme^ fo cal- led, bccaufe it crowns not only the Cornice, but the Entabla- ture, and the whole Order. The French call it the Lar- mier, our Workmen the Drip, as c o c o as ferving, by its great Projedurc, to skreen the rclt of the Build- ing Irom the Rain. Some call it abfolutely the Cornice, as being the principal Member thereof Vitruvmsixc- qucntly ufes the Word Corona for the whole Cornice. 1 he Corona is itfelf crown'd or finifli'd with a RigktorFillet, The Corona, M. Le Cierc (ays, is that large fqnare Moulding immediately under the Cymafe. Jt projects very much, both for the greater Beauty of the Entablature, and for the better fheltcring even of the whole Order He alfo fays, he makes this Part ftronger than the Cymafe, as being the ruling Member of the Entablature, and even of the Order. Underneath tiiis he ufually digs a Channel, for three Rea- fons ; the firrt is to give it more Grace and Ornament ; the fecond is to render it lefs heavy ; and the third is to pre- vent Rain, or other Moifture, from trickling down along the Order, For the Water falling from the Top of the Cornice, not being able to afcend into the Channel, is forced to fall Drop-by-drop on the Ground, by the Means of a little Ledge ; and 'tis on this Account, that the Bottom of the Coiona is called Larmier, or Drip. CORNUCOPIA, inArchi- tedure, Sculpture, ^c. or Horn ot Plenty, is rcprefented under •the Figure.ofa large Horn, out of which ifllie Fruits, Flowers, ^c. CORRIDOR, in Architec- ture, a Gallery, or long Ids, around a Building, leading to leveral Chambers, at a Diftancc from each other. CORSA. This Word, as Fafcia and Txnia, in Fitru- v!Hs, Signifies what is by us cal- led Plaiband. COUCH, in Painting, isufed for each Lay or Impreflion of Colour, whether in Oil, or in Water, wherewit!i the Painter covers the Wall, Wainfcot, or other Matter to be painted. So they fay, a Painting has had its lalf Conch, or Lay. A Ceiling has had VJVO Couches. The Word Couch is alfo ufed for a Lay or Impreflion on any l>iing, to make it more firm and confiiieiit, and to skreen it from the Weather; as Painiing is co- pcr'd with a Couch ot Varnilh. COVING, in Building, when Houfes are biiilt projc6i:ing over the Ground-Plot, and theturn'd Projefture archM with Timber, (turn'd with a Quadrant of a Circle or Semi- Arch,) lathed and plaiftcrcd, under which People may walk dry, (as is much uf d at Tunhridge-li'^ells) on the Up- per Walks,) the Work is com- monly called Coving. Mv.l-{'ing ftys, that the Car- penters Work of Coz-;??^ is worth 4 J. per Square. COUNTER Drawing, m Painting, t^c. is the Copying of a Delign or Painting, by Means of a fine linnen Cloth, an oiled Paper, or other tranfparent Mat- ter, whereon the the Strokes ap- pearing through, are followed and traced with a Pencil, with or without Colour. COUNTER FORTS, But- trefres,Spurs,or Pillars of Mnfon- ry,ferving to prop or fuflainWalf s or J c o C R oi TerraiTes fubjcd to bulge, or be thrown down. Thcfc Works are ufually bent into Arclies, and placed at a Diftance from each other. When any Thin^ is built on the Defcent oi" a Mountain, it mud be Ihcngthened wkhCoufi- tcrfurts well bound to the Wall, and at tlic Diftance of about twelve Yards from each other. Counter Gage, in Carpentry, a Method ufed in mc.ifuriiig the Joi.its, by transferring, v. g. the Breadth of a Mr-rtoile to the Place in the Timber where the Tenon is to be, in order to make them fit each other. Counter Light, in Painting, a Window or Liglit oppofite to anyThing which niukcs it appear to a Difadv-Mitage. Counter Mure '^^ a little If^all Counter IViiU S built clofe to another, to fortify and fecure ir, that it may not receive any Datriages from Buildings made contiguous to it. COURSE, in Architeaure, a continued Range ofStones, le- vel, or of the (ame Height throughout the whole Length of the Building, without being in- terrupted with any Aperture. A Conrfe of Plinths, is the Continuity of a Plinth of Stone or Plafter in the Fjce of a Build- ing, to m.ark the Separation of the Stones. CO U S S I N ET [^ . ^. a Cnjhion'] 'n\ Architecture, fignifies the Stone which crowns a Piedroit or Peer, or that lies immediate- ]v over the Capital of the Im- port, and under the Sweep. The Bed of it is level below, and curved above, receiving the lirlt Rife or Spring of the Arch or Vault. Coujinet is alfo ufed for the Ornament in the Ionic Capital, between the Abacus and the Echinus or Quarter-Round, and which ferves to form the Vo- lutes. It is thus named from its re- prcfenting a (^ufliion or Pillow, prtfs'd by the Weight over it, and bound with the Strap or Girdle, called, by f^itruvins^ Bal- thei's. CR AM POONS,? Pieces of CRAMPONS, SIron that are hooked at the ^.nds, for the the drawing or pulling up of Tiinber, Stones, (jfc. CRANK, a Contrivance or Machine, in manner of an El- bow, only of a fquare Form, projefting out from an Axis or Spindle; and ferving by its Ro- tation, to raife and fall the Pif- tons of Engines for railing Wa- ter, rcfc. CROSETTE, in Architec- ture, the Returns in the Corners of Chambranles,or Door-Cafes, or Window-Frames, called al- fo Ears, Elbows, Ancones, Pro- thyrides. The Crofette of a Luthern is the Plaifter or Covering near a Luthern. CROSS GARNETS. See Hinges CROSS-Gr^;«V. Timber is faid to be crofs-graind, where a Bough or (bme Branch flioots out on a Part of the Trunk of the l>ee ; for the Bough or Branch lliooting forwards, the Grain of chat Branch (hoots for- wards alfo, and fo runs acrofs the Grain oi the Trunk ; and if it C R C U it be well grown together, it will fcarce be perceived in feme Stuffs, but only in working. CROSS Multiplication. See Multiplication. CROWN POST, in Archi- tedure, a" Foft which in fome Buildings (lands upright in the Middle, between two principal Rafters. Cro-jj?i^ in Architedure, the uppcrmoli Member of the Cur- nice, called alio Corona, and Larmier. CROWNING, in Architec- ture, is generally underftood when any Thing terminates or finifhes a Decoration of Archi- tedure: Thus a Cornice, a Pe- diment, Acroteres, CT^iT. are cal- led Crovjnings. And thus alfo the Abacus is faid to crown the Capital : And any Member or Moulding is faid to be crowned, when it has a Fillet over it : And a Niche h crown'd, when it is cover'd with a Capital. CRYP FA [of xp-.V-o,, Gr. to hidv.-] a fubrerraneous Place or Vault, efpecially under a Church, for I'Vi^ Interment of particular Families or Petfons. y'ttruvius ufes the Word for Part of a Building, anfwering nearly to our Cellar. Hence, CRYPTO PORTICO, a fubterraneous Place, arched or vaulted, ufcrd as an Underwork or Pallnge into old Walls The fame Words are alfo ufed for the Decoration at ihe Entry of a Grotto. CUB/\TURE,7is the Cu- CU BAT ION, Sbing of a Solid, or the meafuring of the Vol. I. Space comprehended m a Solid as in a Cone, Pyramid,' Cylin- der, ^c. I'he Cubature has Refpcd to the Content of a Solid as the Quadra- ture has to the Superficies of a Figure: So that the Cubature of the Sphere turns on the fame Thing as the Quadrature of the Circle. CUBE, in Geometry, a re- gular orfulid Body, conliiling oLiix fquare and equal Faces a^ Sides, and its Angles all right, and therefore equal. The Cube is fuppo fed to be generated by the Motion of a iquare Plane along a Lineequal to one of its Sides, and at Right Angles thertto : Whence it fol- lows, thatthe Phuies of all Sec- tions parallel to the Bafe, arc Squares equal thereto, and con- fequently to one another. Cube^ ^ In Arithme- CubickNttmbers^s, tick, is a Number ariling from the Mul- tiplication of a fquare Num- ber by its Root: Thus \i the fquare Number 4 be multiplied by its Root 2, the Faduin 8 is a Cube or Cube Root. Cube is a fquare Solid, com- prehended under fix Geometri- cal Squares, being in the Form of a Dve, to find the folid Con- tent. This is, The RULE, Multiply the Side of the Ca^^ into itfelf, and that Produd a- gain bv the Side, the lafl Pro- dudt will be the Solidity or fo- lid Content of the Cubs. T 17.5- c u c u i7-r 87? IlZf 175- 306.25- 17-5' I5-3I2J- 2I437J 3062 f S3S9-37S the folid Content, Suppofe A B C D E F G a Cu- bical Piece (if Stone or Wood, each Side tb.ereot' being Icven- teen Inches and a hair, multiply 17.5" by 17.5", and the Product is 306.25' ; which being multiply'd by 17.5', the lall Prockid will be 535-9 Iblid Inches and 375 Parts. To reduce the Iblid Inches to Feet, divide by 1728, (becaufe there are fo many Cubical In- ches in a Foot,) and the Tolid Feet in the Cube will be 3, and 175- Cubical Inches remaining. By Scale and Compajfcs. Extend the CompafFes from 1 to 17.5', and that Extent turn'd over twice from 17-5, will reach to 5359 the Iblid Content in Inches : Then extend the Compartes to i, turn'd the lame Way from 53^9, and tht;y will reach to 3.1 Feet. Demonstration. If the Square A BC D be con- ceived to be mov'd down the Plane ADFF always remain- ing parallel to itfelf, there will be generated by fuch a Motion, a Solid having fix Planes ; the two oppofite of- which will be equal and parallel to each other; whence it is called a Parallelo- pipcdon, 01- fquare Prifm. And if the Plane ADEF be n Square equal to the generating Plane A BCD, then will thege- neratt^d Solid be a Cabe. I'vom hence fuch ,':>olids may be conceived to be cojillituted of an infinite Series of equal Squares,each equal to rhe Square ABCD, and AEorDF will be the N anber of I'erms. Therefore, if the Area ot A BCD be multiply'd into the Number of Ferms AE, the i-rodud is the Sum of all that Series, {pef Lemma i.) and conlcquently ths c u c u the Solidity of theParallelopipe- don, otCube. Or if the Bafe A BCD, be- ing divided into little fquare Areas, be muUiply'd into the Height A E, divided into alike M 'fur e for Length; After this Way, you may conceive as m»- ny little Cubes to be generated in the whole Solid, as is the Number of the little Areas of theBafe,multiply'd by the Num- ber of Di villous the Side A E contains. Thus if the Side of the Bafe ABbe 3, that multiply'd into itfelf is 9, which is the Area of the fquare Bafe ABCD; then if AE be likewife 3, multiply 9 by 3, and the Produ6l will be 27, and fo many little Cubes will this Solid be cut into. From this Demonftration, it is very plain, that if you multi- ply the Area of the Bafe of any Parallelogram into its Length, or Height, that Product will be the folid Content of fuch a So- lid. Enradfon of the CuBE Root. To extraft the Cube Root, is nothing elfe but to find fuch a Number, as being firft multiply'd into itfelf, and then into that Produd, produceth the given Number. Which to perform, cbferve thefe following Direc- tions: /Vr/Z, You muft point your given Number, beginning with the Unit's Place, and make a Point or Dot over every third Figure towards the Left Hand. Secondly^ Seek the greateft Cube Number in the firft Point, towards the Left Hand, putting this Root thereofin the Quotient, and the faid Cube Number under the tirrt Point, and fubtracl: it therefrom, and, to the Remain- der bring down the next Point, and call that the Refolvend. Thirdly, Triple the Quotient, and place it under the Refol- vend, the Unit's Place of this, under the Ten's Place, and call this the triple Quotient. Fourthly, Square the Quotient, and triple the Square, and place it under the triple Quotient, the Units of this under the Ten's Place of the triple Quotienr, and call this the triple Square. Fifthly, Add thefe two toge- ther, in the fame Order as they Hand, and the Sum fliall be the Divifor. Sixthly, Seek how often the ' Divifor is contain'd in the Re- folvend, rcjeding the Unit's Place of the Refolvend, (as in the fquare Root,) and put the Anfwer in the Quotient. Seventhly, Cube the Figure laft put into the Quotient, and put the Unit's Place thereof under the Unit's Place of the Refolvend. Eighthly, Multiply the Square of the Figure lad put in the Quo- tient, and place the Produift under the laft, one Place more to the Left Hand. Ninthly, Multiply the triple Square by the Figure laft put in the Quotient, and place it under the laft, one Place more to the Left Hand. Tenthly, Add the three laft Numbers together, in the fame Order as they ftand, and call that the Subtrahend. La^ly, Subtraa the Subtra- hend from the Refolvend, and if T a there c u c u there be another Point, bring It Example i. Let 314432 be a down in the Remainder, and Cubick Number^ whole Root is call that a new Refolvend ; and required, proceed in allRefpefts as before. 314432(68 Root. 216 98432 Refolvend. 18 Triple Quotient of 6. 108 TripleSquare of the Quotient 6. 1098 Divifor. 5-12 Cube of 8, the lafl Figure of the Root. 1 1 5-2 The Square of 8, by the triple Quotient. 864 The triple Square of the Quotient 6 by 8. 98432 The Subtrahend. After you have pointed the given Number, feek what is the greateft Cube Number in 314, you will find the firft Point to be 216, which is the nearcft that is ]eis than 314, and its Root is 6; which put in the Quotient, and 216 under 314, and fiibtrad it therefrom, and there remains 98 ; to which bring down the next Point, 432, and annex to .98 ; lb vi^ill it make 98432 for niie Refolvend. Then triple the Quotient 6, it makes 18, which write down, the Unit's Place, 8, urder 3, the Ten's Ph;ce of the Refolvend. Then fquare the Quotient 6, and triple that Square, and it makes 108, which write undtr the triple Quotient, one Place on the Lett Hand ; then add thofe two Numbers together, and they make 109S for the Divifor. Then feek how often the Divifor is con- tained in the Refolvend, (rejeft- ing the Unit's Place thereof) that is, how often 1098 in 9843, which is 8 Times ; put 8 in the Quotient, and the Cube thereof below the Divifor, the Unit's Place under the Unit's Pi ace of the the Refolvend. Then fquare the 8 laft put in the Quotient, and multiply 64, the Square thereof, by the triple Quotient 18, theProdud is ii5'2; let this under the Cube of 8, the Units of this under the Tens of that. Then multiply the triple Square of the Quotient by 8, the Fi- gure laf> put in the Quotient, the Prodi.ft is 864; lit this down under the lalt Produd, a Place more to the Left Hand. Then draw a Line under thofe three c u c u three, and add them together, and the Sum is 98432, which is cal- led the Subtrahend ; which be- ing fubtradhd from the Refol- vend, the Remainder is nothing ; which fliews the Number to be a true Cubic Number^ whofe Root is 68, that is, if 68 be cubed, it will make 314432. For, if 68 be maltiply'd by 68, the Frodu6l will be 4624; and this Produd, multiply'd a- gain by 68, the lall Produdt is 314432, which Ihews the Work to be right. 68 68 544 The Work 408 4624 68 36992 27744 The Proof 31443a Example 1. Let the Cube Root of 5735'339 be required. After you have pointed the given Number, feek what is the greatelt Cube Number in f, the iirft Point, which you will find to be one; which place under 5*, and I, the Root thereof, in the Quotient; and fubtraft i from 5', and there remains 4 ; to which bring down the next Point, it makes 4735- for the Refolvend. Then triple the i, and it makes 3; and the Square of 1 is i, and the Triple thereof is 3 ; which fet one under another, in their Order, and added, makes 33 for the Divifor, Seek how often the Divifor is in the Refolvend, and proceed as in the laft Ex- ample. f73f339 C U P u hmi9 (179 Root. 473.5- Refolvend. -. The Triple of the Quotient i, the firft Figure. 3 The triple Square of the Quotient i. 33 The Divifor. ^43 The Cube of 7, the fecond Figure of the Root. 147 The Square of 7 muitiplv'd in the triple Qanti.-Tt 3. 21 The uiple Square of the QuoLitut muliiplyM b) 7. 3913 The Subtrahend. 822339 1 he new Refolvend. 5-1 The Triple Quotient 17, the two firft Figures, 867 The triple Square of the Quotient 17. 8721 The Divifor. 729 The Cube of 9, the laft Figure of the Root. 413 1 The Square of 9, inultiply'd bv the triple Quotient 5:1. 7803 The triple Square of the Quotient 867 by 9. 822339 The Subtrahend. In this Example, 33, the firft with 9 or 8, you will find that Divifors feems to be contain'd the Subtrahend will be greater more than feven times in 4735", than the Refolvend, the Refolvend; but if you work Som* c u c u Some more Examples for Tra^ice, SM^i'7S9 (3*9 T^he Root. 5'46i Rcfolvend. 9 The Triple of 3, 27 The triple Square of 3. 279 The Divifor. I The Gz^^ of I, the fecond Figure. 9 The triple Quotient by the Square of i. 27 The triple Square multiply 'd by i, the fecond Figure. 2791 The Subtrahend. 2^7075-9 A new Refolvend. 93 The Triple of 31. 28S3 The triple Square of 31. 28923 The Divifor. 729 The Cul^e of '9, the laft Figure. 7S33 The Square of 9 by 93, the triple Quotient. 25'947 The triple Square 1883 by 9. 267075-9 The Subtrahend. T 4 846^4^131 c u c u 84604^19 C439 The Root. 64 20604 Refolvend. 12 The Triple of 4. 48 The triple Square of 4. 492 The Divifor. 27 The Cube of 3. 108 The Square of 3 by the triple Quotient. 144 The triple Square of 3. ^SS'=>7 The Subtrahend. 5'097'cr9 The Refolvend. 129 The Triple of 43. 55-47 The triple Square of 43. 5'5'5'99 The Divifor. 729 The Cube of 9. 10449 The Square of 9 by 129. 49923 The triple Square by 9. ^ ^097^ 19 The Subtrahend. 259697989 c u c u 25-9697989 (638 116 43697 Refolvend. 18 The Triple of 6. 108 The triple Square of 6. 1098 The Divifor. 27 The Cube of 3, the fecond Figure. 162 The Square ot 3 by 18 324 The triple Square of 108 by 3. 34047 The Subtrahend. 965-0989 Refolvend. 189 The Triple of 63. 11907 The triple Square of 63. 119259 5-12 The Cuhe of 8. 12096 The Square of 8 by 189. 95-2 5-6 The triple Square of 11 907 by 8. 9647072 The Subtrahend. 3917 The Remainder. 25*91 705-5 c u G U 2^9170^6 {19S-9 ■7917 The Refolvend. 6 The Triple of 2. 12 The tripic Square of 2. 126 The Divifor. 729 The Cube of 9, the fecond Figure. 486 The Square oi 9 by 6. ic8 The triple Square by 9. 163S9 The Subtrahend. ipSofd The Refolvend. 87 The Triple of 29. 2^23 The triple Squaic of 29. 2-53 1 7 The Divifor. i2f The Cube of 5-, the third Figure, 217^ The Square of 5- by 87. 12615- The triple Square by 5". 1^^3375' The Subtrahend. 244681000 The Refolvend. 885 The Triple of 295'. 261075- The triple Square of 295. 2611635- The Divifor. 729 The Cube of 9, the laft Figure, 71685- The Square ot 9 by 88f. ^349'575' The triple Square by 9. 2356S5079 The Subtrahend. 8995921 The Remainder. In this Ex- ample I annex 3 Cyphers to the Remain- der , which makes the third Refolvend; by which Means I bring one to the Place of Deci- mals. And fo you may pro- ceed to more decimal Piaces at Pleaiure, by anntxiiig three Cvphcrs to the next Remain- der, and car- tniig on rhe Woik, as be- fore. 3.2069810135' c u 22069SIOI25' (2805: 8 14069 Refolvend. 126 The Triple of 2. The triple Squar^ of 1* c u 126 TheDivifor. 51a The Cube of 8. 384 The Square of 8 by 6. 96 The triple Square by 8, 139^1 Thf Subtrahend, ii7J>ioi2f New Refolvend. 84 The Triple of 28. 235-2 The triple Square of 28. 23604 The Divifor. 840 235-200 The Triple of 280. The triple Square of 280. 235-2840 New Divifor. 125- The Cube of 5-. 21000 The Sqiure of 5- by 840. 1176000 The triple Square by 5-. 117310125 The Subtrahend. In this Ex- ample, 13952 being fubtrad- ed from the Refolv. 14069, the Remain- der is 117; to which bring down 810, the third Point , and it makes 117810, for a new Refol- vend ; and the next Divifor is 23604, which you cannot have in the faid Refolv. (the Unit's Place being re- jeded,) foyou muft put o ill the Quotient, and feek a new Divifor, (af- ter you have brought down your laft Point to the Refol- vend ;) which new Divifor is 2352840 ; whicli you'll find to be con- tained 5 times. So proceed to finifh the reft of the Work. 937^9- cu cu 64 2975-9 The Refolvend. J^ -Ji'^ Triple of 4, the fira Figure. 4^ The triple Square of 4. 492 The Divifor. 27125- Th e Subtrahend. 2634^7^ The Refolvend. 135- The Triple of 45-. - J ^^^ ^"^^^ ^^"^^^ of 45*- 60885- The Divifor. 64 The Gde of 4. 2160 The Square of 4 bv 12 <- ^43°o The triple Square by 4. 245-1664 The Subtrahend. 18291107 The Refolvend. < o'^^o'' I''^ Triple of 45-4. ^6t8348^ The triple Square of 4^.4. ^i^S^i The Divifor. 8 The Cuh of 2. r.^At'^f J!"^ ^'^"^'■^ "f ^ by 1362, ^^36696 1 he triple Square by 2. 123724088 The Subtrahend. 5-9186982 The Remainder. In extrading the Cul;e Root of nine, ^c. Places, that is, always a mix d Number, always ob- to confift of even Points, as in ferve to make the decimal Part the laft Example, where the de- to confift of either three, fix, cimal Places were five, to which I annexed a Cypher to make up fix, and fo I proceed to point it ; and by that Means I haveaPoint falls upon the Unit's Place of whole Numbers, which you muft always obierve. To extraSi the Cube Root 07tt of a Fradioft. This is the fame to do as in whole Numbers, obfcrve but the foregoing Diredbions for the c u true pointing thereof; for, as was before directed, the Deci- mal muft always conlift of three, iix, nine, ^c. Places ; and if it be not fo, it muft be made fo, by annexing of Cyphers, as is abovefaid. If the Cube Root of a vulgar Fradion be required, you muft firft reduce it to a Decimal, and then extrad the Root thereof. Examples of each follow. Example i. Let the Cuh Root of .401719179 be required. .401719179 (.737 Root. 343 5-8719 Refolvend. 21 Triple of 7. 147 Triple Square of 7. 1 49 1 Divifor. 27 Cuh of 3. 189 Square of 3 by 21. 441 Triple Square by 3. 46017 Subtrahend. 1 2702 1 79 Refolvend. 219 Triple of 73. ^S9^7 Triple Square of 73. 1 60.- 89 Divifor. 343 Cuh of 7. 10731 Square of 7 by 219. 1 1 1909 Triple Square by 7. 112985-53 Subtrahend. 1403626 Remainder. Example c u Example i. Let the Culfg Root of .0001416 be required. .000141600 (.Ofi Root. 125- 16600 Refolvend. 15- TheTripleof f. 75 Triple Square of 5-. 765- Divifor. 8 Cube of 1. 60 Square of 2 by i ^. 15-0 Tiiple Square by 2. 15-608 Subtrahend. 992 Remainder. Exaynple 3. Let ^^ be a vul- gar Fradtion, whofe Cul^e Root is required. By this Rule, reduce the vul- gar Fradion to a Decimal. 276) 5'.ooooooooo(.oi8ii5'942 2240 320 440 1640 2600 1 160 560 ^ U .0i8ii5'942 (.262 Root-' 101 1 5" Refolvend. 6 Triple of 2. 12 Triple Square of 2, 126 Divifor. 216 Cuf>e of 6. (of 2. 216 Square of 6 by the Triple 72 The triple Square by 6. 95-76 Subtrahend. 5-39942 Refolvend. 78 Triple of 26, 2028 Tiiple Square of 26. 2035'8 • Divifor. 8 Ode of 2. ■ 3F2 Square of 2 by 78. 405-6 Trip. Square of 2028 (by 2, 408728 Subtrahend. 131 214 Remainder. You may prove the Truth of the Work, by cubing the Root found, as was fliewn in the firll Example; and if any Thing re- mains, add it to the faid Cw^r, and the Sum will be the given Number, it the Work is rightly pcrform'd. 8 I will c u c u I will (hew the Proof of the fifth Example, the given Number being 2,5-9697939, whofe Root is 638, it being a furd Number, there remains 3917. 638 638 5-104 1914 3828 The Square 407044 638 325635-2 1221 13a 2442264 The Cube 2 5'3694072 The Remainder add 4917 Proof equal to the given Number 25-9697989 CUBICLE, a Bed-Chamber. CULINARY, of or belong- ing to a Kitchin. CULVERT AIL, the fame as Dcivctail. CUPOLA, a fpherical Vault, or the Round-Top of the Dome of a Church, in Form of a Cup inverted. Some call it a Lant- horn. CURLING STUFF, in Joinery. See Cross-grain'd. CURTiCONE, in Geome- try, a Cone whofo Top is cue otf by a Plane p:»ralkl to its Balis. CURVATURE of a Line, is its Bendii-ig, or }• lexure, where- by ir becomes a Curve of fuch peculiar Pniperties. CURVE, in Geometr*', a Line. whe;;ein the fevera! Points it coi;lil}s of tend feveial Ways, or arc polltcd towards different Q a utters. In this Senfe the Word h ufed in Oppolition to a ftreight Line, whole fcveral Points arc pointed towards the fame Quar- ter CURVILINEAL, crooked- lined, or conHlling of crooked Lines. Curvi'mcal Figures^ in Geo- metry, are Spaces bounded by crooked Linos; as Circles, El- lipfis, fpherica! Triangles, (^c. CYCLOID, in Geometry, one of the mechanical ; or, as others term them, the tranfcen- dental Curves, calleci alfo the Trochoid. Cycloida! Space., the Space con- tained b-'tween the Cycloid and the Subtenfe thereof CYCLOMETRY, the Art of meafuring Cycles, or Circles, CYLINDER, J c u c u CYLINDER, is a round So- lid, having i:s Bafes circular, equal and parallel, in the Form of a Rolling-Stone. To find- the folid Content^ this is the Rule. Multiply the Area of the Bafe by the Length, and the Produd is the folid Content. Let ABC be a Cylinder^ ■whole Diameter AB is ii.f Lichcs, and the Lencjth CD is i6 P'eet; what is the folid Con- tent ? Firft fquare the Diameter 21.5-, and make it 462. 2f ; which mul- tiplied by .785-4, and the Produd will be 363.05- 1 1 5", Then multiply this by 16, and the Produel will be 580S.S164. Divide this laft Produd by 144, and the Quotient will be 40.34 Feet, the folid Content. J5y Scale and Cornpajfes. Extend the CompafTes from 1 3. 5-4 to 21.5, the Diameter, and that Extent (turned twice over from 16, the Length,) will at laft fall upon 40.34, the folid Content. To find the fnperfitial Content. Firil find the Circumference of the B;Ue 67.5-4; which being divided by 12, the Quotient will be 90.05 Feet, the curved Sur- face : To which add 5.04 Feet, the Sum of the two Bafes, and the Sum will be 95.09 Feet, the whole fuperticial C^jntent. 67-5'4 16 405-24 6754 12) icSo.64 90 05 ^•°^^a 90. 56305 2 dd 95.C9 144) 726 10 (5.04 610 34 By S.jle ;. a Concavo-convex Member, ha- ving its Projedure fubdupie its Height. CYPRESS-TREE is of two Sorts, Wild, and the Sative, or Garden one, themuR pyramidal and beautiful, and which is pre- poUeroufly called the Male, and bears Cones. The Cyprefs is a tall Tree, and (lioors forth from its Roots a ftraight Stalk, divided into feve- ral Branches that bear Leaves very much indented, thick, and of a brownifli-green Colour. At the Ends of thefe Branches grow Flowers like Cats Tails, compofed of feveral little (trait Leaves or Scales, and barren. Thofe who would have Cy- prefs in Standards, and grow wild, which may in Time come to be of large Subftance, fit for the moft immortal of Timber, and, indeed, are the leaft obnoxi- ous to the Rigour of Winter, provided they be never clipped or disbranched, muft plant the Male Sort. It prolpers wonder- fully where the Ground is hot and gravelly. The Venetians make great Profit of this Tree. The Timber of Cvprefs is ufe- ful for Chells, Muflcal Inftru- ments, and other Uiienfils; for it refifts the Worm, and Patre- U 2 fad ion ; D A D E taftion, becaufe of the Bitter- nels of its Juice. It never rifts nor cleaves, but with great Vio- lence. And it may be worth obferv ng, that the ^ worth from 24 j-. to 30/. per Square, according to the Good- ncfs of the Deals. But if the Deals are extraor- dinary, and laid either with Dovetail or Key-Joints (with- out Nails or Pins,) 'tis worth 3)-.r. or 40/. per Square. See f I. OCRS. DECAGON, in Geometry, is a plain Figure of \.q\\ Sides, and as many Angles ; and if all the Sides are equal, and all the Angles, it is called a Regular Vecagoa^ and may be infcribed in a, Circle, If the Side of a Regular De- cagon be I, the the Area thereof will be 8.69; whence as i to S.69,fo is the Side of the Square of any given Decagon to the Area of that Decagon. DECASTYLE, in the an- tient Architefturc, a Building with an Ordonance of ten Co- lunnis in P>onr, as the Temple of ''Jupiter Olympius was. DECIMALS. A Decimal Frucl:on is an artificial Way of fctting down and exprefiing of Natural or Vulgar Fradions, as whole D E D E Numbers : And whereas the Denominators of Vulgar Frac- tions are divers, the Denomina- tors of Decimal Frad'tons arc always certain: For ^Decimal FraH'ton hath always for its De- nominator an Unit, with a Cy- pher or Cyphers annexed to ir, and mud therefore be either lo, I GO, I COO, loooo, ^c. And therefore, in writing down a Decimal FraBion^ there is no Neccflity of writing down the Denominator ; for by bare In- fpcdion it is certainly known, it confiding of an Unit, with as many Cyphers annexed to it, as there are Places (or Figures) in the Numerator. Example. T\\\% Decimal Frac- tion i^j, may be written thus, .25', its Denominator being known to be an Unit with two Cyphers; becaufc there are two Figures in the Numerator. In like ManneriWo may be thus written, .i^if; and M'^A thus, .35-75-; Jind liJ-o thus, .075-; and ■^/^Vo thus, .0065-. As whole Numbers increale in a Decuple, or tenfold Propor- tion, towards the Left Hand, lb, on the contrary, Decimalt decreafe towards the RightHand, in a decuple Proportion, as in the following Scheme. C2 v> , S -'J to a C JZ ,rt to ,0 H'S t- •^-S •' rz uid- S tL jz U4 Vi C ions dred s of uHm dred t« « -5-§ :i: c c 1= *c S 3 sz :-P o Zi t; -a -^ <^ r3 CL, C h-' 1-, -0 0*-^ 765-4321012345-6 Hence it appears, that Cy- phers put on the Right Hand of whole Numbers, do increafethe Value of thofe Numbers in a decuple, or tenfold Proportion; but being annexed to the Right Hand of a 'Decimal Fradion^do neither increafe nor decreafe the Value thereof: So M-o°o is equi- valent to f§^ or .If. And, on the contrary, though in whole Numbers, Cyphers prefixed be- fore them, do neither increafe nor diminilh the Value, yet Cy- phers before a Decimal Fradiott do diminifli its Value in a de- cuple Proportion: For .15-, if you prefix a Cypher before it, be- comes -nhht or -025^ : And .125' is r^ohhh,-, by prefixing two Cy- phers before it, thus, .00125". And therefore, when you are to write a Decimal Fradiion., whofe Denominator hath more Cy- U 3 phers D E D E phers than there are Figures in the Nunieraior, chey muft be fiipply'd by preiixing To many Cyphers before the i'lJures of your Numerator ; as iuppofe ^|^_. were to be written down without its Denominator; here, becaufe there are three Cyphers in the Denominator, and but two Figures in the Numerator, there- fore pretix a Cypher before 19, and fet it down thus, .019. The Integers are fcparated from the 'Decimals feveral Ways, according to Mens Fancies ; but the bcft and moO ufual Way, is by a Point or Period ; and if there be no whole Nnmber, then a Point before the r radion is fufficient: Thus if \o«» were to writedown 317 jVoi,, itmay be thus exprefs'd, 317.217; and J9 roVo o' thus, f 9.002)- ; and y/^Vo • th'js, .0075-. t^Ti-. Reduj2,To reduce a Vulgar Fradion to a ^Decimal: ^SVf&A?*^/)', To find the Value of a Decimal in the known Parts of Coin, Weights, Mea- fijres, id'c. Thirdly^ "T o reduce Coins, Weights, Meafures, ^jfc. to a Decimal. Of thefe,in their Order. 1. To reduce a Vulgar Fradioa io ^Decimal. The RULE. As the Denominator of the given Frav-'lion is to its Nume- rator, fo is an Unit (with a com- petent Number of Cyphers annei'd) to the Decimal re- quir'd. Therefore, if to theNumera- tor given, you annex a compe- tent Number of Cyphers, and divide the Refult by the Deno- minator, the (quotient i> iht De- cimal equivalent to the Vulgar Fradlio'i given. Example I, Let -^ht ^.'iven to be reduced to a De.m^l of two Places, or having 100 for its De- nominator. To 3 (rhe Numerator given) annex two Cyphers, and itm.'kcs 300; which divide bv the I/eno- minator 4, and the Quotient is .7J', the Z)ef/wa7 rcqniied, and is equivalent to \ givtn. Note^ That lo many Cyphers as you annex to the give^i Nu- merator, fo m.my Places muft be pricked off in the Decimal found; and if itflialj happen that there are not fo many Places of Figures in the Quotient, the De- ficiency muft be iupply*d, by pretixing fo many Cyphers before the Quotient-Figures, as in the next Example. Example 2. Let j-f j be re- duced to a Decimal^ having fix Places. To the Numerator annex fix 'Cyphers, and divide by the De- nominator, and the Quotient is jf235-: But it was required to have fix Places, therefore you muft prefix two Cyphers before it, and then it will be .005-235', which is the £)t'f/;«<2/ required, and is equi- valent to jf ,. See the Work of thefe two Examples. 4)3-oo(-75' D E D E 4)3.oor.7; 28 5-73)3.000000(5-233' 20 20 2® 2040 52IO J45 In the fecond Example, there remains 345", which Remainder is very inllgnificant, it being lefs than --— Part of an Unit, mail loooooo* ' and theretore is reje many Places to the Right Hand as there were Places in the 'Deci-mal given ; and multiply thofe Figures pricK'd off by the Number of Parts in the next inferior Denomina- tion and prick off fo many Places as before, and fo continue to do, till you have brought it to the loweft Denon^ination r -quired. Example i. Let .756? of ^ Pound Sterling be given to be reduced to Shillings, Pence, and Farthings. Multiply by 20, by 12, and 4, as the Rule directs, and always prick off four Places to the Right Hand, and you will find it jco make \240 279.25- 139625" 1 1 1 700 1 1 1 700 I24.2662f 4-443 i5'.9^ 3^5-44 399^7 22215' 4449 70.99914 7-35'64 .0126 441384 14712S 73^6 4 .09269064 .0175-32 347 122724 70128 5-25-96 6.083604 32.0752 .0325- 1603760 6415-04 962256 1 .04244400 23.0291 3SAS iooi45'5- 801 I 64 100145-5' 600873 710.0315-95' •75-43^ .0356 45-25-92 377160 226296 .026§5-3792 D E Contraded Muhiplication of Decimals. Becaufe in Multiplication of Decimal Parts and mix'd Num- bers, there is no need to exprcfs all the Figures of the Produft, but in molt Cafes two, three, or four Places of Decimals will be fufficient ; therefore, to con- trad the Work, obferve this fol- lowing RULE. Write the Unit's Place of the Multiplier under that Place of the Multiplicand, vvhofe Place you intend to keep in the Pro- du6l:; then invert the Order of all the other Figures, that is, write them all the contrary Way. Then in multiplying always be- gin at that Figure in the Multi- plicand which ftands over the Figure you are then multiplying withal, and fet down the firll Figure of each particular Pro- dud dire£lly one under the other; but yet a due Regard mud be had to the Increafe ari- /ing from the Figures on the Right Hand of that Figure in the Multiplicand, which you be- gin to multiply at. This will appear more plain by Examples. Example I. Let 2.3S645- be multiply'd by 8.2175, and let there be only four Places retain'd in the Deci- mals of the Produ6l. Firft, D E D E Fir ft, according to the Direc- tions, write down the Multipli- cand, and under it write the Multiplier, thus ; Place 8 (being the Unit's Place of the Multi- plier) under 4, the fourth Place of Decimals in the Multiplicand, and write the reft of the Figures quite contrary to the ulual Way, as in the following Work : Then begin to multiply, firft the 5" which is left out, (only with Regard to the Increafe, which muft be carry'd from it,) faying, 8 times y is 40, carry 4 in your Mind, and fay 8 times 4 is 32, and 4 I carry is 36 ; fet down 6, and carry 3, and proceed through the reft of the Figures, as in common Multiplication : Then begin to multiply with 2, faying, two times 4 is 8, for which I carry i, (becaufe it is above j*,) and Hiy, two times 6 is 12, and i that I carry is 13 ; fet down 3, and carry i, and proceed through the reft of the Figures : Then multiply with i, faying, once 6 is 6, for which carry i, and fay, once 8 is 8, and I is 9 ; fet down 9, and pro- ceed : Then multiply with 7, faying, feven times 8 is 5-6, for which carry 6, (becaufe it is a- bove 5" 5-,) and fay, feven times 3 is 21, and 6 that 1 carry is 27 ; fet down 7, and carry 2, and proceed : Then multiply with f, faying, five times 3 is 15-, for "Which carry 2, and fay, five times 2 is 10, and 2 I carry is 12, which fet down, and add all the groduds together; and the total Produd will be 19,6107. See the Work. 2. 3864 J" 190916 4773 239 167 12 19.6107 Note^ Th;it in multiplying the Figure left out every time next the Right Hand in the Multiplicand, if the Produ6t be y, or upwards to 10, you carry i ; and if it be 15, or upwards to 20, carry 2; and if 25-, or upwards to 30, car- ry 3, '^c. I have here fet down the Work of the laft Example, wrought by the common Way, by which you may fee both the Reafon and Excellency of this Way, all the Figures on the right Hand the Line being whol- ly omitted. 2.3864f 8.2175- II 167 238 4772I90 190916:0 93225- 05-I5- 645- 1 9.6106 y2875- Example 2. Let 375'.! 375-8 be multiplied by 167324, fo that the Product may have but four Pla- ces of jDeclmali. Firft. rj D E D E Firft, fet 6, the Unit's Place of the Multiplier, under 5-, be- ing the t'ourth Place of Decimals in the Multiplicand, (becaufe four Places of Decimals vvere to be prick'd off,) and write all the reft of the Figures backward. Then multiply all the Figures of the Multiplicand by i, after the common Way. Then begin with the fccond Figure of the MaUiplier 6, faying i:x times 8 is 48, for which T carry 5-, (in refpe6t of the 8 left out,) and lix times 5" is 30, and 5- that I carry is 35-; fet down 5- and carry 3, and proceed after the common Method. Then begin with 7, the third Figure of the Multi- plier, and fay, feven times 5; is 35-, for which carry 4, and fay, I'even times 7 is 49, and 4 I car- ry is 5-3 ; fet down 3 under the firft, and carry 5-, and proceed ''•'-r.i;7S'8 the Multiplicand as before. Then beginning with 3^, the fourth Figure of the Multi- plier, and fay, three times 7 is 21, carry 2, and fay three times 3 is 9, and 2 I carry is 1 1 ; fee down I, and carry i, and pro- ceed as before Then begin with 2, the fifth Figure, and lay, two times 3 is 6, for which I carry i, and fay, two times 1 is 2, and I carry is 3 ; fet down 3; and two times 5- is 10; fet down o, and carry i, and proceed as before. Then begin with 4, the laft Figiire of the Multiplier, and fay, four times i is 4, for which I carry nothing, becaufe 'tis lefs than 5" ; then lay, four times ^ is 20; fet down o, and carry 2; and proceed through the reft of the Figures of the Multiplicand. l^hen add all up together^ and the Produd is 6z']6.<)-^io. See the Work. 4237.61 the Multiplier revers'd. oy^i^y^S the Prodnft with I. 225-o82f5' the Product with 6 increas'd wirh 6x8. 2625963 the Produd with 7 increas'd with 7X5-. 112541 theProdud*wirh 3 increas'd with 3^7. ■7^03 the Produft with 2 increafed with 2X3. 1500 the Produd with 4 increas'dwiih o. , 6276 9520 the Produft requir*d. Let D E D E Let the fame Example be repeated, and let only one Place in the Decimals be prick'd off. ojf.i27S^ the Multiplicand. 4237.61 the Multiplier inverted. 375-14 ihe Produ6l by i with the Increafe of 1X7. 225-08 the Produ6t with 6 increafed with <5 x 3. 2626 the Produdt of 7 increfifed with 7x1. 113 the Produd with 3 increafed with 3x5". 7 the Produ6t with 2 increas'd with 2 X7. I the Increafe only of 4x3. 6276.9 the Produd is the fame as before. More Examples for 1^ra£iice. Multiply 39J.3756 by •75'642, and prick off four Places in Decimals. 9p5'. 375-6 the Multiplicand. 2465-7. the Multiplier revers'd. 299.0699 the Produd required. Let the fame Example be repeated, and let there be only one Place of Decimals, 395'-375'6 24657. 1767 the Produd by 7 increafed with 7X 198 the Produd by 5- increafed with yx f. 24 the Produd by 6 increafed with 6 X9-f.6 X 5*. 2 the Increafe of 4 X9-I-4 X 3. 299 I the Produ<2. '". CharaSleri J D E D E Charaders^ and their Signification, Note, That this Mark -f- fig- nifies Addition; as 84-5-, that is, 8 more 5-, or 8 added to f ; and 8-4-3 +7 denotes thele Num- bers are to be added into one Sum. This — (ignifiesSubtraftion, as 9 — 4 lignifies that 4 is to be ta- ken from 9. This Mark X fignifies Multi- plication, as 7X5- lignifies that 7 is to be multiply'd into 5-. This Mark -^ lignifies Divi- fion, as 12 -^4 fignifies 12 is to be divided by 4. This Mark fignifies Equali- ty, or Equation ; that is, when = is placed between Numbers, or Quantities, it denotes them to be equal, as 7-|-)=i2,thac is, 7 more 5- is equal to 12; and 1 5"— 7=8, that is, 15- lefs by 7, is equal to 8, or fubira6l 7 t'rom 15', and there remains 8. This Mark : : is the Sign of Proportion, or the Golden Rule, it being always placed betwixt the two middle Terms or Nu'rbcis in Proportion, thus, 4 : 20 : : 6 : 30, to be thus read, as 4 is to 20, lb is 6 to 30. Divifion of Decimals, Divifion of Decimals is per- form'd after tl^e fame Manner as Diviiion of whole Numbers; but to know the Value or De- nomination of the Quotient, is the only Difficulty; for the re- folving of which, obferve either ot the following RULES. I. The firfl: Figure in the Quotient mud be of the fame Denomination with that Figure in the Dividend which (lands (or is to be fuppofed to ftand) over the Unit's Place in the Divifor, at the firft feeking. _II. When the Work of Di- vifion is ended, count how ma- ny Places of Decimal Vi\xx.s[.\i^XQ are in the Dividend more than in the Divifor, for that Excefs is the Number of Places which muft be fcparated in the Quo- tient for Decimals : But if there be not (o many Figures in the Quotient, as is the faid Excefs, that Deficiency muft be fupply'd with Cyphers in the Quotient, prefixed belbrc the figniricant Figures therc€t", towards tlie Lett Hand, with a Point before them; fo Ihall you plainly dif- cover the Value of the Quotient. Thefe fallowing Dircdions ought alfu to be carefully obfervd. If the Divifor confifts of more Places than the Dividend, there muft be a competent Number of Cyphers annexed to the Divi- dend, to make it confift ot' as many (at leaft) or more Places of Decimals than the Divifor ; for the Cyphers added muft be reckon 'd as Decimals. Conlidec whether there be as ftiany Decimal Parts in the Di- vidend as there are in the Divi- for ; it there be not, make them fo many, or more, by annexing of Cyphers. h D E D E In dividing of whole or mix- ed Numbers, if there be a Re- mainder, you may bring down more Cyphers, and by continu- ing your Divilion, carry the Quotient to as many Places of Decimals as you pleafe. Thel'e Things being confider- ed, I fliall proceed to the Prac- tice of Diviiion of Decimnli^ which I (hall endeavour to ex- plain in as fami'iar and as ealy a Method as poilTble. Example i. Let 48 be divided by 144. In this Example the Divifor 144 is greater than the Dividend 48 ; therefore, according to the Direftions above, I annex acom- petent Number of Cyphers, (viz. four,) with a Point between them, the ufual Way and divide according to i44)48.oocoC.3333 the fecond Rule, there being four Places of Decimals in the Di- vidend, and none in the Divifor; fo the Exccfs of djcimal Fliiccs in the Dividend, above that in the Divifor, is four; fo that when the Divilion is ended, there mull be four Places o^ De- cimals in the Quotient. See the Work. Example 2. Let2i 7.75- be divided by 65-. ^irfl^ in feeking how oft 6s in 217, (the firft 'three Figures of the Dividend,) I find the U- nit's Place of the Divifor to fall under the Unit's Place of the Dividend; therefore the firft Fi- gure in the Quotient will be Ur nits, and all the reft Decimals. Or, by the fecond Ruie, there being two Places of Decimals in the Dividend, and no Deci- mals in the Divifor, there- fore the Excefs of decimal Places in the Dividend, above the Divifor, is two; fo when the Diviiion is ended, feparate two Places in the Quotient to- wards the Right Hand byaPoint. See the Work. But, firft, in feeking how often 144 in 48.0, (the firft three Fi- gures of the Dividend,) I find the Unit's Place of the Divifor to fall under the firft Place of tht Decimals-^ therefore the firft Figure in the Quotient is in the firft Place of Decimals: Or, by Vol. L 65-)2i7.75'(3-35' 227 3^S X Example D E D E Lxwipte r>. Let i6-.is97S be d;\ idcd by 13.2)". ] 3. 2))267.T 5-975(20.163 397)- Iii this Example, 3, the U- nit's Place of the Divilor, falls under 6, the Ten's Place of the Dividend; theiffore (by the fir(t Rule) the lirfl Figure in the Quotient is Tens. Or, by the fecond Rule, the Excefs of De- cimal V\acLr, To there mull ba three Places of Deci/ijah in the Quotient. £xamplc 4. Let rf.67)i)-9 be di\ ded by 375-. 89. 37)-.89)i;.675-T59(.c4i7 ''^39SS 263669 546 In this Example, f, the Unit's Place of the Divifor, talis un- der 7, the fccc-nd Place of De- cirmls in the Dividend ; there- fore (by the firll Rule) the firll F'ijurc in the Quotient is in the fecond Place of Decimals ; fo that you mud put a Cypher be- fore the firft Figure in the Quo- tient: And (by the fecond Rule) the Excefs of decimal Places in the Dividend, above the Num- ber of ri'c-aV^rt/ Places in the Divi- for, is 4; for the decimal ^Hcts in the Dividend is 6, and the Number of Places in the Divi- for but two; therefore there muft be four Places of Decimals in the Quotient. But the Diviilon being tiniOied after the common Way, the Figures in the Quo- tient are but three, therefore you mult prefix a Cypher before the fignificant Figures. Example ^. Let 72.1^64 be divided by -1347. •I347)72.•I5'64C5'3^6S 4806 765-4 9190 1 1080 304 In this Example, the Divifor being a Decimal, the tirfl Figure thereof fills under the Ten's Place m the Dividend; there- fore the Units (if there had been any) fliould fall under the Flun- d red's Place m the Dividend ; and 'Co the fir ft Figure in the Quotient is Hundreds. And, by the fecond Rule, there being four Places Df Decimals in the Dividend, and as many in the Divifor, fo the Excefs is nothing; but in dividing, I put two Cy- phers II D E D E phets to the Remainders, and continue the Divifion in two Places farther, fo I have two Places of Decimals. See the Work. Example 6. Let .125' be divided by .0457. 914 3199 1610 1371 2390 228^ 105- In this Example, the Unk's Place of theDivifor (if there had been any) would fall under the Units Place of the Dividend; therefore the firft Figure cf the Quotient is Units. And by the fecond Rule, there being fevea Places of Decimals in the Divi- dend, and but four Places in the Divifor, fo the Excefs is three; therefore there muft be three Places of Decimals in the Quo- tient. Ifhallfetdownonly the Work of fome few Examples more, and fo proceed to ContraHed Divifion, .O045'6(.ooooo5'979i(.ooi 51 1419 Let it be divided by 2S2. 282)1.0000000(003^-461 fere. 15-40 1300 1720 280 .325'). 400000(1 .2307 75-0 1000 2^00 225" .042) 495'.ooooo (i 1 785'.7i ys 330 360 240 300 60 18 X Divifion D E D E Divijion of Decimals contraSled. In Divillon of Decimals the common Way, when the Divi- for hath many Figures, and it is required to continue the Divilion till the Value ot' the Remainder be but fmall, the Operation will fometimes be large and tedious, but m.ay be exceliently contrad- ed by the following Method. the RULE. By the firfl Rule of this Chap- ter, find what is the Value of the firil Figure in the Quotient ; then, by knowing the firft Fi- gure's Denomination, you may have as many or as few Places of Decimals as you pleafe, by taking as many of the left Hand Figures of the Divifor as you think convenient for the firft Di- vifor ; and then take as many Figures of the Di^ idend as will anfvvcr them; and in dividing, omit one Figure of the Divifur at each following Operation. A few Examples will make ir plain. Example i. Let 721 I75'62 be divided Dy 2 25-743, ^"'^ ^'^^ there be three Places of Decimals in the Quotient. ^^•2^743) 721. i7f 16^(3^9-4^7 6']']xi(^ 43946 22^74 21371 20317 1055- 90? in this Example the Unit's Place of the Divifor falls under the Hundred's Place i:i the Di- vidend, and it is required that liiree Places of Decimals be m the Quotient ; To there mult be iix Places in all, that is, three Places of the whole Numbers, and three Places of Decimals' Then, becaufe I can have the Di- vifor in the fit It fix Figures of the Dividend, I cut off the 62 with a Dafli ot the Pen, as ufe- lels ; then I leek how oft the Divifor in the Dividend, jnd the Anfwer is threeTimes \ put three in D E D E in the Quotient, and multiply and fubtraft as in the common Divilion, and the Rem;iinder is 43946. Then prick off'tiiree in the jjivifor, and feek how often the remaining Figures may be had in 43946, the Remainder, which can be but once; put i in the Quoiicnt, and multiply and fub- tradl, and the next Remainder is 21372. Then prick off tiie 4 in the L)i\ ifor, and leek how often the remaining Figures may be had in 21372, which will be 9 times ; put 9 in the Quotient, multiply thus ; fiying nine times 4 is 36, tor which 1 carry 4, (in refpcd of the 4 Inft prick'd off,) and nine times 7 is 63, and 4 is 67 ; fct down 7, and carry 6, and lb proceed till the Divilion be finiflicd, always rcipcding the Incrcate made from the Figures prick'd off. Obferve the Work, which will bet'er inform you than many Words. ^•i5'743)7ii'i75^2 (319.467 677229 43946 225-74 21372 32 2031687 105- 5" 45-0 902 972 1^2 111 17 15 4780 44f8 03220 80201 23019 I have fct down the Work of this lalt Example at large, ac- cording ro the common Way, that thereby the Learner may fee the Rtafoia of the Rule, all .the Figures on the right Side the per- pendicular Line being wholly omitted. Exar/iple 1. Let 5 1 7 1. 5-91 65* be divided by 8758615-, and let it be required that four Places of Decimals be prick'd off in the Quotient. 8.7^86i0^i7i-5'9i<^l5'(f90-45'77 4379307^ 7922841 7882754 40087 3P34 5-05'3 4379 674 613 61 61 In this Example I can't have 8, the firft Figure in the Divifor, in 5", the firft Figure of the Di- vidend ; fo that the Units Place of theDiviforfalls under the Hun- dred's Place of the Dividend ; fo that there will be feven Figures in the Quotient, that is, three o^ ■whole Numbers, and lour of Decimals ; therefore there muft be leven Figures in the Divifor, X 3 (becaufe D E D E (becaufe the Number of Places in the Divifor andQuiuicnt will be equal,) and there muft be eight Places in the Dividend • fo that I cut otT the Figure f with a Dafh, as ufelefs. I'hus having proporiion'd the Dividf^nd to the Divifor, and both to the Num- ber of Places or Fig ires defired in the Quotient, I proceed to di- vide as before, ftving, how often S in 5-1, which will be five times; put s in the Quotient, and mul- tiply and fubtrad, and the Re- mainder is 7922841. Then I prick off the firll Figure in the Divifor 5-, and feek how often the remiiir.ing Figures of the Di- vifor are in the aforefiid Remain- der,)which Ifind 9 times; put 9 in the Quotient, and multiply there- by, laying, nine times ^ (the Fi- gure prirk'd off) is 45-, tor which - 1 carry 5-; and lay nine times i is 9, and 5" I carry is 14; let down 4, and carry i, and pro- ceed to multiply the refl: of the Figures, and fubtra6l, and the Remainder will be 40087. Tht-n prick off the Figure i, and feek how often 875-86 in the Remain- der 40087, the Anfwer will be o; lb put o in the Quotient, and prick off the Figure 6, md feek how often 8758 in 40087, which will be four times ; put 4 in the Quotient, and multiply, laying, four times 6 ( the Figure lalt prick'd off) is 24, for which I cairy 2; and lay, four times 8 is 32, and 2 I carry is 34; fet dov\n 4 and carry 3 ; multiply the reft of the Figures, and fub- tradt as before, and fo proceed after the fame Mfuncr, until all the' Figures of the Divifor be prick'd off, to the laft Figure, -^ee the VVorA:. Example 3. I>ct 25". 1367 be di- vided by 217.3543, and let there be five Places of Decimals in the Quotient. In this Example, 7, the Unit's Place of the Divifor, falls under I, the firft Place of Decimals ; therefore the firft Figure of the Quotient is in the firft Place of Decimals^ fo the Quotient will be all Decimals : Then be- caufe the Quotient-Figures, and the Figures of the Divifor will be of an equal Number, dafh off the 43 in the Divifor, and the 7 in the Dividend, as ufelefs, and divide as before. 217-35143) 25'-i?6|7Gii564 21735- 3401 2.174 1227 1087 140 130 10 8 Although I have hitherto given Directions for proportioning the Divifor and Dividend, fo as co bring into the Quotient what * Number of decimals you pleafe, yet there is no abfolute Neceffi- ty for it ; but you may carry on your Divifion to what Degree you pleafe, before you begin to prick off the Figures of the Di- vifor, in order to contrad the Work, as in the following Ex- amples, D E D E amples, where it is not required be do le according to Difcrc- to prick off any doterniiiiate (ion. Number of Dccimah\ bat it may ^■JS^JS'^) 74M 7^717 C26S9.671 18 I 190 12)- 5- 1 I 6540536 24720157 22054048 2666109 3^48 1 oSo 185029 J65405 19624 19297 327 276 ■ri 28 21, I X4 12,34254) D E D E ii-34ir4)5'i4-7M9S(4i-7-""f7n 2105-338 123425-4 871084 86397S 7106 6171 93f 864 71 62 PECK-NAILS. See Nails. DECORATION, in Archi- tcdure, an Ornament in a Church, or other pubh'ck Place; or what adorns and inriches a Building, Triumphal Arch, zsfc. either on the Infide or without. The Orders of Architecture contribute a great deal to the Decoration ; but then the feveral Parts of thefe Orders mud have Decor attoKs alfo fignify the Scenes of Theatres. The Deco- rations in Opera's, and other theatrical Periormances, mud be ofceri changed, in Conformity 10 the Subjedt. ' ' The Antients had two Sorts of Decorations for their Theatres : The firft, called i^crfatiles^ ha- ving rhree Sides or Faces, which were turned facctdivcly to the Spe6lators. The other, called DuCiilcs^ which were drawn or Hidden before others. The Ifjtter Sort of Decoration is dill in ufc, and to greater Ad- vantage among us than the An- ticnts, who were under a Ne- ccdity of drawing a Curtaiii whenever a Change was jiiade in the Dec»ration ; where;iS the Change is made in a M >menr, and without fcnrce being per- cciv'd upon our vStagc. DECORUM? 1. e. Decency, DECOR 5 'i* particular- ly uied in Archictdure for the Suitablenefs of a Building, and the feveral Parts and Ornaments thereof, to the Station and Oc- calion. ViiriivtHs is very exaft in this Point, and gives Rules exprefly for the appropriating or fuiting the feveral Orders to their natu- theirjud Proportion, Characters, ral Charadcrs : So that, e.g. a and' Ornaments ; or otherwife the fined Order will bring Con- fulion rather than Richnefs. Decorations in Churches are Paintings, Vafes, Fedoons, er'f. bccafionally placed on or againd the Walls, but fo difcretionally, as not to take oft^any thing from the Form and Beauty of the Ar- chitedure, as is much pradtifed in Italy at the folemn Fcads. Corinthian Column diould not be fct at the Entrance of a Pri- fon or Gate-Houfe, or a 'Tufcan in the Portico of a Church, as has been done by fome of our Builders, who have offended even in the Difpolition of the Ofiices in oLir ordinary Houfes ; vye of- ten finding the Kitchen fet where the Parlour iTiould be ; and that in the fird and the bed Story, which D E D E y.hich fiiould have been con- oemncd to the lowed and word. Some interpret Decorttm to Signify the oblerving a due Re- aped bctVv'ccn the Inhabitant and Habitation ; Whence Palladio concludes, that the principal En- trance muft never be regulated by any certain Dimenfions, but iaccording to the Dignity oi the Perlbn \vho is to live in \x.\ yet to exceed rather in the more than in the lefs, is a Token of Gene- rofity, and may be exculcd with fome notable Emblem or In- fcripcion, as that of the Conti di BaviUuqua over his large Gate at Verona^ (where probably there had been fome Difproportion committed;) 'Patet janua Cor rnagis^ i.e. My Gate is wide, but mv Heart more wide. DECUrLE, ii" Arithmetick, a Term of Relation or Propor- tio'i, implying a Thing to btr ten times as much as another. DECUSSATION, in Geo- metry, Opticks, ^c. the Point in which two Lines, Rays, l^c. crofs or interfcc). each othi:r. DEFICIENT NUMBERS, in Arithmetick, .are fach, whole Parts added together, make lefs than the Integer, e.g. 8, whofe quota Parts are 1,2, and 4, which together make no more than 7. DENTICLES? in Architec- DENTILS S ture, an Or- nament in Corniches, bearing ibmeRefemb'ance to Feeth, par- ticularly atfc6red in the Ionic and Corinthian Orders. They are cut on a little fquare Member, properly called Benti- cnlus\ and the Notches or Orna- ments themfelves Dentes., from Dens., L. as refembling a Row of Teeth, In antient Times Dentils were never ufed in the Ionic Cornice • yet they arc found in the Re- mains of the Theatre of Mar- celliis-, v/hich fome take for an Argument, that ^itruvius had not the Diredion of that Build- ing. (^iiruziiusprai'cnbss the Breadth of each i?^;;;r/7, or I'ooth, to be its Height; and the Indenture or Interval between each two, he direds to be two Thirds of the Breadth of the Dentil, He alio in his fourth Book ob- ferves, that the Creeks never put Di-ntils under Modilionf, be- caufe Modilions reprefent Pur- lins; vjhQv^z^ Dentils reprefent the Ends of Rafters, which can never be placed underneath Pur- lins. The Romans were not fo fcru- pulous as to this Decorum., ex- cept in the Pantheon, where there are no Dentils under the Modi- lions, neither in the Portieo, nor the in/ide of the Building. DESCRIBENF, \n Geome- try, a Term expreffing fome Line or Surface, which by its Motion produces a Plane Fi- gure, or a Solid. DESIGN, m Architedure, Zffc. is the Draught, or the I'houghr, Plan, geometrical Re- prefentation, Dillribution, and Conflrudion of a Building, ^c. In Building, the Term Ichno- graphy may be ufed, when by Defign is only meant the Plan of a Building, or a flat Figure drawn on Paper. And whe:i fome Side or Face of the Build- ing is raifed from the Ground, we may ule the Term Ortho- graphy; and when both Front and D I D I and Sides are feen in Perfpedive, we may call ic Scenography. DESIGNING \'<\he Art of delineating or drawing the Ap- pearance ot natural Objects by Lines on a Plane. DIAGONAL, in Geometry, is a Right Line drawn acrofs a Figure ot'f<;veral Sides, from the Vertex of one Angle. Some Authors call it Diameter, and others Diametral of" the Figure. Fir/}, It is demonftrated, that every Diagonal divides a Parallelogram into two equal Parts. Secondly, That two Dia- gonals drawn in any Parallelo- gram, bife£t each other. 'Thirdly, That the Diagonal of a Square is incommenfurable with one of its Sides. DIAGRAM, in Geometry, a Scheme for the Explanation or Demonltration of any Fi- gure or Proportion belonging to it. DIAL, an Inftrument where- by to know the Hour or Time of the Day, when the Sunfliines. The firft Sun-Dial that was fet up in Rome, was erected by Pa- f\rius Cwrfor, about the Year of the City, 447: For P//»)' fays, ihere was no Mention of any Ac- count of Time, but of the Sun's Setting and Riling. This Dial was fet up in the Temple of ^a/Ww«r, but it went not right. About thirty Years afcer this, M. Valerius Mejfala, i:iys Farro, being Conful, brought our of Sicily^ from the taking of Cnta- na, "^anothcr Dial which he fet up on a Pillar near the Rojlrur/i'-, but it not being made for that particular Latitude, it could not ^o true. Neverthelefs they Wiade ufc of it for eleven Years ; and then Marcius'Philippus,who was Cenfor with Lucius Tau- his, fet up another that was more exad. The Greeks alfo were a long Time without Clocks and Sun- Dials. Some afcribe the In- vention of Sun-Dials to Anaxi- mene% Miletius, and others to Thales. There are many Kinds of Dials mention'd by Fitruvius ; as one invented by Berofus the Chal- dean, which was on a reclining Plain, parallel almofl: to the Equinoftial, there was an half Circle upon it; and thence it was called Hemicyclus. Arijiarchus Samius found out the Hemifphere-DiaU And there were fome Spherical ones with a Needle for a Gnomon. The Difcus of Arijlarchus was an Horizontal Dial, with its Limb raifed up all round to prevent the Shadow from extending it- felf too far off. Dial-Planes are of two Sorts. Firji, Such as are made on the Wall of aBuilding. Ox, Second- ly, luch as are drawn on Tables of Wood, commonly called Dial-Boards. The firft Sort, if they are made on Brick Work is done by Plaiflering on the Wall with Lime, Sand, and Hair mix'd: This, if well drench'd with Lin- feed Oil, after it is dry, or as long as it will drink in any, and afterwards with Oil and white Lead, may be durable enough. But it will be a better Way to temper the Lime, Sand and Hair, with Ox Blood, which will be no great Charge, but of great* Advantage; for this Mixture will equal in Time the Hard- nefs D I D I I nefs of a Freeftone, and keep the Surface as much from the Injuries of the Weather; but it muftibe afterwards pointed v/hite. If you are to work on a Stone, the beft Way is to drench the Stone with Linfeed Oil and White Lead, very thin, till it will drink in no more; then will the Dial you paint upon lalt the longer, and be the better prepared to refift the Ruins of Time Now for Tables or Dial- Boards of Wood, they being moll: common, I (hall give fuch Directions for the making of them, as have been always found moft profitable and fit for the Purpofe. The beft Wood for this Pur- pofe is the cleared Oak, and the reddeft Fir, provided it be not turpentiny. There is but little Difference between thefe two Woods as to their Alteration by the Weather, both being fubjedl to fp'it, in cafe they are bound, and have not iree Li- berty to fhriiik with dry Wea- ther, and to fwell with Wet. Bur as to their lading, Oak feems to be the better of the two : Though good Red Fir that is hard, will ordinarily lafttheAge of a M^in, if it be fecured as fuch 1 hingsought to be. In working eiiher of thefe Kinds of Woods, firft cut the Boards to fuch a Length as you intend the Deal Board Ihould be, and fo many of them as may make up the Breadth dcfigned'; then let them be jointed on the Edges, and planed on both Sides, and afterwards fet to dry : For it has been obferv'd, that though Boards have lain in an Houfe ever fo long, and are ever fodry, yet when they are thus fhot and planed, they will fhrink after- wards beyond Belief, if kept dry. When they have been thought to have been dry enough, and Vv'ill fiirink no more, let them be again fhot with good Joints, and let every Joint be fecured by two Wooden Dove- tails, let in crofs the Jcn'nt on the Backlide; but let this be done when the Boards arcglued 'together, and well dry'd. After they have been thus glued, and the Joints are fuffi- ciently dry'd, th.en let the Face of the Board be well planed, and try'd every Way, that it m.iy be both fmooth and true, and all of a Thicknefs, as Pan- nels of Wainfcc)t are com- monly wrought. The Edges muff be thus true and even, that they mav fit in- to the Rabet of a Moulding put round ir, juft as a Faimel of Wainfcot does in its Frame. This will give Liberty to the Board to flirink, and fwell with- out tearing; whereas Mouldings that are nailed round the Edge, as the common Way is, do fo refirain the Motion ofthcWood, that it cannot flirink wi hout tearing; but Boards wrought af- ter this Manner will lalt a long Time, without cither parting in the Joints, or fplitting In the Wood. Dials are fometimcs drawn on Planes lin'd with Copper or Lend, thnt they may be free from fplitting or tearing; but a Bonrd (if it be made as above direfted) is thought preferable to them in many Befpeds. As, D I D I As, F;Vy?, It is much cheaper. Secondly^ Lead (and Copper too, a little) vili fwell with the Heat of the Sun, and grow in Time hollow outvvrirds or convex, in- ftead of a perftd Flat, lb that the Truth of its Shadow will he much injured. Thirdly^ the Colours will be apt. to peel from the Metal, and the Dial vjWX by that IVieans be in danger to be looner defaced^ than if it were painted on a Wooden Plane. For Cjluing the Joints of Dial Boards, lee the Article Glue. DireSlions for Paintings &c. a Sun-Dial. Four Colours arefufficient for this Woik, I'tz.- -^payiijh Bruwn^ for the Priming, or firlt Colour. 14'bite Lead for the lecond Co- lour, and finilliiug the Face of the Table. I'^ermilii'jn for drawing the Hour- Lines. And, Lamp-Dliick for the Figures in the Margin, refpcding the Lines of every Hour, if it be a plain D.il. Eiit if you -ivould have the Fi- gures gilded, tiicn forne others are required, as Gold, and the Size to lay it on, and Smalt, for a blue Ground, if you would have a rich Colour. But fome lay the Ground where the Figures are gilt, with Ver- miiiion : And that ihews well, if the Figures are lifted with black , and a black Moulding round the Dial. The next Particular ihould be thePrndice of painting the Dial ; but before that can be done, the Draught mult be drawn i and therefore it will not be unfea- Ibnable to dire6l to the btft Au- thors who have wrote on the Subicd ofDtalliug. As, Fnji, Stirrup's Dwlliftg^ aS being of excellent Ufe to ac- quaint a young Learner with the Knowledge of the Sphere, that he may underlknd the Na- ture and Reafon oi Dials. Secondly., Collins\ Dialliifg^ a very uilful Book, Thirdly., Ley bourn's Dialling^ h\ which you have the beft Ways for drawing Eaft ana Welt i)/Wj, and far Deciders. Fourthly., Colitns\ Sector on a ^{udrant: In which you have communicated the Cut of a Scale, that by knowing the De- clination, gives all tlie rell of the Rcquifues of an Upright Decliner, by Infpcdion only, with as great Exadnefs, as by the nicelt Calculation : Bclides, it teaches the Way of drawing the Hours of a Dial by a Tan- gent Line, and alio by the Scale ()f Hours; two of the bLlt and molt e.\pedi:ious Ways that ever were yet found out. The PraSiice of painting Sun- Dials. When according to the Rules given in the Books before men- tioned, you have diawn «>n the Paper the Draught of your Dial., and your Board is ready, and al- io your Colours prepared, ac- cording to the Dire6lions be- fore given, you fhould then in painting your Dial, proceed as follows: Take Spanijlo Brown., that has been well ground, and mixe4 moderately D I D I moderately thin, and withalarge BrilUe-Brulli dipped in ir, colour the Bo:ird or Plane all over, on the Back as well as on theb'ore- lide, to prelcrve it the ijetcer, fo that no Part be let't uncoloui'd; This is cilled the Priming of a Dial. When this tirft Colour is dry, do it over again with more of the fame Colour, temper'd fomewhat thicker; and when this is alfo dry, you may, if you pleafe, do it over again v/ith the liime Colour : The Work will be the fubftantialler, and lalt the longer. VVhen this lafl Time of Co- louring with the Priming is done, then colour the Face of the Dial-P/aae over wich White Lead ; and when that is dry, work ic over again three or four Times more, fucceflivelv after each Drying; and ft) will the Face of the Dial-Piaae be fuf- ficiently defended againihhe ma- ny Years Fury and Violence of the Weather. When the laft Colouring of the White is drav/n, you mud draw on the Plane, with a Black Lead Pencil, a Plorizontal Line, fo far diftant from the uppermolt Edge of the Dial, as your Dif- cretion fliall think fit, or your Experience finds fhall be moA becoming the Plane* Then ftt out the Margin of the Dm/ with Boundary Lines for the Hour, Half Hour, Quarters, and Quarter-Divllions of the Dia/, as vou fee done in mofl: Dia/s. Wiu'u the Margin and Boun- dary Lines of tlie Dial are fee out, then take your Paper- Draught, that has been fairly drawn, and place the Horizon- tal Line of that, on the Hori- zontal Line that you before drew on the Plane; in doing of which, obferve to place the Centre according as the Situa- tion of your Plane, for Conve- nience take, requires. Thus if your Dial be a Full-South Dial, then let the Centre be exactly ill the Middle of the Plane: Biit if your Dial decline from the Sou:h, either La(t or Welt, then pbce not the Centre of your Draught in the Centre of your Plane, but nearer to one Side or other of it, according as it de- clines, having alfo Regard to the Quantity of its Declina- tion. As for Example : U your Dial decline Ealtwards, then let the Centre of your Draught be placed between the Centre and the Eaftern Side of your Plane, the Quaniity thereof mud be according as your Dia^ declines: If it declines but a little, rhen place the Centre of your Draught but a little from the Centre of your Plane; and if it declines much, piace the Centrcof your Dr;''.ng'it the more out of the Centre or your Planc. The Reafon of adviling this, is, that by fo doing you may gain a greater Diftancc for thofe Hour-Lines, which in declinini; Planes, fall nearer together on one Side than they are on the other : For which Reafon, it is nfual fo to do in declining Planes,, except they decline far, as between eighty and ninety Di.'grees : For in this Cafe, th(7 are commonly drawn withoi-t Centres, to gain the greater Dilhncc-for the Hour-Lin-s. When D I D I When the Paper-Draught has been thus artificially placed on the Plane, and taltened with Pins, or Imall Tacks, then let the Draught of it be transferred on the Plane, by laying a Ru- ler over every Hour and Quar- ter-Diviiion, and where the Ru- ler cuts orinterfcfts the Bounda- ry Lines of the Margin, there make Marks, by drawing Lines with a Black Lead Pencil, of luch a Length as each Divilion requires, (or is defign'd by your Boundary Lines,) obferving al- ways to draw the Hour and and Half Hour Lines quite through your Margin, that they may be Guides tor the right placing of the Figures, and for a I'mail Spot that is ufually pla- ced in the Margin, right againft the Half Hour. When this Dial Draught has been thus transferred to the Plane itfelf, you muft not for- i^et to draw the Subllilar Line according as it lies in your Draught, to be a Guide for the light placing the Stile or Cock,; for you nmft be very exad in every Particular, or elfethe Dial will not be right. Every 1 hing that is requir'd being taken from the Draught, and' transferred to the Plane, then take thcDraught oft,and with Vcrmiiliou very well ground and prepar'd, as is before taaght, let the Boundary L'nes of ,your , Dial, as aUb the Hour, Half Hour, and Quartcr-Divilion be drawn therewith: Let your Co- lour be as thick and as ftitf as vou poffibly can work it, fo as to draw a clear and fmooth Line; bccaufe this is to be done but once. When your Vermillion Lines are drawn, then make the Fi- gures vvith Lamp- Black, and a Spot in the Middle of the Margin, right againft the Half Hour Line; and, if you pleafe, in the Margin at the Top of your Plane, you may put the Date of the Year, your Name, and fc^me Sentence as is ufual in Things of this Nature. Then fit in your Cock, fo as to make right Angles with the Plane. So fhall your Dial be drawn, and finiifi'd in ail Refpefts as a plain Dial ought to be. If you would have the Figures in Gold, fee Gilding. DiAxMETER, in Geometry, is a Right Line, pafTing through the Centre of a Circle, and ter- minating on each Side at its Cir- cumference. The Properties of the Diamc ter, are, Firjl^ That it divides the Cir- cumference into three equal Parts. And hence we have a Method of defcribing a Semi- circle upon any Line afTumhiga Point therein for the Centre. Secondly^ The Diameter is the greatelt of all the Chords. Thirdly, To find the Ratio of the Diameter to the Circumfe- rence. Archimidfs has found the Ratio of the Diameter to the Citcuai- ference, as 7 to 22,. Modern Practical Geometri- cians alFume the Diameter to be to the Circumference, as 100 to 314- Ad. Metius gives us the Ratio oi \}\e^ Diameter to the Circum- ference, as 113 to 3j'5', wh'ch is the moft accurate of all (hofe exprefs'd D I D I exprefs'd in fmall Numbers, as not erring 3 in 1 00000000. Diameter of a Column^ \s that taken juft above the Bafe. From this the Module is taken, which meafures all the other Parts of a Column, Diameter of the Swellings is that taken at the Height. Diameter of the D tminution of Columns^ is that taken from the I'op of the Shafts. DIAMOND-GLASS. See Quarry. Diamond-Pavement. See Pa- ving. DIAPHANOUS, tranfpa- rent, or pellucid, i.e. giving Paf- fage to the Rays of Light, as Water, Air, Glafs, Talk, fine Porcelane, ^c. DIAPHANEITY, the Qua- lity of a tranfparent or pellucid Body. DIASTYLE, in the antient Architefture, an Edifice where the Columns (tand at fuch a Diftance one from another, that eight Modules, or four Dia- meters, are allowed for the In- tercolumniation. DIE, a Term apply'd to any fquare Body, as the Trunk or Naked of a Pedeftal, which is that Part included between its Bafe and Cornice. DIGGING. T\\tDiggingoi the Ground for Cellars, and for the Foundations of Build- ings, is commonly done by the Yard foHd, containing twenty- feven folid Feet, which is com- monly counted a Load. Therefore take the Dimen- fion in Feet, multiply the Length by the Breadth, and the Pro- du£l by the Depth, and then di- vide the laft Produdt by ^7, and the Quotient will give the Content in folid Yards. DIMENSION isiheExtcn- fion of a Body confidered as capable of being meafured. Hence, as we conceive a Bo- dy extended, and capable of be- ing meafured in Length, Breadth, and Depth, we conceive a trine Dimenjion.^ viz. Length, Breadth, and Thicknefs. The fii (t is cal- led a Line, the fecond a Sur- face, and the third a Solid DIMINISHING of Columns. See Column, and Diminu- tion. DIMINUTION, in Archi- tefture, is the Coiitra£tion of the upper Part of a Column whereby its Diameter is made lefs than that of the lower Part. All Archite6ls have made their Columns lefs above th:iit below, with Delign to attain thofe two important Points in Architefture, Strength, and the Appearance. Some again have made them a little bigger towards the Mid- dle, than towards the Bottom, which is called the Swelling. Indeed, neither Diminution .^ nor Swelling, are obfcrved by the Go^/^/V^Architedts, who make their Columns perledly Cylin- drical ; for which Reafon they are properly called Pillars, ^m Contradiftinftion to Columns. The Diminution of Columns commences generally from one Third of the Height of the Co- lumn; though fome begin it from the very Bafe of the Co- lumn, and fo go on tapering to the Capital ; but this is not eftcemcd to have fo good an Ef- fect. ViiT»vius D I D I P)truv'!Ui himfolf would have the Dirntraition of Columns be ditferent. according to their Height, 'and not according to their Diameter : As tor Example, he diminiihes a Column of if Feet in Height a fixrh Part of its Diameter, and another of fo only one eighth Part; but this Rule of D'tminution is not found to have been obferved in the Antique. Mr. Terratdt obferves, that a Difference of Orders does not infer a Ditference in Duninu- tiom; there being in difterent Works of the fame Order both fm-.ill and ^xcai ljim!f7Ujtofts ; but however, except ihc'lufcan Or- der, which yitrnv'nis diminilhcs by a fourth Part; though /^^/^/?oA? does it only by a fi.th, and the Tra]f.n Column by a ninth. Btrnmutmn in Antique Build- ings, are very differently adjuft- ed'^ as well as in different mo- dern Authors. M- ^-' Clerc fays, all Diminu- tlorjs of Columns begin to dimi- nifh in Thicknets from one Third of their Height. But in Proportion, as their Orders are more delicate, their Diminution ought to be lefs fenfible. For inftance, in the Tufca-a Order, where the Column is but 14 Modules high, its Semidia- meter under the Aftragal may be diminifhed fix Minutts. In the Tuj'can Order, where the Column is if Modules high, \\.%Biynimni(jn under the Allragal may be but f Minutes and a half. In the l^cric Order, where the Column is 16 Modules, the Dt~ minntion may be but tive Mi- nutes. In the Ionic ^ where the Column is 18 Modules, the Diminution may be but four Minutes and a half. And in the Reman and Corin- thian^ no more than four, that is, VL Diminution of four Minutes on each Side the Axis, is the ut- moft that the Column will un- dergo, though it always incrcafes in Height in Proportion to its Thicknefs. Indeed, fays he, according to foiTie Authors, the Diminution of Columns, even of the fame Or- der, onght to be greater or lefs, according as their Heights are greater or lefs. For li. fiance, a Doric Column, fay they, 20 Feet high, muft have lets Diininution than another of 15- Feet; and one of 30 lefs than one of 20. The Reafon they give for this, is, that the Great- ncfs of the Height cafily impofes on the Sight ; and hence they conclude, that a very tall Co- lumn muft of itlelf appear di- miniflied towards the Top. Nor can it be denied, but that this holds true, where tht Eye is placed near, and looks up from the Bottom to the Top of the Column ; but then it is to be conlidered, that large Columns are never made with delign to be viewed thus near; but always at a Dilfance fuitabie to their Height : And it would be ridi- culous to fpoil their Proportions, out of Complaifance to fuch as fliould pleafe to view them at an improper Diftance. Therefore, fays he, in my Opinion, when any certain Di- mtnution of a Column has been once edablilhed, provided it does but pleafe the Eye when viewed at D I D I at n Diftaiice, it ought never to bo. changed on Occalion of any. Alteration in the Height of the Column, excepting it fliould be found in fome clofe narrow Place ; which yet can never hap- pen, unlefs in the Inlide of a Building : For Inlhnce, of a Dome, or the like; to which a prudent Architeft will always have a particular Regard. Bur, lays he, here it mufl be remcmber'd, that I am here fpealc- ing of Columns of the fame Or- der; for in ditTerent Orders the D :;nh2ution mufl: be different. But as to the Doric Column, for Inftance, be its Height an hun- dred Feet, or be it but ten, its Diminution fliould always be the fame, at leaft, this is my Opi« nion. DIOPTRICKS is the Doc- trine of refrafted Vilion, which are alfo called Diaclajlicks . They are properly the third Branch of Opticks, whofe Office is to con- flder and explain the Effeds of Lighr,refra61:ed by palling through different Mediums of Air, Wa- ter, Glafs, er't-. DIPTERE 7 in the antient DIPTERON3 Architedure, fignified a Temple fiirrounded with two Rows of Columns, which form a fort of Portico's, called /f-Wj or I/les. 'jPfeudo Diptere is the fame, excepting, that infiead of the double Row of Columns, this ■was only encompalfed with a iingle one DIRECT VISION, in Op- ticks, is that which is perform'd by dircet Rays, in Contradiftinc- tion to FiF^on by refra£i:ed or re- fleded Ravs. Vol. I. Dired Vifion is the Subjeil of Opticks, which prefcribes the Laws and Rules thereof. Dired Rays^ are fuch as pafs in direct Lines from the Lumi- nary to the Eye; without being turned out of their rc6tilincary Dircclion by any intermediatu B.idv, cither opakc or pellucid. Dired, in Arithmetick. 7^he Rule of Three Dired^ is that op- poiite to the Inverfe. In the Dired^ the fourth Number re- quired increales the Proportion; and in the Inverfe^ diminillies it. DIRECTION, in Mecha- nicks, or Litie of Diredion, is particularly ufed for a Line pal- ling from the Centre of the Earth through the Centre of Gravity of a Body, and the Support or Fulcrum that bears it. A Maa mult of Neceffity fall down, as foon as the Centre of his Gra- vity is out of the Line of Diree- tion. A,7gle of Diredion^ in Mecha- nicks, is that which is compre- hended between i\\t Lines of Di- redion of two confpiring Powers. Line of Diredion, in Mccha- nicks, is that Line in which a Body moves, or endeavours to proceed. Magnetical Diredion \s ufed. in the general, to lignily theTen- dency or Turning of the Earth, and all magnetical Bodies^ to cer- tain Points. The Situation of our Earth is known to be fuch, that its Axis is the Axis of the Univerfe, and therefore its Poles and Cardinal Points correfpond cxadly to thofe of it. This Situation fome account for hence, that it is the moft Y commodious D I D I commodius, in refpefl to the Afpcds and Influences of the heavenly Bodies, and renders it the fittcfc Habitation for Man. Others maintain, that this Po- fition of t-lie Earth is the Efted ofamagnctick Virtue; andfup- pofe a c'clfftial Pole, wirh a like magnetick Virtae, which extend- ing as far as our Earth, draws the correfpondent Part of it, the Pole, towards itfelf. DIRECTLY, in Geometry, a Teim ufed of two Lines, which arc. faid to be diredly a- gainll each other, wheii tl-.ey are Parts of the fame Right Line. In Mechanioks, a Body is laid to Itrikc directly againll an- other, if it ftrike in a Right Line perpendicular to the Point ot Cont^-.a. A Sphere is fliid to flrike d\- redly againil: another, when the X/ine of Direction palles through both their Cf.Titres. DIRECTRIX? in Geome- DIRIGENF $ try, a Term which expreffes the Line of Mo- tion, along which the defcribent Line or Surface is carried in the Genejis of any Plaoe or folid Figure. DISC^ in Opticks, the Mag- DISK3 nitudc of Pelefcope- Glalles, or the Width of their Apertures, whatever their Figure bo, whether plain, convex, me- Difcus, 'z5'c. DISCREET Proportion-^ DISJUNCT Proportion 3 !S when the Fvatio of two or more Pairs of Numbers, or Quantities, is tr;e fame, but not continual, that is, when the Ratio of the Confe- quent of one Pair of Numbers, or (Quantities, to the Antece- dent of the next Pair, is not the fame as of the Anrecedent of one Pair to its Coiifcquent ; as 3 : 6 : : 8 : 16 are difcreet Proportionals^ becaufe the Ratio of 3 to 6, is equal to the Ratio of 8 to 16 ; but the Ratio of 3 to 6, or 8 to 16, is not the fame as of 6 to 8. D^fcrett ^lantity is fuch as is not coiuuiuous, and joined together ; as Numbers whofe Parts being diftin6i: Units, can- not be united into one Conti- yiuum ; for in a Contv/iuum there are no actual determinate Parts before Diviiion, but they are po- tentially infinite. DISTANCE is properly the fhorteft Line between two Points, Line of DijluKce^ in Perfpec- tive, is a Right Line drawn from the Eye to t^ie principal Point. Point of Lift a-'ice^ in Perfpec- tive, is a Point in the Horizon- tal Line, at fuch Diltance from the principal Point, as is that of the Eye from the fame. DISPOSITION of "Pidures and Paintings; the Manner how and where Gentlemen, cj'^-who are poUelTed of feveral Sorts of them, lliould place them in their Houfes, b'f I. Antique Works, or Grotef- co, may become a Wall, and the Borders and Friezes of other Works ; but if there be any Draughts in Figures of Men and Women to the Life on the W^all, they will be belt of Black and White, or of one Colour heightened: It' rhey be naked, let them be as large as the Place will afford : If oV Marble Co- lumns^ Aqueduds,Arches,Ruins, and D I D I and Catarafls, let them behold, high, and of large Proportion. II. Let the beft Pieces be pla- ced to befcen with lingleLights; for fo the Shadows fall naturally, being always barred to ^n- fwer one Light ; and the more under or below the Light, the better, efpecially in Men's Fa- ces, and large Pieces. III. Let the Porch or En- trance into the Houfe he fetout with ruftick Figures, and Things rural. IV. Letrhe Hall be adorn'd with Shepherds, Peadmts, Neat- Herds, with Milk-Maids, Flocks of Sheep, and the like, in their refpcdive Places, and with pro- per Attendants; as alio Fowls, Fifli, and the like. V. Let the Stair-Cafe be fet off with fome admirable Monu- ment or .Building, either new or ruinous, to be feen and ob- ferved at a View palling up ; and let the Ceiling over the Top- Stair be with Figures fore-fliort- ened, looking down out of the Clouds, with Garlands, and Cornucopia's. VI. Let Landskips, Hunting, Filhing, Fowling, Hiftories,and Antiquities, be put in the Great Chamber. VII. Let the Pi6tures of the King, PrincCjCiff. or their Coats of Arms, be placed in the Di- ning-Room, forbearing to put any other Pidures of the Life, as not being worthy to be their Companions, unlefs at the lower End, two or three of the chief Nobility, as Attendants on their Royal Perfons ; for want of which, you may place fome few cf the neareft Blood. V^III. In the inward, or with- drawing Chambers, put other Draughts of the Life, of Perfons of Honour, intimate, or fpecial Friends, or Acquain- tance; or of Artifts only. IX. In Banquetting-Rooms, pJace chearful and merry Paint- ings, as of Bacchus, Centaurs, Satyrs, Syrens, and the like, for- bearing all oblcene Pidures. X. Hiftories, grave Stories, and the bcft Works become Galleries, where any one may walk, and excrcife their Senfes in viewing, examining, delighting, judging, and cenfuring. XI. Place Caftles, Churches, or fome fair Buildings in Sum- mer-Houfes, and Stone- Walks. In Terraffes, put Bofcage, and wild Works. Upon Chimney- Pieces, only Landskips; for they chiefly adorn. XII. Place your own, your Wife and Childrens Pidures, in in your Bed-Chambers, as only becoming the mod private Room, and your Modefty ; lead (lays our Author,) if your Wife be a Beauty, fome wanton Gueft fhould ga^e on't too long, and commicnd the Work tor her fake. XIII. In hanging Piftures, if they hang high above Reach, let them bend fomewhat forward at the Top; becaufe, other wife, it is obferved, that the vifual Beams of your Eye which extend to the Top of the Pidure, appear further off than thofe of the Foot. DISTEMPER, in Painting, is the Workii'g up of Colo'jrs with fomerhing elfe befides bare Water, or Oil ; as if the Colours Y 1 are D 1 D I src mixed with Size, Whites of Eggs, or any luch proper gluti- noasor uiiclaous Subltance, and not with Oil, then the Painting is laid to be done in Di/iemper, as the admirable Cartoons at tLiynptnft- Court are. DISTINCT BASE, in Op- ticks, is that Diftance from the Pole of a convex Ghifs, in which Objefts beheld through it appear dtjlinft^ and well defined, • and is what is otherwife called the Fncpis. DISTRIBUTION, in Ar- chitecture, as the Dijlribution of the 'Plan^ is the dividing and dil- penfing the feveral Parts and Pieces', which compofe the Plan of a Building. Dijlributivn of Ornaments^ is nn equal orderly placing of the Ornaments in any Member of Architedture. DITRYCLYPH, in Archi- tefture, the Space between two T'ris^lyphs. DIVERGENT, 7 . DIVERGING Lines, 5 '" Geometry, are fuch Lines whofe Diliance is continually incrca- ling. Lines which converge one Way, diverge the oppolite Way. Divergent Rays, ') in Opticl^s, Diverging Rays, 5 arc thofe Rays which ilTue from a Point of a vilible Obje61:,aredifperfed, and continually depart from one another, according as they re- move from the Objecl:. In this Senfe, the Word isop- pofed to Convergent; which im- plies that the Rays approach each other, cr to tend to the Cen- tre, where, when they are ar- rived, they interied, and if con- tinued furiher, they become di- Concave GlaflTes render the Rays diverging, and Convex ones converging. Concave Mirrors make the Rays converge^^n(\ Convex ones diverge. It is demonftrated in Opticks, that as the Diameter of a pretty large Pupil does not exceed two M. or one Fifth of a Digit. Di- verging Rays, flowing from a radiant Point, will enter the Pu- pil, parallel to all Intents and Purpofes, if the Diftance of the Radiant from the Eye be four thoufand Feet. Diverging Hyperbola, is one whofe Legs turn their Convexi- ties towards one another, and run contrary Ways. DIVIDEND, in Arithme- tick, is the Number that is to be divided into equal Parts by another Number. DIVISIBILITY i? that Dif- pofition of a Body whereby it is conceived to have Parts, into which it may adually or men- tally be divided; or it is de- fined a paffive Power, or Proper- ty in Quantity, whereby it be- comes feparable into Parts, ei- ther adually, or at leaft men- tally. Body is divtfible in infinitum^ i.e. you cannot conceive any Part of the Extenfion ever lo fmall, but that ilill there may be a fmaller. There are no fuch Things as Parts infinitely fmall ; but yet the Subiilty of the Parts of fe- veral Bodies is fuch, that they very much pafs our Conception. And there are innnmerable In- ftances in Nature of fuch Parts that are a6tually feparuted from one another. Mr, D I D I Mr. Boyle gives us fevcral 111' ftances : He mentions a Silken Thread that was three hundred Yards long, which weighed but two Grains and a half. He alfo meafured Leaf-Gold, and found that fifty fquare In- ches of Leaf-Gold weighed but one Grain. Now if the Length of an Inch be divided into two hundred Parts, the Eye may diftinguifh them all; there- fore there are in one fquare Inch forty thoufandvihble Parts ; and in one Grain of Gold there are two Millions of fuch Parts; which vifible Parts may be fur- ther divided. DIVISION is one of the four great Rules of Arithmetick, be- ing that whereby we find how often a lefs Quantity is contain- ed in a greater, and the Over- plus. jDivi/io» of Numbers^ is in Reality only a compendious Subtraftion: The Etfcd of it being to take a lefs Number from a greater, as often as it is poflible, that is, as oft as it is' contain'd therein. There are three Numbers contained in Z)/- vifio-a : Firjl^ That given to be divided, called the Dividend. Secondly^ That whereby the Di- vidend is to be divided, which is called the Divifor. Thirdly^ That which exprelfes how oft the Divifor is contained in the Dividend, or the Number refult- ing from the Divifion of the Di- vidend by the Divifor, called the Quotient. DIVISOR, is the Dividing Number, or that which fliews how many Parts the Dividend is to be divided inio. DODECAGON, a regular Polygon, confiding of 12 equaf Sides and Anglos. DODECAEDRON, in Geo- metry, is one of tne regular P/^- tonick Bodies, comprehended un- der 12 equal Sides, each of which is a Pentagon. Or, A Dodecaedron may be con- ceived to confifi: of 12 quin- quanguhir Pyramids, whofc Ver- texes or Tops meet in the (Cen- tre of a Sphere, cojiceivcd to circumfcribe the Solid, and of confequence they may have tlieir Eafes and Altitudes equal, To find the Solidity of the Dodecaedron. Firji^ Find that of one of the Pyramids, and multiply it by the Number of Bafes, viz. 12, and the Produ6t will be the So- lidity of the whole Body; or the Solidity of the whole Body may be found by multiplying the Bafe into one Third of its Di- fiancefrom the Centre i2Times: And to find this Diibnce, take the Difiaiice of two parallel Fa- ces, and the Half will be the Height : Or, Multiply the Area of the Pen- tagonal Faces of it by 12, and then this latter Produdl of it by one 7^hird of the Difiance from the Diftance from the Centre of the ^odecacdro'/iy which is the lame as the circumfcriblngSphere. The Side of a Dodecaedron Infcribed m a Sphere, is the grea- ter P.'-rt of the Side of a Cube infcrib'd in that Sphere, cut into extream and mean Proportion. If the Diameter of the Sphere be 1000, the Side of ixTiodecae- dron infcribed in it, will be .3^682. y ^ All D O D O All Dodecaedrons are fimilar, and are to one another as the Cubes of their Sides; :ind their Surfaces are alio llr)ilir,and are therefore as the Square lif their Sides; vvheiice,as .5-09282 is to 10.5-1462, fo the Square of the Side o|- any Dodecaedron to its Superficie.,; and as .3637 to 2.78516, lb is the Cube of the Side of any Dodecaedron to the Solidity ofir. Let ABCDEFGHIKbea dodecaedron^ each Side of which being 12 Inches, the Iblid Con- tent, and fuperlicial Content is requir'd. The Solidilv of the Dodecae- dron is compoled of 12 Pent- angled Pyramids, -whofe Ver- texes all meet in the Centre. Therefore if we fii^.d the So- lidity of one of thoie Pyiamids, and multiply that by 12, that Produft v.'ill be the Solidity of the 'Dodecaedron. The Altitude ' i one of the Pentangled Pyramids will be found to be 13.36219. The Perpend'cu'rr. of thePen- tagon will be 8.258292.* 847.748760 30 half Sum 247.748760 6o45'4 -4 99099504 9909950 123S744 99099 14S6 1103.487S3 Content of one Pyramid. 12 13 241. 85396 the Solidity oh\\Q Dodecaedron. If DO DO If the Area of the Pentagon be multiplied by 12, the Pro- dud: will be ihe fuperficial Conccac. 247.7487 12 2972.98)'r2 the fuperficial Content. Example i. If the Side of a Dodecaedron be 12 Inches, what i> the Content folid and luperlicial ? 7.6631 19 the tabular Number. 1728 the Cube of the Side. 613049^2 15-326238 53641833 7663119 1 3241. 869632 the folid Goutent, nearly the fame as before. 20.645729 144 825-82916 825-82916 20645-729 2972.9S4976 the fuperficial Content. By Scale and Compajfes. on 1 3241 .86, ^^c. the folid Con- tent. Extend the Compaffes from And if you apply the fame I to 12, (the Side,) that Extent Extent twice from 20.645-729, it being turn'd three Times over will at la(l fall upon 2972.98, trom 7.651 19, will at lalt fall up- Is'c. the fuperficial Content. Y 4 Example D O D O Example z. If the Side of an Odacdron be 20 Inches, what is the iolid and lupcrficial Content ? .4714045' the tabular Number. 80CO the Cube of the Side. 3771.2360000 the folid content. 3.464102 the tabular Number. 400 the Square of the bide. ' i3S5'.64o8co the fuperficial Content. By Scale and Co?KpaJJes. Extend the Compafles from i CO 20, and that Extern: lurn'd three Times over from-.47i404f, will at laft fall upon 3771-236, the folid Content. The fime Extent turn'd twice over from 3.464, ^c. will at laft fall upon i385'.64, the fuper- licial Content. DOME, in Archite6ture,' a fpherical Roof, or a Roof of a fphcrical Form raifcd over the Middle of a Building, as" a Church, Hal!, Pavilion, Vellible, Stair- Cafe, err. by way of crowning. Domes are the fame that the Italians call Couppolas^ and we Cupola's, l^'itrwotus calls them Ti:ols. They are generally made round, or refembliug -the Bell of a great Clock ; but there are fome Indances ot fquare ones, as thofe of the Lonrrc; and alfo fome of them are in the Form of polygons, as that of the Je- fuit's Church in the Rue St-A»- thoine at Paris. Domes have commonly Co- lumns ranged around their Out- fdcs, both for the faKe of Or- nament, and Support to the Vault. DOORS, in Architefture, are Apertures in Walls, to give En- trance and Exit into and out of . a Building, or an Apartment of it; It is laid down as a Rule, that the Dtors of an Houfe be as few in. Number, and as moderate in D'menlions as poflible : For, in a Word, all Openings areWeak- nings. Secondly^ That they do not ap- proach too near the Angles of the Walls, it being a very great Solccifm to weaken that Part which iliould Ibengthen all the relL A Precept well recorded, but illy praftifed by the Italiam^ par- ticularly at Venice. Thirdly.^ That the Doors ^ if pof- fible, be placed over one another, that V^oid may be over Void, and Full over Full ; which will be a great Strengthening to the whole Eabrick. Fourthly^ That, if pofTible, they may be oppofice to each other, in fuch manner, that one may fee from one End of the Houfe to the otner ; which will not only be very graceful, but moft con- venient, y 1 IT B 1: n fn 6" \:,/^, ' D O D O yenient, in refpeft that it affords Means of cooling the Houle in Summer, by letting the Air through the Houfe; and bvkeep- 'ing out the Wind in Winter, which Way focver it fit. Fifthly^ 'Tis not only crna- mental, but very fecure, to turn Arches over Doors; which will dilcharge them, in great Menfnre, of the fuperincumbent Weight. The Proportion of Doors is adjufted by that of a Man. In large Buildings they muft always be larger than in Imall ; bur flionld not be lefs than fix Foot high in any, to admit a Man of ju(t Stature ered And as the Breadth of a Man wich his Arms placed a-kembo, is nearly fubduple his Height, tlaje Width ought never to be I^j^ than three Feet. ^ Some Architects give us thefe Dimenfions following : In fmall Buildings, the Breadth of the 2)oor^ four Feet, or four and a half; in middling Build- ings, five or fix ; in large ones, fcven or ejght; in Chambers of the firft Story, three and a half, three and three Fourths, or four: of the fecond, four, or four and a half; and of the third, five or fix; in Churches, feven or eight; in Gates, nine, ten,* or twelve. Hence their Height is eafily de- termin'd, except for the Gates of Cities, which fiiould only be four tn^'iftjis of their Breadth. Palkdio . has an Obfervation, ihat the principal 2Joor^ or En- rance oi an Houfe muft never be regulated by any certain Di- menfions, but by the Dignity of the Perfon who is to live in it ; yet to exceed rather in the more than the lefs is a Token of Qe- ncrofity, and may be excufed with fome noble Emblem, as that of the Conte di Bcvilacqua^ over his large Gate at P'crona^ where a little Diiproportion had been committed, fatet janua cor mazis. As to the Price of Doors : Thofe that are made of plain. Whole Deal, and rabbeted, are for Stuff, Nails, and Workman- fhip, valued, as ibnie Workmen fay, at ■^d. or 4^. the fuperficial Foot; iheWorkmanfliip only at IS. or zs. 6d. per Door. Double jOoors batten'd, or made Wainfcot-faihion, may be worth -jd. the Foot for Work- manfliip and Materials, and 4 s. or 5-^, per Door^ for VVorkman- fiiip alone. Folding 'Doors and Cafes are ufjally valued at 20/. or ops. per Pair ; and Balcony Doors and Cafes at the fame Rate. Ordinary Doors ^ without plain- ing, are ufually valued at i s. perDoor^ making and hanging up. jJrchiirave Door-Cafes^ in Brick "Buildings, are worth, according to their Mouldings, a Penny an Inch, /'. e. if the Breadth of the Moulding (from the Outfide to the Infidc of the Frame) be nine Inches, it is worth qd. perVooi running Meafure ; if ten Inches, \od. per Foot; and fo either more or lefs, in Proportion. Frontijb Doors., in large Build- ings, with their uiual Ornaments, as Pilafters, cT^. are worrh (ac- cording to their Lirgenefs and Variety of Workmanfliip inclu- ded) from 3/. to 5-. 10, or 20/. or more^ per Door . See Batten Door. M. Le Clerc fays, when a lit- tle Door is mace in the Front of ail D O an ordinary, but regular Building, ic Ihould be railL-d to the jult Height of the Windows that ac- company iti but its Breadth mult a little exceed that of the Windows, leaft while it is ad- jufted to the reft of the Build- ing, it appear ill-proportion'd in itielf. U it is defir'd to have the Doer ^dorn'd with an Order of Columus, it muft be raifed higher. ji Geometrical Rule for a Door, or H^indovj. The Breadth being given^taks it three Times for the Side of a a Square, and draw the Diago- nals, whofe Interfedion willbe the Centre of the Pediment's Arch ; then from the Top of the Pediment, draw Lines to rheop- pofite Angles of the Square, and their Interfedion with the Dia- gonals, is the Height of the Doer. The Breadth of the Door be- ing divided into fix, one is for the Breadth of the Architraves^ one Third to the Spaced two Thirds to the Piladcr b ; the Plinth ^h two Thirds higli ; the Height of the Kneel g cf the Archi:rave is twice its Breadth; the Height of the Ftized is equal to the Breadth or the Architrave, and the Cor- nice e one Fourth higher; the Length of the Trufs^ is from the Top of rlic Frize to the Bottom of the Kneel, For the feveral Members, divide the Breadth of the Architrave a into fix Parts, giving half a Part to the Bead, one and a half to the fir ft Face, half a Part to the fmall Ogee, two to the fecond Face, one to the Ogee, a half Part to the Filler. For the Projedions, the firft D o Face is a half Part, the fecond Face one, and the Whole two. For the plain Cornice b, divide the Height into eigh Parts, giving one and one Fourth to the Cavetto, one Fourth to the Fillet, one and one Fourth to thcOvolo, one Fourth to the Fillet, two to the Coro- na, three Foutths to the Cima Reverfa, one Fourth to the Fil- let, one and a half to the Cima Re6ta, and a half Part to theFil-- let. For the Projeftions, the Cavetto hath one and a half, the Ovolo two and a half\ the Co- rona five and a half, the Cima Reverfa fix and a half, and the Whole eight. For the Dentil Cornice^, divide the Height into ten Parts, giving one and one Fourth to the Ogee, one Fourth to the Fillet, one and a half to the Dentils, (whofe Breadth is two Thirds of their Height,)one Fourth to the Fillet, one and one Fourth to the Ovolo, one Fourth to the Fillet, two and one Fourth to the Corona, three Fourths to the L>ima Re- verfa, one Fourth to the Fillet, one and a half to the Cima Rec- ta, and a half Part to the Fillet. For the Projeiftions, the Ogee hath one and a half, the Dentils two and a half, the Ovolo four, the Corona feven and a half, the Cima Reverfa eight and a half, and the Whole ten. See the Plate. DORIC, in Architecture, is the fecond of the Five Or- ders; and is that between the Tufcan and the lomc. This Order feems the mofl natural and bcft-proportion'd of all the Orders, all the Parts of it being founded on the natural Po- fition of folid Bodies. Accordingly, D O Accordingly, the Doric is the :-:[{ and moft antient of theOr- ccrs of Architedure, and is that which gave the tirft Idea or No- tion of regular Building. It was, indeed, more fimple at its firll Invention than it is at prefent ; and when they came in After-Times to adorn and en-^ rich it more, the Appellanon of Doric was reftrained to this richer Manner ; and then they called the primitive fimple Manner by the new Name of Tufcan. Tradition delivers that Dorm King of Achaia having bnilt a Temple of this Order at A^gos^ dedicated to Juno, caulcd it to be c2i\\Qi^ Doric : Though fome derive its Name from its having been invented or ufed by the D'jriim S >me Time after its Inven- tion, it was reduced to the Pro- portions, Strength, and Beauty of the Body of a Man. Hence as the Foot of a Man was jadgcd the fixth Pun of its Height/they mace thei)or/V Co- lumn fix Diameters high. After that they added anoti.cr Diame- ter to it, and made it feven ; ^hich Augmentation feem'd to bring it nearer to the Proportion of a Man; the human Foot, / at lead, in our Days, not being exaftly a Sixth, but nearly the Seventh of the Body. The Charaders of the Doric Order, as they are now manag'd, are the Height of its Column, which is now eight Diameters; the Prize, which is adorn'dwith Triglyphs, Drops, and Metopes; its Capital, which is without Vo- lutes ; and its admitting of Cy- maciums. D O It has been already obferved, that the Antients had two Do- rics: The firft of which was the more fimple and m.i(rive,and chit-f- ly ufed in Temples ; the fecoiid, which was the more light and delicate, they ufed in Porticoes and Theatres. Indeed, l^itruvius complains of the Doric, as being very troublefome and perplexing on Account of the l^iglyphs and Metopes, fo as to be fcarce ca- pable of being afcd, except in the Pycnoftyie, by placing a Tri- glyph between ea:n two Co- lumns; or in the Aiasollvle, by placing three Triglyphs between each Column. The Doric is ufed bv the Mo- derns on Account or v.s Solidi- ty in large Ifrong Buildings, as in the Gates of Cities and Cita- dels, the Outfides of Churches, and other malTy Works, in which Delicacy of Ornaments would be unfuicable. The moft confiderable antient Monument of this Order, is the the Theatre oi Marcellns at Rome, the Capital, the Height of the Frize, and Projedare of which, are i:uich fmallerthan in the mo- dern Architedure. F/^w/^adjuftsthe Proportions of the Doric Order, as follows: He divides the whole Height of the Order, without the Pedcftal, into twenty Parts, or Modules; one of which he allows to the Bafe,fourteen to the Shaft orFufI, one to the Capital, and four to the Entablature. The particular Proportions of the feveral Parts and Members may be feen under their refpedive Articles. rhe D O D O I'he Doric Order delineated by equal 'Part^^ infiead of Modules and iMinutes. The Height of the Pedeftal be- ing two Diameters and one Third, is divided into four, giv- ing one to the Bafe, whofe Plinth is two Thirds thereof ; the other Part is divided into feven, giving four to the Torus, one to the f'illet, and two to the Hol- low. The Breadth of the Die is a Diameter and one Third. The Projedicm of the Bafe is equal to its H-ight, and the Fil- let hath four of thefe Parts. The Height of the Cornice is half the Bale, being one Eighth of the whole Height; and is divided into nine, giving two to the Hollow, one to the Fillet, live to the Corona, and one to the Fillet; the Projection of the Hollow is three of tliefe Parts, the Corona lix, and the Whole feven. T^ajc oj the Column. The Height is half a Diame- ter, and is divided into lix, giv- ing two to the Plinth, one and a half to the lower Torus, one F^ouith to the Filler, one to the Scotia, :f to the Fillet, and one to the upper Torus. The Fillet above t'ne Torus is equal to the others, and is Part of the Co- lumn. The Projedion is two of thefe Parts, and one Third thereof is for tlie upper Fillet, two Thirds to the upper Torus, and the Fillet under it, is per- pendicular to the Centre. For fwrming the Scotia, di- vide the Height into three, as in the Scheme, and on the Line that feparates the one Part above from the two Parts below, and perpendicular to the Fillet, is the Centre for the firft Quarter- Sweep, and the fame Diftance forwards, on the Line, is the Centre for the other Quarter; and is alfo the Projedlure of the lower Fillet. The Diminifhing of this Co- lumn is one Eighth of the Dia- meter. The Height of the Ca- pital is half a Diameter, and is divided into nine, giving three to I he Prize of the Capital, one to the Fillets, which are three, and are equal, two to theOvo- lo, two to the Abacus, and one to the Ogeel* and Pallet, which is one Third. For the Projeftions, the FiU lets have one of thefe Parts, the Abacus three, andtheW-hole four. The Height of the A.rchitrave is half a Diameter, and is divi- ded into lix Parts, giving two to the firft Face, two to the fe- cond, one to the Bulls ^ and Fil- let, which is one Third, and one to the Band at top. The Projedion is equal to the Band. The Fri7,e is in Height three Fourths of the Diameter, and the IViglyphs d are in Breadth half a Diameter; which are divi- ded into fix, giving one to each of the Channels, half a Part to each Half-Channel, and one to theSpaces between the Channels. The Projedlion from the Na- ked of'theF"rize is three Fourths of a Part, and the Spaces, or Me- topes, between the Trigiyphs, ought to be equal to the Height of the Ffize. The D O The Height of the Cornice Is three Fourths of the Diameter, and is divided into nine, giving one to the Cape of theTriglyph, one to the Hollow and Fillet, which is one Sixth, one to the Ovolo, one to the Mutulef and Fillet under it, which is equal to the other, a half Part to the Cap of the Mutule and Fil- let, which is one Third, one and three Fourths to the Corona, three Fourths to the Cima Re- verfag one Fourth to the Filler, D O one and one Fourth to the Cima Reda, and a half Part to the Fillet. For the Projeftions, the Cap of the Triglyph hath one of thefe Parts, the Hollow one and three Fourths, the Ovolo two and three Fourths, the M: lule eight and three Fourths, tht Co- rona nine and three Fourths, the Cima Peverfa ten and three Fourths, and the Whole twelve Parts. DORMER, D E D E D R B R DORMER, -^in Architec- DORMx'VNT, 3 tefture, is ihe Window made in the Roof of a Houfc, or above the Entabla- ture, being raifsd upon the Raf- ters Dormers are commonly rated at fo much per Piece. Dormant-Tree is a Name given by Workmen to a great Beam lying crofs a Houfe, commonly called, a Summer Dormant -Tiles. See TiLES. DORMITORY, a Gallery in Convents or Religious Hou- fes,' divided into feveral Cells, in which the Religious lleep or lodge. DOUCINE, in Architeaure, is a Moulding or Ornament on the higheft Part of the Cornice, in the Form of a Wave, half convex, and half concave. The Doticine is the fame as a Cymatium, or Gula. DOVE-TAILING, in Car- pentry, is a Manner of faften- ing Boards (or other Timber) together, by letting one Piece in- to another, in the Form of the Tail of a Dove. It is the ftrongeft of the Kinds of Joint- ings or Aflemblages, wherein the Tenon, or Piece of Wood which is put into the other, goes widening to the Extreme ; fo that it cannot be drawn out a- gain by reafon the Extreme or Tip is bigger than the Hole. It ib called by the trench^ ^ueue d'/ironde^ i. e. SivalkvJ- Ta:l\ which Name is alio ufed by the £»^///^ themfelves in For- tification. DRAG. A Door is faid to dr -g., when in opening or fhut- ting, it hangs or grates upon the Floor, or Cell. DRAGON BEAMS aretwo ftrong Braces or Struts which ftand under a Brell-Summer, meeting in an Angle upon the Shoulder of the Kingpiece. DRAPER V, in Sculpture and Painting, the Reprefcntation of the Garments or Ciothing of hu- man Figures. It includes not only Garments, but Tapeltry, Hangings, Curtains, z^^c. DRAUGHT, P in Architec- DRAFT, f ture, is the Figure of an intended Building defcribed on Paper; in which is laid down, by Scale and Com- pafTes, the feveral Divilions and Partitions of the Apartments, Rooms, Doors, PafTiges, Con- veniencies, {^c. i n their due Pro- portion to the whole Build- ing. It is cuftomary, and alfo ex- ceedingly convenient for any Perfon, before he begins to ere6t a Building, to have Deligns or draughts drawn upon Paper or Vellum, wherein the Ichnogra- phy or Ground-Plot of every Floor or Story is delineated or reprefented, as alfo the Form or Fafhion of each Front, with the Windows, Doors, Orna- ments. k3^c, in an Orthography, or Upright. Sometimes the feveral Fronts, ^j^c. are taken and reprefented in the fame Draught., to fhew the Effect of the whole Building, which is called a Scenography or Perfpedive. - But this not being eafi'y un- derftood, except by thofe who undcrfiand rhe Rules of Perfpec- tive, therefore it will be more intelligible to the feveral Work- men, to have a Draught of each From, in a particular Paper by *ilfch'; J D R D R itfelf ; and alfo a Drntight of the Ichiiography or Gruuud- Plot of each Floor or Stery, in a Paper by itfelf; becaufe often- times the Contrivance and Con- venicncies of one Story ditfer from thofe of another, either as to the L-.irgenefs of the Chim- neys or Divifions of theRooms, fome being larger in one Story than another, C5'«". All which Things being well confidered and drawn on Paper before the Bi.iilding is begun, thefe Tir alights will be a great Guide to the Wori^men, and fave them a great deal of Time in contriving their Work ; and, belides, the're will be no need of Alterations, or pulling the Building to Pieces after 'tis be- gun ; which, befides the Hin- deraiice of the Procedure, makes the Building lame and deficient ; nothing being fo well done, vAy^n 'tis put up, and pull'd down, and fet up again, as i^ it were done at firrt. To dravj any ObjeSt in iti OzU- Lines as exacl as the Life^ or Nature. Take a Sheet of thethinneH:, or wliitcft brown Paper, and bruHi it over with Oil of Tur- pentine, which will immcdi-.ue- ly render it tranfparent and then put the Fiiper to dry in the Air ; when \i is dry, flrain it upon a Frame, and fix it againft any Objed you <^ci\^x\ to draw, as an Houfe, ^s'c, then juft before ir p!ace a Piece of Wood with a Hole in it, fit for one Eye to look through ; and as you meet any Outlines of the Objedl you dclire upon the tranfparent Pa- per, trace them over withaPen- cil, fowill you be fure you can- not err; for there wilf be no- thing bnt juft Proportion, and a true Reprefentation of Na- ture. To make this dill of more Elegancy, obferve the Tracing of your Draughts^ where the Shades are, and m^ark them with your Pencil ; for all the Art in the World can never difpofe the Shades' fo regularly, as one may touch by this Method : But the Shades mull be done quickly af- ter the Outlines are drawn, and not at disferent Times, becaufe every Inftant the Sun changes them. In this too, obferve, that in certain Objects, you will have fainter, ftronger, and yet more darlv Shades; and in your Re- marks of them, take fiich Me- morandums, as may direct you how to fiiiiOi them, with Indian Ink, or other Colour, when you fit down to compleat your Work. The beft Way is to prepare three Shells or Gallipots of In- di.in Ink mixed with common Water, before you attempt to trace out your Object:, viz. one of a very faint Black, the next of a middling Black, and the other of an intenfe Black : Number them i, 2, 3, from the lighted to the darketl; and as you make your Obfervation on the Shades of your Objeft, mark upon your Draught the fame Numbers, as they happen to ap- 1 pear; fo that afterwards you ; may finifh with Certainty. j Again, it is neceffary in the j drawing of any Thing afcerthis Manner, to obferve that the L'nes D l( D R Lines on the fliady Side fhou'd be thinner, in Proportion to the Light that falls upon them. ^ AsforExninple ; Inthedarkefl Part a Line may be of that Thicknef;,iu the next Part fome- what thinner, and in the other thus ; unlefs In Things of a great Diftance hardly to be iiu- derftood, or lb faint as hardly to be perceived thus; a inere Shadow, as it were. Some have been guilty o'f a .great Fault, thouf;h'they have taken the Outlines very exact, by making all tiieir Lines ot an equal Thicknefs. If an Objeti be rcprefented at a great Diftance, as half a Mile, or two Miles off, and the Draw- ing be as flrong in that Part of the Pifture, as if it was next the Eye, or not ten or twenty Feet from the Draughts-Man^ it would not appear pleafant or natural to the Eye. A Man muft not be exprefs'd vvith Buttons on his Coat at a Mile's, csr'f. Diltance, no more than they muft be omitted in a Perfon fo near the Eyej as. ten or twenty Feet : Though this has inadvertently been done by fome that palled for great Men : Nor a Capital, ^c. with Carv- ings and Mouldings, ^c. And the Shades, in thofe ^\- ftant Appearances, muft be m Proportion to the Strength of theObjefts as they appear to us, /'. e. imperfedt. Three or four well-dirc6led Touches of the Pencil on the fhady Side, will reprefent a Fi- gure at the Diftance we can di- fcern it, as lively as fome Hun- dreds will near the Eye, The tranfparent Paper, before meiuion'd, is alfo of another Ufe; for if it be laid upon any Piclure or Print, all the Lines may be iftzw through it; and then you may draw or copy it with the greateft Plealbre, You win then, if thePicStures be doiic by a good Maftcr, fee which Lines are ftrong, and which tender or foir, and imitate them. There is yet another Way to take Views and Landskips, which Ibme prefer to the tranPparenc Paper, that is, cither with vvhite, or black Tiffmy or Lawn ftrain- ed upon a Frame, and ufrd in the fame Maimer as the Paper, excepting that the Black Lead Pencil is ufed to the Paper, on the Tiffany and the Lawn, Char- coal, finely pointed, and very fofr, \% ufed; but on the black Tiffmy white Chalk of the tendereft Sort. How to bring thefe Drawings to Ufe^ and to copy from '\prints^ l^aiiitifigs^ &C. If you drav/ upon tranfparent Paper, to take a Drawing from it regularly, get a Piece of Paper of the &me Size, and rub on one Side of it fome Powder of Black Lead, till ic is well and equally black'd, and fo well rubb'd, that a Touch of a Fin- ger will hardly be tinged with it. Then take the Dravjlng you have made, or Prinr, and lay the black'd Paper under it, with the black'd Side downwards, up- on a Piece of white Paper, and pin the three together ^ yj two Z ' ejr D R D R or three Places; take then a Via Chalk, or Red Oker, on the .is Figure III. is exa6lly of the fame Dimenlions of the Plan laid in Perfpcdive at Fig. II. Firlt mark the Line LK m equal Proportions, by the fame Scale of the ground Plan, Fig. II, 0.S (i^ipyC^d, which are fo many Feet in Height ; and they Hand- ing on the Bale of the iirfl: Fi- gure, are Uprights not in Per- fpedive : Then draw a Line pa- rallel with L I, from Number 4, which gives you the Front of the Body you are to raife; if it is to be only three Feet high, draw a Line crofs from Num- ber 4. and that determines the Height, which you will then find to be a Foot wide, and three Feet high by Mcafure : Then f om the Top of the L'ne 4, draw a Line with a Black-Lead Pencil to the Point of Sight; and rnife another Line from 3 paral- lel to the Line 4, till it touches the penciled L'ne pafling from f to the Point of Sight ; which gives you the Side Appearance of the Column or Body, as you will fee it from the Place where you ftund, [the Line from Point 3 fliould bi drawn with a Pen, be- CaUi'e it is to reiiiain ;] then wirh a Pencil draw a Line from C to the Point of Sight, which will determine the other Line, to make the Shape on the l^op of the Column : And then raife q Line parallel with L i, with a Pencil from the Point, till it touches the Line from C to the Point of Sight; then draw a pa- rallel Line £o C f, at 6,7, and D R D U you will hive the Square at the Top of the Pillar or Column, as you can obferve it from the Place where you ftand, which is fuppofed to be at A. [You mud remember, that the Line drawn from z to 6, is only an imaginary Line, to be rubbed out ; for it cannot be feen from the Place where you {land, and therefore muft not appear in the Drawing ; but you iliould not leave it out, becaufc it fliews you where to regulate the Top of the Column, and teaches you to place your Column upon its Bale with Certainty. ] By this Means you may fee Front, and one Side of your Co- lumn : And the Line from i to 2 muft alfo be rubbed out, be- ciufe it can't be feen. Then finifli your Column only with the Lines From I to C From 4 to 5- From 3 to 7 From C to 5" From 6 to 7, and From I to 4. And it will be drawn without any Imperfc6tion, and appear as follows in Fig. IV, When this is done, you may place another Column on any one of the Squares erected in the fame manner, obferving to fling your Shades all on one Side, and then you cannot err : But efpecially mind where the dot- ted Lines are in Fig. III. DRAUGHT COMPASSES are CompaJJes with feveral move- able Points, to draw fine Draughts in Architediire. DK AW-BRIDGE is a Bridge made to draw up, or let down, as Occafion ferves, before the Gate of a Town or Caftle : And they are made after feveral Mm- ners; but the molt common are made with Plyers twice the Length of the Gate, and a Foot in Diameter. I'he inner Square is travcrfcd with a Crofs, which ferves lor a CouDterpoife; and the Chains which hang from the other Ex- tremities of the Plyers, to lift up or let down the Bridge^ are of Iron or Brafs. DRIP, in Architcaurc. See Larimer. Drips are alfo ufed in Build- ing for a certain kind of Steps, made on tiat Roofs to walk up- on ; a Way of Building much ufcd in liaiy^ where the Roof is not made quite flat, but a little raifcd in the Middle with Drips^ or Steps, lying a little to the Horizon. DROPS, in Architefturc, an Ornament in the Doric Enta- blature, repreftnting Drops^ or little Bells, immediately under the Triglyphs. DUPLA Ratio ? i. e. Doul^Ie DUPLE S Ra(w, ill Archircfture, is where the ante- cedent Term is double the Con- fequent ; or where the Exponent of the Ratio is 2 ; thus 6 : 3 is in a Duple Ratio. SUB-DUPLE, or Doidh Sub-Duple Ratio^ is where the confequent Term is double the Antecedent, or the Exponent of the Ratio is 7 ; thus 3 : 6 is a fiib-dnVle Ratio. DUPLICATE Ratio ought to be well diltinguilhed froni 'Duple. In a Series of Geometrical Proportions, the firft Term to the third is faid to be in a Dh^ plicate Ratio of the firlt to the »Z 4 fecondj D U fecond, or as iLS Square is^ to the Souare of the fecond : 1 hus 2.4.8. 16. rhe Ratio ot 2 to 8 is ^but'lic.iw of chat of 2 to 4, or as the Square uf 2 to the Square of 4 • for which Rcafon, Duphcaic Ratio is the Froporiion of Squares, as Triplicate R^tto is ot Cubes, If^c. And the Ratio of 2 to 8, i's laid to be compoanded of that of 2 104, and of 4108. DUPLICATION i.e. Doubling, in Ariihmetick and Geometry, is the multiplying a Quantity difcieet, or continued by two. n 2 c The Term is chiefly ufed of the Cube, as the DupUcraton of the Cube, which is a famous Pro- pofition that the Geometricians have fought this 2000 Years. _ The i)nplicatton of a Cubic^ is to find the Side of a Cube that fnall be equal in Solicaty to a Cube given. This has been attempted oy feve- ral geometrically ; but it is in vain to pretend to ir, for ir cannot be done without the Solution of a cublck Equation ; and fo a Co- iiick Section, or fome higher Curve, muft be ufed for deccr- inining the Problem. DYE, in Architeatire, is any fquare Body, as the Trunk or not:h'd Part of a Pedelhl ; or it is the Middle of the Fedeltal, or that Part included between the Bafe and the Cornice; or is fo called, bccaufc M is often made in the Form of a Cube c)r Dye D^o is aUb ufed for a Cube of Stone^ placed under the Feet of a Statue, and over its Fedeltal, to raife it, and iTiew it the more. DYPTERE^ in the antient DIPTERE > ArchitedUire, ji^i ^ kind of Temple encom- E G pafTcd with a double Row of Columns; and iht PCendo Dyp- terc^ or Falfe Diptere^ was the fiine, only that this was encom- pailcd with a (ingle Row of Co- lumns, inllead oi a double Row, E A V EAGLE, in Architcaure, 5 Figure of that Bird, antiently ufed as an Attribute or Cogni- sance of Jupiter in the Capitals and Friezes of the Columns of Temples confecrated to that God. EAVES, in Architeaure, is^ the Margin or Edge of the Roof of an tioufe; being the lov;eft Tiles, Slates, or the like, that hang over the VValls, to throw off' Water to a Diftance from the Wall. faves-Lrah, is a thick feather- edg'd Board, generally nailed round the Eaves of an Houfe for the lowermoft Tiles, Slates, or Shingles to reft upon. Eaves -Lath arc commonly fold for three Half- pence or Tv^o-pcnce per Foot, (running Mcafure,) according as they ari; in Goodnefs. n:cCENTRICK?inGeo- EXCENTRIC S metry, a Term apply'd where two Cir- cles or Spheres, though contain- ed in fome Meafure within each other, yet have not the fame Centre, and of confequence are not parallel in Oppolition to Concentrick, where they have one and the fame common Cen-» tre^ and are parallel. ECCE^^TRIQT^ Po/nt of di/faji/--e -L^ -^ K vA /■■ / ^.'^yfrt ; I '/ \i \ \ /, m\ / m1\ E G E G ECCENTRICITY > is the EXCENTRICITYS Diftan- ces between the Centres of two Circles or Sphcics, which have not the fame Centre. ECHINUS, in Architedure, is a Member or Ornament near the Bottom of the lomc^ Corin- th'ian^ and Cuinpojite Capitals, ■which the French call ^nnrt de Rotid^ from its circular form or Contour; and the Engl'ijh ^Quar- ter Rjund^ or hotiltin ; the Ita- lians c^W it (9 Wo, from Oviira\ and the French^ Ove^ from the Latin^ Ovum an Egg ; and thence the Efigli/Jj call it Eggs a;-2d /irj- chors. See ANCHOR.. The Greeks call it EjcrygH, a Chclnut, from the Egg's being encompalTed with a Cover fome- thing refembling a Chefnut cut open. ECHO, in Architefture, is a Term applied to certain Kmds of Vaults and Arches, molt com- monly of elliptical and paraboli- cal Figures, ufed to redouble Sounds, and produce artificial Echoes. The Jefuit Blanc^ in his Echo' rnetry^ at the End of his firll Book of the Sf^jcre^ teaches the Method of making an artificial Echo. Fitruvius relates, that in di- vers Parts of Greece and Italy^ there were brazen Vefiels art- fully ranged under the Seats of theTheatres, to render the Sound of the Voices of the Adors more clear, and make a Kind of J^cho ; by which Means, every Perfon of that prodigious Mul- titude who affilted at the Spec- tacles, might hear with Eafe and Pleafnf e. Sff:}o is a Sound rcfle^led or reverberated from a folid con- cave Body, and fo repeated to the Ear. The 'Perjpautich^ who ima- gined Sound to be l know not what Species, or Imigc of the fonorous Body imprclicd on the adjoining Air, account for Echa from a Refilicion or leaping back of the Species, caufcd by its meeting icme Obltacle in the Way. But modern Natural ifts, who know that Sounds coaiid in a certain l remor or Vibration in the fonorous Body, comniuni- cated to the contiguous Air, and by that Means to the Ear, give us a more coniillent Account of Echo. For 'tis evident, that a tremu- lous Body, Ifriking upon another folid Body, may be repelled without deftroying or diminilh- ing its Tremor ; and of confe- quence, that a Sound may be re- doubled by the Relilition of the tremulous Body or Air. But a fimple Reflection of the fonorous Air is not e- nough to folvc the Echo ; for then every pJain Suriice of a folid Body, as being fit to re- flect a Voice or Sound, would redouble it ; which, as is found by Experience, does not hold. Therefore it fliould feem, that a kind of Concimeration or Vaulting were neccflary to pro- duce an Echo^ in order to col- lect ; and by colIc6ting, to heighten and increafe, and after- wards to reflect the Sound; as it is found is the Cafe in refl.dinjj the Rays of Light, where a coiv- cave Mirrour is required. Iq E C In EfFeft, as often as aS^nd ftrikes <)n a Wall perpendicu- larly, behind which, is any Thing of an A.rch, or even another paral- lel Wall, fo often it will be re- verberated, either in the fame Line, or other adjacent ones. Therefore it is neceifary, in order that an Echo be heard, that the Ear be in the Line of Refledion ; and in order that the fame Perfon may hear it e- cho, who mide the Sound, it is necffiry, that he be perpendi- cular to the Place which retiecis it. And as for a tautological or manifold Echo^ it is necef- fary, that there be a Number of Walls and Vaults, or Cavities, either placed behind each other,' or fronting cnch. A fingle Arch or Concavity, cfc". can fcarce ever (top, aiid refled the Sound ; but \t there be a convenient Difpolition be- hind it, Part of the Sound, that is propagated thither, being col- leded and refleded as before, will prcfent another Echo ; or if there be anotlier Concavity oppofed at a due Dilbnce to the former J the Sound rcfiedcd from the one upon the other, will be tofs'd back again upon this lat- ter, ^c. The Bifhop of Le'ghs^ &c. has well conlider'd many of the Phicnomena of Echo. He remarks, that any Sound falling either diredlyor oblique- ly on any dente Body of a fmooth Superficies, whether arched or plain, is retiefted more or lefs. He fays, the Surface muft be fmooth, or elfe the y\ir by Re-^ verberation will be put out of E C its regular Motion, and the Sound thereby broke or extin- guifh'd. He likewife adds, that ft e- choes more or lefs, to fhew that when all Things are, as before defcribed, there Is ftill an £- chotKg^ though it be not alwavs heard, either becaufe the direcl Sound is too weak to be beat quite back again to him that made it, or that it does return to him, but fo weak, that it can- not be difcern'd ; or elfe that he (lands in a wrong Place to re- ceive the refleded Sound, which pafles either over his Head, or under his Feet, or on one Side of hira, and which therefore may be heard by a Man who ftands in the Place where the receding Sound will come, provided no interpofed Body intercept it, but not by him that firll made it. Echoes m.iy be produced with different Circuinlhnces : Eirji, APlaneObftaclerefleds the Sound back in its due Tone and Loudnefs, Allowance being made for the proportionable De- creafc of the Sound according to its Diftance. Secondly., A Convex Obftacle refleSs the Sound fomewhat fmaller, and fomewhat quicker, though weaker than it otherwife would be. Thirdly., A Concave Obftacle echoes back the Sound bigger, flower, and aifo inverted, but never according to the Order of Words, Nor does it feem poffible to contrive any fingle Echo that fiiall invert the^ound, and repeat backwards; becaufe infuchcafe, the Word which was laft fpoken, that E G E C tl;:it is, which lafl occurs to the Oblhcle, muft be repelled firll, which cannot be: For, where, in the mean Time, fiu>uld the firft Words hang and be con- cealed ? or, how after fiich a Paufe, be revived and animated again into Motion ? From the determinate Conca- vity or Archednefs of therefled- ing Bodies, it may happen that Ibme of them fliall only echo back one determinate Note, and only from one Place. Fourthly^ The echoing Body being removed further off, it re- flectii more of the Sound than when nearer; which is the Rca- fon why lome Echoes repeat but one Syllable, fome one Word, and fome many. Fifthly^ Echoing Bodies may be fo contriv'd and placed, as that reflecting the Sound from one to the other, either direftly and mutually, or obliquely and by SuccelfiOn, out of one Sound fhall z Multiple Echo^ or many Echoes arife. To this may be added, that a Multiple Echo may be made by fo placing the echoing Bodies at unequal Diftances, as that they may refled all one Way. and not one on the other; by which Means a manifold fuc- ceffive Sound will he heard : One Clap of the Hands will be heard like many; one Hah^ like a Laughter; one Word, like ma- riv of the fame Tone and Ac- cent ; and fo one Vial like ma- ny of the fame Kind, imitating each other. Lajll\\ Echoing Bodies may be fo order'd, that from any one §ou.id given, ihs;y llial] produce many Echoes^ different both as to. Tone and Intention. By which Means a Mufical Room may be fo contriv'd, uvit not only Playing on an Inltru- ment in it, Hiall feem many of the fame Sort and Size, but even a Confort of different ones, on- ly placing certain echoing 'Bo- dies fo, as that any Note play 'd fliall be return'd by them, in T hirds. Fifths, and Eighths. _ Echoes are dillinguffh'd into divers Kinds, v'lz. I. Smgle Echoes^ which return the Voice but once ; of which fome are Tonical, which only return a Voice when modulated in fome particular"! one. Others Polyfyllabical, which may return many Syllables Words, and Sentences. II. Multiple or 'Tautological Echoes^ which may return Syl- lables the fame oVtentimes re- peated. In Echoes^ the Placje where the Speaker ftands, is called the Centrum l-^honiciim^ and the Object or Place which returns tlie Voice, Centrttm 'Thomcamf- ttcHra. At the Sepulchre of Metelk^ Wife of Crcjjns^ was an Echo whicii repeated what a Man faid five Times. And Authors men- tion a Tower at CyzicuSy where the Echo was repeated fcvcii Times. EFFECTiON, in Geomitrr, is ufed in tne fame Senfe with the Geometrical Conflrudion of Propoiitions, and often of Pro- blems and Praftices; which, when they are reducible from, or founded upon fome general Propoijtioii, are culled the Geo- metrical E L a L the wettlcal Effcdions thereunto be- Fibres with which Bodies were longing. "^ form'd. EFFICIENTS, in Arithme- The Ehjlichy of Fibres coa- tical Progreffion, are the Num- fifls in this, that they can be bers given for an Operation of extended, and taking away the Multiplication called Faftors. Force by which they are lengthen Thefe Efficients are the Multi- plicand, and the Multiplicator EFFIGIES, ■? a Portrait Fi- EFFIG Y, 5 gure or Repre- fentation of a Perlbn to the Life. EGGS, in Architecture, an Ornament in that Form, cut in the Echinus or Quarter-Round of the hnic and Conipofac'Cip'\ ed, they will return to Length they had at firll. Fibres have no Elajlicity, un- lefs they are extended with a certain Force; as it appears ia Strings which have their Ends fix'd without being ftretch'd ; for if you remove them a little from their Polition, they do not return to it ; but what the De- tals. The Profile or Contour of gree of Tendon is, which gives an Echinus is enrich'd with E^gs beginning to their Elajlidiy^is not and Anchors placed alternately. ELABORATORY. See Laboratory. ELASTICIFY is that Pro- perty of Bodies whereby they re- turn tb their former Figure, when it has been altered by any Force: For if a compa6l Body be dented in, without the Parts falling into that Dent,the Body will return to its former Figure, from the mutual AttrasSiion of its Parrs. All Bodies, in which we ob- fcrv e Elafiic:i\\ confilt of fmall Threads or " Filaments, or at lead may be conceived as con- fifting of fuchThreads ; and it may be fiippos'd that thofe 'Fhreads laid together make Vp one Body : T hereforc that we may examine Ebjliciiy in the Cafe which is the ]eafl complex, we mu(t confider Strings of IVIulical Inftrumcnts, and fuch as are of Metal; for Cat-Gut Strings have a fpiral Twilt, and cannot be conlider'd in the lame Manner as thofe yet determin'd by Ei^periments. When a i'ibre is extended with too much Force, and this De- gree of Teniion is alfo un- known : This we do know, that the Degree of Teniion ifi Fibres, which confiitutes Ebfiicity^ is confin'd to certain Limits. Hence appears the Difference of Bodies that are Ebliick, and fuch as are not fo ; why a Body lofes its Elajliciiy, and how a Body deftirute of Elafticity^ ac- quires thatProperty. A Plate of Metal, by repeated Blows of an Hammer, becomes Elaftick, and by being heated, does again lofe that Virtue. Between the Limits of Ten- fion that terminate Elaflicity^ there is a different Force requir'd for different Degrees of Teniion in, or to ftretch Cords to.certaiii Lengths. What this Proportion is, muft be determin'd by Ex- periments; whicli mult t>emade with Chords of Metal. ELBOW, in Architeaure, a Term ufed for an Obtufe Angle of E L E L of a Wall, Building, Road,^^'^. which divides it trom its Right Line. ELEMENTS, by Geome- tricians, Natural "Philofophcrs, ^c. are iifually taken to lignify the fame as Principles or Rudi- jnents of any Science. So when Natural Philofophcrs fay, the Elementary Principles of mixed Bodies^ they mean the fimple Particles out of which the mixed Body is compos'd, and into which it is ultimately refjlvable. ELLIPSIS, in Geometry, I's one of theConick Seftions.^ pro- perly call'd an Oval or Oblong. EUipfis^ or Oval^ is a Figure bounded by a regular Curve Line, returning^ into itfcif ; but of its two Diameters cutting each other in the Centre, one is longer than the other, in which it ditFers from the Circle. To find the Area thereof, this is theKUhY.. Multiply the Trs.nfverfe Dia- meter by the Conjugate, and multiply that Produd'by .785-4, and this lall Produft will be the Area of the EiUpfis. \ \ 61.6. the Tranfverfe Diameter. 44-4 2464 2464 2464 i735'04 •7854^ I 0940 I 6 12675-20 2188022 19I45-2S 2 1 48. 1 004 1 6 the Area of the OvaL Demonstration. If you circumfcribe any El- i'tpfis with a Circle, and fuppofe an infinite Number of Chord Lin©* drnwn therein, till p^rgllel to the Conjugate Diameter, as ttiofe in the Figure above, then it will be. As DA the Diameter of the Circle is to N« the Conjugate Diameter of the Ellipjh^ to is S aB any Chord in the Circle to E L E L bah^ Its refpc^live Ordinate in For, according to the Proper- the EllipJiS' ty of [he Circle, It is 1 I 1 flS X T^= D B« by the Property ot the EllipCis. and 2 n TC : NC ::Sx T^: D^^ • icis I 3 DTC : NC : : □ B« \ub, I. z 14I TC : N C: : 13d : ^^. 3 Hence Confeqn. That is 2 TC : iNC :: B^ : ^^ DA : N» :: B^B : bab. But the Sum of an infinite Series of fuch Chords as B^Z-do conftitute the Area of theCircle ; and the Sum of the like Series of their refpeclive Ordinate?, •xs.bab^ do conftitute the Area of the Ei- lipfis. Therefore TS : N » : : Circle'.',- Area : the Ellipjis Jreabm T S :N« :: D TS : TS'XN«; whence it tbilows that DTS : Circle's Area : :T S X N a : EUipJis Area. Confequently, as i is to .7S)'4, lb is the Rcttangleor Product of the Tranverfe "and Conjugate Diameter of any Ellipfis to its Area. Hence it is eafy to conceive that the fqunreRoot of the Pro- dud of tiie Tranfi'crfe and Con- jogate Diameters will be the Dia- meter of a Circle equal to the Ellipfis. ELLIPTICK, ? of or per- ELLIPTiCAL, S tainiiigto an Ellipfis. Serlio-, IL.rtman^ Cj'c. demonftrate, that the bell Form for Arches or Vaults, is Elliptical. Elliptic k Space Is the Area con - tain'd within the Circumference or Curve of the Elllplis. Elliptical Co}7?pa(Jcs^ an Inftru- ment ufually made of BraCs for drawing an Elliplis or Oval at one Revolution of an Index. ELM E M ELM is of fingular Ufes, TVhere it may lie continually wet or dry in Extreams, therefore proper for Water-Works, Mills, Ladles, and Soles of Wheel- Pipes, Aqueduds, Pales, Ship- Planks, beneath theWater-Line. Some of it found in Bogs has lurn'd like the moft polifh'd and hardeft Ebony. It is alfo of Ufe for Wheel- ivrights, Handles for fingle Saws, the knotty Parts for Naves, and Hubbs ; the flraight and fmooth for Axletrees; and the very Roots for curioully dap- pled Works, Kerbs of Cop- pers, Feathercdge, and Weather- Boards, Trunks, Coffins, and Shovel-Board Tables. The Te- nor of the Grain makes it alfo fit for all Kinds of Carved Work, and mod Ornaments be- longing to Architedure. Vitruvius commends it for Tenons and Mortoifes. EMBOSSING, I inArchitec- IMBOSSING, 3ture,Sculp- turc, eff, IS the forming, or fafhioning of Works in Relievo, whether cut with a Chiffel, or otherwife ; it is a kind of Sculp- ture or Engraving, wherein the Figures ftick out from the Plane whereon it Is engraven, and ac- cording as they are more or lefs protuberant. It is called by the ItaUans^ Baffo, Me7Z0, or Alto Relievo, and by the Engliflj, Bafs-Relief, Mean Relief, or High Relief. EMBRASURE, in Archi- tedurc, is the Enlargement made of a Gap or Aperture of a Door or Window on the Inlide of a Wall. Its Ufe is to give the greater Play for the opening of the E N Door, Wicket, Cafement, ^c. or to take in the more Light, The Emhrajure coming flo- ping inwards, renders the inner Angles obtufe. When the Wall is very thick, tney fometimes make Emhralures on the Out- fide. EMPASTING, \n Painting, is the laying on Colours thick and bold; or the applyin^^ fe- veral Lays of Colours, to the End that they may appear thick EN DECAGON, ~)va Geo- HENDECAGON, 5 metry, a Figure having eleven Angles and confequently as many Sides! ENGINE, in general, is any Mechanick Inftrumcnr composM of Wheels, Screws, Pullies, efr. by the Help of which, a Body is cither mov'd or hindred from moving. Erjl^ When the Quantities of Motion, in the Weight and Power, are equal, the Engine fhall Hand tn aquilibrio^ but Wihen they are unequal, the greater Quantity of Motion fliail overcome and work the En- gine. Secondly^ Of Forces In them- felves equal, that which is near- efl: to that Point of the En- gine^ about which the Weight and Pov/cr move, or uppn which they fullain each other, is relatively the weakcfl upon the Engine ; for as the Engine works the nearefl Force moves the flowed, and therefore has the leaft Quantity of Motion. Thirdly, The EffcQ of any Force upon the Engine, wiil not be changed, if, without changing the Line of Dire d ion, n is only placed in fomc other Point: of the UimeLine, T!e E isf E N The Nature of any Engine is cxplain'd, when it is known in what Circumlkuces the Weight and Power will be in aqmitbrio upon that Engine, * Fourthly^ In all Efigincs •whatlbever, the Weight and Power will be in (cquilibrio^ when their Quantities arc in the reciprocal Proportion of the Velocities, which the Working of the Engine will give them. If an Engine be compounded of feveral fimple E.ngtnes^ the Power is to the ReliRance, when it counterbalances it in a Raiio. compounded of all the Ratio's which the Powers in each fimple Engine would have to the Refinance, if they were fepnrately apply'd. fiNNEAGON, a Figure of nine Angles and nine Sides. Ei\TABLArURE,7 inAr- ENTABLEMENT, 3 chi- tcfture, which Vitniviui and i'ignola call Ornameni, is that Part of an Order of a Column, which is over the Capita], and comprehends the Architrave, Prize, and Cornice. The E^ntablattirc Js alfo cal- led the Trabeation, and feems borrow 'd from the Latin Trabs^ a Beam. But Ibme derive it from TabHlatny,]^ L. a Ceiling ; bccaufe the Prize is fuppofed to be p)rm'd by the Ends of the Jollts, which bear upon the Ar- chitrave. It is different in ditierent Or- ders : Indeed, it does confiil of the three grand Parts or Di- vilions nbove meniioned in all ; biu fhofe l^uts conlill of a great or kfs Number (^f particular Members or bubdivilions, ac- cording as the Order is more or lefs rich. flgnola makes the Entablature a quarter of the Height of the whole Column in all the Or- ders. In the Tufc-an^ and Doric ^ the Architrave, Prize, and Cornice, are all of the fame Height. In the Icnic^ Corinthian^ and Compofite^ the whole Entabla-. tare being fifteen Parts,- five of thefc go to the Architrave, four to the Prize, and fix to the Cor- nice. Entablature^ 1 in Mafonry, is Entablement , ^ u fed fo r the laft Row of Scones on the Top of the Wall of a Building, 011 which the Timber and the Co- vering reft. It is often made to project be- yond the Naked of a Wall, to carry off the Rain. 'I he Entablement of the T'uf^ f^» Order, fays M. Le Clerc^ con- lilts of three principril Parts ; a Cornice, a Prize, and an Archi- trave. To the fiifl, that is, the Cor- nice, he gives about two Fifchs of the Height of the Entable- ment. TheFrizehc makes fomewhat higher than the Architrave, to the End that thofetwo Members may appear to have nearly the fame Height; the Overplus given to the Prize, being intended to fupply the Place of that Part hidden from the Eye by theTss- nia, which finillics the Archi- trave. And this fame Rule, he fays, he ufes in all his Entable- ment i. Of the E.ntnhlemcnt of the Column raifcd on a Pedtflal, he tells E N tells US, he always makes two Defigns of an Entablement; the one a fmall Matter higher than the other; the fir(l for Columns that have no Pcdcftals, and the fecond for thofe that have. This Difference of Entablement \s a Thing highly reafonable, in re- gard Columns that have Fede- rals, are in a more rtatcly Or- donnance than thofe which have none, provided the Co- lumns be but equal in other Refpeds. Whence 'tis apparent, the Entablement oh\-\tf\K{\.i\\o\i\d be ftronger than that of the laft: Accordingly, making one Enta- blement three Modules and fif- teen Minutes, which is the com- mon Height, he fays, he could not think it advifeable to make the other, which is for Columns without Pedeftals, above three Modules, ten Minutes; which comes five Minutes fliort of the former. I am fenfible, fays he, that were we only to have Regard to the Laws of Strength and Weaknefs, we fhould diminifh the Entablements of Columns that have Pedeftals, rather than thofe which have none. But we are here, fays he,con- fulting Beauty, not Strength ; and it may be obferved, 1 don't augment the Strength of this£»- tahiement^ but diminifh that of the former, where the Porticoes are Icfs grand, and the Columns lea diftant. Oi Entablatures which have Breaks, and prnjeft unequally, M. Le Clerc fays, the Entabla- ture is fometimes made to give back or retreat a little between the Columns ; but on etraordi- nary Occatious, and for fpccial Vol. I, Reafons, as where there are not large Stone> fufficient to carry out the whole Entablature to its due Pitch ; or where a great Pro- je6lure between the Columns might intercept the Light neccf- fary underneath, or prevent the View of any Thing above. Bur, however, it mufi not be forgot: that the principal End of the Entablature:^ is to flielter what is underneath; which, in this Cafe, it only does by Halves, as having nothing biw the bare Pro- jefture of the Cornice for that Purpofe. ENTERSOLE, in Architec- ture, a kind of little Story, fometimes called a Mexanzine, contriv'd occafionally at the Top of the firfl: Story, for the Con- veniencyof a Wardrobe, ^c. ENTRY, a Door, Gate, Pallage, cfrV. through which we arrive at any Place. EPICYCLOID, in Geome- try, a Curve, generated by the Revolution of a Point of the Periphery of a Circle along the convex or concave Part of ano- ther Circle. EPISTYLE, in the antient Architedure, a Term ufed by the Greeks^ for what we call Architrave. viz.'Oi malTive Piece of Stone or Wood laid imme- diately over the Capital of a Co- lumn. EQUAL is a Term of Rela- tion between two or more Things of the fame Magnitude, Quantity, or Quality. Equal Circles are thofe whofe Diameters are equal. Eonal Angles are thofe whofe Sides arc inclin'd alike to each other, or that are meafured by iimilar Parts of their Circles. A a Equal Areas 'are ' equal ^ whether the Figures be fimilar or not. Equal Solids are fuch as cohl- prehend orcoV)t$tift each as much as the other,' or 'whole Solidi- ties and Capa(^;ties are equal. Efual Geornetrkal Ratio's are thole whofe leaft Terms are Iimi- lar aliquot or aliquant Parts of *the greater. Equal Ar'tthmetical B.atio's are thole wherein the Diti'crence of the two lefs Terms is equal to the Difference of the two greater. ^ '--'^m ■.\\>.; \- •. EVEN NUMBER -is >th« which can be divided [into two equal Parts, as 4. 6, 8, ^c, EVENLY-EVEN Number, is that which an even Number meafures by an even one ; as 16 is an Evenly-even Number, be- caufe 8 an even Number mea- fures it by 2, an even Number. Evenly-odd Number is that "which an even Number meafures by an odd one, as 20, which the even Number 4 meafures by the odd one f. EVOLVENT, in Geometry, a Term ufed by fome Writers for the Curve which refults from the Evolution of a Curve, in Contradiftih6lion to the Evo- lute, which is the firft Curve fuppofed to be opened or evol^ ved. EVOLUTE, in the Higher Geometry, a Curve fuppofed to be evolv'd or open'd, and which in opening defcribes other Curves. EVOLUTION, in Geome- try, is the Unfolding or Open- ing of a Curve, and raaking^ it defcribe a Volute. ..loini, Evolut'mn is alfo ufe^ for the Extradion of Roots out of Powers ; in which Senfe it is diredly contrary to Involution. EURITHMY, in Architec- ture, Sculpture, and Painting, is a certain Majefty, Elegance, ai^d Eafiiiefs, appeariiig.iiii \^^^ Qf§n- TOl " ■ - 3^ pofitlon of, diver? Members or Parts of -a, Body,, Painting, or Sculpture, and , refuking from the fine Proportion of It. ^ Fitruv'tHS ranks the Euriihmicz among the elfcntial I^artsof Ar- chitefture. He defcribes it as confining in the Beanty of the Conftruilion or Aifemblage of the feveral Parts of -the Work, which render its Afped, or its whole Appearance grateful; e.g. when the Pleight corref- ponds to the Breadth, and the Breadth to the Length, ^c. From thefe three Ideas, or Defigns, w';;;. Orthography, Sce- nography, and Profile, it is, that the fame EKritbmia, ma- jeftick and beautiful Appear- ance of an Ediiice, does refult; which creates that agreeable Har- mony between the feveral Di- racnfions, i, e. between the Length, Breadth^ and Height of each Room in a Fabrick, fo that nothing leems difproportiona!, too long for this, or too broad for that, but correlponds in a jull and regular Symmetry and Con^ fent of all the Parts, with the Whole. Evelyns Accaunt pf Architeclt. "' ,. ' , EUSTYLE, in'.^fchiteaure, a fort of Building \\\ which the Pillars are placed at the moil convenient Diilance one from another ; the Intercolumniations being all juft two Diameters, and a quarter of the Column; except thofe in the Middle of the Face, before and behind,, which are three Diameters diftant. EXAGGERATION, fn Painting, is a Method of repre-. fenting Things wherein they are A a 2 pflrpng ; EF^Y' F A flrong either in refpedl to th.e Defi,;^n or tiie Colonring, ■■'-">'' EXAGON. See Hexagon: EXPERIMENTUM Cruds IS a capital" leading or decifive Experiment, thus called, as ci- ther like a Crofs, or Poft of Dircfticn placed in the Meeting of feveral Roads : It guides and dircds Men t^ the true Know- ledge of the Nature of the Thing, as it were, extorted by Violence. EXPONENT, in Arithme- tick, or. Exponent of a Powcr^ the Number which cxprtiVcs the Degree of the Power; or which Ihevvs how often a given Power is to be divided by its Root, be- fore it be brought down to Uni- ty. EYE, in Architeaure. isufed to fignify any round Window- made in a Pediment, an Attick, the Reins of a Vault, or the like. Eye of a Dome is an Aperture jit the Top of the Dome ; as that of the ^pantheon at Rome, or of St. Piiurs at Londoti. It is ufu- silly cover'd with a Lanthorn. Eye of the f^olaie^ in Architec- ture, is the Centre of the Vo- lutes, or that Point in which the Helix' or Spiral, of which it is Ibrm'd, commences: Or it is the little Circle in the Middle of the Volutes, in which are found ,the thirteen Centres for the de- fcribing the Circumvolutions of it. E\e'BTOii\ in ArchiteSure, is n(ed'' in the fame Seius as Lilt or Fillet. F A FABRIC K, the Strudure or Conltrudion of any Thing, particularly a Building, as an Houfe, Hall, Church, FACADE,^ in Archiicaure, fWCE, 5 ^^^ Eront of ^a Building, or the Side on which the chiet Entrance is. Alio it is fometimes ufed for the Side rliar it prefents to u Street. Gar- den, Court, ^c. Andfumetimes for any Side oppofite to the Eye. FACE, -pin Architedure, is FACIA, Ca flat Member, ha- FASCIA, 3viiig a coniidera- ble Breadth, and but afmallPro- jedurc; as the Bands of an Ar- chitrave, Larmier, l^c. Face of a Stom^ in Mafonry, is the Superficies or Plane of the Stone that is to lie in the Front of the Work ; which is very eali- ly known, when the Face is icapted, the Face being always oppofite to the Back ; and the Back going rough as it comes from the Quarry. But in rough Stones, Work- men generally chufe to make one of thofe Sides the Face^ which, when in the Quarry, lay perpendicular to the Horizon, and confequcntly the breaking, and not the cleaving Way of the Stone. ' -^ '' '^ ■ For a better underilanding of which, fee Stohe. FACEING, F A F E FACEING of rimher Build' ing with Brick. The Manner of this is as fellows : All betwixt the Timber and the Wall is a Brick's Length thick, (or a nine Inch Wall,) and againft the Timber but half a Brick, or a four and a half Inch Wall. But this Way of facing Tim- ber Buildings is not approved of, by reafon that the Mortar does lo extremely burn the Timber. FACIA ■) in Architedure, FASCIA C according to M. FACIO r Perrauh, figni- FACE J fiesanydatMem- ber, as the Band of an Archi- trave, ^c. Some write it Fa- fce^ as though from the Latin., Fafcia^ a Swathe, or largeTurban, which Vitrnvius ufes on the like Occafion. In effcd it is no more than a broad Lift, or Fil- ler. They are commonly made \\\ Architraves, and in the Cornices of Pedellals. Fafcia's., in Brick Buildings, are certain Juttings-out of the Bricks over the Windows of each Story, except the upper one. And thefe are fometimes plain, like thofe of Columns ; but fometimes they are moulded, which make a very handfome Appearaace : And this Mould- ing is ufually a Scima Reverfa at the Bottom, above which are two plain Courfes of Bricks, then an Aftragal, and laftly a Boultin. It is the fame in Stone Build- ings as it is in Brick, and they are alfo fometimes plain, and fometimes moulded with a Scima Reverfa, or Ogee. The Price of Fafcia^s is, if the Workman finds materials, ufual- ly about lod. per Foot running Meafure; but Workmanfliip on- ly, is . ^k^VL%,6 d. /Qi . 8 d. per Foot.) MM Tl^ iiv.f") l/itruv'ms means by the Term Fafcia., (as alfo Tania and Corfu.,') what we call TUtBa-dd. FACTORS, in Ariihmetick, is a Name given to the Multi- plicand and Multiplicator, be- caufe they do facere produdum., i.e. make or conftitute the Pro- duft. FACTUM, in Arithmetick, the ProduQ of two Quantities multiplied by each other. FEATHER -EDG'D Boards or Planks., are fuch as are thicker on one Side than the other. FELLING of Timber. See Timber. FENCING with "Pales : As Paling with three Rails, cleft Pales, Rails, and Pofts, cleaving and fetting up, is ufually done at 3x. 6d. the Rod, reckoning the telling of the Timber into the Bargain ; but then their Mate- rials are laid down to their Hands. Fencing with fingle Rails and Pofts, together with felling, clea- ving, and fetting up, is ufually done at %d. or lod. the Rod ; but then alfo their Materials muft be laid down to their Hands, that they may have no carrying. Some fay, that they have known it done for 4Ycve delired ; as on Triurriphal Arches, Tourna- inents, ^c. FESTOONS, in Architeaure, cff. a Decoration ufed by Ar- chitc6i:s. Painter?, Joiners, ^c. to enrich their Works. It con- fiils of a String or Column of Flowers, Fruits, and Leaves ty- ed together, fomewhat biggeft in the iMiddJe, and extended by the two Ex?f ernes ; bt fides which, the main Pin which fiiUs down in an Arch, two le/Ter Parts hang perpendicularly. See the Figure. _;::■.:;! J .• i^e/^ac-jflff ar*e HOItr^'dhiefly tifi-d in Friezes, and other vacant l^lace^, which require to be fiil'd up and adorn'd. ' This Orn*TW/rnt is made in Imitation of the FeflooMs^ or long Cinders of Fl&wers, which the P V Ahtren» ^Taeed on the Doors of then- Temple^^l^S^. om feflivaP Occafions,' '■v.^*^ '\^ yu:-.'. '\ j.iib^ FIGURE 'fs the Surface or terminating Extremes of a Body. F/j^nre alfo fignines all Repre- fentations or Images of Things in Sculpture, Prints, ^c. ^' Fi^m-e^ in Geometry, fignifies a Surface inclos'd, or circum- fcribed with one or more Lines; as Circles, Ellipfes, Triangles, Squares, Polygons, ^frV. Figures are either reftilineal or curvilineal, or mix'd, accord- ing as the Perimeter confilfs of Right 'tiiireji .' Curve Lines, or both. ' Re/ci!ineal Figures are thofe which have their Extremities all Right Lines, as Triangles, Qua- drilaterals, ^c. Polygons Re- gular, Irregular, ere- CurvHiyteal Fi_zures are fuch as have iheir Extremities crook- ed ; as Circles Ellipfes, ^c. Mix'd Figures are fuch as are bounded partly by Right Lines, and partly by crooked ones ; as a Semi-Circle, Segment of a Circle, (ffc. '■Playie Figures, or Plane Sur- faces, are fi.ich as are terminated and bounded by Right Lines only. ip.-j-ir.j^ A Regular Figure^ M that which is equilateral and equi- anglar. An Irregular Figure^ is that which is not both. • tigfire, in Conic Sections, ac- cording 10 Apollontus^ is theRe6t- angle under the Latns Refcwm ^ Tra/rfoerfum in the H) betbola and Elliplis. Figure of the Diameter^ the Redapgle under any Diameter, and and its proper P&ramete^niSjAiy. the Elliplis and Hyp«rbo)3^{ caflit} ed the Figure of that t)iametei\i , Figure^ in Painting and Dc- ligning, is the Lines and Colours that Form the ReprefentatiGii\of a Man, or other Animal, j i -^ Figure^ in Architecture, ^c. fignifies the Reprefentation^ of Things made in folid Matter, as Statues, eTf . Figures^ in Arithmetick, are the nine Digits, or numerical Chara6ters,i,z,3,4,5-,6,7,8,9,o; or thofe by which Numbers are exprefled or written. FILLET > in Architefture, a FILET 5 little fquareMerar ber, or Ornament, or Moulding, ufed in divers Places, and upon divers Occalions ; bat generally as a Corona or Crowning over a greater Moulding. The Filet is the fame that is by the Italians called Lifta^ or Liflella ; by the French^ Reglet ; and by others Band^ and Bande- lette. Fillet^ in Painting, Gilding, eff. is a little Rule, or Reglet of Leaf Gold drawn over fome Mouldings ; or on the Edges of Frames, Pan nels, cffiT. efpecially when painted white by Way of Enrichment. FINISHING, with Archi- teds, ^c. is frequently ufed of a Crowning, Acroter,C5'V. railed over a Piece of Building, to ter- minate and finiflj^i.Qi eompieat FIRE-STONE, a fort of Stone called alfo Rygate-Stonc, of the Name of the Place from whence it is chiefly brought, be- ing very good for l^'re- Hearths, Ovens, Stoves, zjfci.' gjgasjja/jt j , As tQthq Price (^f^/T/r^.^S'/^j;/^, Hearths at: it,, are uiually fold at I s. per FoQti .and Chimney- Gorner Stones at los. per Pair ; and Blocks for fetting up Cop- pers, eagh being about three Feet long, one and a half broad, and eight or nine Incpjss- tbipit,:.at 6s. S d. /'(fr Piece,'. •' rr > < FLEMISH BRICK5, a nqat ftrong Sort of Bricks, of a yel- low ifli Colour, brought front Flanders ^ and much ufed in paving Yards, Stables, ^c. be- ing much neater and /tronger, than common or Clay Bricks. Thefe Bricks are fix Inches and a quarter in Length, two and a half in Breadth, and one and a quarter thick. Now al- lowing one Fourth of an Inch for the Joint, 72 of them will pave a Yard fquare ; but if they be fet edge-ways, then a Yard fquare will require lop. Thefe Bricks are ufually fold for 2 s. per Hundred FLIGHT of a Stair-Cafe. See Stair-Case. , y FLINT VVAt ' 1 The Foot is of SifFerent Lengths in different Countries. The ^aris Royal Foot exceeds the Efiglip by 7 Lines and a half. The antient Roman Foot of the Capital confifted of four Palms, equal to four Inches and feven Tenths Fnglijlo. The Rbtnla»d or hey den Faot^ by which all the Northern Na- tions reckon, is to the Roman Foot as 95*0 to 1000. The Proportion of the prin- cipal Feet of feveral Nations, compared with the Engli[l3 and French^ are as follows : The Englip Foot being di- vided into 1000 Parts, or into 12 Inches, the other Feet will bs as follows : Fc. Inc. Lin. London Foot 1000 0120 Puris^ the Royal Foot 1068 I GO 8 Amfterdiim Foot 942 Oil 3 Ayitwerp Foot 946 OH Z Dort Foot 1 1 84 12 2 Khinland^ or hey den Foot 1033 I 04 Mechlin Foot 919 II IMiddleburg Foot 991 0119 Strasburg Foot 920 II Lor rain Foot 95-8 II 4 Cologn Foot 95-4 0114 Bremen Foot 964 II 6 , ,^ ,, i,. Frankfort on theMayn Foot 948 II 4 ,bni/oiO Spanijjj Foot loor n o' : i^rr Toledo Foot 899 10 y .A :ii: -3(1 J 1 Roman Foot 967 .^."jJTiliJ^ij^ R \o •ine fifbvb, Molonia Foot 1204 JM1.>2J ^, 2i jr lO V 11 ma Mauma^ri^mh t)uiul Foot i5'69 %■' '''(^J^jilj wood '■mil lo r^Vefice^ (Wi^ulu siorn io ,t)3n3qxi^i^«^.'.31§ Copenhagen WOl 'Pi&H ■^3irii 3ri3 CopenhagmiB^Nl smslFoiot ■ 96^) Qiidljfcjfj^'jjq;).'] .-.., -^^r.^jitga . znoflnsmiC Foot. 1831,1 i^a3'ft:jj> ,,- The Grff^fioul olduD Foot 1007,- 'forijaQw i.^jV (?/<^ AtfJKtfwsi'^ 3riT Foot 970 on o The Tarts Foot being fuppofed to contain 1440 Parts, the reft will be as follows : .,- r<.T PoQf Foot Foot Foot Foot Foot Foot Foot Foot Paris ^~- Rhifiland Roman London SwedifJj Damjh Venetian Conjlantintp olitan Bononian Strasburg Norimbcrg Dantzick Italy Foot Foot Foot Foot 1 140 1320 13SO 1320 1403 15-40 1320 1682 1282 1346 1721 1320 FOOT-PACE,") is a Part of HALF-PACE, ra Pair of Stairs, whereon, after four or fix Steps, you arrive at a broad Pjace, where you may take two or three Paces before you afcend another Step, by that Means to eafe the Legs in alcending the reft of the Steps. FORNICATION is anArch- ing or Vaulting. '' FOUN DATION is that Part of a Building, which is under Ground, or the Mafs of Stone, Brick, ^c. which fnpports a Building,or upon which theWalls of a Superllrudure areraifed Or it is the CotFer or Bed dug below the Level of the Ground, to raife a Building upon; in which Senfe, the Foundation ei- ther goes to the whole Area or Extent of the Building ; as when there are to be Vaults, Cellars, or the like ; or it is drawn in Cuts or Trenches, as when only Walls are to be raifed. The Foundation is properly fo much of the Mafonry, or Bricklayers Work, as reaches as high as the Surface of the Ground, and ought always :o be proportion'd to the Load or Weight of the Building that it is to bear. Sometimes the Foundation is mallive, and continu'd under the whole Building, as in the an- tique Arches and Aquedn6h, and fome Amphitheatre^; : But it is more ufually in Spaces or Inter- vals, either to aVoid^xpence, or becaufe ihQ Vacuities are at too great great aDiftance, in which latter Caie,they make ufc of infulated J Pillars, bound together by Arches. ■ Of Digging for, and Laying of Foundations. There are feveral Things to be well conlider'd in laying the Foundations of a Building, the moll: niateriai of which are here extracted from the be/l Architects Anticnt and Modern. That we may found our Ha- bitation iirmly, requires the ex- adell Care : For, fays Sir Henry IVooton^ if the Foundation dance, "twill mart all the Mirth in the Houfe. Therefore, fays that excellent Arcliite61:, we muftfirlt examine the Bed of Earth upon which ■we are to build, and then the under Fillings or Subftrudion, as the Antients called it. For the former, we have a general Precept in PitruDiiis, cvvice repeated by him as a Point indeed of main Confequence ; SnbjiruBlonis Fundationes fodi- a-/it:ir^ fi qaennt inveniri ad fali- dum ^ in folido : By which, he recommends nor only a diligent, but even jealous Examination what the Soil will bear; adviling lis not to rert upon any appear- ing Solidity, unlefs the whole Mould through which we cut, havti likewife been folid. But he has no where deter- miii'd how far we iTiould go in this Search, as perhaps depend- ing more upon Difcretion than Regularity, according to the Weight of the Work. But yet Palladio has ventured to icduce it to a Rule; and al- F O lows a ;fixth Part of the Height of the whole Building for the Cuvafione, i. e. hollowing or under- digging, unlefs there be Cellara under Ground ; in which Cafe, he would have it fome- w^hat lower. See Sir Henry Wootot^s Elements of Architec- ture. Palladia alfo lays down feve- ral Rules to know if the Earth be firm enough for the Fonnda- //o;?,(vvithout artificial Helps,) by Obfervations from the digging of Wells, Cifterns, and the like, (which he would have to be done in the firlt Place) and from Herbs growing there, if there be fuch as ufually fpring up in firm Ground; alfo if a great Weight be thrown on the Ground, it neither founds nor fhakes ; or if a Drum being fet on the Ground, or lightly touch'd, it does not refound again, nor fl^akethe Wa- ter in a Veifel fet near it. Thefe, fays he, are Signs of firm Ground But the beft Way to difcover the Nature of the Soil, is to try it with an Iron Crow, or elfe with a Borer, fuch as is ufed by WclKDiggers. Architects ought to ufe the utmofl: Diligence in this Point ; for, of all tlie Errors tliat may happen in^ building, thofe are the moit pernicious, which are com- mitted in the Foundatiovi ; becaufe they bring with them the Rufn of the whole Building; nor can they be amended without very gre;it Difficulty. Foundations are either na- tural, or artificial: Natural, as when we build on a RocTt, or very folid Earth; m which Cafe, we need not fcek for any fur- • • ■ ther F O F O ther Strengthening: For thefe, without Digging, or other ar- tificial Helps, are of them- felves excellent Fonndatiotts^ and molt fit to uphold the greateft Buildings. But it" the Ground be fandy or marfhy, or have lately been dug, in fuch Cafe, Recourfe muft be had to Art. In the former Cafe, the Architeft mud adjuft the Depth of the Foundation by the Height, Weight, i^c. of the Building: A fixth Part of the whole Height is looked upon as a Medium; and as toThicknefs, double that of the Width of a Wall is a good Rule. If you build up(m mofly and loofe Earth, then you muft dig till you find found Ground. This found Ground (fit to uphold a Building) is of divers Kinds ; (as Alberti well obferves,) in fome Places 'tis fo hard, as hardly to be cut with Iron, in other Places very ftitf, in other Places blackifh, in odiers whi- tifh, (which is accounted the the weakeft,) in others like Chalk, and in others fandy; but of all thefe, that is the beft that requires moft Labour in cutting or digging, and when wet, does not difolve into Dirt. If the Earth to be built on is very foft,as in Moorifh Grounds, or fuch that the natural Founda- tion cannot be trulkd, then you muft get good Pieces of Oak, whofc Length muft be the Breadth of the Trench, or about two Foot longer than theBreadth of the Wall : Thefe muft belaid crofs the Foundation^ about two Feet afuuder, and being well ramm'd down, lay long Flanks Vol, I. upon them ; which Planks need not lie fo broad as the Pieces are long, but only about four Inches of a Side wider than the Bafisor Foot of the Wall is to be, and pinn'd or fpik'd down to the Pieces of Oak on which they lie. But if the Ground be fo very bad, that this will not do, then you muft provide good Piles of Oak of fuch a Length as will reach the good Ground, and whofe Diameter muft he about one twelfth Part of their Length. Thefe Piles muft be forced or drove down with aCommander, or a Machine or Engine for that Purpofe, and muft be placed as clofe as one can ftand by ano- ther; then lay long Planks upon them, and fpike or pin them down faft. But if the Ground be faulty, but here and there a Place, and the reft of the Ground be good, you may turn Arches over thefe loofe Places, which will dif- charge them of the Weight. You muft not forget to place the Piles not only under the outer Walls, but alfo under the inner Walls that divide the Building; for if thefs (hould fink, it would be a Means to make the outer Wall crack, and fo ruin the whole Building. Having thus far ccuifider'd the Bed of Earth on which the Build- ing is to beerefted, we fhall ne?\t confider the Subftru6tion, as it was called by the Antients, but the Moderns generally call it the Foundation . This is the Ground-Work of the whole Edifice which muft fuftain the Walls, and is a kind of Artificial, as the other was Natural: As to which, thefe B b Things eveH' therefore- layti §tpi?fn v-w jg^v > foundation pould Platforihi ofi.ga»©d Board.'j ■; ^p; Jt^ and if unlit Con- liners any. where, then they are more efpedaljy :fi> in tile: Euun- to iiave moft Strength in their natural Pofuion. This Precept is generally ob- ferv'd by all good modern Ar- tills, not only in the Foundatiov^ but alio in all the Parts of the Super Oructure; and that for a better Realbn than that bare Gon- jei^lure, viz. becaufe they iind the Stones to have a cleaving Grain, or that they are fubjedl to Thirdly^ That the Breadth of cleave that Way of the Stone the Subllruciion be at ieatt dou- ble the Breadth of the Wall that is to be r^fed Upon it. Bat even m this Cafe, Art ought fc.give way.toDifcretion; and the Subftrudion may be made either broader or narrower, ac-cording as the Goodnefs of the Ground, andthePonderofity of the Editice requires. F'jurtljjy, That the Fou:4datton he made tp.diminifh as it rifes, but yet fo, tjjat there may be as much left .00 the one Side as the otiier; fo that theMiddlo of that ;ibovc .m&y bei perpendicularly over th$iPv^i44le_of that below: ^AVhich pngljc^jin l/ke manner to -;l>e obtkiH'<^] iA;:diminifliing the WaUs/flbo^'e (ground; for by this M^an?,' ith§;^]§!4iiding will be- 'corwie oJiiUfib jfeonger than it that lay horiiontally in the Quarry: And for that Reafon, if the horizontal Pofuion of the Scones in the Quarry fhould be placed vertically in the Build- ing, ttie fiipcr-incumbent Weight would be apt to cleave them, and lo render the Building rui- nous For, as it has been ob- ferv'd by 'Philip D'Ormc, the Breaking or Yielding of a Stone in the. Fou>idation.^ although it fliou'd be but the Breadth of the J3ack of a Knife, it will make a Cleft of mope than half a Foot in the Fabrick aloft. See Stone- Bed^ and F.m of a Stone. V Jjl fome Places they found the Peer^ of Bridges, and other Baildings' near the Water, on Sacks of Wool laid like Ma- . tf.aires, Y(hich being well prefs'd . aiisd grtiaiy, \vill ne\L«i: giveiW»y ; 3¥ 1--\'-^-^ -- -i '^fii ,^"\k^n'}4liuppn,'the .Ruins of an uoi-jy^'diiM ^/**. iFouudanons* .• o!^^/'W]f4^;«*''^uUuletS; yqu ;are noJrjtiK' viiK 1 . >.M :■ Well '^ifym^ \^h~}\^ RsR'^^iu!^'^ I! ,vMrji j?i/^//Ay^i tells as there are ■.that,i»s Strengtjf i^-iggjoieji^ip y^fiy\?raA'^Yay^ of valuing i^o/r»^- fteatjhe'i^iiiWiHSfi v/ ,jl Cfjj mi . :t/>>r-fi9r: Years Purchafe. hh.lf^tiig attempts to demon- ftrate, that this Way of valuing Foundations is better, and to be preferred to any other. The Foundattom of Bridgeu Of all the Antients (fays M. Gautier) in Archite6lure, who have given us any Rules for the founding of Bridges, Scamozzi is the only one that has faid any Thing to the Purpofe. He tells us, that xhtFounda- tions are laid after different Man- ners, The firfl: is by cncloling all round the Space of Ground you would build upon, by Dams made with Piles fet deep in the Ground in double Rows, well ftrengtnened and bound together with crofs Pieces and Cords, and filling the vacant Spaces between them with Chalk or other earthy Matter. . This being dohe,'tli>e Water muft be cmpty'd mu, and the FouKdation digged according to the Quality of the Ground, driving down Piles, if it be ne- B b 2 oefi.iry F O eeflary ; upon which the Walls of the Foundation mil ft be laid. But this Method is only pra6ticable in building on fuch Rivers where the Water is nei- ther very rapid, nor very deep. The iecond is done by laying the Fo^^f^^ii/w or. Grate-Work, Rafts offtoutOak well bound together and made faftat the Sur- face of the Water with Cables or Machines, and building upon them large Quarters of Stone cr.inip'd together, and joined with good Mortar or Cement, and afterwards letting them dc- fc:nd fonly by thofe Cables and Machines perpendicularly to the Bottom of the Water; as he f-iys, was done in the Time of the Emperor Claudtms^ at the Fort of Ofiia ; and as Dragnet Keys did in the kut Age at Coa- Jiatzunopls^ in the fine Mofquc that he built upon the Sea. This Manner requires a good Bottom, equal and very even. The third is by drawing off all or the greated Part of liie Wa- ter of the River ii:ito fon;e other Place, or by digging it ano- ther Bed, or letting it out into deep Ditches ; in which, liiys he, great Diligence muft be ufed, to have all the Materials ready, and to have Workmen enough rea- dy, fiiflicient to compleac it in a fliort Time, to the End that the Mafonry may be well confirm'd and iettled before there is a Ne- ceflicy ro let the River into its former Bed. ,,,. i., ji'rV, The lall Methodj which is that which Scamozz't fays, he believes Trnjaa made ufe of in fcuilding a Bridge over the Da- Tiube^ h to dig a new Bed for the River, in a Place which fcgms, as it were, to meet itfelf, after ha- ving made a great Elbow or Compafs about; which being done, the Bridge may be built with Eafe, and that dry-fhod, in that Place. And when the Bridge has been well fettled, to open the PafTage of the Current at the two Ends, flopping the Bed up with ftrong Banks or Moles, and fo the River will take to its old Courfe again ; this, fays he, is the furefl Me- thod of all. To lay the Foundation of the Piers of a Bridge, if the Earth be foft, it muft be piled, after as much of it has been carried away as can well be. The ■ fame is to be done, if it be Sand or Gravel ; which muft be dug out as deep as can be, all round about, to a reafonable Di- ftance; which muft be furround- ed with pointed Piles or Stakes well faftened to one another, til- iing the Spaces between Pile and Pile with Chalk or folid Earth well rammed in ; which will for a Time, hinder the Car- rent from wafhing away the Piles andSand, and ruining the Work. The Piles ought to he made tapering from Top to Bottom ; the Arches unequal in Number, and carried up higher than the higheft Inundation. The Archi- tcfture of BriH.gcs ought to be plain and ruftick. Scamozzi afterwards gives the Defign of his fine Bridge' of Stone, and another of Car-^ pentry. The Profile of thij-' iaft may be feen in Monfieur'^ !De La Hirers Treaiife of Car' peatry. lO Jo .iv. ^ ; M. Blonde! relates the Method he made ufe of in laying the tQundatim \ F O -ri -lajk 3falJi Josm b) ,313 w li Fiyundattdfi "of the Btldge of' Xa'tntes^ which he caufed to be built over the C^rtnz»?f. The ancient Bridge had beeiv born down, it having been built on Potters Earth or Clay, and piled, fo that the SweUing of the Foundation had raifed the Piles, and threw downthe Bridge. The Piles, by the Swelling of the Clay, ftarted out above a Foot higher than the Level of the reft. The Plummets went into this Clay, to the Depth of lixty Feer, made with a large Borer, the Arms of which were of Iron, each three Feet in Length, and well jointed one into another with good Pins. After they had caufed it to be dug feven Feet below the Bot- tem of the Water, all the Work being counterguarded and en- compalTcd with a good Dam, and the Hollownefs rak'd level, then a Grate-Work of good Oaken Wood was laid all over Jthe Foundation^ of twelve or fourteen Inches in Thicknefs, and fquare the whole Length and Breadth of the Building, not only that Part that was piled, but aUb the Opening or Space between the Piers and Abutments of the Bridge, or the void Spa- ces of the Arches. The Chambers of the Grille^ or Grate-Work, filled withgood Quarters of hewn Stone, and the upper Part covered with Planks of five or fix Inches thick, well faftened on with Pins all over the Grate- Work. Afterwards, upon this Work of Carpentry, is laid a Foundation of Mafonry five Foot thick, all kvel, with F O allcW 3ri} Haulw noq;; . godd lieWrf Sfotifes^^el I Tiftened together withCraiflp-Irons. Upon this flat Foundation of five Feet thick, the Piers are erected; which for the firft Year are brought no higher than the Imports, to the End that they may fettle well during ^k Win- ter. -M HiJii:"! t>t>/;iTtt>n&TJi;]:;j:iO* M. Bfdndeltn^W% itaj^pear," that whatever Precautions Ar- chite6ts take to fecure their Works by good Foundations^ yet they are very conjedural and un- certain. He in this compares an Ar- chited to a Phyfician, who pro- ceeds only upon Gonjeflures. For who can venture to fay, fays he, that building upon a Foundation of Confiftence, as it appears to him tobe,thatheilialI not meet with foft or bad Ground underneath , which the Weight of the Building will prefs down and fink into, and by that Means be overturn'd. '^^ ' ' Upon this Ocdafidn, %sM. G<2a!;/>r,IcangiveanExamplethat happen'd in one of the Illes of 0/eron^ or R^e, where the King caufing Fortifications to be built, one Face of the Wall funk, or fell down, notwithftanding it was built on a Bank of Rock; becaufe it had a Hollow under- neath, which could not- be, or was not difcovered. '^''^' ' ''•' ' M. Blondel relates" fn Gonfir- mation of what he has faid, that the vaft Walls of the Church of t^alde Grace ^ funk in on one Side, though built upon a good Foun- dation; becaufe there were under- neath large HolloWs which had been made in former Times, for taking oiH of Stones fome Fa- Bh ^ thorns ¥6 tnoms lower, tner^^havjijig bp<^fi.'- a'Qaarrv there, ,, ,1 •; ' j'luicffael /Jn^e JSonarote cauiea the Flfl^'j«'M^ork may ht'ir(laquilibt'}o. This Building thus" raifed, his lijcceeded pet- feaiy well/' '-'^ ' M. Bfr^Jcl rerfiarks further, that the Materials ar 'Paris not being of the fame Solidity as thole of lia/y^ as perhaps Mar- ble, and harder, will not permit to make Bridges at Paris with fo much Delicacy, and fo dif- cngaged as ihofe which are made in Italy ; which have a great deal lels Thicknefs at the Place of the Keys of the Arcades. Artificial FOUNTAIN, a Machine whereby the Water is violently fpouted or darted out, called by the brunch a Jet d'Eau. Of thefe thee are divers Kinds, dime founded on the PrefTurc or Weight of the Wa- ter, and o'.hers on the PrelFure or Weight of the Air. Itbe ConflrnStion of a^ artificial Fountain flaying by the 'Pref- jure or IVeight of the IVater. The Fund or Refervoir of Water mu ft be placed conlider- ably higher than the Fountain it- felf, (whether the Fund or Re- fervoir has been placed there by Nature, or whether it has been raifed by Art for that Purpofe by any Kind of Machine, as Pump, Siphon, or th© like,) and from the Refervoir vertical Tubes muft be laid for the Water to defcend through; to which vertical Tubes horizontal ones are to be fitted under Ground, to convey the Water to the Place where the Fountain is to play. Lallly, vertical Tubes muft be eredled from thefe horizontal cries. or' J^Sji.Their.AUitudes mull be. much leifs than that .pf the Tubes,' whereby the Water was brougf.c' from the Ref^y^(^ic^.w t^ 1^1-' zontal ones. . ...j^-.^^iyj <. j. If this be dohe^ tTie water" will, by the PrefFure of the fuper- incumbent Column, be fpouted up at thefe Jets, and that to the Height or Level of the Water in the Refeivoir ; and this will be, though the Tubes be bent and in- cur vaied after any Mamie-r wb^t:- loever. . -si . , i, By this Means Water may h'e fpouted to any given Height at Pleafure; and the Tubes may be fo proportioned, as to yield any given Quantity of Water in a given Time ; or feveral Tubes of tiie fame Fountain may be made to yield Water in any given Ratio ; or different Tubes may may oe made to proje6l the Wa- ter to different Altitudes. As for Ifi (lance ;■ In. 4 Fountain that flo all ff out the Wa- ter in various Dire^ioffs, Suppofe the verticaTTube Or Spout, in which the Water rifes, to be B A, [fee the Plate, Fig. I.] into this fit feveral other Tubes, fome horizontal, others oblique, fome inclining, others reclining, as PO, NM, LF, ^c. Then as all Water retains the Direc- tion of the x^perture through which it is fpouted, that iffiiing through B will rife perpendicu- larly ; and that through H, L, P,N, E, will defcribe Arches of different Magnitudes^ fnd.\fe^id diff'eient Ways. . . ' .' • rj - ' / IS9 Or thus : Suppofe the vertical T\:te rA7Cfe^WP^ate,Fig.II.) through which ^^he'Watcr riles, tooe ffopped atih^T6p,^asin B, and inftead of P&e§ -or;}ets, let it be only'peVfOTsted with little Holes all around, or only half its Surface ; then will the Water fpirt or fpin forth ih all Direc- tions through the little Apertures, and to a Diftance proportional to the Height^ of, tl>6' Fall of the Water.' '■'■■- -'^'-' ^'■' And hence, if the Tube BA be fuppofed to be the' Height of a Man,and befurnidied with a Cock atD, uDon the opening the Cock, the Standers-by not being appre- henfive of any fuch Thing, will be covered and furrounded with a Shower. But here this is to be obferved, that the Diamciers Of the Aper- tures out of which the Water is emitted, muff be a great deal lefs than that of the Tube in which the Water is conducted, left the Refiftance of the Air and other Impediments br^ak'the Force df the Water. '"•,' ''-■^■ ,--1 ■■-• ■- •• '-i' b y:.L-u.i\'' :• . ; ter in Manner of a Shower^ U tlous.conJiruSlf<^. ■■ ■ -t ._ To the Tube'wliefein the Wa- ter is to rife, fit a Head that is in the Form of a Sphere or Lens, as in the Plate, Fig. HI. made of a Plate of Metal, and perforated at the Top with a^reat many fmall Apertures. - ' ••-• - . And then the Water "rifing with a great Force towards BA, \.will be there parted into innu- * inerable little Threads, which ll5f:jn^Svv :.!'J A^n^O Vf,.'^ '■Will F Q) q F OO ^ •will afterwards break and dif- tuation, and always retains the perfe.uu/^4h?fifie(^,%(^^^3 -^'DiFe^ioft of the- Apertures or X -tn ,-> A vv.V- ^ '>:•'.•,-: Holes, all that is required T^e 'pmjir^Siii/p 0/7: .'Fouritaih, making fuch Fountains^ is to tl)e Stream of which raifes and flayi a B raj's Bull. See'the i^rocii^-ii. hollow Globe ^.i Ball mSej'of thin Plate, whofe Weight mari not be too heavy fof' thi1_Force of the Water. Let theTu'be CB, through which the Water riles, be exaftly per- pendicuiar to the Horixon. Then Vet thei3aU be laid in the Bottom of the Cup or Bafon C, i^n^ it will be forced up by the Stream, and fuCtaiiiM at a con- fiderable't-icight, as at A, vibra- ting alternately, or playing up arid down. And as the Figure of the Ball docs not contribute any Thing to its riling and falling recipro- cally, any other Body, in feveral other Forms, that are not too^ heavy, may be ufed inftead of it, e. g. a Bird with its Wings ftretched forth, ^f. But this Sort of Fountain fhould only be play'd in a Place that is not eijpofed to the Wind. And it is alfo necelTary, that the Ball,' When on the Defcent, fhould kceif) ^he|fame precife Per- pendicular in which it role, fince otherwife it 'would mifs the Stream, and fall downrightj^ ^j. m clofe Tubes within the Figures of thofe Animals, having their Orifices in thole Parts out of •^which the Water is to fpout. 1 heret'ore, from the Principles before laid down, it will be very eafy to deduce whatfoever re- lates to the Furniture of Foun- tains^ and the various Forms that Water may be put into by their ■ Means: All which depend on the Magnitude, Figure, and the Diredion of the Ajutages or Apertures. T'he ConJlriiSiion of a Fountain which fpreads the It^ater in the Form of a Cloth. Solder two fpherical Segments D and G to the Tube BA, Fi- gure V. almod touching each other, with a Screw F, that fo you may either contra6l or en- large the Interftice or Chink be- tween them at Pleafure. Or you may make a fmooth even Nitch in a ipherical or len- ticular Head, fitted upon the Tube; and then the Water fpout-^.: ing through the Chink or Nitch,,,' will expand itfelf in manner of a Cloth. So much may fuffice, as to,, fuch Fountains as play by MeanSiJS • .' - - . , , , ',. of the PrslTureor Weight of thcdj Tj&ff Co;^r«S'/:(jtf ^ Fodiitains, ' Water. -.oqi whiih J^dkt iVater' oH( of the ^i^ ii^-y ''- f- FiZt{rnJ>f M:n and other Aiii-\ ,, -M Tn^^E ^M larlio ri0B5 mort Since Water may be derfvM „. Tk^ ^X convey'd by Tubes in any St- «- . F CP ^ F 6^ '^ '^T'/^? ConJlrmioH'of ^ 'Fountain ■fi The Conftrud'iOfi of dti jlttifichl Fountain, ivhich plays by the Spring or Elajlieity of the Ai^. See the Plate, Fig. Yh - ^1' Provide a Veflfel' of Metdl, Gluls, or the like, proper for a Refervoir, ending in a fmall Neclt d at the Top. Put the Tube db through this Neclc, traverfing the Middle of the VefTel till its lower Orifice e does almoft, but not quite, reach the Bottom of the VefTel, the VefTel being firft half fill'd with Water. The Neck is to be fo contriv'd, as that a Syringe or condciifing Pipe may be fcrew'd upon the Tube ; by Means of which a large Quantity of Air may be in- truded through the Tube into the Water, out of which it will difengage itfelf, and emerge into the vacant Part of the VefTel, and lie over the Surface of the Water DC. Now the Water here con- tain'd being thus prefs'd by the Air,-^ which is, e.g. twice as denfe as the external Air, and the elaftick Force of Air being equal to its gravitating Force, the Effed will be the fame as if the Weight, or the Column of A.ir over the Surface of the Wa- ter, were double that of the Co- lumn prefTing in the Tube ; fo that the Water mufl of neceflity fpout up through the Tube, with a Force equal to the Excefs of PrefTure of the included, above that of the external Air. which will play by the Draught ■, of the Breath. Seb'^he Plate, to ■Fig.vir. , ,, ., Suppofe a Spher'e' be made of Glafs, or Metal, into which a Tube is fitted DC, having a lit- tle Orifice in C, and reaching al- moft to D, the Bottom of the Sphere; if now theAir befuck'd out of the Tube DC, and the Orifice C be immediately im- merfed under cold Water, the Water will afcend through the Tube into the Sphere. Thus proceeding by repeatecj Exfudions, till the Veffel be a- bove half full of Water, and then applying the Mouth to C, and blowing Air into the Tube, upon removing the Mouth, the Water will fpout forth. '"^'■'/.. Or, if the Sphere be put m hot VVater, the Air being there- by rarefied, will make the Wa- fpout nut as before. This Kind of Fountain is call- ed Ptla Heronis., i. e. Hero V Ball., from the Name of its In- ventor. T'he CoMjlruSiion of a Fountain which., when it has done [pout- ing., may be turned like anHour- Glafs. See the Plate, Fig. VIII. Be provided with two VefTel s, ML and ON, to be fo mucti>^ the bigger, as the Fountain is to play the longer ; aqd placed at To much the greater Diftaucc from each other N P, as the Water is detired tQ fpout the higher. , . Let Let B AC be n crooked ThS^, furniftied in C with a Cock ; and" FED, another crooked Tube, furnifhed with a Cock in D : In I and K let theie be -other lefTer Tubes, Open at both Ends, and reaching near to the Bottoms of the Vdlels NO and LM, to which the Tabes QR and ST are likcwife to reach. If now the V-effel LM be filled with Water, it will de- fccnd through the Tube BA, and upon opening the Cock C, ■will rpoui: up near to the Height of K; and after it is fall again, "Will (ink throvgh the little Tube I into the Veflel NO, and ex- pel the Air through the Tube QO. At length, when all the Wa- ter is emptied oat of the Veiiel LM, by turning the Machine upHde down, the VefTel NO T.'ill be the Reft^rvoir, and make the Water fpout up through the Cock D. Hence, if the VefTels LM and NO contain juil as much Wnter as v^'ill be fpouted up in an HoiJr's Time, there will be a fpoutiug C'epfydra, or Water Clock, whicii may be graduated or divided into Qmit-ters, Mi- nutes, er'f. _ See the Figure. I'kc ConJlfuSihn of a Foumain '■ ivh'ich be^'tris to pLiy upon the lightifjg of'Candlef^ and ccnfes as jhev 7o oiit, ' ' See Fig. IX. 'Tkkfe'rW'o cvUndtical VeiTels i^'B a\id CP, ^'nd conned them 'SyT"^5 open at both Ends KL, BF,^^F R To Itbe Tubes folder, Candle- flicks jH,^(r. ftnd to the holiow Cover of the iQwer Vellel CK fit a little Tube or Jet FE, fur- nifhed with a Cock G, and reach- ing almoil to the Bottom of the VefTels. In G let there be an Aperture furniOicd with a Screw, whereby Water may be poured into C D. . Then upon lighting the Candle, H, i^c_. the Air in the contigu- \ ous Tubes becoming rarefied thereby, the VVater will begin to fpout through EF. By the fame Contrivance may a Statue be made to fhed Tears \ upon the Prefence of the Sun, or the lighting of a Candle, ^r. all that is here required being to lay Tubes from the Cavity where- in the Air is rarefied to fome Cavities near the Eyes, and full of Water. Vulgar FRAGTI9NS, q. d, a broken Number, in Arithme- tick, ia a Part or Dis ifion of an Unite or Integer ; or it may be defined to be a Num.bcr that fiands in Relation to an Unite, as a Fart to irs Whole. Vulgar Fradions^ alfo called Jimple FradioKS^ are alv/ays ex- prelfvrd by two Numbers, the one written over the other, with a fliort Line drawn between them. The upper Number, which, is called the Nuimrator oftheFrac tion^ eypreffes the Farts given of the Denominator ; and the lower Number, which is called the/)*?- noniinator of thi FraSiion^ denotes the Unite or Whole, which is divided into Farts. -' ''*, ■'-*' -f " T&us FH mwi 1 hus three Fourths oP^fi tihie, ,o,r other Thing, are written A,' where the Denominator 4 fhews that the whole Line is fuppos'd to be divided into four equal Parts, and the Numerator 3 in- dicates, or afligns three of luch Parts. 1 '-fOi34/-. Again, feven Twelfth's is writ- ten i\y where the Numerator 7 exprelfes feven Parts of an Inte- ger divided into twelve; and the Denominator 12 gives the Deno- mination of thele Parts, which are called Twelfths. In all FraBtons^ as the Nume- rator is to the Denominaror, fo is the Fradion itfelf to the Whole of which it is a Fradion. Thas, fuppoling :| of a Ponnd equal to 1 5 J. it is evident, that 3:4 : : 15" : 20 ; whence it Follows, that there may be infi- nite Fradions of the fame Value with one another, inafmuch as theie may be infinite Numbers found, which fhall have the Ra- tio of 3 to 4. Fra^tioKs ^\c "iftinguiflied into proper and ir,7proper : A proper Fradion is one whole Numera- tor is lefs than its Denominator, and ccrifcouently the Fratlion lefs th.:. i.c Whole, or Integer, ^'- ' An improper Fradion is one •jvhofe Denominator is either equal to, or bigger than the De- nominator ; and confequently the Fradion equal to, or greater than the Whole, as |f or rf . "Fradions are alfo diftinguifh'd liito JimpU and yompound: Sim- ple Fradions are fuch as conlilf of one Numerator and one De- pQmiiiator, as t%^ i\^^, CS'f, .C^ifitpovftii,Friidi^s3i:/^ foch as con fill of feveral, Num2M#or«A and Denominators, mA cd' '^^^ of 71, bi'c. Thefe are alfo 5?ftlle '^^^ 5=^t,and7=!|. It no Denominator be given, the Number is reduced to a Frac- tion by writing i under it as a Denominator, as f, -f, ^j. ,\ Secondly^ To reduce a given Ffadion to its loweflTerms, i.e. to find zFradion equivalent to agi- venin^^^(/«,as:;f7,divicie both the Numerr!t,)r 12, and the Denomi- n .tor 48 by fome one Number that will divide them both with- out any Remainder, as here by 4, the Quotients 3 and 12 make a new Fradion., as ^2. ^re equal to -- And if the Divifion be per- formed by the greateft Number that will divide them both, then will the FradioK be reduced into its lowed: Terms. Now to find the greateft com- mon Divifor of two Quantitic;, divide the greater by the lefs; then divide the Divifor of the Divifion by the Remainder there- of Again, divide the Divifor of FR of the fccond Dtvifion by the Remainder of the fecond, and fo on till there remain nothing ; and thelaftDiviforwiilbe thegreateft common Meaiure of the given Numbers. If it happen that Unity is the only common Meafure of the Numerator and Denominator, then the Fra^ton cannot be re- duced any lower. Thirdly^ To reduce two or moie Frad'tons to the fame De- nomination, i. e. to find Frac- tions equal to the given ones, and with the lame Denominators ; If only two Fradions be gi- ven, multiply the Numerator and Denominator of each into the Produd of the Denominator of the other, and the i'roduds gi- ven wiil bs the new FraSiions required. Thus f ) 4, and 3) f, make If and ff : If more than two be given, multiply both the Nume- rator and Denominator of each into the Produtt of the Deno- minators of the relt : Thus 24)7, 12)^, 18)4:, are = ^!, H, ^^• FoHrthh\ To tind the Value of a Fratttm in the known Parts of its Integer; e.gr. As fuppofe it were required to know what is the Value of i"^ of a Pounn, multiply theNumerator 9 by 20, and divide the Frodud by the Denominator x6, and the Quo- tient will be ir J. Then multiply the Remainder 4 by 12, the Number of known Parts in the next inferior Deno- mination; and dividing the Pro- dud by 16, as before, the Quo- tient will be 3^/. fo that j-^ of a Pound is= 11/. 3^. Fifthly^ To reduce a mix'd Number, as 6 xi, into an im- F R proper FraB'ton of the fame Va- lue; Multiply Ithe Integer 6 by 12, the Denominator of the Frac- tion^ and to the Produd 72 add the Numerator : The Sum 83 fet over the former Denomina- tor H", conilitutes the Fraction required : Sixthly^ To reduce an impro- per FrcdVion into its equivalent mix'd Number. Suppofe the given Fraction to be ^, divide the Numerator by the Denominator, and the Quo- tient 3 1^2 is the Number fought. Seventhly^ To reduce a com- pound Frad'ion into a fimple one, multiply all the Numera- tors into each other, for a new Numerator; and all the Deno- minators for a new Denomina- tor thus, 7 of i of |- will be II. Addition of Vugar Fradions. Ftrfl^ If the given FraSiions have ditferent Denominators, re- duce them into the fime ; then add the Numerators together, and under the Sum write the com- mon Denominator, thus, e. g. f -f f =if-f.|^=i x^^.andf Secondly^ If compound FraC' tiom are given to be added, they mud firfl be reduced to fimplc ones : and if the Fratiions be of ditferent Denominations, as ^ of a Pound, and \ of a Shil- ling, they mult be firft reduced to Frndions of the fame Deno- mination of Pounds. Thirdly^ To add mix'd Num- bers, the Integers are firft to be added sm ^ F R added, then the Fraftioiia! Parts ; and if their Sum be a proper Fradion, only annex it to the Sum of the Integers. If it be an improper Fradiiotf, reduce it to a mix'd Number, adding the Integral Part thereof to the Sum of the Integers, and the Fraii'toml Part after it, as III. SHkra(^io}tofFra6i\ons. Firft, If they have the fame common Denominator, fubtraft the leiTer Numerator from the greater, and fet the Remain- der over the common Denomi- nator. Thus from ri fake j-^, and there will remain f^. Secondh^ if they have not a common Dcnominator,they muft be reduced to Fradiom of the fame Value, having a common Denominator ;and then as in the firft Rule, Thirdly , To fubtract a whole Number from a mix'd Number, or one mix'd Number for ano- ther, or reduce the whole, or mix'd Numbers to improper Fradions, then proceed, as in the firftand fecond Rule. IV. Multiplication of Fraftions. Firjl^ If the Fraiiions propos'd be both lingle, multiply the Numerators one by another for a new Numerator, and the De- nominators for a new Denomi- nator. Thus i being muliiply'd by f , produces f f. Secondly^ If one of them be a . F R mix'd, or whole Number, it muft be reduced to an improper Vradion \ and then you are to proceed as in the laflRule, Thus^ being multiply'd into i£. A.S. I — OiJ- In Multiplication of Fr^if?/Wx, it \^ to be obferv'd, that th» Produft is lefs in Value, than either the Multiplicand andMul- tiplicator; becaufe in all Mul- tiplications, as Unity is to the Multiplicator, fo is the Multi- plicand to the ProduQ. But Unity is bigger than either Fador, if the Frahions be pro- per ; and therefore either of them mull be greater than the Pro- duft. Thus, in whole Numbers, if 5* be multiply'd by 8, it will be as I : 5* : : 8 : 40 ; or 1:8 : : f : 40. Wherefore in FraBions alfo, as I i I : i : : ^ : ii ; or as But I is greater than either 4- or ^^ wherefore either of them muft be bigger than ^f. V. Divifion of Fradions. Firjl^ I f the Fraiiions propos'd be both iimple, multiply the Denominator of the Divifor by the Dividend, and the Produt^ will be the Numerator of the Quotient. Then muUiply the Numera- tor of the Divifor by the Deno- minator of the Dividend, and the Product will be the Denomi- nator of the Quotient, Thus ^)^(ff. Secovdly^ If either Dividend, Divifor, or both, b; whole, or mixed .TiplK ^^ix^d Wiiti^e^^, redtfce them to ^improper Pra'^hfis:, arid if they ^ ,Jt compduhd FraStions^ reduce ;them td'ifmple Dries ; and then ' iroceed as in the firft Rule. In Divifion of Fra^ions it is to be dbferv'd, that the Quotient !s always greater than the Di- vidend i becaufe in all Divifion, as the Divifor is to Unity, fo is the Dividend to the Quotient; is if 3 divide li , it will be as a, i i . . 12 . ^^ f '. . ■> , -^ Now '^ fs g'^eatei* ' thart Ir'; wherefore ii inufl: be greater than 4; but in Fradions as I : : f : 77, where f is lefs than I ; wherefore f muft be al- fo lefs than '- J. 7 ' FRAMING 0/ in Architefture, . -FRIEZE 5 is properly a large flat Face or Member, fe- parating the Architrave from the Cornice, and that Part of the En- tablature between the Architrave and Cornice. This Member was called by the Antients Zoophorus^ becaufe it, was commonly inriched with 'the Figures of Animals. .^., ■( ^■,^,;fFrieze is faid to be forrp-ed iirom the Latin., Phrygio an Em- broiderer, becaufe utually adorr^- .ed with Sculptures in Bajl'a- Re- ^ieiio^ injitating Embroidery. ,,, j -.iT\\^ Frieze is foppoie^ t6i>e -^efigued to reprelent Lhd Heads of the tranfvcrfe Beams .whiph fuiiain the Roof or Covering'.^fj V- This Member is quite plain In thg7«/?i?» Order;, but'is iarich'd with Triglyphs in .the DoriV^,^I,s ftmetimes nnde arch'd pc. fvvelj- ing in the /oaiV^;Wi,-;vf;hich,CiLe particularly, Fitrnvins calls "it ,the Corintkuiti and CorAppfits ic i^ frequently joined to the 'Ar- chitrave by a little Sweep,. ?.nd fometimes to the Cornice : And in thefe richer Orders, it is com- monly .idorned with Sculpture, Figures, Compnrtiments,, Hifto- ries. Foliages, Feftoons,.rj;'V As to the Height oit\i& Frieze^ h is in the general much the fame as that of the Architrave. l^itruvius makes the Tiife^n Frieze flat and plani, .at^d in Height 30 Minutes.. \;,,.;^!^..,, Palladia., who makes it con- vex or fwelling, gives it but ^G Minutes -. And Scamozzi^:Kk^% it plain, and in Height 4a M\- nutes. ,, /^ .,;^ TheZ)or;V: f^itruvuis njidf'^i^- mla make this Frieze ^n^ only carved with Triglyphs and Me- topes, and its Height .30 or 40 Minutes. And Palladia and Sea- mozzim?kQ it Wkcl^itrwuius^ and in Height 45- Min. The loMu : ^ifruvm malies this Fr/V.::i? flat, only csrved with Acanthus Leaves, Lipn.9, Mt-n efr. _and in Height :jp M;|v, f^j^l Kolcif^ic alfo makes ir,fJr.r,jajid al- lows it 4j Min. 'hnn}?ofite : \rfh m K/lnnvw 1.5 Jtj^ "with.^Carroi-Te?, and carved'berwceivthcrr£'fs 5-2' J^jn, l^igK.la mak' cj It ^jk e ^/ ->-/'! -nifr^^'"? who mattes it te litit\ Frc m FR P R From thefe Variety of Inrich- ments which adorn the Freezes^ they obtain various Denomina- tions. Convex Freezes 7 are fuch PuhtHUted Freezes 5 w hofe Profile is a Curve ; the beft Pro- portion of which, is when drawn on the Bafe of an equilateral Triangle. In fome the Swelling is only at Top, as in a Confole ; in o- thers at Bottom, as in a Bal- lufter. Flour'tp'^d Freezes are fuch as are inrich'd with Rinds of ima- ginary Foliages; as x\^z. Corhnhi- an Freeze of the Frontifpiece of Nero\ or with natural Leaves, either in Cluftcrs or Ciarlands ; or continued as in the Ionic of the Gallery of Apollo in the Louvre. Hijiorical Freezes are fuch as are adorn'd with Bafs Relievo's, reprefenting Hirtury, S;Jcrificcs, ^c. as the Arch of Jitus at Rorne. Marine Freezes are fuch as represent Sea-Horles, Tritons, and other Attributes of the Sea ; or Shells, Baths, Grotto's, ^c. Rufltc Freezes are fuch whofe Courfcs are rudicated or im- bofs'd, )is in the Tufcan Freeze of Palladio. Symbolical Freezes are thofe adorned with the Attributes of Religion, as the Corinthian of the Temple behind the Capital at Rome.^ whereon arc reptefcntcd the Inlhuments and Apparatus of Sacrifice. AVe fometimes, fays M. Le Clcrc, make the Frieze of the Entablature convex ; but then this ftiould never be done with- out fome good Reafon, mere Caprice being not fufficient to" warrant fuch an Alteration. When one Order is raifed over another, and the upper Co- lumn has its due Bignefs, its Pedeftal neverthelefs goes beyond the Naked of the under Column, which to fomePerfons has a dif- agreeable EfFe£t. This, fays he, inclines me to think, that the firft Architeft who made a convex Frieze.^ did it with a Defign to extenuate this Appearance of a Defeft I'his is evident, that as the Naked of a Frieze is hidden by this Swelling, the Fedeftal of the upper Order appears lefs, to ex- ceed the Naked of the under Or- der, as may be eafily obferved where the two Orders are i^tn over each other. Were it not on this Account, the convex /r/>^?,juft mentioned, ought not, fays he, in my Opinion, to be imitated : The Frieze may be made convex in all the Orders except in the Doric, where this Swelling can't be allow'd, by reafon of the Triglyphs. FRESCO, a Method of Paint- ing, or rather Plaftering on Walls to endure the Weather, and reprefenting Birds, Beails, Herbs, Fruits, ^c. in Relief. It is performed on frefn Pla- fter, or on a Wall laid with Mortar, not yet dry, and with Water Colours. Fhis Sort of Painting has a great Adantage by its incorpora- ting with the Mortar, and dry- ing along with it, it is rendered extreme durable, and never fails or falls but along with it. Of the Method of this Paint- ing : To make the Comport or Plafter of old rubbilh Stones, and a f R and mk it with well-burnt Flint '(or Lime) and Water; "but Hvafii out the Saltiiefs of the Lim6,'by often pouring the Water, and putting frefh to*it. This fhould not be done in moift Weather, becaufe that has a great Influence on the Walls. And in order to render the Plaider the more durable, they ftrilve into the Joints of the Brick or Stone Wall Stumps of Horfe Nails, at about iix Inches Di- ftance, to prevent the Plaiftcr from peeling off. Wirh this Plaifter thsWall is firfttobeplaiftered agoodl'hick- nefs, and left for fome Time to dry; and the Defign and Colours being firft ready prepared. This Painting is chiefly per- formed on Walls and Vaults newly plaiftered with Lime and Sand; but the Plailkr is only to be laid in Proportion as the Painting goes on, no more being to be done at once than the Painter can difpatch in a Day, while it is dry. Before the Painting is begun, there is ufually a Cartoon or De- fign made on Paper, to be calk'd and transferred to the Wall, a- bouthalf an Hour after the Plai- ner has been laid on. The Colour being prepared and mingled, the Wall is to be plaiftered over again a fecond Time about the' Thicknefs of Half-a-Crowa, but only fo rnuch as you intend prefcntly to Work upon; and while it is wet, you jnufl; work the Colours therein, which will mix and incorporate iyhh the Plainer, fo as never to wafli out. The Painting niUfl be, for'tha Work to come put in all ft? Vol. I. R EeaiUy,v.Tought -. . .nd with a free Hand; lor there can^ be no Alteration after the firllPuiiu- ing, and therefore make your Colour high enough at firft; you may deepen, but not t^fily heighten.' . " ; , ■ 7 Nor mud they, /ever be re- touch'd dry, with Colours' inixd up with the White of an Egg, or Size or Gum, as fome Work- men do, by reafon fach Colours grow black ifli ; nor do any pre- ferve themfelves,' but fuch as were laid on haftily at firlt. In this Painting all the com- pound and artificial Colours, and almoil all the Minerals are fet alide, and fcarce any Thing ufed but Earths ; w hich are capable of preferving their Colour, de- fending it from the burning of the Lime, and relilling its Salt, which ritruviu.s (:aX\s ip Bitter- iiefs. The Colours ufed are White made of Lime llack'd long ago, and white Marble Duft; Oker, both red and yellow, Violet Red, Verditer, Lapis Lazuli, Smalt, Earth, black Spanifli Brown, Spanifli White, erV. All which are only ground and work'd up with Water ; and molt of them grow brighter and brighter as the Prcfco dries. ,; ^. -.^ . The Bruflies and Peacfis for' this Work muiVbe ' long and foft, or elTe they wiU rake and raze the Painting: The Colours muft be full, and flowing from the BruHi; the D'efign pexfed in the Image or Paper Copy; for in this W^ork you cannot .alter or add uron any Golpur. .■« Ihis Sort oX Painting has a great Advaiuage, by its incorpo- rating w&l^i^? ^lert^'fj ^^ 4ry- ' C'c ' in» F R F R ing along with it, is rendered ey- treamly durable, and never fails nor fafls but along with it. The Antients painted on Stuck ; And it is worthy Obfervation in Vitrmius^ what in finite Care they took in making the Incrulbtion orPlaillering of their Buildings, to render them beautiful and lad- ing : Though the modern Pain- ters find a Piaifter made of Lime and Sand preferrable to Stuck, both becaufe it does not dry too hailily, and as being a little brownifh, it is fitter to lay Co- lours on, than a Ground i^o white as Stuck. This Kind of Painting was the antient Grecian'^ xy of Paint- ing, and fincc much ufcd by the Romans. Plutarch informs ns, that/fr^- tas^ the great Commander under Ptolemy King of E^^ypi^ (in a Compliment to the Emperor's Atfedions that Way,) forbore to fack a stealthy City, merely for the Excellency of the Frefco Painting upon the Walls of the Houfes. There have been feveral whole Towns of this Work in Ger- raany^ excellently well done, but now^ ruin'd by Wars. «>At Rome there are three Cham- bers (in the '■Popes Palace) of Frefco.^ done by Raphael Urbia^ and 'JtiVio Romano, (his Difciple) who finiihed his Mailer's Work, ■which is yet caHcd Raphael's befign. There are other Places done by Andrea d<^l Sexto and Michael ylftgeloy and Tome other Artifts. There is an excellent Frefco Work at Foitnta'inbleazi'm France. It is the continued Travels of Vlyffs^ in lixty Piece Sj dene by Bollmneo Martin Roufe^ a Flore»' tine., and others. FRET l in Architeaure, FRETTE5 is a Kind of Knot or Ornament, confiding of two Lifts or fmall Fillets va- rioufly interlaced or interwove, and running at parallelDiftances equal to their Breadth. Every Return and Interfeftion of thefe Frets muft be at Right Angles. This is fo indifpenfibly neceirary,that they have no Beau- ty without ir, but become per- fe6tly Gothic. Sometimes the Fret confifts butof afingleFillet, which how- ever may be fo ordered, as to fill its Space exceedingly well, if well managed. Thefe Frets were very much in ufe among the Antients, who apply'd them chiefly on even fiat Members, or Parts of Buildings ; as the Faces of the Corona, and Eves of Cornices ; under the Roofs, Soffits, C!'<^. on the Plinths of Bafes. t':ff. The Name Frette was hence occafion'd, that Frette literally fignifies the Timber- Work of a Roof; which confifts chiefly of Beams, Rafters, ^c. laid acrofs each other, and, as it were, fretted. FRET-WORK, an Enrich- ment of Frettc^oiz. Place adorn- ed with fomething in the Man- ner thereof. , IFret' F R F R Fret-Work is fometimes ufed for the filling up and enriching flat empty Spaces, but it is prin- cipally pradifed in Roofs which are fretted over with Plaifter- Work. The Italians alfo ufe Fret- Work in the Mantlings of Chim- neys with great Figures, a cheap Piece of Magnificence, and as durable almoft within Doors, as harder Matters in the Weather. FRICTION, in Mechanicks, is the Refinance which a moving Body meets withal from the Surface on which it moves. Fridion is produced by the Afperity or Roughnefs of the Surface of the Body mov'd on, and that of the Body moving. .For fuch Surfaces confifting alternately of Eminencies, and Cavities, either the Eminencies of the one mull be railed over thofe of the other, or they muft be both broken or worn off: But neither of thefe can happen with- out Motion ; nor can Motion be produced without a Force imprefs'd. Hence the Force apply'd to move the Body is either wholly or partly fpent on this Effed, and of Confequence there ariles a Refiftance or Frit^ion^ which will be be greater, cceteris pari- bus^ as the Eminencies are the greater, and the Subftance the harder. And as the Body by continual Fridton grows more and more polifli'd, the Fridion d.\m\u\?[\ts. Hence ft follows, that the Surfaces of the Parts of Ma- chines, which touch each other, ought to be as fmooth and po- lifU'd as poffible. But as no Body can be Co much polifli'd, as to take all In- equality quite away; witnefs thofe numerous PJdges which may be difcover'd by the Help of a Microfcope on the fmoothell Surfaces ; hence arifcs the Ne- cellity of anointing the Parts that touch with Oil, or other fatty Matter. The Laws of FriS^iofz are, Frrjl^ As the Weight of a Body moving on another, is in- creafed, fo hhsFriSio;i. This is experimentally feeniti a Balance ; which v/hen only charged with a fmall Weight, eafily turns ; but with a grea- ter, a greater Force is re- quired. Hence if the Line of Direc* tioit of a moving Body be ob- lique to the Surface moved on, the Fridion is the greater; this having the Effed as the Incrcafe of Weight. And hence again, as a perpen- dicular. Stroke or ImprelTion is to an oblique one ; as the whole Sine is to the S\r^ft of the Angle of Incidence; and the Sine of the greater Angle \s greater, and that of the lefTer lefs ; the Fridion is greater, as the Line of Di red ion approaches nearer to a Perpendicular. This is eafily obfervable, and efpecially in the Teeth of Wheels, which are frequently broke oii this very Account. The Fridion therefore is ta- ken away, if the Line of Di- redion of the moving Body be parallel to the Surface. Secondly^ The Frid'ton is lefs in a Body that rolls, than ic would be, w^ere the fame Body €c % {3 F R to Hide ; as is eafily demonftra- tcd. For fuppofe a dented Ruler, nnd fuppofe a dented Wheel to move along it, with its Teeth perpendicular to the Circumfe- rence : If now the Body were to Aide, the Tooth, when it touch'd the Ruler, would defcribe a Right Line on the Surface thereof; and as the Tooth of the Ruler relills the fame, it could not pro- ceed without either removing or breaking either the Tooth of the Wheel, or its own. And the fame will hold of the Hiding of any rough Surface upon another, where all the ¥ridwn will take Place^ that can any way arife from the Roughnefs of the Sur- face. But if the Wheel roll along the Ruler, then the Tooth will no longer refift its Motion, on- ly as it is to be hoilted out of tliQ Cavity over the Eminence of the Tooth; and the fame holds in the rubbing of any rough Body over the Surface of another. Hence in Machines, lead the FuUlm (houid employ a good Pjirt of the Power, Care is to be taken that no Part of the Ma- chine Aide along another, if it can be avoided, but rather that they roll or turn upon each other. With this View, it may be proper to lay the Axes of Cylin- ders, not as is ufually done in a Groove, or concave Matrix, but between little Wheels moveable on their refpcdive Axes. This was long ago recomend- «!wd by V. Capiiits ; and it is C91- F R firm'd by Experience, that a great deal of Force is faved by it. Hence alfo it is, that a Fully moveable on its Axis, refifts lefs-. than if it was fixed; and the. ftme may be obferv'd of th* Wheels of Coaches, and other Carriages. From thefe Principles, with a little further Help from the Higher Geometry, Olaas Roemer determin'd the Figure of the Teeth of Wheels, that fhould make the leaft Refiftance polii- ble, and which would be Epicy- cloidal ; and the fame was after- wards demonftrated by M. De La Hire, Though the Thing is not yet taken into Praclice. Hence, in Sawing-Mills, the Sides of the Wooden Re6tangle, the Saws are fitted into, (hould be furnifli'd with Rotules or lit- tle Wheels, which would great- ly leifen the Fridion\ and the like in other Cafes. Add, that as Winches, or curved Axes pre- vent all Fridion^ thofe fhould be ufed inftead of Wheels, as often as poflible. The Calculatiot2 of the ^ianttty or Value of Fridtioa. The' FriBion is a Point of the utmofl: Importance in Machines, and by all Means to be confider- ed in calculating the Force there- of; yet it is generally overlook'd in fuch Calculations : But this, principally, by reafon the precifc Value is not known. it is not yet reduced to certain and infallible Rules. The com- mon Method is barely to com- pute . what . the Advantage is which a movyigPowfr has. from the T R F R the Machine, either on account of its Diftance from a fixed Point, or of the Diredion in which it a6ls. And in all the Demon- flrations, it is fuppofed, that the Surfaces of Bodies are perfedly Imooih and polifh'd. Indeed, the Engineers exped that in the Praflice they (liould lofe Partjof the Advantage of their Force by their Fridion ; but how much it is fuppofed, nothing but the Pradice can de- termine. M. /f>7zo«^o»j, indeed, has made an Attempt to fettle by Experi- ment a Foundation for a precife Calculation of the Quantity of Fridion; and M. Parent has confirm'd it by Reafoning and Geometry: But their Theory, however warranted, is not gene- rally and fully received. l!A.AmontoMs'% Principle is, that the Fr'iilion of two Bodies de- pend on the Weight oriForce wherewith they bear on each other ; and only increafes as the Bodies are more ftrongly prefs'd and apply 'd again ft each other ; or are charged with a greater Weight ; and that it is a vulgar Error, that the Quantity of FnV- tion has any Dependance upon the Bignefs of the Surfaces rub- bed againlt each other; or that the FriSiion increafes as the Sur- faces do. Upon the firft Propofal of this Paradox, M. De La Hire had Recourfe to Experiments, which fucceeded much in Favour of the new Syftem. He laid feveral Pieces of rough Wood on a rough Ta- ble: Their Sizes were unequal; hm he laid Weights upou them, fo as to render them all equal- ly heavy, and he found th.it the limie precife Force or Weight apply'd to them, by a little Pul- ly, was required to put each in Motion, notwithftanding all the Inequality of the Surfaces. The Experiment fucceeded in the fame Manner, in Pieces of Marble laid on a Marble Table. Upon this M. Be La Hire apply'd himfelf to confider the Rationale of theThing; and has^ given us a Phylical Solution of the Effea. And M. Jr^ofitom fettled a Calculus of the Value of Fridion^ and theLofs fuftain- ed thereby in Machines, upon the Footing of the new Prin- cijifle. In Wood, Iron, Lead, and Brafs, which are the principal Materials ufed in Machines, he finds the Re ii fiance can fed by Fridion to be nearly the fame, when thofe Materials are anoint- ed with Oil, or other fatty Mat- ter: And this Refiftance, inde- pendant of the Quantity of the Surface, he makes to be nearly equal to a third Part of the Force wherewith the Bodies areprefled againff each other. Befide the PreiTion, the Mag- nitude whereof determines that of the Fridion^ there is another Circumffance to be confidcred, -viz. Velocity. 'V\\zFrit1ton is the greater, and the more difficult to furmount, as the Parts are rubb'd together with the greater Swiftnefs : So that this Velocity mufl be com.- pared with that of the Power neceffary to move the Machine, and overcome the Fridion. If the Velocity of the Power be double that of the Parts rubb'd, it acquires by that Means C 3 aii F R F R an Advantage, that makes it double, or, which amounts to the fame, diminifhes the contrary Force of FriSlton by one half, and reduces it to a fixth Part of the Weight or Prcffion. ]3ut this Velocity, M. Amon- lons only coufidcrs as aCircum- ftance that only augments or dimininies the Effcd of the Preffion, i.e. the Difficulty of tliC Motion ; fo that the Fridion Confirmations and Illuftrations of the Theory of Fridion^ t\\t Publick, nor even the Academy itfelf, where it was propofed, could not be brought fully to acquiefce in it. It is granted, the Preffion has a great Effedl, and is, in many Cafes, the only Thing to be confidered in tndiotts. But it will behardto perfwade us abfo-^ lutely to exclude the Confidera- Uill follows the Proportion of tion of the Surface AndinEffedl, the Weight. Only we are hereby dired- ed to difpofe the Parts of Ma- chines that rub againft each other in fuch Manner, as that they may have the lead Veloci- ty polfible. And thus the Dia- meter of the Axis of a Wheel fhould be as fmall as poflJble, xvith Regard to that oftheWheel, in that the lefler the Axis, the flower will be Motion ot the Surfaces rnbbing againft each other, fince the Velocity of a circular Motion always goes di- minifhing from tlie Circumfe- rence to the Centie. And for the fame Reafon, the Teeth of dented Wheels fliould be as fmall and as thin as polfi- the contrary feems capable of a Metaphylical Demonllration. If two Bodies witn plain Sur- faces, fuppos'd infinitely hard and polifh'd, be moved along each other, the Fridion -wxW either be none, or infinitely fmall : But if inltead of fuch Snppofition, which has no Place in Nature, we fnppofe two Bodies witU rough uneven Surfaces, the Dif- ficulty of moving one of them upon the other muft arife either from this, that the firft muft be raifed,in order to cifengage the Parts,catch'd or lock'dinto the iecond ; or that the Parts muft be broke or worn off, or both. In the firft Cafe, the Difficulty of railing one of the Bodies, t>ie ; for a Tooth catching on a makes that of the Motion; and Notch, ciff. rubs one of" its Sides ofconfequence the Fridiott aiiCes againlt a Surface equal to its wholly from the Weight or own ; and is to difcngage itfelf Preffion, arni the Surface has no- m a certain Time by palling over a thing to do. 6pace equal to the Surface ; con- fequently the lefs the Surface, the lefs Space it has to move, the Liitlenefs of the Surface di- ininilhing the Refiftance of the Fridion ; not that it is a lefs Sur- face that rubs, but as there is a Icf^ Space to move. Bat notwithftanding all the In the fecond Cafe, the Mag- nitude of the Surface would be all, were it poffible this fecond Cafe could be ablblutely extrad- ed from the firft, i. e. could the Parts of one Body be rubb'd and worn again ft thofe of the other, without raifing one of them ; it being vifible, that a greater Num- ,, bef F R F R ber of Parts to be broke would make a greater Refinance than a lels. But as in Praftice, we never rub or grind without railing the Body, the Refiftauce arifingfrom the Greatnefs of the Surface, is always combin'd in the fecond Cafe with that of the Preffion ; whereas in the former Cafe, that arifing from the PrelTion, may be alone, and uncom- pounded. Add to this, that what is wore off a Body, is ordinarily very little, with Regard to the great Number of Times the Body muft have been raifed during the Fr/V- tio»^ and all the little Heights added together, which the Body muft have been raifed to. Hence as the Reliftance from Preffion may be fmgle, and as the fame always accompanies that ariling from the Magnitude of the Surfaces, and is ufually the much more confiderable of the two, when it does accompa- ny It; for thefe Reafons, in moft of the Experiments that are made, it is the only one perceived, and the only one that needs to be confidered. But then, as 'tis poflible, in certain Cafes for the Preflion to be very llender, and the Num- ber of Parts to be rubb'd,very great, it muft needs be own'd, there are Cafes wherein the Fridion follows very fenfibly the Proportion of the Surfaces. FRIEZE, ^in Architefture, FRIZE, Cis a Member or FREEZE, ^Divifion of the Entablature of Columns, by the Antients called Zoophorus. FRIGERATORY, a Place to make or keep Things cool in Summer. FRONT, in Architefture, is the principal Face or Side of a Building, or th.it which is pre- fented to the chief Afpect or View. Of Setting of Fronts. The Setttng (_rh.it is making) o^ the Frcnts of great Buildings, viz. Afhiar (or Stones) Archi- trave Windows, or Doors, with the Ground-Table, Fafcias,and other Members, {^\x.Wing fays) are worth from 3/. \os. to 5-/. per Rod, according to theGood- nefs of the Work. trant^ in Perfptclive, i-s a Pro- jedtion or Reprefentation of the Face or Forepart of anObjed, or of that Part diredly oppolite to the Eye; which is more .ufu- ally called the Orthography. FRONTAL, alittie Frontoq or Pediment, fometimes placed over a little Door or Window. FRONTISPIECE, in Archi- tefiure, the Portrait, or princi- pal Face of a Building. FR0NTON,inArchiteaure, an Ornament which is more ufually called among us, Fedi- meiit. FROWEY. Workmen; fay Timber is froivey^ when it is evenly tempered all the Way, and works freely without tear- ing. FRUSTUM, in Mathema- ticks, a Piece cut off, and fepa- rated from a Body. Thus the Frujlum of a Pyramid^ or Cone^ is^ a Part or Piece of it cut off ufually by a Plane parallel to the Bafe. C c 4 Frnjlnm F R F R Frujlriarn of a Pyramid^ is the the Side of the greater Bafe iS remaining Parr, when the Top Inches, and the Side of the lelTcr IS cut off by a Plane parallel to the Bafe. o u^o find the (olid Come Jit ^ there are fever al Rules: RULE I. To the Redangle, (or Pro- eua) of the Sides of the two B^^Xcs^ add the Sum of their Squares ; that Sum being multi- ply'd into one I'hird of the Height of the Fnijlum^ will give its Solidity, \( the Bafes be Iquare. Or thus, which is the fame in ' EiTed: Multiply the Areas of the two Eafes together, and add the two Areas to the fquare Root ; and that Snm multiply'd by one Third of the Height, gives the Solidity of any Fruflum, either aquare or mul tangled. RULE If. Add one third Part of the Square of their Difference to the lledangle of the Sides of two Bafes; and that Sum being mul- tiply^d into the Height, will, if ihc Bafcs be fquare, produce the Solidity : But if they be triangu- 3ar, or multangular, the faid Hedlangle of the Sides, with the third Part of the Square of their Difference, will be the Square of a mean Side; and the fquare Root t, are the fame., in effect., as for the Frultum of a Pyramid. RULE I.' To the Reftangle of the Dia- meters of the two Bafes add the Squares of the faid Diame- ters, and multiply the Sum by .!78)-4, the Produd will be the IVipie of the mean Area ; which multiplied by one Third of the perpendicular Height, that Pro- dudl will be the folid Content. Or thus : Multiply the Area's of the greater and leffer Bafes together, and out of the Produ6l extraft the fquare Root ; then add the fquare Root and two Area's to- gether, and multiply the Sum by one Third of the perpendicular Height, and the Produd will be the Iblid Content. RULE r IS. r K. RULE II. To the Rectangle of the greater and lefTer Diameters add | Part of the Square of their Difference, and multiply the Sum by •785-4, the Produft will be a mean Area ; which multiplied by the perpen- dicular Height, the Produdlwill be the Solidity. Example. Let ABCD be the Frujium of a Cune^ whofe greater Diameter CD is 18 In- ches,^ and the lefler Diameter A B is 9 Inches, aad the Length 14.25- Feet, which is the folid Content. Multiply 18 by 9, and the Produd will be 162 ; and the Difference between 18 and 9 is 9, whofe Square is 81, a third Part of which is 27 ; which add to 162, and the Sum will be 189: This being multiply'd by 785-4, the Produd will be 14844; which being divided by 144, the Quotient will be 1.03 Feet, the Area of the mean Bale ; which maltiply 14.25- Feet, the Height, the Produd is 14.677J Feet, the folid Content. Or thus, by the firfi Rule. The Square of 18 (the greater Diameter) is 324, and the Square of 9 (the lefler Diameter) is 81, and the Redtangle or Produft of 18 by 9 is 162 ; the Sum of thefe three is 5-67, which multiply'd ^y •7S5'4, theProdud is445-.32i8 ; which divided by 144, the Quo- tient is 3.09 Feet, the triple Area of a mean Bafe: This multiply'd by 4.75-, a Third of the Height, the Piodu6t will be 14.6775" Feet, the Solidity the fame as before. ,^cs F R F R See the Operation. .78^4 189 70686 7854 144) 148.441^6 (i.03; 144 444 Height 14.25- Feet. 43 z AreaBafe 1.03 Feet- 18 18 From 9 9 Subt. 162. 9 Rem. Add 27 9 Sum 189 3) 81 Square. 27 a Third 12 4279 1425- Solid Content i^-^yys Feet. 324 the Square of 18. 162 the Reaangle. 81 the Square of 9. 5-67 the triple Square of a mean Diameter. ; . 785-4 3-09 ^5-7 ^.j^ which multiply'd by 14.25- Feetj — ^ and the Produft is 604.36, (j'c. ^4978 i5'45- which divided by 12, the Quo- 74124 2163 t'cnt is 5-0.36 Feet, the Curve- ^0270 1236 Surface; to which add the Sum :. of the two Bafes 2.21 Feet, the I44)445'.32li8 Solid. 14.6775- Sum is 5'z.j7 Feet, the whole , ^ — fuperficial Content. 133^ To meafure the Frujlum of 36 a reftangled Pyramid, called a Prifntoid^ whofe Bafes arc pa- ^ . , , - r ■ I ^ rallel to one another, but dif- To find ibe fuperficial Conte:-7S. proportional. You will tind the Circumfe- rence of ih? greater Bafe to be The RULE. ^6.5-488, and of the leller Bafe 28 2744 ; the Sum of both is To the greateft Length add 84 8232, thchaU t)um i!>42.4i 16; half the Icfler Length, and mul- liply F R F R tiply the fame by the Breadth of the greater Bafe, and referve the Product. Then to the lefTer add half the greater Length, and multi- ply the Sum by the Breadth of the lefTer Bafe; and add thisPro- du6l: to the other Produ6t re- ferved, and multiply that Sum by a third Part of the Height, and the Product will be the fo- lid Content. Example. Let ABCDEFGH be a Prifmoid given, the Length of the greater Bafe AB 38 In- ches, and its Breadth AC 16 In- ches ; and the Length of the lelfer Bafe E F is 30 Inches, and its Breadth 12 Inches, and the Height 6 Feet: What is the folid Content ? To the greater Length A B 38,^ add half the lelfer Length EF ij', the Sum will be 35- ; which being multiply'd by 16, the greater Breadth, the Produd will be 848; which referve. Again, to EF 30 add half AB 19, and the Sum will be 49; which multiply by 12, the leller Breadth EG, and the Produd will be 5-88 : To which add 848, the referv'd Produd, and the Sum will be 1436 ; which being multiply'd by 2, a third Part of the Height, the Produd will be 2872 ; this Produd divide by 114, and the Quotient will be 19.14 Feet, the folid Content. If! 16: 5-3 848 588 1436 2 2,872 8 = AB. 30=EF. iEF. i9:=iAB. AC. 49 12«=:EG. ^8S 144)2872(19.94 Feet, the Content. 1360 640 64^ « a third Part of the Height* F R P R T'o prove this Rule : Let it be fuppofed the Solid cat into Pieces, fo as to make it capable of being mealured by the fore- going Rules, thus : Let ABCD reprefent the greater Bafe, and EFGH the Idler Bafe; and let the Solid be fappoled to be cut offthrouj^h by the Lines ac, bd^ and e f, gh^ from the Top to the Bo'tcom; fo will there be a Parallelopipedon, having its Bales equal to the lefler Bafe EFGlrl, and its Height, 6 Feet, equal to the Height of the Solid : Mul- tiply 30 (the Length of the Bafe) by 12 (the Breadth thereof) and the Produd: is 360; which mul- tiply by the Height 6 .^eet, and the Product is 2160. Thaa there are two Wedge- like Pieces, whofe Bafes are ah EF, and GH, cd-^ if thefetwo Pieces are laid together, the thick End of one to the thin End of the other, they will compofe a redtangled Parallelopipedon ; which, to meafure, multiply the Length of the Bafe 30 by its Breadth z, and the Produdt will be 60 ; which multiply by 6, the Height, the Produft is 363, Then there are two other W dges like Pieces, whofe Bafes a-e e E, ^ G, and /F, h H ; thefe two laid together, will compofe a reftangled Parallelopipedon: To meafure this, multiply the Length of the Bafe 11 by the Breadth 4, the Produft is 48 ; which multiply by 6, the Height, theProdud is 288. A a / iS ( ^- / n O o And la^ly, there are four re£t • angled Pyramids at each Corner ; which, to meafure, multiply the Length of one of the Bafes 4 "by its Breadth 2, the Produd is 8 ; which multiply'd by 2, (a third Part of the Height,) the Produ6l is 16 ; and that muU;- ply'd by 4, becaufe there are four of them, the Produ6t is 64; then add all thefe together, and the Sum is 2872 ; and divide by 144, the Quotient is 19.94 Feet, the fame as before, which (hews the Rule to be true. See F U F U See the ©pcratioii : IZ 30 12 4 30 a 4 2 360 60 48 8 6 6 6 2 2160 360 288 16 360 4 288 64 64 144) 2872 (19.94 Feet the whole Content. To fiMrithe fuperficial Content. Half the Perimeter of the greater Bafe is 5-4, and half the Perimeter of thelelFer Bafe 1542; which being added together, the Sum is 96 ; which being multi- ply'd by 6 (the Height) the Pro- duft will bf, 5-76: Then divide this Produft by 12, and the Quo- tient is 48 Feet ; to which add the Sum of the two Bafes 6 72 Feet, and the Sum will be 54.72 Feet, the whole fuperficial Con- tent. FUNNELS o/ai»2»^p. The Funnel is the Shaft, or fmalleft Part from the Walle, where 'tis gathered into its leart Dimen- sions. Palladto directs, That the Funnels of Chimneys be carried through the Roof, three, four, or five Feet at the leaft, that they may carry the Smoke clear from the Houfc into the Air. He advifes alfo, that Care be taken as to the Width of them; for that if they be too wide, the Wind will drive back the Smoke into the Room i aud if Vol. 1. they be too narrow, the Smolce will not be able to make its Way. Therefore Chamber Chimneys mud not be made narrower than ten oreleven Inches, nor broader than fifteen ; which is the ordina- ry Depth of the Funnels of great Kitchen Chimneys,whofeBreadtli is four or five Feet within the Work, from the Place where the Brell ends, to the Top of the pHnnel. Now the faid Bread reaches from the Mantle-Tree to theCeil- ing or Pitch of the Arch, al- ways dimini(hing within the Work, till you come to the Meafures of Depth and Breadth before mentioned ; and from thence to the End of the Funnel^ it mufl; be carried up as even as it poflibly can be ;. for if there be a Failure in this, the Smoke happens to be otfenlive. FURRING, in Architefture, is the making good the Rafters Feet in the Cornice. Thus, when Rafters are cut with a Knee, thele Furrings are Pieces which go ftraight along with the Rafter, from the Top of the Knee to the Cornice. D d Alf« r F U Alfo when Rafters are rotteHiJ^ ©r funk hollow in the Middk;^ there are Pieces cut thickeft itt the Middle, and tnpering towards each End, which are nailed up- on them, to make tnem ftraight. Such Pieces are called Furs^ and the Putting them on, Furring the Rafters. FUSAROLE, in Architec- ture, is a Moulding or Orna- ment placed immediately under the'Echinus in the Doric ^ Ionic ^ and Cumpofite Qz^'maXs . The FufaroU is a round Mem- ber carv'd in Manner of a Col- Jar or Chaplet with oval Beads. The Fufarols fhould always an- Iwer exa6tly under the Eye of the Volute, in the Ionic Ca- pital. FUST, in Architedure, is the Shaft of a Column, or that Part comprehended between the Bafe and the Capital. Alfo cal- led the Naked. The Fuji is 'that cylindrical Part which makes, as it were, the Body or Trunk of the Co- lumn, exclulive of the Head and Feet. The Word is French.^ and literally (igniries a Cask. But fome derive it from the Lattn Fuji-Sy a C/uL G A^ G A Q ABLE-END of a Houfe, h ^^ the upri,;ht triangular End from the Cornice or Eaves to the Top of its Roof. 1 pnibc!)! looQ -.y^-' c ,3TAi ^'- rito tn'eaffire a Gable-End; ^'8 ^« Multiply the Breadth at Bot- tom by half of the Perpendi- cular, or Line from the Angle of the Top to the Middle of the Bottom, or multiply half the former by the whole of the latter, and the Produft will give the Content in fuch Meafures as the Dimenlions were taken in. GAIN, the Bevelling Shoul- der of the Joilh, or other Stuff. 'Tis alfo ufed for the lapping of the Eiid of the Joifts, ^c. upon a Trimmer or Girder ; and then theThickncfs of the Shoul- der is cut into the Trimmer, alfo bevelling upwards, that it may juft receive the Gain., and fo the Joifl and Trimmer lie even and level with their Surface. This Way of working is ufed in Floors and Hearths. GALLERY, inArchiteaure, is a covered Place in a Houfe, much longer than broad, and which is ufually on the Wings of a Building, ferving to walk in. Gallery is alfo a little Ifle or Walk, ferving as a common Palfage to feveral Rooms, placed in a Line or Row. Their Length (according to Palladia) ought to be at leaft five Times their Breadth. They maybe fix, feven, or eight Times their Breadth, but mull not ex- ceed. GARD MANGER, aStore- houfe or Room to fet Meat in. GATE, GATE, a large Door leading or giving Entrance iiuo a City, Town, Callle, Palace, or other confiderable Building ; or a Place for Palfage ofPerfons, or Horfcs, Coaches, or Waggons, ^c. As to their Propoiiion : The principal Gates for Entrance, through which Coaches and Waggons are to pafs, ought ne- ver to be lefs than feven I* oot in Breadth, nor more than twelve Foot; which lafl: Dimenlion is fit for large Buildings. As to the Height of a Gate, it ought to be one and a half of the Breadth and fomething more. But as for common Gates in Inns, under which Waggons go loaded with Phy and Straw, eT^-. the Height of them may be twice their Breadth. Of the Price of fame Sorts o/Gates. As to the Price of Gates, it is various, according to the Sorts of Gates ; which again will differ - according to the Dimenlions and Workmanfnip. I fhall at prefent mention only, Pallifadoe and ^old- Gates . Of Pallifadoe Gates. Mr.^ JVing fays, in RHtland- pjlre, if the Gates be fix or feven Feet high, and the Workman find Timber and Workmanfliip, they are worth about 9 or los. per lineal Yard ; but if he find only Workmanfliip, then it is worth but 6 or yx. per Yard. If they are Serai- Pallifadoe, ■with kneeling Rails at the Top, handfomely moulded on both Sides, ^nd fguare Pallifadoes, G A rnipad :• Panft€:lsy;a.i>^ , Bifocllon- Mouldings on . boHr Sides, the Gates about eight Feet high, and the Pods a Foot fquare^ opened in the I'ront, or revailed with a Moulding ftruck in it on botli Sides the Revail, a Bate and Ca- pital laid on the Ports, and the Heads cut into one of the 'Pla- tonick Bodies; as fuppofe an Icofaedron, and the Pods were about ten or eleven Feet above Ground, then the Workman- fliip is worth iz or 13/. a Yard lineal ; but if the Workmen find Timber, it will be worth up- wards of 20 J. a Yard lineal ; iii fuch Gates, to find all Iron- Work, Painting, Is^c. it would be worth above 30/. a Yard lineal. Of Pold Gates. Thefe are fuch as are fet up in P^ences, for Cutting up the Paf- fages into Fields, and other In- clofures. Thefe are of two Sorts, ei- ther of fa wed, or cleit Timber. For the making one of fiiwri Timber, fetting it up, and its J^ofts, the Price in diffeientPla- xes, is rrom3x. 6d. to ^s.. But if the Carpenter pay for the Saw-, ing, then the Price is from ^s. to 6 s. 6d. Such a Gate, Tim- ber and Work, is worth from 7 J. to 10/. according to the Goodnefs; but with Polls, from ii.r. to 1 5- J. but Gate and Iron- Work, from IOJ-. to 13/. and Polls from ifj-. to 18 j. Cleft Fold-Gates, Cleaving, Making, and Hanging, from 4 j. to 5-;. and fo proportionably for all Fimber, Iron, and Polls. The Reafon why the Prices are diffe- D d 2 rent, E G E rent,is,becaufe they are according Names or Denominations, by. to the CuftOmS- of different Pla- wh'(ch Money/Weights, Mea""^ ces. G'WEL i's ufed for what is more nfuanv ciiJl the Gallic GENERATED? in Mathe- GENITED 5ticks,isusM to Ifguify whatever is produced either in Arithmet'ck, by the Multiplication, Divilion, orEx- tradion of Roots ; or in Geo- metry, by the finding out the fares, ^c. are generally known^ or. particularly divided by thp"^^ Laws and Cuftoiiis of fevei;at Nati.^.r.s. GEOGRAPHY isthe Science that reaches and explains the Properties of the Earth, and the Parts thereof that dep^^nd upon Quantity. GEOMETRICAL, of or Contents, Areas, and Sides, or of pertaining to Geometry. e.x'tream and mean Proportionals, without Arithmetical Addition, and Subrrailion. GENERATING LINE, or h^ure, in Geometry, is that Geomefrical 'T la;ie .See Plane. Geometrical Place. See Lo* cus. Geometrical Solution of a Pro- blem^ is when the Thing is fol- which, by Its Motion or Revolu- ved according to the Rules of tion, produces any other Figure, Geometry, and by fuch Lines plane ,or folid : Thus a Right as are truly Geometrical.^ and Line, mov'd any way parallel to agreeable to the Nature of the. itfelf, ^£';?^r^z/£'j- a Parallelogram; Problem. round a Point,-jnthe fume Plane, with oneEnd faften'd in thatPoint, n generates a Circle; one entire Revolution ' of a Circle in the fame Plane, generates the Cy- cloid ; the Revolution of a Se- micircle round fts Diameter, ^^- nerates a Sphere, l^c. GEOMETRY originally lig- nify'd the Art of Meafuring the Earth ; but it is now the Science of whatever is extended, fo far as it is, fuch, that is of Lines, Superficies, and Solids. It is very probable, that Geo- metry had it firft Rife in Egypt^ GENESIS, in Geometry, is where the Nile annually over the Formation of any Plane or#fio\ving the Country, and co- folid Fij^ure by the Motion vering it vvith Mud, obliged Men of fome Line or Surfice; which ' Line or Surface is always call'd the DcJcriLynt ; and that Line, according to which the Motion h made, is called the DiyigsKt. GEOCENTRICK is apply "d to iiny Thing %vhich has the Earth for its Centre. to diltinguilh their Lands one from another, by the Confidcra- tion of their Figure; and to be able aUb to meafure the Quantity of it, and to know how to plot ir, and to lay it out again in its ! jail: Dimenfions, Figure, and Proportion. After which, 'tis GEOD/ESIA, Surveying, gr likely, a farther Contemplation . the Art of mcafliring Land. of th6(e Draughts and Figures, GEODEriCAL Numbers^ help them to difcover many ex- ^ lire fuch Numbers as are confi-. cellcnt andwonderfn! Properties ^cred accoi;|ij|:p^ to thqfe \;i^lg^r^.[ belonging to them ; which Spe- ,j, . .a i>a culation SP g? a culatfon continually wa^ fj;^T^^ ttK|n^ay,y^ur (ipld^pn, it would proving, apd is ftni t9 liii% v^fy^, fo drown it, that it would have Day. [)^'^ ' \{i'r;Uriinrc ' ^^ Luftre: But on the other But the ueome try <|r ng-.Floors, do" not place your binding orftrong, joills ahdVe four or five Feet apart; nor let your Bridgings or common Joifls be above twelve Inches apart, that is, between one Joift and another. ■ : ■> j, It fhould alfo be obferv*d ne- ver to make double Tenants or Tenons for bearing U^es, fuch as Binding joiQs, common Joifts or Purlins ; for in rhe tirft Place, it weakens very much whatever you frame it into; and, in the fecand Place, it is a Rariry to have a Draught in both Tenons, that is, ro dr.iA' your Joint ciofe bf the Pin : for the hiid Pir, by p.dfmg through boih T<:i!on>, if there is a D lUiht in <;uch. muft bend it fo much, that except the Pin be as tough as W'te, it muft needs break in driving, and c.m- fequi-ntly do more Hnrt than Good. GIRT. See Fillet. Given is a Word often ufed in the MaihcmaticKs, and ligni- fies fomething which is fupposM to be known. Thus if a Magnitude be known, or we can find another equal to it, we fay, it is aCtven Maz,nitude^ or that fuch a Thing \s given in Magnitude if the Pofition of any Thing be fuppofed as known, then fay. Given in 'J^ofition. Thus if a Circle be adually defcribcd upon any Plane, they fay, its Centre is given i» ^Po/i- ti>jn\ its Circumference is gvoen in M(7gnitHde^ and the Circles is given both in Pojition and Mag- mtude. But a Circle may be given in Magnitude only ; as when on- ly its Diameter is given^ and the Circle not actually defcribed. Ir the Kind or Species of any Figure be ^/Vw, they fay. Given in Specie ; if the Ratio between any two Quantities, is known, they are faid to hegweft in Pro- ^urtiun. GLACIS, in Building, ^c. is an eafy infenfibJe Slope or De- clivity, GLASS, GLASS, -a Diai>hanous or Tranfparent Body» made by Art, of Sand and Nitre, as P//»y fays. It is alfo made of white gUllenng Flints mixed with Sal Alkali^ or the Salt of the Herb Glafswort, or Saltof Fern- AOies, for common 07«/}, Ibme fay. M. Blanconrt lays, the FenC' t'tans ule white Fh'nts, and alfo a rich Sand, and likewife a fort of White Marble. He likewife 9dds, that all "white tranfparent Stones, which will not burn to Lime, are fit to make; andthatall Stones that are fit toltrikefire, are capable to be made into Glafs. A certain learned and curious Author gives us the following Charaders or Properties of GUfs^ whereby it is dillinguifli'd from all other Bodies, "viz. 1. That it is an artificial Con- crete of Salt, Sand, or Stones. 2. That it hfufible by a ftrong Fire. 3. That when fu(ed, it is tena- cious and coherent. 4. That it does not wafte or con fume in the Fire. f. That when melted, it cleaves to Iron. 6. That when it is red-hot, it Js duftile, and capable of being fafliion'dinto any Form, but not malleable ; and capable of being blown iutoaHoUownels, which no Mineral is. 7. That it is frangible when thin, without annealing. 8. That it is friable when cold. 9. That it is always Diapha- nous, whether hot or cold. 10. That it. is flexible and elaltick. . ,-. . , 11. That it is diflblirble by Cold and Moifture.,^l^AdD ylivfb G L !jj;/'That it! ij Qjily. capable of being graven or cut! ivith a Dia- mond and Emery, t ^v-. 13. That ir receives any Co- lour or DyCpbQ^ externalJy and internally, .lo ^Irii biii -jH;. ■ 14. That it is not dfflciluble by Aqua Fortis, Aqua Regia, or Mercury. 15'. Neither acid Juices, nor ^ny other Matter, extrad either Colour or Tafte, nor any other Quality from it, 16. It admits of PoliOiing. 17. That it neither lofes of Weight nor Subftance, by the longell and moft frequent Ufe. 1 8. That it gives Fulion to other Metals, and foftens them, 19. That it is the moft pliable Thing in the World ; and that it bell retains the Fafhion given ir. 20. That it is not capable of being calcin'd. 21. That an optnGlafs filled with Water intheSummer-Time will gather Drops of Water on the Outfidc, fo far as the Water on the Inlidc reaches ; and a Man's Breath blown upon it will manifeftly moilten it, 22. Little Glafs Balls, filled with Waier, Mercury, or other ^ Liquor, and thrown into the Fire; as alfo Drops of green Glafs broken, fly afunder with a loud Noife. 23. That neither Wine, Beer, nor any other Liquor, will make it multy, or change its Colour, nor rulf it. ' ;- ' ;'J'/f' ;• 24. That it may be cemented, as Stones and Metals, • -' if. That a Drinking-Glafs partly filled with Water, and rubbed on rtW'^^Brim vfrith a wet -s(i h'r^\(i(j j^ ojf^ i^'-' Finger, o^jofifl&T 3lduoi> sjlem f *- l G L G L Finger, yields^ ihufical Notes, higlifcr, or lower, as the G/afu is more or lels full, and makes the Liquor frisk and leap Tbe Sorts of Glafs. There are various Sorts of (7 /(?/>, which are made ufe of in the World ; but at prefent, I fliall only fpeak of thole Sorts of (ylafs which Glaziers com- monly ufe here in Eftgland^ which are thefe following, vtz. Crown Glafs ^ which is of two Sorts ; I . Lamheth and RatcUff. 2. French or Norr/iandy Glafs. j>. German Glafs of two Sorts, White, end Green. 4. jDutch Glafs. f. Newcaflle Glafs. 6. Staff or djhire Glafs. 7. Brijiol Glafs. ^.Look'm^GUifs. <). 'Jealous Glafs. Of which Sorts, I (hall treat fuccindtly in their Order. Crown Glafs is of two Sorts, RatcUff and Lambeth Crown Gbfs. That Sort of Crown Glafs that goes by the Name of Ratcltf Crown Glafs.^ is the bell and cleared Sort of Crdwn Glafs ; which Sort was ar firft made at the Bear-Garden^ on the Bank- lide, in Souihwark^ in the Year 1691. which was publiified m the Gazette^ and commended, as follows, and called Crown tVtndovj-Glnfs., much exceeding French Glafs in all its Qualifica- tions. But the Maker of this Sort of Crown Glafs being now removed to RatcUff.^ it therefore now bears the Name of RatcUff Crown Glafs., as it did at firft of the Bear-Garden Crown Glafs. This Sort of Crown Glafs is of a light Sky-blue Colour, which may. be very dillinftly feen if it be laid on. a Piece of a white Paper. It has been reported, that an Fnglifjj Glafs-Maker went over to France on Furpofe to learn the French Way of making Glafs ; which he having attained to, came over again into England., and fet up Making of Crown Glafs., and in the Performance, outftripp'd the French his Teachers, as ^»^- Ufljr/ien ufunlly do. There are twenty-four Tables of this Glafs to the Cafe, the Tables being of a circular Form about three Foot, fiv, feven or eight Inches in Diameter, and confequently each Table will be in Area about nine or ten Feet, and the Cafe betwixt two hun- dred and twenty, and two hun- dred and forty. This Glafs is brought from RatcUff m fuch kind of Frames as Newcajlle Glafs is brought up to Town in, only the Newcaflle Glafs is brought on Shipboard ; and this RatcUff Glafi upon Staves by two Men. 1. This C7/rfyi called RatcUff Crown Glajs^ has been fold tor about 9^/. a Foot in London^ cut into Squares, and when wrought in Lead, and fet up, for about 18^. a Foot. 2. Lar/jbeth Crown Glafs takes its Name alfo from the Place where it is njade. It is of a darker Colour than RatcUff Crown Glafs., and more inclining to the Green. This Sort is fold for ^d. 1 Foot cut into Squares; and be- ing wrought and fet up into Windows with Lead, its Price is faid to be worth about 16 d. a Foot. French G L French Glafs^-aMo called Nor- mandy Glafs^ becaufe it was for- merly made at Cherburg^ in Nor- mandy ; and alfoZi0rra«»c7/«/}, be- caufe made there. Now it is rnade wholly in theNineGlafs- Works ; five whereof are in the Forcll of h^om ; four in the County of Eu ; the Icaft at Beaumont^ near Rouen. They alfo make Glaj's at Never s in Orleans^ and like- wife at St. Gob'tn., near La Fere in 'Pkardy; but from which of thefe Places, any French Glafs comes, that is ufed in England^ is uncertain. It is a thinner and more tranf- parent Glafs than our Neivcaftle Glafs^ and when laid on a Piece of white Paper, it appears of a dirtyifli green Colour. Itufed to be of a middle Price, betwixt Crown and Nevjcafile Glafs., which has been fold for 12 . a Foot, wrought in Lead, and fet up. Of this Glafs., there is but twenty-five Tables to the Cafe. German Glafs. Of this there are two Sorts, White and Green. The White German Glafs is of a whitifh Colour, and free from thofe Spots and Blemiflies which our Nevjcafile Glafs is fubjed to; but it has commonly fome fine or fmall carved Lines or Streak'd Lines, as the Newcaflle Glafs hath. Green GerrnanGlafs. This, be- fides itsgreenifl-iColour,is fubje6l: to havethofe fineLines or Streaks which the White is; but both the Green and the White Ger- man are ftraighter, and not fo vvarp'd as the Newcaflle Glafs is. Both thefe Sorts of Glafs are brought over from Germany., and yet is generally as cheao asiVew- (aflk Glafs. G L Butch Glafs does not differ much from Neivcaftle Glafs m its Colour and Price. *Tis fre- quently much warp'd like that, and the Tables are but fmol I. Newcaflle GJafs, is that which is moftly ufed in Ey,gland. 'Tis of an Afli Colour, and fubjed to Specks, Screaks, and other Bleniifl-jes, .md belides, is fre- quently warp'd and crooked. Mr. Leybuurn fays there are forty-five Fables to the Ca(e, each Table containing five fu- perficial Vtti:, and conlcquently a Cafe <^f forty-five Tables to the Cafe will contain two hun- dred and twenty-five Y^tf, tho' fome fay, there are but thirty-five Tables, and (ix Feet in each Ta- ble; which amount but to two hundred and ten Feet. Mr. Leybourn fays, that aCafe of forty-five Tables, five Feet to a Table, equal to two hundred and twenty-five Feet, wcM^hs about two hundredweight, and confequently nine Feet will Weigh about eight Pound. As to the Price of Newcaflle Glafs., it is uncertain : For when Coals are plenty, then Glafs is cheap; and when Coals are'dear at London., then Nevjcaflle Glafs is fo likewife; not that they want Coals at Newcaflle., but be- caufe they have no "other Con- veyance for it to London: So that at fome Times it has been ar 30 X. a Cafe, and at other Times 40 i-. But fome fay, that the moll common Price is 34 /. the Otic. Some fay, 'tis worth 6 or -js. to cut a Cafe of this Glafs into Quarries Diamond Fafliion (with Halfs, and Quarters, and Three Quarters of Quarries, as thcGlafs falls out ;) and others again have fald theyji^puli do J5 for half the Money.- . - > ' ^ '•? i Nevjicajlle GUfs^ cut into large Squares, are fold from 22 x. to 2ss:per hundred Feet, according to their Size; and fni all Squares from 19;. to 22 J. per hundred Feet; aod Quarries of Newcafile Glafi jfpf, about ^6tfn/»tff!hupdred Feet.',, b •" riVciiDr* vli 'ir j-^i Glazing done with this Nevj- cajlle GlaJs^vAih Quarries, Band- ing, Soldering, and Finning the Cafemcnts, being included, the tifaal Price in London \s-rd. ox6d. per Foot. But in ftveral Parts of the Country, they iiave 6d.per Foot, and will be paid for pin- ning the Cafements beiide. Glazing, in fume Places of Eff gland, as in RutlntiJ^ and other Parts towards the North, is done with Quarries of New c^i file Glafs at 4<^. -T or ^ d. per Foot; and Squares wrought into Lead, and fet up, for 6d. per Foot. But in Sujj'exy Keyit^ and the vSouth Parts of England, they will not work fo cheap; becaufti the Glafs colls them fomething dearer. They ufually reckon 'jd per Foot for Glazing with Squares of Nt-wcaftle Glafs^ and thev will be paid for pinning the Cafements befides, ■^taffordfljire GUfs^ is a fort of tjlafs that is feldom ufcd but in that and the neighbouring Coun- ties. BriJiolGlafi is fo cal led, becaufe it is. made at the City of Brifiol ; hut very little of it comes to L'j'/tdoN, by reafon they have not the Convenience of fending it by Sea, as they have from New- caftle by Coal Ships; though this IS as cheap, and better than Nevj- cajlh Glafs. G L Looking Glaff. As to Looking Glajs Plates, they are made either at rhe Old Bear-Gar den in South' vjark^ or at l^aux-Hall^ near Lambeth, I am not certain, whether this Sort of Glafs be not made with the Sort of Sand which V>x.Grew mentions in hisMufiCura ^^egalis Secietatis, p. ^^6. Fine Sand, fays l;e, from a Sand-Pit near Bromley in Kent^ of which is made the cleareft and belt Englijh Glafs : It con- fi(h of fome Grains as clear as Chrylhil ; ' which being mixed with others obfcure, give a whitifli Aih.Colonr to the whole Mifs. Some have a Way of examin- ing which is the whteft and clear- eft Glafs; which is as fellows : Thev take it up clofe by one Edge, betwixt the Edges of the Middle and Forefinger ; and tnen looking again ft the cut or broken Edge,' the Eye> being thus skreen'd by the Edges of the two l-'inger>, they fay, 'tis cafy bv this Method to difcerr; wiiich is the whiteft and cleareft Glafs. Thefe Looking Glafs Plate? are ground fmooth and flat, and polilh'd. They are fometimes uled in Salhes, or Sa(h-Win- dows, Bul 'tis a dear fort of Glafs ; for they ask ^s. a Foot for fuch Squares, and if they are large, 'tis much more. LooktKg Glajfes, being foil'd, being in Vogue for Ornaments over Chimneys in Parlours, l^fc I (hall fay fomething briefly con- cerning them. Sir 14 Warn. Petty tells us, that the V^Xmq of Looking Glafs Plates conlifts in a duplicate Pro-. portion G L J .v\ ^o t C 6 T 1 SO I so I so I ' fO 12 -r I 7^ I 2,f 1 iV. S. Here are dx diftincl Win- dows, viz. the two upper ones fire three-light Windows ; and of the four lower ones, there is one of three Lights, two Tingle Lights, and one double' one. N.B. A Number (landing at the Top (of the oblong Figure in the S'chemc above) is the Height of the Light; that at the Bot- tom the Breadth, and that NunVocr in the Aliddle the upper one for the Number of Squares in Height, and the lower one for the Number in Breadth. N. B. a!fo. That the firfl and fe- cond Windows (which are three-light Windows,) have their Dimenfions fet down in b'tict^ and duodecimal Parts of Feet; e.^^. In the firft Win- dow you have this Number 3 6 o at the Top, which iig- uifics the Height of the Light to be q Feet and 6 duodecimal Parts of a Foot ; in the Mid- dle there is I^-, vs'hich iignities there is 6 Squares in Height and 4 in Breadth, (equal to 24 m the whole Light; and be- low there (lands 2 I o, which iigni(ies 2 Feet, and one duo- decimal Part of a Foot. In the fccond or middle Light, there is a C, fet to (liew that there muft be a Cafement in that Light, and confequently that the upper Squares and lower ones muft be cut fome- what fhorter, (becaufe of the Frame of the Cafement,) and the Side Squares muft be cut fomething narrower, and the four Corner-ones both (horter and narrower. Now by fuch a Draught a London Glazier ^vihtin his Country Curtomers fend to him for fuch a certain Parcel of Glafs, he knows immediately how to cut it ro fit his Work, and the Country Gla- zier knows how to work up his Glafs by it; lb that it (hall fit each Window, though he be fifty Miles diftantfrom it, as well as W he were by it. The London Glafs -Cutters commonly mark (with a Letter or P^igure over them) all the Windows that are of one Size, and write the fame Mark on a Piece of Paper, which is put in among that Parcel of Squares which belong to thofe Lights that are all of one Size. This Piece of Paper is fo put in, that the Chara6ter is vifible above the Edges of the Squares ; by which diftinguiniingChara£l:er,theC?^»- try Glazier readily knows which Squares to take for any Window. I fliall w G L G L I fliall add, as to this Article cf Draughts^ that thofe Glaziers who underftand decimal Arith- mctick^ lit down their Dimen- lions ill Decimals, which better fuits the London Glafs- Cutters^ becnufc they have their Rules centeHmally divided for that Purpofe. For that Reafoii I have here fet down the Dimenfions of the four lower Windows in i^'eet, and centefima! Parts : hs fur Example; in the third Windovi^, at the Top, you have thefe Num- bers 4 5^0, which iignify that the Height of the i^iglu is 4 Feet, and 50 centelimal Farts ; and at the Bottom there are thefe Num- bers I 5-0, wtiich fignify i Foot 50 centchmal Parts ; and fo of the. reft. Of Meafuring GfalierV Work. I fliall firfi confider the Cuf- toms ufed among them, (for Cuftom is to be the greateft Guide in a!! manner of Mea- fures;) and fe coldly ^ the taking the Dimenfions, and computing the Quantity. Note I. That in Gtazhtg^ when Windows have a femicircular Top, (or any other curved Forms,) theCuftom is to taiie the full Height as if they were fquare. 2. That all Windows confifting of intire Circles, or Ovals, or any other curved Form, the Dimenfions are taken the two longeft Ways at Right Angles one to another, and from thefe Dimenfions the Areas are found as if they were fquare. Vol. L 3. That all Crochet Windows iti Stone- Work, are all mea- fured by their full Dimenfions , in Height and Breadth, as if they were fquare, and nut carved. 4. That there is very good Rea- fon for all thefe Cuftoms, if we confider, Ftrft^ TheTrouble in taking Di- menlions to make ihem by. Secondly^ The Wafte of Glafsin working it to thefe Forms.' And, Thirdly^ The extraordinary Time expended in fetting it up, more than in that of fquare Lights. Of the takifig Dimenfions. Glaziers generally take them to Parts of Inches, and compute to the Nicety of a Fraction of an Inch, which may be done fe- veral Ways; four of which are pradifed by fome Surveyors and Workmen ; which are, firjl^ by Vulgar Fractions; fecondk\ by Crofs Multiplication of "Peer, Inches, and Parts ; thirdly^ by Duodecimals; 2ind^ fourthly^ by Decimals, Bur becaufe Glaziers ufually take Dimenfions to the Parts of an Inch, the beft and readielt Way to compute the Areas, is to take the Dimenfions with a SlidirgRule, fuch as is. generally ufed by GLi^ziers^ which Rule is divided centefiinally; the Di- menfions being thus taken, and fet down, are multiplied one in- to the other, as eafily in Vulgar Arithmetick,as whole Numbers are. Ee As G L G L As for the Manner of com- puting th€ Quantity, ite Cross Multiplication. Of tke Price of divers Sorts of Glaziers ffWk. I. Glazing with Squares : For the Price of French^ German^ D'Atch^ ^nd E»glijb Ct own Glafs, wi ought in Lead, and let up, lee before. As to the Price of Square- Work, the Malkr finding Glafs, and the Glazier Lead, Solder, and Workmanlliip, it is valued at about two Pence half-penny fer Foot ; but the Country Gla- ziers will be paid three Pence a Cafement for pinning of them, (which is the putting of Leaden Pins through the Iron Frame, and foldering them, to fix the Glafs to the Frame,) viz. Cafe- ments of four Foot and a half long, and fo in Proportion, if they find Lead and Solder for it. But for workiiig up Squares, and fetring up, and finding no- thing but Workmanfliip, it is worth about one Penny, or three Ha'f-pcnce fer Foot. 2. Of Glazing vjisb ^tarries J which' is for the mod Part done with A>UT.7/iiV Glafs. See for the Price of new Work nnd Mate- riils, wh.at is faid before in the Article Nevjcajllc Glafs. •But if the Glazier find only Lead, Solder, and Workman- Ihip, it is worth about t^jree Pence /jfr Foot : But if they find nothing but Work, then three Half-penc^ or two Pence is a llifticicMit Price: For taking do wn Quarry Glafs, fcowering and (bidcring it anew, and banding and fitting up again, the ufual Price is three Half- pence per Foot. But in Churches, where they fay they have ufually more for Banding, c/f. the Price is two Vcnce per Foot; and fo likewili; for taking down, fcowering, foldering, banding, and fetting up again ot old-talhion'd Work, compofed of Pieces of Glafs of ditferent Sizes and Figures, the Price is two Pence per Foot. Mr. Leybourn icWs us, that in London they generally ufe that Size of Quarries called lis. which he defcribes as follows : Quarries are for the moll Part fix Inches in Length, from one Acute Angle to the other ; and in Breadth, from Obtufe Angle to Obtufe Angle, four Inches ; fo that each Quarry contains twelve fuperficial Inches ; which Sort is that they cdiW Lung Quar- ries. See Quarries. N. B. There are fevcral Ap- pelladons given to the va- rious Dimenfions, ^c. of Quarries, viz^ 1. The Range, which is a Perpendicular let fall from one of the Obtufe Angles to the op- pofitc Side. 2. And the Length is the long- eft Diagonal, from one Acute Angle to the other. 3. The Breadth is'the Ihorteft Diagonal, which is drawn be- tween the two Obtufe Angles ; us for the Sides, and Area of the Quarry, that is very well known to all. You will find in the Word Quarries, that there have been, or fiill are twelve Sorts ofQuar- riev, froin whence arife divers Propofitiuns G L G L Propofitions of great Ufe to Glaziers. As, 1. To tind any of the fi/e fore-cit°d Diineniions, asRnnge, Side, Length, Breadth, and Area of any of the Sort of Quarries. 2. To tind the Area of any Sort of Quarries. 3. Having any of the Dimen- fions ^ivcn, v'tz. Range, Side, Breadth, or Length, to iind the Niune or Denomination of the She., viz. whether %s. 10 s. 12 j. 4. Having the Area of a Quar- ry given, to find of what Sort or Size it is. y. To find whether a Window hit glazed with thofe they call fquare Quarries, or long ones ; for it is to be obferved, that there are fix Sorts of Sizes of fquare Quarries, and i\^ Sixes of long Quarries; which make 12 Sorts in all. Glazii^r's U^ork is meafurcd by the Foot fquate ; fo that the Length and Breadth of a Pane of Glafs in Feet, being multi- ply'd into each other, produceth the Content. It is to be noted. That 6" A^^r^.'^rj ufually take their Dimenfions to a quLUter of an Inch ; and in multiplying Feet, Inches, and Parts, the Inch is divided into 12 Parts, as the Foot is, and each Part is divided into ii,$ir'f. Example I. If a Pane of Gl afs be four Feet eight Inches, and three Quarters long ; and one Foot, four Inches, and one Quar- ter broad, how many Feet of Glafs does it contain .^ •Tu -Tk • 1 r ^ 8 Inches 4 > . <^ .729 TheDecmialof ^_^j^^^^^^t^is^7^^ F. /. "P. 4 § 9 I 4 3 4 8 5» I 6 II I : 2 : 2 : 3 4.729 135-4 I89I6 23^45' 14187 4729 6.403066 FacH 6 Feet 4 Inches. J5y Scale ond Cvynpajfes. Extend the CompafTes from i to i.35'4, and that Extent will reach from 4.729, to 6.4 Feet, the Content. E e Example Example II. If there be ei^ht one Quarter broad, how many Panes of Glafs, each tour Ftet Fi-et cirGiiH^'are contain'd iii fovea Inches three Quarters long, thy faideieht Panes ? and one Foot five Inches >nd; 'Aua^jd ,^ji • E l. P. 4 7 9 I S 4 7 9 • I If 1 9 I I 11 n 3 6 : 8 : I : 8 3 8 S3 : S : I : 6 : o .464 •437 33^22, 1393^ 185-84 6.6y620i 5-3.4104(6 Fucit 5*3 Feet j- Inches. By Scale and Compajfes. Extend the Compafles from i to 1.437, and that Extent wiil reach from 4646 to 6.676; then extend the CompafTes from i to S, and that Extent will reach from 6 676 to 5-3.4, the Content. ExamplelW. If there arefixteen Panes of Glafs, each four Feet five Inches and a half long, and one Foot four Inches and three Quarters broad, how many Feet of Glafs is contauied in them? F. L y. 4.4^8 4 : 5- : 6 1.395- 1:4:9 ———-—- 22290 I : 5- MO : o 13374 3 : 4:1:6 44^8 6 : 2 ,; 8 : I : 6 6.218910 24 -^W^if^hfi • ^ .u£fn.iii4-875-^4 '■•.. ■ ' ^^-.■-. 4 ^ ;;4 3ri^ \>' 4 ~ -"— ■- 9£j jj 1i ^^11; . , .99,f:i^r -P:,^^ , >V '? o y£V7 3vi^ i> 99-f02s6 ra£ ^iB4i3qqu.3rij noavfiD rist/o#'f'?99 Feet 6 Inches. It J^ G'L <^ O It may be obferved, that xin-l ftead of multiplying by i6, I have muitipiied by 4 twice, becaufe tbur Times 4 is 16 By Scale and Compaffes. Extend the CompafTes from i to 1.395", and that Extent will reach from 4.458 to 6 219, then extend the Compailcs from i to 16, and that Extent vviil reach from 6.219 ^^ 99 Feet, the Con- tent. It mufl be obferved, that when Windows have Half Rcninds at the Top, they arc to be meafiired at their full Height, as if they were fquare. in like manner Round or Oval Windows are mcafured at the full Length and Breadth of their Dianieters. So a'fj :ire Crocket Windows in Scnni.-Work mcalured by their full Square'^. The iL.Ubn is, that the Trou- ble of taking their Dimendons to work by, the VVafle of Ciiufs in workirii;, and the Time fpcni in fetripg them up, is far more than the Value of the Glafs. GLUE. To make the belt Clue -iox gluing the Joints of Deal Boards. Set a Quart of Water on the Fire; then put in about half a Pound of good 6'/«e, and boil them gently together over a foft Fire, till the Ghe be entirely dilTolved, and. of a due • Coiv fiitence; for if it be too thin, the Wood will fo drink it up, that there will not remain a Body fufficient to bind the Parts to- gether : On the contrary, if it be too thick, it will not give way for the Joint to fhutcloie enough to be ftrongly joined ; for though it i^!G(«^,that maizes the Joints ilick, yet where there is fo much of ir, that ihe'Joint cannot clofe exadly, it will never hold firm. When Clue is ufed, it mult be made thoroughly hot ; for Clue never takes firm hold of the Wood, when it is not thorough- ly hot. And fee that the Joints to be glued have not been touch'd with Oij or Greafe ; for if fo, the G/uc will never take fad hold. The Joints of tRe boards be- ing (hot true, and the Glue hot, fet both tiic Faces of the Joint clofe together, and both turn'd upwards ; then dip a Btufli in the Glue, and befmear the Faces of the Joints as quick as polTible, and clap the two Faces of the Joint together, and Hide or rub tiiem long Ways one upon an- other two or three Times, to fettle them clofe, and fo let them ftand til! they arc dry and firm. GOLDEN RULE, in Arith- me.ick, a Rule or Praxis of great Ufe and Extent in the Art of Numbers, w-hcrcby we find a fourth Proportional to three Quantities given. It is alfo cal- led the Rul? of three^ and Rule of proportion. GORGE, in Architeaure, is a fort of Concave Moulding, wider, but not fo deep as aSfco- tia, chiefly ufed in Frames, Ch-am- branles, l^c' Gorge of a Chimney, is the Part between the Chambranle and the Crowning of thel^lantle. Of &AS there are diverS Forms, (Iraight, perpendicular, in Form of a Bell, y^. Gorge_ is alfo fometimes ufed for a Moulding, which is con- cave on the upper Part, and con- £ c 3 vex G O GO vex at Bottom, more properly called Gui.i and Cymcitium. Gorge is allbufed tor the Neck of a Column, which is more properly called Collartn and Gor- . gertMe. GOTHIC Archkca::re is that which deviates from the Pro- portions, Charafters, eff. of the Antique. The Gothic ArchiteSlure is fre- qucjuly very folid, heavy, and maffive ; and Ibmetimes, on the contrary, e):(;eedingly light, deli- cate, and rich. The Abundance ol' little, v\'himlica1, wild, and chimerical Ornaments, are its moft ufual Charaders. The Pro- files of this arc generally very in- correft. Authors diftinguini Gothick Ar- chiceflure into two Kinds, viz. A'/Jtient and Modcrtt. The Antient is that which the Goths brought vv?ich them out of the North into German\' in the Fifth Crntury. The Edifices built in tills Manner were ex- ceeding mnfiive, heavy, and coarfe; from Gr r?;ij^/7y it has been introduced into other Countries. Thofc of the Alodcnt Gothic run into the other Extream, be- ing ligh:, delicate, and rich tO Excefs ; wltnefs Wc(lmi?7fler- Ahhew rhcCithedral ^iLttchficld^ the Oofs ar Coventry ^ b.z. The lad Kind coiicinucd long in ufe, efpecially in lial)\ viz. from thiz Thirteenth Century, to the Rcfioration of the Antique Building in the Sixteenth. All the antient Cathedrals are of this Kind. It is not to be doubted, but that the Inventors of the Gothic Architecli'.:e thought they had far furpaffed the Greek Archfte6ls. A Greek Building has not one Ornament, but wnat addsaBeau- ty to the Whole. . The Parts neceflary to fuflain or flielter it, as the CoUmins, Cornices, cSTr. derive all their Beauty from their Proportions : Every Thing is limplc,mcafur'd, and rellrain'd to the Ufe it is intended for. No daring ouL-of-the-way Strokes, nothing qraint to im- pofo on the Eye. The Propor- tions are fo jull, that nothing ap- .pears very grand of itfelf, al- though the Whole is grand. On the contrary, :n the Go- thic Architcfture, we fee hugh Vaults raifed on flender Pillars, which one would exped every Minute to tumble down, though they v.'iil fiand for many Ages. Every T.iing is cramm'd with Windows, Rofes, Crolfes, Fi- gures, zs/c. Gothic Column is any round Pillar in a Gothic Building, titiier too thick, or too fmail for its Height. 1 here arc fome of them found twenty Diameters in Height, without either Diminution or Swelling. To dravj a Gothic Arch by the Interfedion of Right Lines. Firji, Draw the Bafe Line a b^ and divide i.t in the Middle at /, and fet up the Height of the Arch from / to ^ ; then draw the Lines a c and h d perpendicular to a ^, and equal to half the Height of the Arch /iB^ fame "Mag- n that in be, tremi- coni- to be _i^arths, ~ er'f. which refore are of ,/^:ferent neous 'oJy is Ti tlie irts of leBo- ler of lagni- ecifick than H heavy I Re- solute. lis the flireeiy iir, or. othing .'dium. Stone abfo - which hen it Aerial falls. Force ^fcend gclfe, t Me- an 'm~ cliii'd i? ffoizhnoi vLo3 /ni: .-!-)f^w v< H ^^y. A ; 2 j^ A ^ /" _B ^ =1 ^/.//.' .^sr. ^/./. D ^ G R G R by which any Body tends towards the Centre of the Earth. Relative Grafky is that where- with a Body dclctnds after ha- ving fpeiii part of its Weight in overcoming feme Reliftancc. Such is- that wherewith aBody defccnds along an iuclin'd Plane, where fome Part is employed in overcoming the Refiltance or Fridion of the Plane. Accelerate Gravity is the Force of Gravity^ coniidcred as grow- ing greater, the nearer it is to the attnifting Body or Point. Gravity or Weighty is the Hea- vinefs of Matter, and is the na- tural Inclination which is in hea- vy Bodies to move downwards when they are not fuftain'd or held up, and fall towards the been con- fidered in thefe Feints, all is con- founded by the Flues under it, v/hich convey the Heal from the Stoves. Befides G R G R Befides what is commonly called a Green- Houfe^ it has been curtornary to provide Glafs Cafes of itveral Kinds, and Stoves, for the Preiervacion of Plants brought front diftcrcnt Coun- tries. But an ingenious Author has found them to be fo many un- neccllary Espences ; and that a good Green -Houfe^ well con- trived, WiiH do all that is re- quired for the Welfare of any Pbnc 'n\ the Winter ; and that it may be fo ordered, as to flielter at one Time Oran,i;e - Trees, Plants from the Cape of Good Ilope^ I'^irgwia^ Cirolim, and in- deed fuch as grow within ten Degrees of the Line. 1'he fame Author fiys, that when he was firll acquainted with Aloes, Ifidiafi Figs, and fuch like Plants, he conlelles he thou|;;ht they could never have Heat enough, and that he de- llroy'd many by that too com- mon Noiion ; he could hardly venture them out of the Hot- Beds in the moft extreme Heats of Summer; and that in the Win- ter, they were half-roafted with fuhterraneous Fires he n.ade un- der the Glafs Cafes where they flood. A good Crcen-Houfe ought to be iKuated on t:)e dried Ground, lo he as fee from Lumps as poffible ; fubllantial Provih'on ought likewifc to be nr^de for Jtceping out the Cold, and yet upon Occafion to let in Air free- ly ; but chiefly to contrive that i\e Front of the Houfe be fo difpofed, that nothing may ob- (lru6t the Paflnge of the Sun's Ravs, in the VVinter, into the Houfc. Itis gieaerally allowed, that the South Afpeft is the bell for a Grecn-Hurtfc^ as it will m that Expofure receive the Sun for the greatelt Part of the Day ; but in cafe that cannot be had with Conveniency, the South -Weft Afpe6t is next to be coveted ; and it wtmld be pleafant, as well >j as beneficial to Plants, if the Confervatory was always join- ed lo the Dwelling-Houfe. Nothing can be more agree- able ill VVinter, than to have a View from a Parlour or Study through Ranges of Orange- Trees, and curious Plants of foreign Countries, bloflbming and bear- ing Fruit,* when the Gardens without Doors are, as it were, in a Siate of Death ; and to walk among thofe Curiolities of Na- ture, as in the molt temperate Climate, vvitiiout any Senfe of the Froft, or pinching Cold that reigns abroad; and befides, there is this Conveniency in joining the Confervatorv lo the Houfe, that in c )ld Wcatlier you may go into it, without letting in the cold Air, or blighting Winds from abioad. Thus much as to the Situa- tion : The next Thing to be confidercd is the Proportion of the Building, and that chiefly in Relation to the Height and Breadth of the Room; which a certain Author direds, that for the better Admiflion of the Sun's Rays to pifs all over the Houfe, the B'cadth of it be no more than the FI i^ht from the Floor to the Ceiling, which may be from ten to eighteen Feet. 'I'hat the Walls towards the North and theEalt, be of a good 'I'hickncfs, and the Front to- wards G R G R wards the South be all of Glaft, except a low Wall about a F'oot high from the Ground ; that there be no Piers of Brick-Work or Timber in the gla2,'d Part, for they caft more Shade into the Houfe, in Proportion to their Bignefs, than it can receive L'ght through the Glafs; where- as, every one who undcrilands exotick Plants will allow, that they fhould have all the Advan- tages of the Sun's Rays in Win- ter, that they poffibly can re- ceive : And for this End, he is of Opinion, that it would be proper, in the colder Parts of England^ to build the Front of a Grcea-Houfe xxx a Sweep, or in the Form of a Semicircle, which would then receive the Rays of the Sun from the Time of its Riling, till its Setting. That the Glafs in the Front, whether it be in Sathcs or Cafe- ments, be fo contrived, that it may either be made to Hide quite below or above the Frames, or to be taken away, as Occa- fion (hall oftl-r, to give Air to the Plants, which tor about a Fofcnight or three Weeks after they are fet into the Houfe, and as loiig before the Plants come abroadj fhould be quite open Night and Day, if the Frofts or biighcing Winds are not abroad. Some have pra6lifed, with good Succcfs, to lay the Win- dows of their Grecn-Hcnfes Ho- ping about ten Inches; but he is of Opinion, that they will do as well upright. Ht adviles, that the Door be in the Middle of rhe Front, and at leaft four Foot wide, to ad- mit large Plants; that it beglaz'd, to which ftroiig Shutters Ibould be added, at leaft art Inch thick, which in the Wii'uerTime fhould be fliut every Night, for fear of Froft; and alfo in extraordinary cold Weather, when violent* Winds blow right- ' agairift the Houfe, T hat for the better Security of the Plants from Cold, a Place for the laying up the Gardiner's Tools be built at the Green- Houfe^ and over it a Fruitery or Seed-Room, or in the Lieu of the latter, the Room may be fill- ed with dry Scraw. The beft Paveinent for nGreen- Houfe^ he fays, is that made with fquare Tiles, which quickly fucks up Wet, and never fweat, as Marble, or fuch Kinds of hard Stone ufuiilly do; and that for lining of the Walls, nothing is prefeirable to Dutch glaz'd Tiles, which are foon warmed with the Sun, and refl<;6i: a great Heat into the Houfe. That in the Difpofition of the Shelves in the Green- floufe^ one Third of the Floor be allowed for them to Hand upon, one Third from the firlt Shelf to the Windows, and as much from the hift Shelf to the Back of the Houfe; fo that a Perfon may walk round the Plants, which being placed in the middle Line of the Houfe, are fafe from the extreme Cold, which is general- ly nearer the Walls or Glafles. The Chimi;ty for warming the Air, he dirttls to be built between the W;;;dows and the tirft Shelf at one End of the Houfe, about a Foot above the Floor, which will rife after- wards, and fpread itfclf over the Whole. But G R G R But the ingenious Mr. Philip Milter has given us a more ac- curate Dciigu of aGrcen-HofifCj which lie defcribes as follows : As to the Length of theHoafe, he lays, ihac fliould be propor- tioned to the Number of Plants if is to contain, or the P'ancy of the Owner; but as to the Depth, that fliould never be more than fixteen Feet in the C'ear, and the Length of the Windows fhould be at lead equal to the Depth of the Houfe; and if they are ibme- thing longer, it will be Hill the better. Tliefe Windows fiiould be carried up quire to the Ceiling, that there may be no Room for dead Air in the upper Part of the Houfe, and they ought to come down within about ten Inches or a Foot of the Floor ; their Breadth fhotild be proportioned to the Length of the Houfe, "which in a fmall Green- Houfe may be four Feet broad, but in a large one they (liould be lix Feer. The Piers between thefe Win- dows (hould be as narrow as polTii^Ie they may be, to fupport the Building, tor which Reafon he chufes to have them either of Stone or folid Oak ; for it they are built with fine nibbed Brici\S, they are generally Co foft, that the Piers will require to be made thicker than can be allow'd, otherwifc the Building will be in danger of falling in a fliort 7^'nie, efpccially if any Rooms be built over the Green- Hot^fe ; which would be of great Ufc in keeping out the Froli in very hard VV inters. if the Piers arc made with Stone, he direds that they be twenty Inches broad in Front, and floped off backwards to a- bout ten Inches broad ; whereby the Riys of the Sun will not be taken off, or obftrudcd by the Corners of the Piers; which it would be, if they were fquare. And if the Piers are made of fo'idOak, eighteen Inches fquare he accounts (trong enough to fupport the Euildiug ; and alfo floped off, after the Manner be- fore dirc6kd as to thofe of Stone. A Tool-Houfe may alfo be erefted at the Back of theBuild- mg, which may alfo fcrve for nrany other Furpofes, and will alfo be extremely uftful, by pre- venting Froll from entering that Way; fo that the Wall between thefe need not be more than two Bricks in Thicknefs; whereas if it were quite expofed, behind it ought to be two Brick and a half, or three Bricks in Thick- nefs. And thus alfo, if you have a Mind to make ahandfome Build- ing, and to have a noble Room over th« Green- Hou[e^ you may make the Room to come over the Tool-Houfe, and carry up the Stair-Cafe in the Back, fo as not to be \Q.Q.Vi in the Green- Houfe : And by this Means you have a Room twenty or twenty- two Feet in Width, and of a proportionable Length. And under this Stair- Cafe there may be a private Door into the Creen-Hoiife^ at which rhe Gar- diner may enter in hard frofcy VVcather, when it will not be fafc to open any of the Glalfes in the Front. The Floor of the Grecn-Houfe may be laid with Marble, Stone, or G R G R or broad Tiles, according as the Owner pleafes, and mud be raifed two Feet above the Level of the Ground on which the Houfe is lituate, which will be fufficient, if the Soil be dry ; but if moid and fpringy, and there- by fubjeft to Damps, it will be necefTary to raile it at leaft three Feet above the Surface. He advifes alfo, to inake a Flue of about ten Inches in Width, and two Feet in Depth, under the Floor, about two Feet from the Front; which Flue is to be carried the whole Length of the Houfe, which may be re- turned along the back Part, and be carried up in proper Funnels adjoining to the Tool-FIoufe, by which the Smoak may pafs off. The Fire-PIace may be con- triv'd at one End of the Houfe, and the Door at which the Fuel is put in, as alfo the Afli-Grate, may be contrived to open into the Tool -Houfe; fo as to be quite hid from the Sight, and be in the dry; and the Fuel may be laid in the fame Place, and fo will always be at Hand for Ufe. He alfo advifes to have good ftrong Shutters to "the Win- dows in the Front of theGreefi- Houfe^ hung on Hinges to fold back, fo that they may fall back quite clofe to the Piers, fo as not to obftrudl the Rays of the Sun. Thefe Shutters may be an Inch thick, or a little more, made to join fo clofe, as to be able to keep out our common Frofts ; and when the Weather is fo cold as to endanger the freezing in the Houfe, it is but making a Fire in the Flue, and that will eff*;61:ually pacvcut it. The back Part of the Houfe Ihould be plailkred wich Mon:ir, and white- wafli'd ; or if lined with Wainfcot, fhould be paint- ed white, as Qiould the C.iijig, and alfo every Part wltniniiae the Houfe ; for White rtfl 61:s the Ravs of Light in a much greater Quantity, than any other Colour ; and is ot very great Service to Plants, efpecially in the Winter Seafon, when the Houfe is pretty much closed, fo that but a fmall Share of Light is admitted through the Win- dows : For he fays, he has ob- ferved, that at fuch Times, where a Green Houfe has been painted black, or any dark Co- lour, the Plants have calf moll of their Leaves. He adds, that to avoid the In- convenience •I'hich attends the placing Plants of very diftl-renc Natures in the fame Houfe, ic will be very proper to have two Wings added to the m^mGreen- Houfe^ which will greatly add to the Beauty of the Building, and alfo colled a greater Share of Heat. Fhe Green- Houfe^ according to his Plan, is placed exadtly fronting the South, and one of the Wings faces the South-Eafl, and the other the South- Weft; fo that from the Time of the Sun's firft Appearance upon any Part of the Building, until it goes off at Night, it is conftantly reflect- ed from one Part to the other, and the cold Winds are alfo kept off from the Front of the main Creen-Houfe hereby. And in the Area of this Place you may fo coiutivc, as to place man y w G R G R many of the moft tender exotick Plants, which will bear to be ex- pofed in the Summer Seafon ; and in the Spring, before the Wea:her will permit you to let out the Plants, the Beds and Bor- ders of this Area miy be full of if\ncmonies. Ranunculus's, early Tulips, klfc. In the Centre of this Area may be contrived a fmall Bafon for Warer, which will be very convenient for water!. ig Plants, and \\'\{\ alio very much add to to the Bejiu of the Place ; be- lidcs, the Water being thus li- luated, will be fofccned by the Heat which will be rcflefted from the Gb.flcs upon it, where- by it will be render'd much bet- ter than raw cold Water for ten- der Plants. The two Wings of the Build- ing fhould be fo coritrivcd, as to be fit for placing nants of diffe- rent Degrees of Hardnefs, which mull be etf;;6ted by the Situation and Extent of the Fire- Place, and the Manner of conducting the Flues. For which, fee the Articles Stoves. I'he Wing facing the South- EaO: fhould always be preferred tor the warnielt Stove^ its Situa- tion being fuch, as that the Sun, upon his tirft Appearance in the Morning, lliincs dire(^^'-^ upon the Glalfes; which is ui great Service in wanning the Air of the Houfe, and adding Life to the Plants, after having been flmt up during the long Nights in the Winter SeaU'U. Thefe Wings may be allowM fixty Feet in Length, and may be divide'd in the Middle by Par- titions ofGlafs,wi:hGlafs Doors to pals from one to the oihcr. And the Fire-Place may be fo ordered as to warm both Divi- lions, by placing an Iron Regu- lator in the Flue, fo thut the Smoak may pafs through the F^lues of which Part focver you pleafe. By this Contrivance you may keep fiich Plants as require the fame Degree or Heat in one Part of ihe HouL', and thofe which will thrive in a much lefs Warmth in the other Part ; but this will be more fully explain- ed under the Article Stove. The other Wing of die Houfe facing the South-Weft, may al- fo be divided in the fame Man- ner, and Flues carried through both Parts, which may be ufed accort'ing to the Seafons, or the particular Sorts of Plants which are placed therein. So that' by this Difpofition here will be four Divifions in the Wings, each of which may be kept up to a different Degree of Heat; which, together with the Green-Hotife^ will be fufficient to entertain Plants from all the feveral Countries of the World. And without having thefe fe- veral Degrees of Warmth, it will be impofT.ble to preferve the various Kinds of Plants from the feveral Parts of Africa and Ame- rica^ which are every Year intro- duced into the Engltjh Gardens. For when Plants frc^m very different Climates are placed in the fame Green- Hvufe^ fome pe- rifli for want of Heat, while others are dcftroy'd by having too much of it; and this is often the Cafe in fuch Green- Houfes^ where there are large Colledions of Plants. 1 G R G R 7i GRIND Colours in Oil : LfCt the Grinding-Sfone be placed about the Height of your Mid- dle, let it ftand firm and fall, ib that it joggle not up and down ; then take a fmall Quantity of thcJ Colour you intend to grind^ (two Spoonfuls is enough,) for the lefs Is ground at a I'ime, the ea- fier, and finer, will the Colour be ground. Lay thefe two Spoonfuls of the Colour in the Middle of the Stone, and put a little Linfeed Oil to it, (but take Care not to put too much at firft ;) then mix it together a little with thcMul- ier, and turn the Muller five or fix Times about; and if you find there be notOil enough, put a little more, ^nd grind it till it come to the Conliftence of an Ointment, or appears free from any vSort of Lumps, and fmooth as the moft curious Sort of Butter ; for it grinds much better and fooner when it is ftiffifh, than when it is fo thin as to run about the Stone ; and in grinding^ you mulf often briag the Colour that has fpread together into the Middle of the Stone with a Piece of Laathora Irlorn. And in Grinding hold your Mailer down as hard as you caivi and alfo move it with fuch -u' Slight, as to gather the Colour under it; and that no Knots or Grittinefs remains, and that it is become as fine as Butter itfelf. When it is ground enough, cleanfe It off the Scone with the Horn into a Gallipot cr Piin, and lay on more CQiqiir, and pro- ceed as before, till you have ground what Quantity you want. Vol. I. li: you grind a confiderable Quantity, to be ufed not till fome Time after, put it inro Bladders, tie it up clofe, and hang it up. Thofe who care not for the Trouble to grind the Colours, may have all Mrancr of Colours leady ground at Colour Shops. How to order Colours for workings after they have keen ground. When you ufe Colours, you muft add more Oil to them, but not fo much as to make them ib thin, that they will let the Ground be feen through them, or run a- bout ; and if your Colour be as ^itF as it ought to be, once do- ing will be more than twice do- ing with thin Colour. Painters make ufe of a com- mon Fraud and Deceit, when they agree to do Work by the Yard at a common Price, to be coloured three Times over. In painting with fucli thin Colours that at three Times doing over, it is not fo fublfantial as. one Time would be, if the Colour had a thick and fubllantial Body. Three Times colouring with fubltantiil and well-bodied Co- lour, will hit ten Times as long as that which has been fo flightly coloured, 1 he Priming Colour indeed ought to be very thin, that it may have Oil enough to peiie- trate into the Wood, which tends much to its Prefervation ; but the fecond muft be thicker than the firft. Ff Z« G R G R To find the An^le of a regular \ Ftrft^ Draw the LirH. of P, ( - jifftion AB, alio che JVljtre Lmv; I1>B; then xvill AD he at Right Angles with A B-; then from A Alike the Quadrant C B, and draw the Line AC, which will be at Right Angles with AB; divide A (3 any (iow,- either into ^ual or un.cqualg.ai'ts, and from thofe J>T"^iiop«^raifc Perpendi- culars fioiTf' tacrine AB to touch -th'e Arp^r^C :\j^iib co.;- tinue ihefe "Kight^Jiirnes to cut the Miter LiiTp'-ED, aj^you fee bv the dotted' Lines-, which will divide 'the Line'DB into" the fame Nunj0fr of Par-f^', and, in Propotfi6"n wi.hi^'e Line AB ; then from tbolc' Diviiions made by the dotted Lines on the Line D B, rirtfe Perpendiculars at Plea- lure, and take the Line AC in vour CompalTes, and let it up thcfirft Line, as from D to E ; then take the Line i, i, on the Quadrant, and fet it up the Line I, I ; alfo from 2,2, to 2,2, from 3.3^ ^^ 3. 3. and from 44, to 4, 4, aiid fo on, till the Points are laid down ; into Avhich Points -yoa mull -fttike Nails ; then 6end a thin Lath round them, and by its Edge ftrike the Arch for the Groin or Mttre Bracket N.B. This is work'd in the fame Manner, let the given ArchBC be what it will, or let the Line BD be true Mitre, or irregular. ^0 -riak: Centrds for regular or \ irregular Groins, fo that the I -Mitres pall ie true. This Figure reprefcnts an ir- regular Groin^ bccaafe a b \s Iv'ii!dcr than ac Let the Arch cfd be given, and let tke-Curve be what you will. What muft be the Curve of nkc^ fo that when the two diffe- rent Centres are fet in their Piaccs, their Mitre or Angle fnall G R G R /hall be perpendicular over the Angle Line ad"^. Or if the Groin be of Wood for the Ceiling of a Room, then you mufl: find the Arch d h a^ which muft be your Hip to fallen the other Ribs to. Firjl^ Defcribe the Figure abcd^ and draw the Line a d; then ftrike the Arch efd from the Point «-, and divide the Line cd any how ; from which raife Perpendiculars to touch the Arch £fd^ and continue thole Per- pendiculars to the Line ad, as by the dotted Lines which divides the Line ad into the fame Num- ber of Parts, and in Proportion to cd ; then from thufe Divilions created by the dotted Lines, raife Perpendiculars at Pleafure from the Line ad: Having done this, lay your fquare or patallel Rul<;r at Right Angles with the Line aci and from the Divifions on the Line ad, draw Perpendicu- lars from the Line ac of a Length at Pleafure, which -will divide the Line ac into the fame Number of Parts, and in Pro- portion with thofe on the Lines cd and ad; then you muft take the Line i, i, on the Arch cfd, and fet it on the firft Perpendi- culars on the Lines ad and ac, as from i to i ; and fo that eve- ry Line marked with the fame Figures are of an equal Length, as I, I, to I, I, =3 2, 2, to 2, 2, 3,3 = 3i3. 4,4=4,4, alfo ^ /:» and tk to e f ; and fo of the other Lines, as they follow. And when the Points 1,2,3,4, and all the reft are found by the foregoing Method , you m.uft ftrike a Nail in every one of t^icm, and^ bending a thin Lath round them, draw the Arches aJic and abd, and thofe yod find will anfwer the Purpofe de- figned. See the Plate. Houf to prepare the Boardw^ for the Covering of the Centyes of any Kind oj Groins, and to cut them to their right LcKgths and Bevels, before the Centres are fet in their \Poftt:on. Let ABCD reprcfentthePian of an irregular Groin ; draw the Curves of the two different Cen- tiesBFC and CDG, by the Rule laid down in the foregoing Fi- gure for making of Centres of Groins, &c. in the preceding Fi- gure. Then continue the Line BC both Ways from B to I and from G to K, fo that I K be equal in Length to the Girt of the Curve BFC; and draw IH and KH, which are each equal in Length to the Girt of the Curves at the groining or mitering of tl'.c two different Centres ; and draw the Lines lO and KP perpendicular to IK. Then will thePlaneHlOPK be equal in Quantity to the Back of the Centre BFC. TofindthcBevelsoftheBoard?, lay them all down together", juft as many as will fit between the Lines lO and CP, letiing their Ends reach over the Lines IH and HK. Then ftrike a Line on their Ends, as from I to H, and from H to K, which is the true Bevel of every Board that covers the Centre BFC; and for thofe on tiie Centre C D G, do in the fame M inner. As flu Example; : F f i Produce G R Produce C D, from C to L, and froniD toM, fo that LM is equal in Lci'gtii to the Girt of the CarveCGD; and draw the Lines LH tind MH; alfo the Lines LQ and MR perpendicular to LM. Tnen will the Plane HLQRM be equal in Quantity with the Bacit of the Centre CGD, and confcqucntly the covering Boards G R mufl be equal ; therefore, as on th« Plane H L O P K, lay the Boards on rhe Plane HLQRM, letting their Ends reach over the Lines L H and HM, on. which ftrikea Line from L to H, and from M to H, which will give the true Bevels for the Boards on the Centre CDG; which was to be done. See the Figure. GROTESQUE^Awild, GROTESK > whim- GROTESCO 3ficalFi- gure of a Painter or Carver, con- taining fomething whimfical, ri- diculous, extravagant, and even »}onfttous in it. The Word is alfo particularly apply'd to a Work or Compofi- tion in 6>culpture or Painting in the Grotefque Manner or Tafte ; confining either of Things that are merely imaginary, and have no Exifleace in Nature, or of Things G R G R Things turned and diftorted out of the Way of Nature, fo as to raifc Surprife and Ridicule. Grotesk Work is the fame with what is fometimes called Antique. The Name is faid to have taken its Rife hence, that Figures of this Kind were in antient Times much ufcd in adorning the Grot- to's, wherein the Tombs of emi- nent Perfons or Families were inclofed ; fuch as that of Ovul., whofe Grotto was difcovered near Rome not fixty Years fince. GROTESQUES? are ufed GROTESKS S particu- larly to fignify thofe fanciful Or- naments of Animals, interfpers'd among Foliages, Fruit, ^c. as thofe painted by Raphael Urb'm in the Vatican., and thofe carved by Michael Angela.^ in the Ceil- ings of the Portico of the Ca- pitol. Thefe Kind of Compartiments are called ^by Vitriivim Harpa- genituli. GROTTO ? is a large, deep GROTTAS Cavern or Den in a Mountain or Rock. Grotto is alfo ufed for a fmall artificial Edifice made in a Gar- den, in Imitation of a natural Grotto. The Outfides of thefe Grottoes areufually adorned withRultick Architedure, and their Inlide Shell-Work; and alfo furniflicd with various Jet d'Eaux^ or Fountains, ^c. GROUND to build on. See Foundation. GROUND, in Painting, is ufed to lignify the Surface upon which the Figures and other Ob- jcds are raifed and repxefented. The Ground is properly under- ftood of fuch Parts of the Piece, as have nothing painted on them; but retain the original Colours upon which the other Colours are applied to make the Repre- fentations. A Building is faid to ferve as a Ground to a Figure, when the Figure is painted on the Build- ing. GROUND GUTS. See Alder. GROUNDSELL, or PLATE. See Sell. GROUND- PLAT, or PLOT, a Piece of Ground on which a Building is to be ered- ed. GROVE ? in Joinery, I'fc GROOVE 5 aTerm ufed to fignify the Channel that is made by their .Plough in the Edge of a Moulding, or Stile, or Rail, b'r. to put their Pan nels in, in Wainf- cotting. GROUP, in Painting, Sculp- ture, y«-. is aTerm ufed to ex- prefs the Afifemblage or Knot of two or more Figures of Men, Beafts, Trees, Fruits, or the like, which have fome apparent Re- lation to each other. A Group of Columns., in Archi- tedure, is ufed when we fpeak of three or four Columns joined together on the fame Pedeftal ; but when there are but two, the Word Couple is ufed, and not a Group of Columns. GRY, a Meafure containing one Tenth of a Line. A Line is one Tenth of a Digit, and a Digit one Tenth of a Foot, and a PhilofophicalFoot one T bird' of a Pendul u m, w hofe Ff 5 Diidrcmes G U t)iidroiTies or Vibrations, in the Latitude of forty- five Degrees, are each equal to one Second of Time, or one Sixtieth of a Mi- nute. GUEULE, in Architedure. Sec GULA. GULE -> in Archiceaure, GULA C a wavy Mcm- ■ GOLA 3 ber, the Contour of which rcitmbles the Letter Sj which the Greeks call Cyma- fium^ q. d. a liule Wave; and cur Architeds an Ogee. This Member is of two Kinds : Rcdii and Inverfa. The fird and principal has its Civitics or Hollows above, and Cor,vexities below. This al- ways makes the Top of the Co- rona of the Cornice, jetting over the Drip of the Cornice, like a Wave ready to fall. It is called Gula Rerta^ and by the French^ Douc'im. \x. is fomctimes called abfo- luccly the Entablature^ as being tiie firft or uppermcft Member of ir. The fecond, or Gula Invcrfa^ is exaftly the Rcverfe of the former, the Cavity or ii..riow- ncft of it being at the Bottom; i<^ that with refpcdi to the for- mer. It appears inverted. This is uCed in the Architrave, and Ibmccimes in the Cornice, along with the former, only feparated by a Rcglet. Some derive the Term G:ila from the Refemblnnce thefc Members bear to the Gula^ or Throat of a Man : Others from Giteles^ aTeim in Heraldry, as luppniinv^ the M 'ulding iorm'd frt m thcaniiei'.i Manner uf wear- G U ing their Garments, which con- lilkd of Slips, or Swathes, alter- nately, Furr and Stuff' of various Colours ; the Intervals between which were Gules^ or Guales. GUNTER's LINE.is a Line of Numbers which is upon the ordinary Two-Feet, or Eighteen- Inch Rules, commonly ufed by Carpenters, Joiners, ^c. This Line being the Scale re- commended to in thofe Opera- tions in this Book, that are wrought with Scale and Com- pafll'S, I (hall give ibme Direc- tions for the Ufe of it, as fol- lows : If the Number you would find on the Line, confifts only of Unites, then the Figures upon the Line reprefent the Number fought. Thus if the Number be 1,2,3, ^c. then 1,2,3, b't-. "P" on the Line,reprefents the Num- ber fought. But if the Number confiffs of two Figures, that is, of Units and Tens, then the Fi- gure upon the Rule (lands for Tens, and the larger Divi(ions ftand for Units: Thus, if 34 were to be found upon the Line, the Figure 3 upon the Line is 30, and 4, of thelargeDivifions, (count- ed forward,) is the Point repre- fenting 34 ; and if 340 were to be found, it will be at the fame Point upon the Line; and if 304 were to be found, then the 3 up- on the Line is 3C0, and 4, of the fmaller Divilions, (counted forward,) is the Point rcprefent- ing 304. If the Number con- lills of four Places, or Thou- lands, then the Figure upon the Line (lands for Thoufands, and and the larger Divilions are Hun- dreds, G U G U dreds, the leffer Divifions are Tens, and the Tenth Parts of thofe lefTer Divifions are Units. Thus, if 2735* were to be found, then the 2 is 2000 ; and the 7 larger Divifions (counted forward) is 700 more; and :^ of the leflcr Divilions is 30 more ; and half of one of the IcfTcr Di- vifions is 5" more, which is the Point reprefenting 2735'. You muft remember, that between each Figure upon the Line there are 10 Parts, which are called the larger Divifions; and each of thofe larger Divifions are fubdi- vided (or fuppofed fo to be) in - to 10 other Parts, which are called the fmaller Divifions ; and each of thofe Pans fuppofed to be fubdivided again into 10 other Parts ^ ^c. You muft alfo re- member, that if one in the Mid- dle of the Line, (lands only for I, then I at the upper End will be 10, and i at the lower End will only be /^ ; but if i at the lower End fignifies i, then I in the Middleftandsfor 10, and I at the upper End is 100, t'^c. There is one Thing more which I would have my Reader to underftand ; and that is, how to find all fuch proportional Numbers made ufe of in the Proportions about a Circle, and of a Cylinder, and in other Pla- ces; which Thing may be of good Ufe, to know how to correal a Number which may happen to be falfe printed, or to enlarge any Number to more decimal Places, for more Exaclncft; for though it is mentioned what fuch Num- bers are, yet it has not been flievvn how to find them; which a Learner may be a liule at a Nonplus to do; though they are eafily found by the Rules there laid down. I fliall therefore give two or three Examples, in tliis Place, of finding fuch N^mibers, which may enable my Reader to find out the reft, And, firft, let it be required to find the Area of a Circle, whofe Diameter is an Unit. By the Proportion o^ Van Cu^ len^ if the Diameter be i, the Circumference will be 3. 1415-926, (^c. whereof 3.1416 is fulHcicn!: in moft Cafes. Then the Rule teaches to multiply half the Cir- cumference by half rhe Diame- ter, and the Produdl i<^ the Area, that is, multiply 1,5-708 by .5-' {viz. half 3.1416 by half i) and the Product is' .785-4, which is the Area of the Circle vvhofe Diameter is i. Again, if the Area be required, when the Circumference is 1, firft find what the Diameter will be, thus, as 3.7416 : i : : fo is i to .318309, which is the Diame- ter when the Circumference is one. Then multiply half .318309 by half i, that is .15-9 15-4 by .5-, and the Prod ud is .0795-77, which is the Area of a Circle whofc Cir- cumference is I. If the Area be given to find the Side of the Square equal, you need but extrad the fquareRoot of the Area given, and it is done. So the fquare Root of .785-3 is .8*3.62, which is the Side of a Square equal when the Diameter is 1. And if you extracl the fquare Root of .0795-77, it will be .2821, which is the ^'\<^iQ. of the Square equal to the Circle whofc Circumference isi. Ff4 If G U G U If the Side of a Square within a Circle be required, if youfquare the Semidiameter, and double that Square, and out of that Sum cxtradl the Iquare Pvoot, that fhall be the Side of the Square v»*hich may be infcribed in that Circle; fo if the Diameter of the Circle be i, then the Half is .5, whic'i 0.]uared, is .25", and this doubled, is ,5-, whofe fquarcRoot is .7071, the Side of the Square iiifcrio'd. Again, if the Diameter of a Globe be i, to find the Solidity. it is demonIlrated,that the Globe is 4 of a Cylinder of the fame Diameter and Altitude. Thus, if the Cylinder's Diameter be i,and its Altitude or Length be alio i, find the Soh'dity thereof, and take J of it, and that will be the So- lidity of the Globe required . Now if the Diameter be i, the Area of the Circle, or Bafc of the Cylinder, is .785'4, (as is above fliewn ;) which multi- ply'd by I, the Altitude of the Cylinder, and the Product is aifo .785-4, the Solidity of the Cylin- der; J whereof is .5'2.36, which is the Solidity of the Globe, whofe Diameter is i. GUTTiE,in Architeaure,are Ornaments in the Form of little Cones, ufcd in the Platfond of the Dqric Cornice, or on the Ar- chitrave underneath theTrigiyphs, reprefentiiig a fort of Drops or Bells, and ufually fi.v in Num- ber. GUTTERS, in Archite^ure, arc a kind of Valleys in the Roofs of Buildings, ferving to receive and dmii off the Raia Waters. Thefe Gutters are of two Kinds in refpedtto their Pofition; for they arc cither fuch as come fomething near a Parallelifm with the Horizon, or fuch as in- cline towards a vertical Pofition to the Horizon. 1 he firft Kind ol Gutters may be called Parallel Gutters^ and may be diliinguifh'd into three Sorts, which are covered with Lead : For, F'trfl^ Either it is a Gutter be- tween two Roofs, which (land parallel to each other, being made upon the Feet of the Ratters of two Roofs, which meet toge- ther. Or, Secondly^ A Gutter^ where a Building has a Cantaliver orMo- dillion Cornice, which projeds one Foot and a half, or two Feet (according to theDefign of the Building) beyond the Walls; then the Roof is fet with the Feet of the R.^fters no farther out than the Wall, but rather within it ; fo that the Joilts of the upper Floor lie out beyond the Walls, and alfo beyond the Feet of the Rafters, which is yet cover'd with Lead. The third Sort of thefe ^^r^/- lel Gutters are in flat Roofs, which are ufually called Plat- forms ; where arc alfo Gutters for the Water that run from the Platform to defcend to, which is from thence convey'd otf from the Building, either by Spouts or Pipes. Sectnclly^ Vert'ical Gutters are fuch as are made by two Roofs meeting at Right Angles one to another, or (which is the fame Thing) ina.d<; by ihc End of one PvCOf GU Roof joining to the Side of another Js for Example: If a Build- ing be in the Form of a Roman L, it is then common to have one Gutter on the Inlide of the L; but if the Building be in the Form of a T, it has two Gtit- iers ; but if in the Form of an H, it has four. Thefe Gutters alfo are of two Sorts, viz. either of Lead or Tile: All which fhall be treated of in Order. Of the Laying of Parallel Lead Gutters. In fpeaking to this Head, I fliall firft give a necelFary Cau- tion, which is, z'iz. firft to take care that the Gutter-Boards^ ^c. lie not too near parallel with the Horizon ; but in fuch a Pofition, that there maybeagood Current, (as the Workmen phrafe it,) for if it belaid too near a Level, the Water will be very fubjedi to fland in Plaflies, if the Gutter chances to (tick a little in the Middle, ISc. which fome Gut- ters are apt to do: But this is according as they are pofited in the Building. Some Gutters have a Layer of Sand for the Lead to lie upon ; but th?re are two Reafons that may render this Method not ap- proveable. Firfi^ Becaufe fome Sorts of Sand does very much corrode and decay the Timber that lies near it. Secondly., That when a Gutter is laid on Sand, but a very little fquatting, viz. by jumping upon G IJ ft with the Heels of one's Shoes will make Dents in it, and in thole Dents the Water will fland • and this will be a Means cf de- caying the Lead the fooner. In laying of Leads for Gutters upon Boards^ 'tis common for Plumbers, to folder them, when they are fo long, that a Sheet of Lead will not reach. To do this, they ufually cut a Channel crofs the Gutter-Boards at the End of the Sheet where theSol- dering is to be, and to beat down the Ends of both the Sheets (that are to meet there) into the Chan- nel ; which, when it is done, there will remain a little Cavity, which is filled up by the Solder level with the rell, when it has been foldered. The Lead which is ufually laid in Gutters is that which weighs about eight or nine Pound to the Foot. See Lead. Of Vertical Gutters. Thefe Gutters are made ei- ther of Lead, or Tile. As to thofe made with Lead, I ftall forbear faying any Thing, be- caufe they are almoft the fame in Etfecft as the Parallel ones. But, that unlefs the Builder will be at the Charge, they need net be altogether fo thick for thefe Vertical ones, as for the Parallel ones: For thefe Vertical ones will laft as long, if laid with Lead of about fix or feven Pound to the Foot, as Parallel ones with Lead of eight, nine, or ten Pound to the Foot. Gutters laid with Tiles., arc al- fo of two Kinds : Thofc made of G U G U of Concave or GuUer-TtUs^ and ^Pla'in Tiles. Of which I (hall omit fpcakiiig here, but recom- mend to the Ariicie Gutter- Tiles. Plain T'ile-G utters are alfo di- ftinguifli'd into two Sorts, viz. I. Plaiit Tile-Gutters., (properly fi) called.) And, II. Point-G utters. Qiho\.\\ which I fliall treat in their Order. Firft, Of Plain Tile-Gutters, (properly fo called.) In thefe Plai>t Tile-Gutters, there is a Gutter-Board laid, which raifes them from pointing to «a Angle. And in laying on the Tiles, the Workman begins at one Side of the Gutter^ and fo works acrofs, as if it were plain Work, and then brings the next Row of Tiles back again; fo that he works forth and back, or to and fro, from Right to Left. So that Gutters which are laid after this Manner, are not angular, but of a kind of di- florted car\'ilineal Form ; by which Means they are not fo fabje£l: to be furr'd up with the Mortar which wafhes out of the adjacent Tiles. II. Of Three-Point Gutters. Middle of the Gutter ; and then they lay another on the other Part of the Roof, with its Corner juft in the Middle of ihe;C«««r, alfo that the Corner ofthefecondTile is contingent with the firit ; and then Jay another Tile in the Gutter., with its Corner, as it were, betwixt the other two, and to them. When they have done thus, they proceed in the Work, and lay a Tile on each Part of the Roof, as before, and ano- ther betwixt them in the Gutter., proceeding in their Work in this Manner, till they have finifh'd the Gutter. And this is what is called a Three-Point Gutter : For three Points, or Angles of Tiles, always cometogether,w.^. one Angle of three dillind Rules, which makes it very uniform and handfome. Here you are to take notice, that only three Inches fquare of the middle Tile is vilible (if the Gage be feven Inches,) the reft of that Tile being covered with the next Row of Tiles above it. But noiwithftanding thefe C^/f- ters are very handfome, and if well done, fecurealfo; yet if they let the Water into theHoufe (by reafon of fome Stoppage, or broken Tile in the Gutter.,) they are very iroublefome to mend. Thefe are the fecond Sort of Of MeafuringG.\in&i% orYaWtys. Gutters., which arc hiid with plain Tiles : In laying of which they begin and lay one Tile on one Part of the Roof, (it is no Mat- ter which Part firll) and lav one Corner of the Tile juft in the There are ufually different Cufioms in different Parts of the Kingdom, as to the meafuring of Glitters or Valleys in liling: For ill fome Places, they but feldom, \y G U G U feldom, If ever, allow any Thing for the Gutters ; but include them in the reft of the Roof at Flat and Half. And fomc fay, at London^ they very feldom meafure the G'^^er/, but only as they are Part of the Roof; fo they are included in the Flat and Half-Meafure. Some Workmen 2xTunhyidge- IVells never demand any other, but only as it is included in the Plain Meafure; which is an Area found by Multiplication of twice the Length of the Rafters by the Length of the Building; or, which is the f^ime Thing (when it is three quarters pitch,) the Flat and Flalf-Flat. In laying oi Gutters vf\th con- cave Tiles, the Workmen in fome Pars of St/JJ'ex and Kent^ have brought up a Cuftom of be- ing allowed fo many Feet more than the Plain Mealure, as there are G utter -T'iles^ ("and alfo inclu- ding Corner-TUes^ Ridge-Tiles^ and Dormav-Ti/es.) in the whole Roof. At fome other Places, they claim fo many Feet more to be added to the Plain Meafure, as the Gutters (and alfo Corners) are in Length, including Gut- ters at the Sides of Dormans and Lutherns, it there be any Dor- man-Tiles ufed. In fome Places, the Work- men inlift upon a Cuftom of ha- ving double Meafure allowed for Plain-Tile (efpecially, Three- Poi'fit) Gutters^ e. g. if there were but one Gutter in a Roof, and this Gutter fifteen Feet long, then their Cuftom is to have thir- ty Feet more than the Area of the Roof amounts to ; and this Allowance fome Workmen claim in both Sorts of Gutters VJitb Plain Tiles. Either ot'thefe Plain-Tile Gutters are cheaper to the Mafter-Buil- der, than Concave ones; becaufe Plain Tiles are cheaper than Gutter-Tiles^ they being in many Places not above one fourth Part of the Price. And befides, if the Workmen be allow'd lo many Feet more than the Area of the Roof, as there are Gutter-Tiles that will be one half as much more as the Double Meafure ; for \i it be gaged fo flight as eight Inches, then in a Gutter of fif- teen Feet long, there would be forty-five Tiles, which will be reckon'd forty- five Feet; where- as at Double Meafure, it amount- ed but to thirty Feet. There is another Way of computing Double Mealure ; for the Account of which, I fliall refer you to the Article Sla- ting. GUTTERING, in Carpen- try, is ufually done bv the Lineal Foot, which is by fome valued at London^ for Materials and Workmanftiip, at i.f. GUTTER-TILES are whilft they are flat and plain, (be- fore they are bent fit for theUfe they are intended,) feemingly at a Diftance, a kind of Triangle, with one convex Side. But al- though they lecm to be fo at a Diftance, they are not in Reality fo ; for they are of a quadran- gular Form, confifting of two ftreight Sides, of about ten, or ten Inches and a half long, (for G U (for fo much they onght to be,) and of two circular Sides, the one convex, the other concave ; the convex Side is about four- teen Inches, and the concave one about two Inches. This is their Form as to their Edges or Sides. 1 thall next defcribe the Form of them, in rcfpea of the Fluue ; at the h'ttle End they are bent circular, and fo likewife at the convex great End, at firll like a Corner rile ; but then they bend the Corners of the great End back again ; fa that if a Per- fon look againli the Edge of the broad End, it confifts of a cir- cular Line betwixt two ftrcight ones, like the upper Part of the Chaniftcr of the Sign Libra :^ : This, you muft underfrand, is when you hold the concave Side of the Tile downwards. Thefe Tiles are laid with their broad Ends and hollow Sides up- wards. yfj to the IVe'ight of GM\.tcX'T\\Q%. Thefe '/"//(T/, whofeDimenfions were lo Inches on the freight Edges, 14 Inches on the great convex Edge, when prefs'd down flir, as they were in the Mould, and two Inches at the concave Edge, and about J Inch thick ; 100 of them weigh about 321 or 322 Pounds, and conftqucntly loco would weigh about 3210 or 3220 W- which is near 29 C. Wei,-;ht, and confcqucntly 6S2 would be a Ton Weight. As p^^ibeirJ^rice. ,,,- ...,.\ •^ Ifeft^ .ti> o .:i 139 i VJ Mr. Leyboum favs,, that they, arc iuld at Lofuim at lU ^ oi% H A 2 d. per Tikj or between 10 and ifs. per 100. In fome Places their conftanc Price is id. ^ per Piece, or 12/. per 100. H A ■LTAIR, with Plaifterers, is •*--■■ Bullocks //^/V, &c. which is ufcd in white Mortar ; a cer- tain Quantity of which is put to a certain Quantity of Lime. See Lime and Mortar. yh t9 the Price : This varies, according to the Plenty or Scar- city of it in London. In fome Places in Kent it has been fold for feven Pence per Bufhel j and in Sujfex for ten Pence and twelve Pence ; fo that a Horfc-Load, which is fix- ty Budiels, may be from thirty Shillings to three Pounds, more or lefs. HALF-ROUND. See Ca- pital. HALL, in Archite£ture, is a large Room at the Entrance of a fine Houfe, Palace, or the like. Vitrwviiii mentions three Sorts of Halls : The Tetraftylc^ which has four Columns, fupporting the Plafond or Ceiling ; the Corin- thian^ which has Columns all around let into the Wall, and is vaulted over ; and the E^yptian^ which had a Penjlyle of infola- ted C'jfinthian Columns, bear- ing a 1 ccond Order with a Ceil- Tji-Xfee Hall is properly the firft qfid-finelt Partition or Member of an Apartment ; and in the Houfes H A Jrx A Houfes of Minifters of State, publick Magiftrates, zs'c. is that wherein they difpatch Bufiiiefs, and give Audience. In very magnificent Buildings, where the Hall is larger and loftier than ordinary, and placed in the Middle of the Houfe, it is called a Saloon. Of their U^imenfions. A certain woitdiFrench Archi- te£t direds, that the Length of a Hall be at leaft twice and a quarter its Breadth, and that in great Buildings you may allow it three Times the Breadth ; which laft Length, he fays, will be the moft beautiful and conve- nieMt, As to the Height of HalU^ it may be two Thirds of the Breadth, or fixteen or eighteen . Feet in noble Buildings. In large and ftately Buildings, the //<«///, and other Rooms of the firfl Story, may be arched; by which Means they will be rendered much handforaer, and lefs fubjeft to Fire. The Height is to be found by dividing the Breadth of the Hall into fix Parts, and five of thofe fliall limit the Height of the Room, from the Floor to the under Side of the Key of the Arch. HALLS and Antichambers, and other Rooms of the firfl- Story that are arched, which will be much more handfome, and lefs fubjcft to Fire ; their Height may be adjufted by dividing the Breadth into fix Parts, and taking five of them for the Height from the Floor to the Superficies, un- to the Bottom of the Key of the Arch. As for Example : Let the Fi- gure be twenty -four Feet in Breadth, more or lefs, and ba divided into fix equal Parts ; iake five of them, which will be twenty Feet in Height from the Floor unto the Bottf-m of the Key of the Arch. SeetheFigure. O. Bi'Jiffi'ra L H is 1 !Z ^ 4 S6~ And if you would have ft higher, you muft divide the faid Breadth into eight Parts, and take feven of them for the Height, which will make twenty -one Feet, And if you divide the fame Breadth into twelve Parts, take eleven of them, which will make theHeighl twenty-two Feet from the Floor to the Bottom of the Key of the Arch. The Chambers of the fecond Story muft be a fixth Part lefs in Height, than the Chambers be- low. As if the firfl; Story be twenty Feet in Height, divide the twen- ty Feet into fix equal Parts, and take five of them, which will make the fecond Story fixteen Feet H E H E Feet eight Inches from the Foor to the Joift. Again, if the firft Story be twenty oue Feet in Height, di- vide the twenty- one Feet into 111' equal Parts; takelive of them, and they will make the fecond Story leventecn Feet fix Inches from the Height of the Floor to the Joid. . If tiie firil Story be twenty- two Feet in Height, divide the twenty two Feet into fix equal Parts, and take five of them, which will make the fecond ei^hreen Feet four Inches in Hcighi. H\MMER HARDENING is mo(t!y ufed on Iron and Steel Piares for Saws, ^c. To HANG OVER. See to Batter. HANSE. See Arches. HKAD, in Architecture, ^c. h an Oru.iment of carved Work or Sculpture, frequently fer- ving as the Key of an Arch, or Plat- Bind on other Occafions. Thefe fort of Heads ufually reprefent fome of the Heathen Divinities, Virtues, Seafons, Ages; with their Attributes, as a Fhunderbolt for 'Jupiter^ a Diadem lor Ja^o]^ a Trident for Neptune^ a Crown of Ears of Corn for Ceres ^ a Heimet for Mars^ a Caduceus for Mercury^ The Heads of Beafts are alfo ufed in Places fuitable , as an I-iorfe's //(['di^ for an Equerry, a Deer's or Boar's for a Park or Foreft, a Dog'.s for a Kennel, a Bullock's or Sheep's for a Sham- bles or Market-Houfe. In the Metopes and Friezes,and otherPartsofcertain>4y!/;/i^.7cZ)or/V Temples, we fee ReprefeHtaiions of Bullocks or Rams Heads flead, as a Symbol of the Sacri" fices offered there. HEADS, wirh Bricklayers, a Term uled to fignify half a Tile in Length ; but to the fall Breadth of a Tile : Thefe they ufed to lay at the Eaves of a Roof HEADING Architrave. See Architrave. HEALING, in Architecture, fignifies the covering the Roof of a Building, either with Lead, Tiles, Sla^e, Horfliam Stone, Shingles, Reeds, Straw, fjrV. HEARTH vS^o^f J. SeeFiRE- Stoxes. HEAT, in Smithery. See Iron. HEEL, in Carpentry, an in- verted Ogee. HEIGHT is the third Dim.eii- fion of a Body, confidered with refped to its Elevation above the Ground. Altimctrta is an Art or Science, which teaches the Meafuring of all riei^h^ both acceflible and inaccelfible. The Inflruments chiefly ufed in taking Heights^ are the Qua- drant, and the Geometrical Qua- drant. HELIGOID Parabola, or the 'Parabollck Spiral^ is a Curve a- rifing upon a Suppofition of the Axis of the common Apollonian Parabola's., being bent round in- to the Periphery of a Circle. The Helicoid Parabola then is a Line paffing through the Ex- tremities of the Ordinate, which now converfe towards the Cen- tre of the faid Circle. HELIOSCOPE, in Opticks, a Sort of Tellefcope peculiarly fitted {ov viewing and obfeiving the H E the Sun, as his Spots, Eclipfes, HELIX, the Word is Greek, and literally fignifies a Wreath, or Winding, Helix, in Architefture, is the Caulicolcs, or little Volutes un- der the Flower of the Corinthian Capital, called alio Urilla. Helix, in Geometry, is a Spiral Line, but fome Authors in Ar- chitedure make a Difference be- tween Helix and Spiral A Stair -Cafe, according to 2)az)ilcr, is an Helix, or is helia- cal, when the Stairs or Steps wind round a cylindrical Newel ; whereas the Spiral winds round a Cone, and is continually ap- proaching nearer and nearer its Axis. HEMISPHERE, in Geome- try, is one half of a Globe or Sphere, when divided into two, by a Plane pafling through its Centre. HEMISPHEROIDAL, in Geometry, approaching near to the Figure of a Hemifphere, but is not juftly fo. HEPTAGON, in Geometry, a Figure conlifting of feven Sides and (even Angles ; which, if the Sides be all equal, is called a regular Heptagon. HEPTAGON AL Numbers, are a Sort of Polygonal Num- bers, wherein the Difference of the Terms of the correfponding arithmetical Progreffion is five. One Property, among others of thefe Numbers, is, that if they be multiply'd by 40, and 9 be added to the Produd, the Sum is a fquare Number. . HEXAEDRON \ in Geo- HEXAHEDRQN,^^ ^i&iq^^ H I is one of the five regular Bodies properly called a Cube. HEXAGON, in Geometry, a Figure of fix Sides, and as ma- ny Angles. If thcle Sides and Angles be equal, it is called a regular Hexagon. Fhe Side of a Hexagon is de- monffrated to be equal to the Radius of a Circle circumfcrii)ed about the fame. Hence a regular Hexagon is m- fcribed in a Circle, by fetting the Radius off* fix Times upon the Periphery. HEXASTYLE, in the an- tient Architefture, a Biiilding, having fix Columns in Pront. HINGES, in Building, are thofe neceflary Irons by Means of which Doors, Lids, Folds of Tables, ^c. whether of Houfes or other Buildings, make their Motion, whether of opening or fliutting, or folding, zjfc. The Sorts or Kinds are many ; as Beds, Box, Euts, , Cafemcnt^ Lancajhire and Smooth - filed \ Cafling, Cheft'black Lancajhire, Smooth-filed Coach, Deik, jDove- 'Tails, Ejjes, Folding, Garnets, jDozen-H'are long, ''2)ozen-H'^are jhoTt, li'' eighty long. Weighty fijort^ Larnbt-Heads, Port- Side Lanca- ffire , Side Smooth -filed, and Smooth-filed, Side with Squares, Side with rijing Joints, Lane a' Jhire and Smooth -filed Stall; Trunk of fundry Sorts; Screw, Scuttle, Shutter, Lancafjire Joints, Lancaftjire Dozen-H'^are with Hooks, 2)ozen - Ware long.^ Dozen-Ware port. Weighty long.^ Weighty Jh or t. ^ The H I H I The Price of fome of thefe Hinges are as follows: Bed-Hwgcs^ from 5-/. to 7/. per Dozen. Box-Hinges^ {torn is. to ^s. per Dot. ' Synall Brafs ones, from 2 /. to 2 J. 6d. per D02. 'Jjove-Tails^ from is. to /\s. per Doz; Hooks and Hinges., &c. ^cr /i^« from 3<^.+ to 4^. Side- Hinges.^ from 3;. to 16 /. /"^r Doz. W;tn a Square, from 20 s. to 36/. /"^r Do2. Sere oj' Hinge s ^ from 30 J. to 48 J. per Doz. HIPS, in Carpentry, are thofe Pieces of Timber which are placed at the Corner of a Roof. l"he Hips are much longer than the Rafters, by realbn of their oblique Pofuion ; and are planted not with a right or fquare Angle, but a very oblique one; and confequently are not, or at leart ought not to be fquare at any Angle, as Rafters are not at ^H, bat level at every one of them ; and which is yet more, as Rafters have but tour Planes, thefe commonly have five. They arc commonly, by CountryWork- men, called Corners., and fome call them principal Rafters.^ and others Sleepers. The Truth is. Hips znd Sleepers are much the fame, only the Sleepers lie in the Valleys, (and join at the Top with the Hips ,) but thofe Surfaces or Planes which make the Back of the ///)>, are the under Sides of the Sleeper. The Backs of a Hip are thofe two Superficies or Planes on the Outfide of the Hip., which lie parallel, both in refped of the Length and Breadth with the Su- perticies of the adjoining Side, and End of the Roof. Hip- Mould is by fome ufed for the Back of the Hip: But others underftand it to mean the Prototype, or Pattern, common- ly made of a thin Piece of Wainf- cot, by which the Back and Sides of the Hip are fet out. I fhall here give you the Me- thod of finding the Length and Backs of Hips., &cc. in fquare Frames, and alfo of the Rafters, Diagonals, Half Diagonal, and Perpendicular, as follows ; As 20 :: Breadth of the Houfe ten of the Rafter. J ten of the Hip. .Perpendicular. Diagonal, neareft Diftance. Hit> Angles at Foot 38 — 22 at Top fi — 28 at Back 116 — 12 :RafterAng,cs<«J«P^^no The Angles are always the fame in all fquare Frames that arc true Pitch. Hip H I Htp-Roof^ with Carpenters, called alfo Italian Roof] is a Roof which has neither Gakle- Head^ Shread-Head^ not Jsrkin- Head; (by which is meant luch Heads as are both Gah/e and Hip at the fame End :) For 'tis a Gable or Upright as high as the Collar Beam; and then there are two fliort Hips^ which fhut up with their Tops to the Tops of a Pair of Rafters, which Coun- try Carpenters call Singlan. For a Hip-Roof hath Rafters as long, and with the Angles at the Foot, efr. at the Ends of Buildings, as it has at the Sides ; and the Feet of the Rafters on the Ends of fach Buildings as have Hip-Roofs^ (land on the fame Plane, viz. parallel with the Horizon, and at the fame Height from the Foundation with Rafters on the Sides of the Roof. Thefe are the Hip-Roofs that are by fome called Italian Roofs. The Method of Meafuring Hip-Roofs. If they are three quarters, or true Pitch, as it is commonly called, then it is only multiply- ing the Length of the Building by the Breadth, and adding half as much more to the Area found ; or elfe multiplying the Length by the Breadth and half, or the Breadth hy the Length and half : Either of thefe three Ways will produce the Flat and half,v/hich is equal to the Content of the Roof in plain Meafure, if no- thing be allowed for Hips and Valleys ; but if the Roofh-xvc no Cornice, but the Rafters have feet, then they muft b« added ; Vol. I. H I and alfo the Eaves-Board, la a Bill of Meafurement. Or you may meafure fuch a Roof, by multiplying the Length of it by the Length of the Raf- ter, and it will give the Half Content ; or elfe by multiplying the Length of the Building by twice the Length of the Rafter; which will give thcwholeContenr. How to find the Curve - Lengths and Backs of the Hip, ei- ther bevel or fquare of Roofs in general^ objerve the follow- ing Examples. See Plate XII. The Figure I. is an Hexagon 'Plan^ and an Ogee Rafter. Firfl^ Draw the Plan abcdefy alfo draw the Line b h ; then divide the Line ah in the Mid- dle at/, and draw the Line ih\ then will hh be the Bafe of the ///>, and th the Bafe of the Rafter : From h draw a Line to ^, perpendicular to ;7;, and equal in Length to the Perpendicular of the Rafter ; alfo from h dravr a Line to ^, perpendicular to bh.^ and equal \Qhk\ then draw the moulding Part of the Rafter i k in what Form you pleafe : Having fo done, divide the Line /■ h any how ; from which Di- vifions raifc perpendicular Lines to touch the Curve Line ik\ continue thofe Lines to touch the Line bh^ as the dotted Lines in theExamplelhew, which will divide the Line bh into the fame Number of Parts and Propor- tion with the Line « h ; then from thofe Divifions raife per- pendicular Lines at Pleafure, and take the perpendicular Line i, i,^ on the Line i h, to the Curve of Gg tl*e H I the Rafter tk in your Compares, and let it up tlie correfpondent perpendicular Line on the Line ^A, as I, [ ; alio the Line a, 2 ; and 3,3; iind lb of nil the relt : And in each of thcfe Points flick a Nail, and bend a thin Latn round, to touch them all at once ; then on the Edge of it draw the Curve of the Hijj g b; which was to be done. 7%/j Fig. II. reprefents the Hip bg in Fig. I. and 1,2,3,4, at . the Point e, repreferas the Sole of the Foot of the Hip, before the Back is vjork'd. Firfl^ Draw the Lines on the Hip, at any convenient Diftance, parallel to the Foot of the Bale ac ; then draw the Sole of the Fool of the Hip^ as 1.2,3,4, at the Point e^ of the preceding Fi- gure, Number I. and take in your Compaffes the Dillance between the Point i to the Line e f or from 2 to the Line cd, and fet it Ironi the Back of the Hip ab on thofe parallel Lines which you fee marked by Dots ; then Ihike a Nail into each of thefe Dots or Points, and bend a thin Lath to touch them all at once, and on the Edge of it flrikc a Curve Line ; then drav/ a mid- dle Line down the Back of the Hip, and between that Line and the Curve, which is created by thele Dots, hew oit' the fuper- fiuous Wood, which will make the uue Rack of the Hip ;. and Xo of all other Roofs ^ in what Form Ibevcr : But only you muft obfcrve, if your Plan is be- vel, as one End of 5, to fet the Superfluity of the Sole of the //;f> at the Point f, which is from HI 3 to the Line c b, and from 4 to the Line c d^ on their proper Sides 01 ih^- Hip, becaufe one Side will be wider than thf other, which is the Cafe on the Back of all bevel Hips. The Plan ^^f<^r?/, in Fig. III. j is a H(x.i^nr7, the fame as Fig, L I and the Lines oh, ^ h, h k, and | h i in the one, is equal to b h, ih, hg, and hk in the other; fo alfo are the Soles of the Feet of the Hips I, 2, 3, 4, at the two Points r; and there is no other Difference than the Curves of theRafters, and, of confequence, needs no other Explanation; and fo likewife of the two Hps, Fig. I[. and Fig. IV. the two laft Figures being laid down on- ly for Variety fake. Hovj to find the Length and Be- vel, and the Mould for a Hip, either bevel or fcjuare, ivhether it be above 'Pitch, or under Tttch. Piate XllJ. Brfl, Draw the Plan ah c d^ and let one End be bevel, as be, and the other End fquare, as a d, which divide in the Middle by the dotted Line tv. Then draw the Une e f pa- rallel to ad, and diftant as tar as at or tdy and draw the Lines ia and id. Then take the Line ad m your Compulfes, and fet it on the Line ab, as km, and drav«r the Lines kl and ml, to repre- fent the Pitch of the Rafters, and let fall the Perpendicular In; which take in your CompafTes, and fet it from / to^, and frim / loh^ in a ftraight Line with id and ia, and draw the Lines ga and kfi. Then H I H,I Then draw the Line r s pa- rallel tc bc^ and dilbnt fo much as e i or / 1. Then, draw the Line w j^ through the Point />, and paral- lel to e j\ and draw the Lines bf and c -p. Then take the Perpendicular /», and fet it from /> to o, and from/? to ^, in Right Lines witli b f> and f />, and draw the Lines b and c q. Then is bo^ cq^ d h^ and ag^ the Length of the four Hips. , And if the Lines p o and p q were raifed up, they would meet perpendicular over the Point p ; fo would the Lines ig and i h meet over the Point /'; then draw the Breadth of the H'tp parallel to the Line ag. To finci the Back of the Hip. Set its Splay or Foot in its Polition on its proper Place ; the Sole of which is reprefcnted by its proper Figures 1,2,3,4, in this Example; and ftrike it by on the under Side or Sole of the Hip to the Line ab and a a', which will fliew you how much of it hangs over the Plates a d and a b, as from i lO the Line ad., and from i to the Line a b ^t the Angle a, and from the Extremity of thofe Strokes, ftrike a Line on each Side the Hip pa- rallel to the Back or Line ag. Then ftrike another Line on the Middle of the Back, and thofe three Lines give its true Bevels, to anfwer both Sides of the Roof, whether it be bevel or fquare, b-. hewing off the fu- perfluous Wood between Line and Line. N. B. If you do not approve of fetting the Hip up in its Po- lition, you may find its Back by drawing a Line on the Angle of your Plate, as at-, alfo a middle Line on the Sole of the Foot of the Hip\ and take the Bevels from the Line ; a and ^, and / a and d, and fet them on the Foot or Underilde of the Splay, which v^ill be of the fame Effeft, as fetting it up in its Polition. To find the Length of the Hip, and Aloiildfor its Back., another M^ay, Plate XIV. Draw the Plan ac db., and di- vide it in the Middle by ^», and draw the Line iq parallel to ab., and equal 10 an or nb\ alfo the Line zy parallel to c d., and di- ftant equal to « ; ; then draw the Line gx through the Point vj., parallel to iq; and draw the Lines c d., dw.^ af and bf. Having done this, take the Width of the Span a ^, and fet it on the Line ac any where, as" eg, and draw the Lines for the Pitch of the Rafter ef and gf; alfo the Perpendicular Line fh^ which take in your Coirpaffes, and fet it from vjto f, and from ■uj to a, in a ftraight Line with c vj and<^ty ; alfo from/to /^, and from J to r, in a ftraight Line wkhfa and fb\ and draw the Lines for the Length of the ///px f /', ^», rt^, and br. To draw the Lines jor the Mould for the Back of the Hip. Lay a ftraight Rule from i to », anil make the Point m from Gg 2 n, H O H O /I to f , and make the Point o ; alio from zio b make the Point rt, and from h to y make the Point c ; then take the Compaf- fes, and fa one Fcx)t in the Point w?, and move the other Foot, till it touches the nearefl Place of the Hip- Line ak ; which move about and make the Point /, and draw the Lines ?'/and/^, then is iln the Mould for the Back of the Hip nk-, alfo npq for the Hip br. The fame Method is ufed for the Bcwi Htps ydhy as Is for the 13ack of the Hip d re, and ^^ :5,for the Hip c t \ which was to be done. See Plate XIV. HIP-TILES. See Corner- Tiles. HOLLOW, in Architedure, a concave Moulding about a Qua- drant of a Circle, by fomc cal- led C.iff-meiii^ by others Jlbacus. HOLLY. The Timber of Holly is the whitefl of all hard Wood, and therefore ufed by the Inlayers. It is alfo rtt for all llurdy Ufes ; the Mill- Wright, Turner, and Engraver, prefer it to all others. It makes the bell Handles and Stocks for Pools, Flails, Carters Whips, Bowls, Shivers, and Pins for Blocks, k is excellent for Door- Bars, l^c. HOMOLOGOUS, in Geo- metry, is apply'u to the Sides of timilar Figures, which are faid to be HjmologoHs^ or in Proportion the one to the other. Thus the Bafe of one Triangle is Humolo- S^ous to the Bafe of another limi- lar Triangle, 1^o in llmilar Tri- angles, the Sides oppolite to equal Angles, arc ftid to be Ho- mo! igo»S- HOOKS, in Building, are a neceffary Sort of Utenlils which are ufeful for feveral Purpofcs. They are of various Sorts, fome of Iron, and others of Brafs : Some of the Names of which are as follows: I. Armour-Hooks. Thefe are generally of Brafs, and are to lay up Arms upon, as Guns, Muf- kets, Halbcrts, HaIf-Pikcs,Pikes, Javelins, l^c. Z. Cafement-Hooks . 3. Chimney- Hooks , which are made both of Brafs and Iron, and of different Fafliions. Their Ufe is to fet the Tongs, Fire- Shovcl, c^c. againll. Thefe are fold from 2J. to 2j dd. aPair; the Iron ones from i /. to \s. dd, a Pair. 4. Curtain- Hooks. 5". Hooks for Doors^ Gates., &C. Thefe are from 3.^«»d A£i^ of the ilth of King George I. That it lliall not be lawful to make or have in any Party-Wall of ^ny Houfe ^ which after the 24th of June iJiS- fliall be ereftcd or built within the preceding Bonndnries or Limits, any Door-Cafe, Window, Len- til, Breft-Summer, or Story-Pofls or Plates whatfoever, unlefs \There two or more Houfcs are joined or laid together, and fo ufed as one lingle Houfe ; and that to be no longer than during the Time of fuch Ufage, upon Pain or Penalty, that the Owner of every fuch Houfe^ for every fuch Offence, (hall forfeit the Sum of j-o /. And \\\ confideration that Party -Walls built upon old Foundations may decay, and be- come dangerous, and needful to be rebuilt ; and whereas Dilfe- rences have, and may again arifc between the two Landlords, concerning the Expences of ta- king down the fame, fhoring up the Floors, and rebuilding them again ; it is therefore by the aforc- faid Ad enaSled^ Thatfrom and after the 241 h Day of Jtme^ 1725-. all and every Perfoii and Pcrfons, inhabiting in any Place or Places, in and about the Cities of London and IVcJl- minfler^ or any other Place or Places compriz'd within the Weekly Bills of Mortality, or within the Pariflies of St. Mary Ic Bone and Paddingion^ or with- in the Pariflies of Chtlfea and St.Tancras^ who fliall build, or caufe to be built, any Houfe or Houfes.^ upon any Foundation, old or new, and who fliall find it abfolutely neceffary to take down any dccay'd Party-Wall b^^ween fuch Houfe and the next adjoining Houfe., (hall give Notice thereof in Writing to the Owner or Occupier of fuch adjoining Houfe., full three Months before fuch Party- Wall fhall be begun to be pulled down, to the Intent that the fame may be viewed by fourabfe Workmen, within the Space of one Month next after the Service of fuch Notice ; which four Workmen are to be equally ap- pointed by both Parties, that is, each H O H O each Perfon to appoint two of thein, or more, if required, when they both do agree thereto. But in cafe that the Landlord or Occupier of the next adjoin- ing Houfc^ wi]l not agree to the rebuilding of fuch Party-Wall, or Walls, or is uncapable of paying the immediate Moiety thereto, and (hall ncgleft to no- minate and appoint, within three Weeks next after the Service of Notice, as aforefaid, fuch Work- men, that then the orher of the faid Parties fhall nominate or ap- point four or more able Work- men, who (hall view the Party- Wall required to be taken down and rebuilt ; which Workmen, or the major Part of them, (hall certify in Writing under their Hands to the Juliices of the Peace, in the next General or Quarter Sellions of the Peace, holden fur the City or County where fuch Party -Wall is fitu- ated and being, and that fuch Party -Wall is ruinous, and needful to be rebuilt, ^c. And provided that any Perfon or Pcrfbns whomfoever, fliall think him, her, or themfelves in- jured by fuch Certificate, the laid Judices (hall fummon before them one or more of the faid Workmen, or other Perfon or Perfons whom they (hall think fit, and fliall examine the Matter upon Oath, and their Determi- nation (hall be final and conclu- five to all Parties, without any Appeal from the fam-e. But \t is lO be obferved, that a Copy of the Workman's Cer- tificate vnud be delivered to the Occupier or Owner of fuch next adjoining Houfe^ or left there, within three Days after fuch Cer- tificate (hall be made to the Juf- tices, as aforefaid ; and if there fliall be no Appeal from the fame within three Months after, in every fuch Cafe, if fuch Land- lord or Occupier fliall refufe or ncgleft to fliore up and fupport his, her, or their Houfcs^ within (ix Days after the Expiration of the faid three Months Notice, that then the firft Builder or Builders, with his or their Work- men, (giving Notice as afore- faid,) may javv'fully enter into fuch Hoiife or Hotifes (at all fea- fonable Times,) with Workmen and Materials, and therewith fliore up and lupport the fame ; the Expcnce whereof fliall be paid by the Landlord or Occu- pier; as alfo the half Expence of the Party-Wall built by the firft Builder, after the Rate of 5-/. fcr Pod, for every Rod of Work contained therein. And when the firft Builder fliall have built the faid Party- Wall, he fliall leave at fuch next Houfe with the Landlord or Oc- cupier a true Meafurenient of the Quantity of Brick -Work contained therein, widiin ten Days after fuch Party- Wall fliall be fo built and compleated; of which one half Moiety, at the Rate aforefaid, as a! To the Ex- pence of flioring and fbpporting, (hall be paid by the Landlord or Landlords thereof, or their Te- nants or Occupiers, who are hereby empowered to pay and dedud the fame out of the next Rent that fliall become due. And provided, Thar Ncgle61: or Refufai of the Money fo due be made, and remain unpaid for the tpace of twenty -one Days after Dwma;id thereof; then it flial! ] H O HO fhall and may be lawful to and for luch Hrlt Builder or Buil- ders, his, her, or their Execu- tors and Adminillrators, to fue fuch L iidlord or Landlords for fuch Sums foproportionably due, by Adlion of Debt, or on the Cafe, Bill, Pbiinr, or luforma- tioi), in any C'Aut of Record at Wejlminfier^ &c. And here note^ That the Lav^r here delivered relating to the re- building of decay'd Party Walls, of either Brick or Stone, the fame is to be under Hood and ob- ferved of old Honfes^ where in- ftead of having one Party- Wall between them, as this A61: di- refts, have two Timber Walls or Partitions, one belonging to each Houfe^ and fcparate from one another ; therefore be it un- derwood on all Sides, That who- foever, for the S;'fety of his or their Houfes^ will pull down his own Wooden Walls or Parti- tions, and inftead thereof build a Party-Wall of Brick or Stone, he or they are alfo empowered to pull down the next Wooden "Wall or Partition of the next adjoining Huufc or Houfcs^ (if the Landlord will not agree thereto,) and proceed in every Step, as before delivered for the rebuilding of decay'd Party- Walls of Brick or Stone. Which new-built Wall muft be placed equally on both Pre- mifes, that is to fay, half the T'hicku'^fs of the Foundation on one Landlord's Land, and the other half on the other ; and that all Settings-off in theFoun- dation be equally the fame on both Sides, as directed in the Beginning thereof. The feveral Rates of Honfes^ or Btiildr/tgs, sppointed after the Fire in 1666. were foar. Firjl^ 1 hofe of Allies, By- Lanei, ^c. were termed build- ings of the firlt Rate, and 'vere ordained to confiit but of two Stories, exciuiive of the Cel- lars and Garrets, whofe re- fpedive Heights were fettled as follows, viz. the Height of the Cellar is fix Feet and a half, the Height of the firfl and fe- cond Stories each nine Feet, and the Height of the Garrets at Pleafure. The Scantlings appointed for the Timber of thefe Buildings, are as follows : Summers or Girders, whofe Lengths are not to exceed 15* Feet, muft confift of 12 Inches in Breadth, and 8 Inches in Depth orThicknefs; and Wall- Plates 7 Inches by 5- Inches. Principal Rafters, under ij Feet, to be 8 Inches by 6 In- ches at their Feet, and 5" Inches by 6 Inches at their Top. Single Rafters to be 4 Inches by 3 In- ches; and Joifts, whofe Lengths are more than 10 Feet, muft be 7 Inches deep, and 3 Inches in Breadth ; excepting thofe for the Garret Floors, which muft be 3 Inches by 6 Inches. And here obferve^ Stat. 22. Czr. II. That no Joifts or Raf- ters be laid at greater Diftance from one another, than 12 In- ches, and no Quarters at greater than 14 Inches. Secondly^ Houfei of the fecond Rate are fuch as front Streets and Lanes of Note, conlifting of three Stories 'in Height, ex- clufive H O H O clufive of the Cellars and Gar- rets. The Height of the Cellars mull be 6 Feet and a half, (if Springs will allow it ;) the Height of the fictf and fecond Stories lo Feet each, the Height of the third Story 9 Feet, and the Height of the Garrets at Pleafure. The Scantlings appointed for the Timber of thefe Buildings, are as follows : Summers or Gir- ders in Length , from Jolfts which bear 10 Feet, muft have in . Thicknefs 3 Inches, and in Depth Firjl^ for the Floors. muft have in their Deoths Inches and Breadth Inches,, where the Depth of the Girder Binding Joifts, with their Trimming Jolfts, 5- Inches in Breadth, their Depth equal to their own Floors. Wall-Plates, or Railing-Pieces and Beams Lintels of Oak in the firft, fecond, and third Inches, and Story, and Inches. Principal Rafters, whole J Lengths are .from 18 Secondly^ for the Roof. 21 5 Foot 9 1 1nches, ") 7 Inches X Top 7 *) and 5 thick. v.to^ Foot 10 > Inches, 7 o t u Top 8 5 and 5^^°^hes. 21 Ki^ \x6J Feet, ^murtbe _ gj ^ Foot 12 -i Inches, and U Inches. i Top 9 5 C Foot 12 > Inches,? ^ T , >Top 9S «nd S^^"''"''- Purl ns, H O H O Purlins, whofe Lengths are from ;^^° C r S ? Feet, muft have in their Squares 9? Inc. C 87 6 12 > by ^95-^ Single Rafters, whofe Lengths do not exceed 9^ Feet, muft have .63 in their Squares 5" "^Inches .4b by ^li Inch. Thirdly^ Buildings of the third Rate, are fuch as front the molt priiicip.il Streets of Trade, as Cheapfide^ Fleet- Street^ the Straml^ ^c. confiding of four Stories in Height, exclufive of the Cel- lars and Garrets. The Height of the Cellars are as in the lall preceding, the Height of the firft Story 10 Feet, the fccond 10 Feet and a half, the third 9 Feet, the fourth 8 Feet and a half, and the Garrets at Pleafure. The Scantlings of Timber ap- pointed for this third Rate of Hoztfes^ are the fame of thofe of the fccond. The fourth Rate of Huufes being fuch as ajre appointed fur Perfons of extraordinary Quali- ty, fituare in magnificent Squares, i^c. may have the Height of their Stories and Scantlings of their Tifnber at Pleafure ; but they muft not exceed four Stories in Height, exclulive of the Cellars and Garrets. And here it is to be mteJjThzt the Height of the firft Floor over the Cellars, in Houfes of the fe- cond and third Rates, fliall not be more than 18 Inches above* the Pavement of the Street, nor lefs than 6 Inches, with a circu- lar Step without the Building. Scantlings of Stone appointed for the firlt, fecond, and third Rates of Buildings. Fir ft Rate. Corner Piers ■ — Middle or Single Piers — — Double Piers between Houfe and Houfe Door Jaumbs and Heads Inches. 18 Inches. = iif'^i Second and Third Rates. Corner Piers Middle or Single Piers Double Piers between Houfe and Hoiife Door Jaujnbs and Heads — . 14 Inches by 10, ^ H O H O ^s to Materials: And fir fl of Quartering. Feet. Single ■> Quarters, whofeC 87 muflS 3'"^ and in fi. I "^ Inches in Double 3 Lengths are ^S Shave ^4 S Breadth C3i 3 Thickncfs Laths, whofe^^-" Lengths are ^4 Secondly^ 0/ Laths. Feet, muft have one C 5:"^ of an Inch in Inch in Breadth, and c ^ 5 Thicknef';. Ai to the Front and Rear U^alh. By the Stat. 19 of Car. II. Houfes of the Hrlt Rate Qiall have their Cellar Walls in Front and Rear of two Bricks in Thick- nefs, the firft and fecond Stories of one Brick and a half, and the Garrets of one Brick only. Houfes of the fecond Rate fhall have theii Cellar Walls in Front and Rear two Bricks and a half in Thicknefs, the tiiftand fecond Stories two Bricks, the third Story one Brick and a half, and the Garrets one Brick only. Houfes of the third Rate fhall have their Cellar Walls in Front and Rear three Bricks thick, in the firft Story two Bricks and a half, in the fecond, third, and fourth Stories one i3rick and a hnlf, and in the Garrets one Brick only. Houfes of the fourth Rate, be- ing chiefly for Noblemen, i^c. have their Thicknefs le^'t to the Difcretion of the Architect. By Stat. 7 of Queen Jnne^ no Modilion or Cornice of Wood or Timber fhould here- VOL. I. after be made, or futTcred to i>e made, or fut^ered to be fixed un- der the Eaves of any Houfe.^ or again ft any Front or Rear Wall thereof; but the Front and Rear Wal 1 s of every Huufe and Houfes^ fhall be built intirely of Brick or Stone, (the Windows and Doors excepted,) to be carried two Feet and a half high above tiic Garret Floor, and coped or co- vered with Stone or Brick. Alfo by Stacy, of Queen /^»;??, it is enafled, Fhat ail Jaunibs and Backs of Chimneys, which lliall or may be built, iliall con- lift of one Brick in Thicicners at the leaft, from the Cellars to the Roof; that all the Iniides of fuch Chimneys ftiall be four in- ches and a half in Breadth; that a'i Funnels fliall be plaiftered or pargetted within, from the Bot- tom to the Top ; that all Chim- nevs be turned or arched with a Trimmer under the Hearths with Brick, the Ground Floor ex* ccpted; and that iio Timber ftiall be nearer than uve Inches Hh to ^ t9 n R to any Chimney, Funnel, or nearer than five Inches to any Fire-Piace ; .. that :\11 . ^lantles Fire-Place or Flue. between "the ^aOrfiU'i^ atched^ '"' Bill by::$tati 22, Car. II. h is ■'.virh Brick or Stq^efj and no '"iyja^ed^ That no Timber be Wood or Wainfcot fhall be pla- la-d within twelve Inches of the ced or affixed io the Front of Forefide of Chimney Jaunibs ; any Jaumb or Mantle-Tree of and that all Jorfts on the Back any Chimney, nearer than five of every Chimney be laid with Inches from the Infide there- a Trimmer of fix Inches Dif- of, tance therefrom ; and that no That all Stoves, Boilers, Cop- Timber be laid within the Fun- pers^ and Ovens, fhall not be nel of any Chimney, on Penalty nearer than nine Inches, at the to the Workman for every De- lead, to rhe adjoining Honfe; fault 10^ and 10/. more every snd no Timber or Wood to be Week it remains unreformed :£8 A Table i ^ dH H O H O A T A B L E for one Brick in Thicknefs,';! oyirfiiwad Half of Two Bricks. -'^''^ f^'Wr A lo boo //^ 1 he J deight ot the Walls m Ji^eet. ■ 'I) VflE; Foot Halt- I II III IV yr.i[i long. Brick. Brick. Bricks. Bricks. Bricks. Brick&> I S II 22 33 ii SS 2 II 22 44 66 88 no 3 16 ■"% D3 66 99 13^ i6s 4 22 44 88 132 176 220 - S 2-7 SS no 165- 220 275 6 33 66 132 199 264 3?^ 7 39 77 15-4 231 3^9 386 8 44 88 176 264 353 441 9 S<^ 99 198 298 397 496 10 SS no 220 33^ 441 551 II 61 ' 121 244 364 4S5 606 12 66 132 264 397 529 661 13 72 143 286 431 573 716 14 77 iH 309 462 617 771 IS 83 i6s 331 496 661 826 16 88 176 3SS 529 705 8S2 17 94 187 375" 5-62 749 937 18 99 198 397 5-95- 793 992 19 105- 209 419 628 ^37 1047 20 no 220 441 661 882 1102 21 116 231 4^3 694 926 1157 22 121 242 48r 726 970 1212 ^3 127. 2-53 507 760 1014 1267 2,4 13^ 264 5-29 793 105-8 1322 2.S 138 275- SS"^ 826 1102 1377 16 143 286 573 860 1 1 46 1432 27 1^4 309 617 926 1234 1543 28 16s 331 661 992 1322 165-3 29 220 441 881 1322 ^763 2204 30 275" SSI 1 102 165-2 2204 2755 Hh 2 A Table Kd^ H O Ai T A^i^Biifbp one Brick: in Thiclmefs, or the ifjctiHaif ! of t^'o Bricks. TheTHeight of the Walls ?n Feet. r Foot VI VII VIII XA- X ' Johg.s •Bricks, t Bricks. Bricks. Bilcfis/' Bricks. I - 60 i 1 77 85- 99 no ■^. 2 OC132 j 15-4 176 \ li'L thoie_J'urpores, but alio the Laws tif the Motion of Fluid Bodies. I ! , .'^r Hydratiluki^ therefore, '.com- prehends theArt of condiiiding Water into Pipes, Canals, Ii)rai:is, ^c. Alfo the railing it, with the feveral Engines employ'd for that PurpofeJ ixs^Siphonf^ Pumps^ Sy Tinges^ Fuu.nta]ns^ 'Jets cVBans^ ¥ire- Engine 5^ Mills), dec. HYDROS! ATICKS, [of "TSojp V\fater,. and carme, Gr. Staticks\ a Science that explains i\\Q Equilibrium of Fluids, or the Gravitation of Plluids a? red: Upon the kemoval of that £^/i/- lihrium^ Motion enfues,; and here HydrauUcks commence. Hydraulicks^ therefore fuppofc H'^drofiaticks ; and' the General ity or Writers, from the immediate Relation between ihefetwb, join them together, and calif tliem both either Hydraulicks^ i^r Hy- dro flat icks. ' ;■' But Mr. Harris^ in hWXexi- conTechnicum^ blames Mr.c>^<3- iiarn for^iiixing ani^ confounding Hydrojl'^ticks and Hydraulicks the onevvith the other; lince'by the firfl Is explained thf natural f./a/- librium or Motionjof Water and other Fluids ; and by the^ latter, the Force of nlecljanical Elngines Tbr'tTieFofcihg' it up to great Heights. Hh 4 HYP4^THR0N H Y H Y HYF;ETHR0N7 inamient HYPiE fHROS 5 Archirec- lure, a kind ut' Temple open at me Top. f'itruvius fays it is an open Building or Portico, fuch as lonie antient Temples \vcre, which had no Roof or Covering, as the Temple of Jupiter Olym- fiii!^ b'lilt by Cojjntins^ a Roman Archiccct at /it hens. HYi^HRBOLA, in Geome- try, is one of the two Lines lorined by the Se6tion of a Co'ie. Th^ Hyperbola arifes when the Plane that cuts the Cone is not parullc' to one of the Sides, as it f5 Olr-the^'p£*^^^A^ ; but diver- ges from it outwards, not in- wards. K YPERBOLIFORM Ftguret, are fuch Curves as approach in their Properties to the Nature of the Hyperbola^ called alfo Hy- perboloids. ' HYPERTHYRON, in the antient Architefture, is a fort of Table ufed after the Manner of a Frieze over the Jaumbs of Dorick Doors and Gates, and the Lentils of Windows. It lies immediately under the Corona; and our Workmen ufually call it the King'-Piece. The ENT> of the Firfl Volume. ' ■ ' ^ ' ■ t ;W. The following are Addition^ and Corrections communicated to the Compiler of this Work after the Sheets were printed oft^; there- fore not being willing to omit any Thing that may be of Service to thePublick,but to make this Work as Compleat as poffible, we have inferted them here by Way of SUPPLEMENT. A S IN the Article ASHLERING, iuftead of 4 ^. to 6 d. read from 18^. to 2 J. per Square. In BALUSTER, for 3^. per Yard, read 3 s. per Yard; tho' the Prices are various, according to the Goodnefs of Worianan- fliip. Ill the Article BARNS, have no Dependance on the Prices fet down. In the Article BATTEN JDoors^ as to their Price, have no Dependance; for no Price can B A be fep on them, without know- ing the Dimenfions. BATTER is a Term ufed by Workmen, tofigaify that aWall, Piece of Timber, or the like, doth not (land upright, but leans into the Building ; if it leans from the Building, they fay it over-hun^s. .. BAULKS? Are fmall young BALKS S Fit-Trees, the {lender Tops being cut off, and hew'd up, brought from Nor- vjay. B E #P -.11 I'M«(:.B.4ULK.§^,flre I^^ge .^^pretchercjtoJ^e^i^nY'fV which 3iifiiegp^SiP>,.pu:X'^^''^'^fty''^^'^^''^ '''^'^"'" 'P"'^ <^^'''f i^^''^' '^'-^r'^Tfider jkfQ^Jg\)hi^ffh'^'^i^^yc;' nat;,^' Header, and lb on (i-Miih the.^ATiic'.e BtAU Fit- ,,fajt%, fij|cl,pt^e,WaH';vvhich ^tri'ooc "they <:,^\\J^pJliJb ^md •jcha* b(^n>giy*'i> for, Workman- fhip, where it has been trouble- rR)i"^t^::aSrin a Country Church, '=i(Dr AvMfierl', tjiey have been obliged to icaffold;,. (9«:. .y^e; . Iqn^ ^,ad- icders.: >lAr> -jbhiA -Jiii l1 . B Q S Pi ?i Term among ,r^Workn\^i?v chiefly Bricklayers, ti *who iay^ -Make ^ood BokU ; by ; wnich th<2y; mean fo to dilpofe ■the Bricks To tbeTwicfe BO U LDFR- WAL^S^add^ So?P^ Workmen lay iLati'S^/iii the .Wall angle- ways, and'then crofs them Ibme- . what , like a Ntjt, every two or '.three Feet in Height, which pre- Vemjs ')t falling down in moirt and rainy Weather. In ihq Article BRICK- WORK, inftead of thinner^ read thicker. Alio to that Paragraph, the ^^-^afi^of the Gable^ in the lame . Firlt,., a yB^jcl^Jiyer Jays, a ■ Jirticle, add, or the Bale of the Stretcher, or Bripk long -ways Gable being 24 Feet, take three ?, in the BuHding, beginning at the V Corner^ ^nd;fo on all Stretchers in th:tt Courlc ; ihen upon that 17 he lays next a Header, beginning srtat tJie.-&me Corner; iKxt to that a Ckjfer, which is Part of a Brick, about tx^ti finches; which, with the Heaisr akef^dy laid, is about fix Inches. a?i.aM, which they^call Fieyn'tjh i?b(i:Of ftrdlttiey Ja^ aHtea^^j^tthen 5'.' a Clofcc;UeKt!4->Stre;cher, then ci a Header^ctiexrt a Str,etcher>,fand .r>. fo on to^fhe^End ^f jtKe- Wall ; '^ Chen oil the next Courfe a 3f B R are halved into th6 Ppftr;' alfo let cc he the bearing Beams; and let ddtdd be the binding Joifts, ■which are let into the bearing Beams, as in the Plate G* D* atT; alfo let ^e-ee be the Plan of the feveral King-Pofts. And in B obferve, that // is the Top of the Water at its com- mon Level, and let gg be the Butments or Support to each Shore ; alfo let hh bt the tying Beams, as halved into the Polls ; let /■/ be the Plate for theBraces //to reft on, which fupport the Ports kk\ fo do the Braces m m difcharge the whole Weight ; and let nn be Struts to help the Strength, as by butting againil each Brace ; let o o o be the top Place or Rail, and p ;> a Plank weathered to throw the Water off. N.B. The additional Beams cf ^ do add prodigioufjy to its Strength. And in C*, v/hich is the Sec- tion by a larger Scale, let q q be the Ports, and r r the bearing Beam, framed therein, and let ss be the binding Joifts : Alfo -,let 1 1 h^ the top Rail, being J^'^yvider than the rert, to preferve jj«,the Joints the better ; and let utt 3[j-be the Plank weathered to throw j^^liie Water ;off;. yet better, as at' It is neceffary tp Yet the tying- .^pBeam into thePofts^lliiallMat- p: j;er, becaufe the Plank xx bears jfjoOn 't, as well as oii the binding haV^'^^ ' ^^^ '^'J ^^ Straps of Iron ^'y,>olted thK)ueh ihql^aAs'm.oT^ 97i5 C A der to strengthen the fame ; the lower Bolt goes through the faid Strap, and cotnes under the bearing Beam, and which, with the Joggle zz^ preferves a good Bearing for the Beam, which ought to be trufs'd, as fhewn in the Plate B ; and ^ ef is the Gravel and Paving. r To preferve the Timber the better, let the Truft B* >cbe boarded on each Side. In the Article CANT,- for t»rn it about ^ read tr^rn it over. In the Article CEILING, is to the Price, add, 7 his is to be undcrrtood of the Journeyman's Price from the Mailer ; and alfo the Price, with Materials, is for common Camp Work ; for Work which is done v€f y wellis worth twice that Sum.- ' , • 'r.. To the Article CHIMNEYS add this, which is a more eafy and natural Method. Let the Stack of Chimmys to be meafured^^^^e ^^ itt :the Plate. '•'■^V' V . . . i'irft, prepare the Meafuring- Book, by ruling it into ten Co- lumns ; the firrt for Remarks, the fecond for fo many Times aver as' you are to mcafure Things of the fam6 Dimeniions. As for Exampk: If you h^\ two Hearths in a Stack of Chu-. ncys of the fame Dimtnfion, and on one Floor^ yUii he-ed. let but one down iif yOat ^ook, and jfay twice over, that'is^ pur down 2 in the fecond Column, and puc down doubhe'tHti'"p£^dU(9: under that Word, fiftK^^lumn;: if the firft- Dirncnlfoh^Miasi^tOutfe^donQ *t.vi(^c^;bver,--'jliu'*fet'-dowfn 2 in C H C H the fecond Column over-againft -0F. 61. and make the Produ6t 1^ Feet 8 Inches. The third C'jlumn is for the '"Dimcnfions ; the tourth for lo many Bricks as theWall is thick ; the fifth tor the Produd of the Dimenfions, when multiplied to- gether ; the (ixth for theProduds of the Deductions ; the fcventh for reducing the Produdls into 17 Brick thick, as the eighth is for one Brick ; and the other two for reducing the Deductions to their Thicknefs. If you are to reduce the fird: Dimenfions, whofe Produ(^ is 4 10, and 5- Bricks thick, mul- tiply it by f, which is 24 2 in one Brick. The next Dimen- fion is 6 6 by 11, whofe Pro- du6l: is 7 Feet (not regarding the odd 6 Parts) and 4 Bricks thick; put 7 twice down in the feventh Column, which is t Three-Brick Wall, and i down in the eighth Column for one Brick more, which is the four Bricks Thick- nefs. If you are to reduce the Pro dud of 13 r, which is a De- duction, and '.27 Bricks thick, put firit 13 ijin the ninth Co- lumn, and 13 1 in the tenth. If vou are to reduce the Pro- dua of 9 2, F. 1 I Brick thick, pot 9 2 in the eighth Co- lumn, and 7 of 9 2 under it in the fame Column, for that will be 1 2 2 in one Brick in Thick- nefs, and fomething more ; but thofe odd Parts are feldom re- garded in Pra6tice^ it gives the Turn of the Scale to the Ma- tter, and amounts to a very fmall Matter at the End. When all this is done, you add up the four laft Columns ; the firft, or feventh Column is 331 3 reduced to i ^ Brick ; the next 216 4 of I Brick thick, then you dcdu6t the third or ninth Column of i i Brick from 331 3, there remains 312 8 ; then deduct the lalt Column 61 8 from the eighth, 216 4, there remains i5'4 8 ; which multiply by 2, and divide by 3, which brings 103 the Thicknefs of I t Brick, which add to 312 8, is in all 415^ 8, the Stan- dard Thicknefs of a Brick and half Wall ; which divide by 272 (the -\ being not regarded in this Work) there will be i Rod 143 Feet, which divide by 68, will bring it to Quarters and 7 Feet remaining; which is in all i Rod i and 7 Feet, as will appear by the TaDle. Remarks, .oLifi loHlo arfJ no iool ■V3aor/i olrti ziiii ^nnd_uj_ Remarks. o 11 o . p . S 2 « 3 ^« H=: -^ ^ a 'Li y. T?-^ 3 CQ -13 JJ 3 o ,f:i « M w (i. Ih P^ <=> j ° .2 -3 S •J-c;^ Fronting of Chimney Foundation above lilting ofF Dedua Firft Story Dcduft Chimney Second Story F. I. 6 9 6 6 I I 3 6 I 7 9 7 3 6 3 '9 5 6 Deduct Chimney 3 9 3 c Part of lower Funnel Is 7 Third Story Deduft Chimney 7 6 4 3 3 3 2 9 Part of lower Funnel Part of the other 5 o I lO Shaft 9 o 4 3 4; lO 7 5 6 ^■5 I 47 13 I 31 10 II 3 8 II 38 3 272) 415 (i Rods. ^8) JJI (2 Quarters. __( ■ Standard Feet In all 1 4 Rod and 7 Feet, at 5 /. 15/. per Rod, •5 5: 55 II 55 II 47 2 47, 2 31 10 F. J. 24 2 7 IL ,„■,,{ 55 II 47 2 : tjil 15 9 3« 3 15 II 5 6 9 2 3 o 38 3 l3,i 3I216 4 ij I II 3 -II 3 2 9 S II 8 M 18 7 61 8 312 8 103 154 81 2 Uic 8 308 I 4 3) I'^'g 4; 18 7 61 8 ( i<^3 To bring tiiis into Money, look on the other Side C-H C H At five Pounds fifreen Shitllllgs^ ;>^'R6d, what fs-the Amount of one Rod and a haff and Teven^Fcfet ^ Firft, One Rod is ' Half a Rod is Seven P^eet is as below -^^f M'- 17 06 •At-»§flr.^-c6l 02 Ili Whole Amount 8 if 05-^ For the 7 Feet biing the Pounds into Shillinj^s, which is 115-; W'hich muUipIy by 12, ro bring it into Pence, which is i38oPence, the Pence in five Pounds fifteen Shillings: Then fay, If 272 Feet be worth 1380 Pence, what i« 7 Feet ? 272) 9660 (3J Pence. 816 1 5-00 1360 Divided by 68) 140 (2 Farthings. 136 4 Whrdh% the Quarter of 272^ which will bring it into Farthings; s to wh^it ttfraains, iS' but '^^j of if 'Faf thing,' and hot worth re- :Jitdrngf-^ ••^' / . .-. 1 . ir.sy to .uuBj-.td .,fij jt -'■ ^i'€fe*^»^ys Proportion, accofdlftg't^fome Moderns. =,-K.i-tOhen— rnrr . Chimn.eys in (-.Brea^tjj, .=-rTi rrorrr Tnr dH?MS033Eq6 3rij vlnw.i; ■tnfrifT trrt rTTrTmrmTT ;SV^?tfAf^?.tW.Mfif.<^fe|-^--^ .^9^3 n^ 6,8, or 10 4, 5-7 "r (^ -Tf \ ■ ■ ■;•- Height. ,, P^pth. ih f, «r 6 ii or 3' 4,Pr 4i 2, or 2-3 5^-9 t9,4 22l^ic'hes. 3-<^^o5-9 'i8ip9l?^. To C L D E To the Article CLINKERS fldd, a fort of fm^ll yppens to be infert- ed beneaih it. Next to this fu- perior Echinus are the Modilions ; but initead of ihtm. Dentils are thought to have been firlt inlii- tuted, and for that Reafon fliper- fiuoufly join'd where Aiutules are ; and therefore, where we find Tsenia under Modilions, it is not properly divided into Teeth ; nor is it raOily to be imitated, though we have fome great Examples to countenance it. l^har of the Pantheon may fafth guide us herein, where it is left plain tbr this very Caufe, and that the Reafon of the Thing docs not in l^uth allow it. How- ever, itmurt be acknowledged, nothing hii:s been more grofly abufid; even ;^mongft our molt rcncv.vncd Mifters. In the Article DIAL, and in the Par:igraph, The bell Wood for this Purpole is the cJcareJl t E y^, aMd the reddeji Fir, if it be nut turpeftti»)\ read the ckareji H'ai»fcot^ and yellow Fir^ clear of dead Turpentine Knots, In the Article DOORS, and Paragraph beginning thus. In fmall Buildings, zs'c, add, the Moderns feldom exceed three Feet for the Front Doors of fmall Buildings, and the Cham- bers from two Feet four to two Feer ten, and two Diameters and one Third in Height. In the Article FACIA, and to the Paragraph beginning thus. The Price of Fafcia's is, ^c. add, the Price of Brick Fafcia's, with Materials, is one Shilling two Pence per Foot fuperlicial Meafurc, Moulding on the fame is one Shi 11 ins; and ten Pence /'^r Foot fuperficial Meafure. In the Article FEATHER" EDG'D, initead of Side read Fd\ie. To the Article FENCING, add, thefe Priced of Fencing here mentioned, may be what poor labouring Alcn may have in the IVeald of SuJJcx, but are not fit for the reft of the Kingdom. Paling with three Rails and Pales, is v;orth in fome Parts of Kent fifteen or llxteen Shillings per Rod, if done well, finding all Materials. And 'Paling W\ih two Rails and Pales, is worth tiiirteen or fourteen Shillings per itod ; Ports and Rails crbfs a Field is worth four Shillings /^f-r Rod, finding all Materials. In the Article^FLOORS, and in Paragraph l he Price, ^c. after eleven Shillings^ add the Word H'^orkmanpip. T« F t F R To the Article FLOOR- ning thus, ?vlr. Le^l;or^f-H fay?^ ING, to the Paragraph begin- ^V. add, The Price of Boarding Floors in and about LcndoTt^ is as follows: Boarding with whole yellow Deals, with folding Joints from twenty-two to twenty-four Shillings per Square. iDkto^ Sap-fifted, thai is, the Sap cut ail out, two Pounds per Square. Common ftraight Joint Boarding, thirty-five Shillin finds the Timber into that and it vviil be a5out a Sujex Price. Price for Oak. If you would efiimate the Value of a Square of Framing for a Barn after the Suffex Method, for fbme Place near London it is thus : ' To twenty.five Feet of M^r^^? Fir Timber, at thirty 7 ' * ' Shillings per Load — S° ^^ ^ To fawing ditto • . ,. m .. - o c o To Framing — ^ — , — ■■ ' — O Cf O To Weather-Boards, fixteen at nine Pence per Piece, > and C,)in Boards 50 13 o To Work and Nails . . . o o<- o 2 oi o This is above three Times fawed out of; the Sawing too the Sujfex Price ; but it is eafy little by one 1 hird, for he fup- to fee where he failed in pofeth rough Timber : In fliort, his Eftimate : He has under- it is all Blunders, valued the Timber much, a? 13ut if the Workman would to Price ; has accounted for faw- make a true Eftimate of a JSarn, mg the Boards, but fays nothing the Scantlings mutt be all afcei- about the Timber they are to be tained and fi^.cd, the Dimen- F R F R fioiTS of the Barn given, as the Lenc^th, Width, and Height, if the Planks be Oak, and the rcit Fir. Firft, cube the Plates, thnt is, meafure how many folid Fcct there is in the (liid Plates; then cube the Fir, thit is, find the fo- lid Content in Feet in the whok Carc^fe in the large and fmall Timbers ; then find how many Squares of Weather-Boarding, and Squares of T-hatching, with what Locks, Hinges, &c. is .^wanted, according to your A- greement ; then make a fair Bill of it all, as if it were already -done, as under : This will take ;up fonreTime, (for I would ad- viife the Workman to draw it •all up m\ Paper, with the feve- ral Scanilings, which will mak-e it very eafy to compute, and he will avoid Mitbkes,) but it will Jsnfwer his End, for he will be ■fbre of his Gain before-hand, ;ind not work by Guefs, as is the Way among mort Workmen that are not acquainted with Fi- gures. And here I cunnot but condemn the Method ufcd by the ordinary Workmen in Loft- cioa^ of meafuring the Area or Ground Plat of ihe Building on- ly, and making their Eftimate from thence, as erroneous. For let the Plan be ten Feet fquare, as for Inftance, a Sum- mer-Houfe, the Walls of that Building will be forty Feet a- bout, and the Area one Square ; then admit another Building of twenty Feet fquare, which is four fquare on the Plane or Area, the Wall of this Building will be So Feet about ; fo the build- ing of one Square hath Walls half the Quantity of that of four fquare : Bur this is but one Er- ror among a great many that ac- crue in this Method of eftima- trng ; and I would advife the young Workman to have no Re- gard to this lazy and idle Me- thod, Icll he pay too dear for it inihe End. The Mtrnner of the Bill for an Eftimate. A To fiwed cub'd Oak In Plates^ 40 Feet at 31. 06 To fa wed cub'd Fir in Carcafe, ^-ji Feet at 20 i. 47 Tt) i-S "Squares 7f Ft. broad Weather-boarding, at 18/. 25- T(> i8 Squares Pantiling, at \%s. 16 To 160 Feet Uuderpiiming, at 6d. per Foot 04 To-Hinges, Lock^ and Staples, b"*-, — — <^o s. 00 II 17 04 00 14 d. o S 6 o o o 100 07 o Jbe above Prices are the Z.c'?.^* Prices for Work and Stuff. FRONT ^H r^-l A- ^ nJm vm ^•^ Wi mi-^m. Vo 'f ^^ TT^ ■fc-'^^^L^^^^^'-^''^^- t« ^^ ^^S2^ ^:.^mm aiis^^^s: 22^, ^^ p/^r^ xrv. t V &k' 4 -3 4 -3 2 i.£/^^^ . 9, i. Br/cA^ 3/ C^:^ V- 4 . £/v/:^j mxc^ . ^^£:^:}y^^^^ II r- — I 1 Jii. 2 i £n^L. 4.£nc/b t/vuil 3/ 4. Bivh /Aiz-l J^^/^ J(V. re 2f '^C 4.^ ^^ ^'^ ^^ G U H O FRONT. To this Article add, There is no certain Price for tiiis Work by the Rod, but ic is always done by the F(jut, the Price more or lefs, according to the Goodnefs and Variety of the Workmanfhip. GUTTERS. To this Ar- ticle add, Guuert fhould never have lefs than a quarter of an Inch to a Foot tor Drip, and tin; Soldering crofs the Gutter is al- ways to be avoided, and the Length of the Lead, from Fall to Fall, fliould never exceed 14 Feer. In the Article HOUSE, to the Paragraph beginning thus. Some Workmen pitch the Ends of Timber, ^c. add, The bed Way to preferve the Ends of Timber iu the Walls, is to let them have Air, and nothing to touch them. In the Article about LA.THS, inllead of four Inches in Breadth mud have half an Inch in'Fhick- nefs, read, a quarter of an Inch, N.B. We hope the Reader will make all proper Allowances m Prices, when better Work or Materials fhal I exceed the Scheme of theie Computations. In the Trefs^ An Introduction to xh^MATHEMATICKS: Being Mathematical Lectures read in the publick Schools at the Univerfity of Cambridge. By Isaac Barrow D. D. Profellbr of the Mathematkks^ and Matter of Trinity College. To which is prefix'd, The Oratorical Preface 01 our Learned Author, fpoke before the Univerfity on his being eledred Lucasian Profeflbr of the JMathematicks. TranfliUed by John Kirkby A. M. Likewife in the Trefey GEOMETRICAL LECTURES, Read before theUniverlity of Cambridge. By Isaac Barrow D. D. Tranflated by Edmund Stone F. R. S. N.B. Thefe Two Volumes of the Learned Dr. Barrow's Lec tures were never before tranflated, and will be publilLcd iu February next. Printed for Stephen Austen, at the J»gel and B':b!e in St. Paul's Church'Yrvd. BOOKS Tri/ited for A. Bettefworth ^WC. Hlicb, iu Patcr-nofter-Row j and S. Auften, in St. Paul's Church-Yard. A Book of Ffolmodr, contain-ng Chanting Tunes for Fenit^ ExultemuSy Te Deum Laudamus^ Benediche^ 'Jubilate Deo^ Magnificat^ Ntmc 1)imitt'is^ and the Reading Plalms ; with i8 Anthems, and Variety of Pfalm Tunes. In Four Parts. The Seventh Edition, Correded and Enlarged by James Green. Price flitch'd l s. being the compleateft Book extant. 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